Electronic Structure and Bonding in Pyrrolic Macrocycle-Supported Complexes of Actinides

A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering.

2018

Kieran Thomas Patrick O’Brien

School of Chemistry

Contents

Section Page number List of tables 5 List of figures 9 Abstract 15 Declaration 16 Copyright Statement 17 Publications 18 Abbreviations 19 Acknowledgements 23

Part I. Introduction

Chapter 1. Theoretical background and methodology 26 1. Aims and objectives 26 2. Quantum chemistry 27 3. Density functional theory 33 4. Mulliken and Hirshfeld population analysis 37 5. Natural bond orbital analysis 39 6. The quantum theory of atoms in molecules 41 7. Energy decomposition analysis 46 8. Nucleus-independent chemical shifts 46 9. References 48

Chapter 2. Organometallic chemistry of the f-elements 52 1. Background and chemistry of organoactinides 52 2. Computational organometallic chemistry of the f- 56 elements 2.1. DFT and orbital-based partition methods 57

Contents

2.2. QTAIM analysis of organometallics of the f-block 62 elements 2.3. Non-partition-based methods – EDA and NICS 63 analysis 3. Recent developments in carbocyclic organoactinide 65 chemistry 3.1. The trans-calix[2]benzene[2]pyrrolide ligand 66 4. References 69

Chapter 3. Methodology 77 1. Model complexes 77 2. Computational methodology 80 3. References 82

Part II. Results and Discussion

Chapter 4. Geometry optimisations and electronic 85 structures 1. Geometry optimisations of Th(IV) complexes 86 2. Geometry optimisations of U(III) complexes 91 3. Geometry optimisations of Th(III) complexes 98 4. Partial charge analyses of Th(IV), U(III) and Th(III) 101 complexes 5. QTAIM analysis 107 6. NBO analysis 116 6.1. Transition metal complexes 125 7. Mulliken population analysis of the An-X interaction 138 8. Nucleus-independent chemical shift analysis 143 9. Mulliken population analysis of the An-arene 149 interaction 10. Conclusions and future work 153 11. References 157

Contents

Chapter 5. The strength of the An-X interactions 159 1. Introduction 159 2. Methodologies 159 3. Results 162 4. Heterolytic reactions 165 5. Homolytic reactions 170 6. Functional dependence of QTAIM vs bond energies 177 7. QTAIM metrics vs EDA data for [LAnX]n+ complexes 180 7.1. QTAIM metrics vs EDA data for [LAnX’]n+ complexes 184 7.2. QTAIM metrics vs EDA data for [LAnX*]n+ complexes 188 7.3. QTAIM metrics vs EDA data for [LAnX’’]n+ complexes 190 7.4. QTAIM metrics vs EDA data for [LAnX**]n+ 194 complexes 7.5. QTAIM metrics vs EDA data for [LAnX†]n+ complexes 195 8. Conclusions and future work 199 9. References 201

Chapter 6. Bimetallic L2-/4- alkyl and alkynyl complexes 202 1. Introduction 202 2. Computational details 204 3. Results – Complexes 1 and 2 204 4. Complexes 3, 4 and 5 208 5. Complexes 6 and 7 212 5.1 Dipoles of Th6 and Th7 215 5.2 Molecular orbitals of Th6 and Th7 217 5.3 Comparisons with M(IV) and other An(IV) centres 227 for 6 5.4 Comparisons with other An(IV) centres for 7 237 6. Conclusions and future work 245 7. References 248

Contents

Chapter 7. Overall conclusions and future work 249 1. Geometry optimisations and electronic structures 249 2. The strength of the An-X interactions 250 3. Bimetallic L2-/4- alkyl and alkynyl complexes 251 4. Concluding remarks 252 5. References 254

Appendix 255 1. PBE0 Cartesian coordinates (Å) and SCF energies 256 (Hartrees) of all complexes studied in chapter 4. 2. PBE0 Cartesian coordinates (Å) and SCF energies 264 (Hartrees) of all complexes studied in chapter 5. 3. PBE0 (unless stated otherwise) Cartesian coordinates 278 (Å) and SCF energies (Hartrees) of all complexes studied in chapter 6.

List of tables

Chapter 4 Page number

Table

4.1. Key bond lengths of thorium and uranium 88 complexes with experimental data. 4.2 Key bond angles of thorium and uranium 88 complexes with experimental data 4.3 MAD analysis for PBE and PBE0 for N(av) 96 4.4 MAD analysis for PBE and PBE0 for An-Ar1 96 4.5 MAD analysis for PBE and PBE0 for An-Ar2 97 4.6 MAD analysis for PBE and PBE0 for An-X 97 4.7 MAD analysis for PBE and PBE0 for Ar-An-Ar 97 4.8 MAD analysis for PBE and PBE0 for N-An-N 98 4.9 MAD analysis for PBE and PBE0 for interplanar 98 angles 4.10 Key bond lengths and angles for Th(III) complexes 99 4.11 Differences of bond lengths for LUIIIX and [LThIVX]+ 100 4.12 Partial charges for Th(IV) complexes 102 4.13 Partial charges for U(III) complexes 102 4.14 Partial charges for Th(III) complexes 102 4.15 QTAIM metrics for [LAnX]n+ 107 4.16 R2 values from trends in figures 4.21 to 4.23. 112

4.17 QTAIM metrics for [LAnNH2]n+ 113 4.18 R2 values from trends in figures 4.24 to 4.26. 115 4.19 NBO data for Th(IV) and Th(III) 117 4.20 R2 values for figure 4.26. 119 4.21 R2 values for figure 4.27. 120 4.22 R2 values for figures 4.28 to 4.30. 122 4.23 R2 values for figures 4.31 to 4.33 125 4.24 M-X bond lengths for Hf(IV) and W(III) 127

List of tables

4.25 QTAIM metrics for [LMX]n+ 129 4.26 NBO data for Hf(IV) and W(III) 133 4.27 Mulliken KS-MO data for [LAnX]n+ An centre 138 4.28 Mulliken KS-MO data for [LAnX]n+ X ligand 139 4.29 R2 values for figures 4.49 to 4.51 142 4.30 NICS data for [LThX]+ 145 4.31 Mulliken KS-MO data for [LAnX]n+ An-arene 150 4.32 HOMO energies for [LAnX]n+ 153

Chapter 5 Page number

Table 5.1 Key bond lengths for [LAnX]n+ 161 5.2 Key bond angles for [LAnX]n+ 161 5.3 SCF energies ZPE and thermal corrections for the 162 [LThIVX]+ 5.4 SCF energies ZPE and thermal corrections for the 162 LThIIIX 5.5 SCF energies ZPE and thermal corrections for the 163 LUIIIX 5.6 Energies of molecular ionic fragments with ZPE 163 and thermal corrections 5.7 Energies of molecular radical fragments with ZPE 164 and thermal corrections 5.8 Heterolytic bond enthalpies and Gibbs free 165 energies for [LThIVX]+ 5.9 Heterolytic bond enthalpies and Gibbs free 165 energies for LThIIIX 5.10 Heterolytic bond enthalpies and Gibbs free energies 166 for LUIIIX 5.11 Homolytic bond enthalpies and Gibbs free energies for 171 IV + [LTh X] 5.12 Homolytic bond enthalpies and Gibbs free 171 energies for LThIIIX

List of tables

5.13 Homolytic bond enthalpies and Gibbs free 172 energies for LUIIIX 5.14 QTAIM charge and interaction energies for Th(IV) 176 and Th(III) 5.15 PBE ΔE values for [LAnX]n+ 178 5.16 QTAIM PBE metrics 178 5.17 Th(IV)-X EDA energies 180 5.18 Th(III)-X EDA energies 180 5.19 U-X EDA energies 181 5.20 An-X EDA energies for [LAnX’]n+ 185 5.21 QTAIM metrics for [LAnX’]n+ 185 5.22 R2 values for EDA vs QTAIM for [LAnX’]n+ 186 5.23 R2 values for EDA vs QTAIM for [LThX]+ and 187 [LThX’]+ 5.24 R2 values for EDA vs QTAIM for LThX and LThX’ 187 5.25 R2 values for EDA vs QTAIM for LUX and LUX’ 187 5.26 An-X EDA energies for [LAnX*]n+ 198 5.27 QTAIM metrics for [LAnX*]n+ 198 5.28 R2 values for EDA vs QTAIM for [LAnX*]n+ 199 5.29 R2 values for EDA vs QTAIM for all [LAnX’]n+ and 190 [LAnX*]n+ 5.30 R2 values for EDA vs QTAIM for all [LThX’]n+ and 192 [LThX*]n+ 5.31 An-X EDA energies for [LAnX’’]n+ 193 5.32 QTAIM metrics for [LAnX’’]n+ 193 5.33 R2 values for EDA vs QTAIM for [LAnX’’]n+ 194 5.34 An-X EDA energies for [LAnX**]n+ 194 5.35 QTAIM metrics for [LAnX**]n+ 195 5.36 R2 values for EDA vs QTAIM for [LAnX**]n+ 195 5.37 An-X EDA energies for [LAnX†]n+ 196 5.38 QTAIM metrics for [LAnX†]n+ 196 5.39 R2 values for EDA vs QTAIM for [LAnX†]n+ 197

List of tables

Chapter 6 Page number

Table

6.1 M-N separation distances for complex 1 207 6.2 Li-N separation distances for different functionals 208 6.3 Energies of reaction for 1/2 to 3/4/5 209 6.4 Energies of reaction for 1 to 3/4/5 for different 211 methods

6.5 Bond lengths of Th6 for PBE0 and experimental data 213 6.6 SCF, enthalpy and Gibbs free energies of Th6 and Th7 214 6.7 SCF, enthalpy and Gibbs free energies of Th6’ and 214 Th7’ 6.8 ΔE, ΔH and ΔG values between a and b of 6 and 7 215 6.9 Dipole moments of Th6 and Th7 216 6.10 SCF energies in PCM model 216 6.11 Energy differences of a and b forms in PCM model 217 6.12 Selected MO energies for Th6 and Th7 218 6.13 Metal contributions to selected MOs (%, Mulliken 219 analysis) for Th6 and Th7 6.14 Selected MO energies for Th6’ and Th7’ 224 6.15 Metal contributions to selected MOs (%, Mulliken 224 analysis) for Th6’ and Th7’ 6.16 PBE energies for An6 complexes (An = Th-Am) 228 6.17 MO energies for An6 230 6.18 SOMO energies for open-shell An6 234 6.19 Total energy differences between An6a and An6b 235 for various combinations of MOs and SOMOs 6.20 PBE energies for An7 complexes (An = Th-Am) 238 6.21 MO energies for An7 239 6.22 SOMO energies for open-shell An7 242 6.23 Total energy differences between An7a and An7b 243 for various combinations of MOs and SOMOs

List of figures

Chapter 1 Page number Figure 1.1 Schematic representation of model chemistries 36 according to Pople 1.2 Classification of all types of QTAIM critical points 43 possible in 3D space

Chapter 2 Page number

Figure

2.1 Representations of 5f and 6d-bonding interactions 54 in actinocenes 2.2 Representations of 5f and 6d-bonding interactions 55

in bis-arene and bis-C5H5

2.3 Chemical structure of [N’’2U]2(C6H6) 60 2.4 Chemical structure of TODGA 60 2.5 Neutral form of trans-calix[2]benzene[2]pyrrolide 66 2.6 Different bonding motifs of L2- and L4- with 67 various metal centres

Chapter 3 Page number Figure 3.1 The simplified X ligands 77 3.2 [LAnX]n+ complex with labelled arene and pyrrole 78 rings

3.3 Schematic of M[LAnR] and LAnR’2 79

3.4 Schematic of the [LTh(CCSiMe3)2][NiPR3] 80 complexes (R = Cy, Ph) in the a form and b form

List of figures

Chapter 4 Page number

Figure

4.1 The average bond length of the two Th-N(py) 89 bonds vs the Th-X bonds for PBE and PBE0 for [LThIVX]+ complexes 4.2 Bond angles for N(py)-Th-N(py) and Ar-Th-Ar 90 against X ligand for PBE and PBE0 4.3 Interplanar angles against X ligand for PBE and 90 PBE0

4.4 X-ray structure for [LTN(TMS)2]+ and PBE 91

geometry for [LThN(SiH3)2]+ 4.5 The average bond length of the two U-N(py) 92 bonds vs the U-X bonds for PBE and PBE0 for LUIIIX complexes 4.6 X-ray structure for LUDTBP and PBE0 geometry 93 for LUOPh 4.7 Bond angles for N-U-N and Ar-U-Ar against X 94 ligand for PBE and PBE0 for LUIIIX complexes 4.8 Interplanar angles against X ligand for PBE and 95 PBE0 for LUX complexes 4.9 An-X bond distances for [LAnX]n+ complexes 99 4.10 Partial charges of Th(IV) as a function of X ligand 103 4.11 Partial charges of X as a function of X ligand 103 4.12 Hirshfeld An-X charge difference as a function of X 105 ligand 4.13 Mulliken An-X charge difference as a function of X 105 ligand 4.14 Natural An-X charge difference as a function of X 106 ligand 4.15 QTAIM An-X charge difference as a function of X 106 ligand 4.16 δ(An,X) against An-X bond length 108

List of figures

4.17 QTAIM ρ against An-X bond length 108 4.18 QTAIM H against An-X bond length 109 4.19 QTAIM ρ against An-X QTAIM charge difference 110 4.20 δ(An,X) against An-X QTAIM charge difference 110 4.21 QTAIM H against An-X QTAIM charge difference 111 4.22 QTAIM ρ against An-X QTAIM charge difference 114

with NH2 4.23 δ(An,X) against An-X QTAIM charge difference 114

with NH2 4.24 QTAIM H against An-X QTAIM charge difference 115

with NH2 4.25 NBOs of An-B and An-O bonds 118 4.26 An-X charge difference against An orbital 119 contribution to An-X NBO 4.27 An-X charge difference against An orbital 120

contribution to An-X NBO (NH2) 4.28 QTAIM ρ against An orbital contribution to An-X 121 NBO 4.29 δ(An,X) against An orbital contribution to An-X 121 NBO 4.30 QTAIM H against An orbital contribution to An-X 122 NBO 4.31 QTAIM ρ against An orbital contribution to An-X 123 NBO at fixed An-X bond length 4.32 δ(An,X) against An orbital contribution to An-X 124 NBO at fixed An-X bond length 4.33 QTAIM H against An orbital contribution to An-X 124 NBO at fixed An-X bond length 4.34 Partial charges of Hf(IV) as a function of X ligand 127 4.35 Partial charges of W(III) as a function of X ligand 128 4.36 QTAIM ρ against M-X bond length 129 4.37 δ(An,X) against M-X bond length 130 4.38 QTAIM H against M-X bond length 130

List of figures

4.39 QTAIM ρ against M-X QTAIM charge difference 131 4.40 δ(An,X) against M-X QTAIM charge difference 132 4.41 QTAIM H against M-X QTAIM charge difference 132 4.42 QTAIM ρ against M orbital contribution to M-X NBO 134 4.43 δ(An,X) against M orbital contribution to M-X NBO 134 4.44 QTAIM H against M orbital contribution to M-X NBO 135 4.45 QTAIM ρ against M orbital contribution to M-X 136 NBO at fixed M-X bond length 4.46 δ(An,X) against M orbital contribution to M-X 136 NBO at fixed M-X bond length 4.47 QTAIM H against M orbital contribution to M-X 137 NBO at fixed M-X bond length 4.48 KS-MOs of An-B and An-O bonds 140 4.49 QTAIM ρ against An orbital contribution to An-X 141 KS-MO 4.50 δ(An,X) against An orbital contribution to An-X 141 KS-MO 4.51 QTAIM H against An orbital contribution to An-X 142 KS-MO 4.52 NICS(0), NICS(1) and NICS(2) points in [LThMe]+ 144 4.53 δ(C,C)p values against NICS(0) isotropic values for 145 [LThX]+ complexes on Ar1 4.54 δ(Th,X) values against NICS(0), NICS(1) and 146 NICS(2) isotropic values for [LThX]+ complexes on Ar1 4.55 δ(Th,X) values against δ(C,C)p values for [LThX]+ 147 complexes on Ar1 4.56 δ(Th,X) values against NICS(1) and NICS(2) 148 isotropic values for [LThX]+ complexes on Ar1. [LThBO2C2H4]+ omitted from data set. 4.57 Total Th(IV) orbital contribution to the Th-Ar MO 151 against NICS(1) and NICS(2) isotropies 4.58 HOMO of LThIIIBO2CcH4 and LThIIIOPh 152

List of figures

Chapter 5 Page number

Figure

5.1 Heterolytic An-X ΔH298 and ΔG298 against An-X 167 bond length

5.2 Heterolytic An-X ΔH298 and ΔG298 against δ(An,X) 168

5.3 Heterolytic An-X ΔH298 and ΔG298 against QTAIM 168 charge difference

5.4 Heterolytic An-X ΔH298 and ΔG298 against QTAIM ρ 169

5.5 Heterolytic An-X ΔH298 and ΔG298 against QTAIM H 170

5.6 Homolytic An-X ΔH298 and ΔG298 against An-X 174 bond length

5.7 Homolytic An-X ΔH298 and ΔG298 against QTAIM 173 charge difference

5.8 Homolytic An-X ΔH298 and ΔG298 against δ(An,X) 174

5.9 Homolytic An-X ΔH298 and ΔG298 against QTAIM ρ 175

5.10 Homolytic An-X ΔH298 and ΔG298 against QTAIM H 175 5.11 Change in QTAIM charge of An centre from 177 fragment to full complex against An-X interaction energy 5.12 PBE ΔE for An-X reaction energies against QTAIM 179 metrics

5.13 QTAIM metrics vs EDA EB for An-X 182

5.14 QTAIM metrics vs EDA EO for An-X 182

5.15 QTAIM metrics vs EDA EP for An-X 183

5.16 QTAIM metrics vs EDA EE for An-X 183

5.17 QTAIM metrics vs EDA EO for Th-X’ and Th-X* 191

5.18 QTAIM metrics vs EDA EO for Th-X’/X’’/X*/X**/X† 198

Chapter 6 Page number

Figure

6.1 Schematic of the M[LThR] complexes 1 and 2 202

List of figures

6.2 Schematic of the LTh(CCR’)2 complexes 3, 4 and 5 203

6.3 Schematic of the [LTh(CCSiMe3)2][NiPR3] 203 complexes Th6 and Th7 6.4 Experimental and PBE0-optimised structure of Li1 205 6.5 Experimental and PBE0-optimised structure of K2 206 6.6 Reaction scheme for 1 going to 3, 4 and 5 208 6.7 Experimental and PBE0-optimised structure of Li1 210 with THF 6.8 Experimental and PBE0-optimised structure of 212 Th6a and Th6b 6.9 Energies of MOs of complexes Th6a and Th6b 213 6.10 Representations of MO 255 in Th6b 220 6.11 Energies of MOs of complexes Th7a and Th7b 221

6.12 MO 256 in Th7a splitting to MO 257 and 243 in Th7b 222 6.13 Energies of MOs of complexes Th6a’ and Th6b’ 225 6.14 Energies of MOs of complexes Th7a’ and Th7b’ 226 6.15 Energy differences between a and b forms of An6 229 as a function of An centre 6.16 Energies of MOs of complexes An6a and An6b 231 6.17 MO energies vs enthalpies for An6 complexes 232 6.18 Key f-orbital SOMOs for open-shell An6 complexes 233 6.19 MO, MO + SOMO and SOMO energies vs enthalpies 236 for open-shell An6 complexes 6.20 Energy differences between a and b forms of An7 238 as a function of An centre 6.21 Energies of MOs of complexes An7a and An7b 241 6.22 MO energies vs enthalpies for An7 complexes 242 6.23 MO, MO + SOMO and SOMO energies vs enthalpies 244 for open-shell An7 complexes

Abstract

Chemistry of the early actinides has undergone a lot of developments in recent years, and due to the need of specialised laboratories to handle these often highly radioactive complexes, computational chemistry has become a powerful aid in understanding the physical properties of these unique systems.

This thesis describes a systematic computational study of organoactinide and organometallic model complexes of the form [LAnX]n+ where L is the macrocyclic trans- calix[2]benzene[2]pyrrolide ligand using density functional theory (DFT) in conjunction with a variety of partition-based methods – Mulliken populations analysis (MPA), Hirshfield population analysis (HPA), natural population analysis (NPA) and the quantum theory of atoms in molecules (QTAIM) – with the aim of probing the electronic structure of the An-X and An-arene bonds as a function of the X ligand. Natural bond orbital (NBO) analysis was also used to study the nature of the An-X bonds, with these results compared to the QTAIM descriptions of covalency and ionicity in the [LAnX]n+ complexes. Analogous transition metal complexes of the form [LMX]n+ (M = Hf, W) have also been studied with the QTAIM and NBO approaches to compare with the actinide-based systems. Nucleus independent chemical shift (NICS) analysis was carried out to probe the extent of aromaticity of the arene rings of the L2- ligand in the closed- shell [LThX]+ complexes as a function of X ligand, and was compared with QTAIM measurements of aromaticity. The MPA also revealed δ-bonding to the arene rings of the L2- ligand and was compared to the NICS data.

Bond energies and bond energy decomposition analysis (EDA) of An-X were further analysed and compared to the QTAIM data. These same analyses were carried out on complexes where the X-type ligand series was extended to include a larger set of first and second-row p-block based ligands.

Finally, other, bi-metallic actinide-based complexes including the L2-/4- ligand were studied with the aim of understanding the thermal stabilities of these experimentally-characterised complexes, with analogous model complexes modelled to find potential synthetic targets. The Kohn-Sham molecular orbitals (KS-MOs) of some of these complexes were also analysed to try and find a rationale, based on their electronic structure, for the energetic preference for one binding mode of L-An over another.

Declaration

No portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning.

1. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the “Copyright”) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes.

2. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made.

3. The ownership of certain Copyright, patents, designs, trade marks and other intellectual property (the “Intellectual Property”) and any reproductions of copyright works in this thesis, for example graphs and tables (“Reproductions”), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions.

4. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property University IP Policy (see http://documents.manchester.ac.uk/display.aspx?DocID=24420), in any relevant Thesis restriction declarations deposited in the University Library, The University Library’s regulations (see http://www.library.manchester.ac.uk/about/regulations/) and in The University’s policy on Presentation of Theses.

Publications

K. T. P. O’Brien and N. Kaltsoyannis, “Computational study of An–X bonding (An = Th, U; X = p-block-based ligands) in pyrrolic macrocycle-supported complexes from the quantum theory of atoms in molecules and bond energy decomposition analysis”, Dalton Trans. 2017, 46, 760.

M. Suvova, K. T. P. O’Brien, J. H. Farnaby, J. B. Love, N. Kaltsoyannis and P. L. Arnold, “Thorium(IV) and Uranium(IV) trans-Calix[2]benzene[2]pyrrolide Alkyl and Alkynyl Complexes: Synthesis, Reactivity, and Electronic Structure”, Organometallics, 2017, 36, 4669.

Abbreviations

1 – M[LThMe]

2 – M[LThCH2Ph]

3 – LTh(CCSiH3)2

4 – LTh(CCSiMe3)2

5 – LTh(CCSiiPr3)2

6 – [LAn(CCSiMe3)2][NiPCy3]

6’ – [LTh(CCSiMe3)2][PtPCy3]

7 – [LAn(CCSiMe3)2][NiPPh3]

7’ – [LTh(CCSiMe3)2][PtPPh3]

ADF – Amsterdam density functional

An – actinide

ANO – atomic natural orbital

AO – atomic orbital

Ar – arene

B3 – Becke hybrid exchange functional

B3LYP – Becke-Lee-Yang-Parr hybrid functional

B88 – Becke functional

BCP – bond critical point

BH4 – borohydride

BO – bond order

BO2C2H4 – bis-pinacolato boron without methyl groups

Abbreviations

CASSCF – complete active space self-consistent field

CCP – cage critical point

CGTO – contracted Gaussian type orbital

COT – 1,3,5,7-cyclooctatetraene

CP – critical point

DFT – density function theory

DTBP – 2,6-di-tert-butylphenoxide

ECP – effective core potential

EDA – energy decomposition analysis

ESI-MS – electrospray ionisation mass spectrometry

FF – Fukui function

GGA – generalised gradient approximation

GTO – Gaussian type orbital

H – energy density at bond critical point

HF – Hartree-Fock

HOMO – highest occupied molecular orbital

HPA – Hirshfeld population analysis

KS – Kohn-Sham

KS-MO – Kohn-Sham molecular orbital

L – trans-calix[2]benzene[2]pyrrolide

L2- – trans-calix[2]benzene[2]pyrrolide without H on N(py)

L4- – trans-calix[2]benzene[2]pyrrolide without H on N(py) and without one H on each Ar ring

LAnX – full actinide complex with L and X ligands

Abbreviations

LCAO – linear combination of atomic orbitals

LDA – local density approximation

LSDA – local spin density approximation

L-type – Lewis type

LUMO – lowest unoccupied molecular orbital

LYP – Lee-Yang-Parr functional

MAD – mean absolute deviation

Me – methyl

MO – molecular orbital

MPA – Mulliken population analysis

N(py) – pyrrolide nitrogen

NAO – natural atomic orbital

NBO – natural bond orbital

NCP – nuclear critical point

NICS – nucleus-independent chemical shift

NL-type –non-Lewis type

NPA – natural population analysis

OPh – phenol

PBE – Perdew-Burke-Ernzerhof functional

PBE0 – Perdew-Burke-Ernzerhof hybrid functional

PP – pseudopotential

PW86/91 – Perdew-Wang exchange-correlation functional

QTAIM – quantum theory of atoms in molecules

RCP – ring critical point

Abbreviations

SCF – self-consistent field

SOMO – Singly-occupied molecular orbital

STO – Slater type orbital

TF – Thomas-Fermi model

TFD – Thomas-Fermi-Dirac model

TMS – tetramethylsilane

TODGA – N,N,N’,N’-tetraoctyl-diglycolamide

X – BH4, BO2C2H4, Me, N(SiH3)2 and OPh ligands

X’ – CH3, NH2, OH and F ligands

X’’ – CH2Ph, NHPh and OPh ligands

X* – SiH3, PH2, SH and Cl ligands

X** – SiH2Ph, PHPh and SPh ligands

X† – CPh3, SiPh3, NPh2, PPh2, OPh and SPh ligands

δ(A,B) – delocalisation index between atoms A and B

ηx – haptic bonding to x number of arene carbons

κx – haptic bonding to x number of pyrrole carbons or nitrogens

μ-Hx – bridging bond from x number of hydrogens

ρ – electron density at bond critical point

Acknowledgements

I would like to thank Prof. Nikolas Kaltsoyannis at the University of Manchester for all his supervision and guidance throughout my postgraduate studies. I would also like to thank Prof. Polly L. Arnold and Dr Marketa Suvova at the University of Edinburgh for providing important experimental data.

Particular thanks to Claire O’Brien for her help and advice regarding my thesis, and my family, Lainey, and friends in room 7.04 for putting up with me for three years!

Also a special thanks to the University of Manchester for funding this PhD, the National Service for Computational Chemistry Software (NSCCS), UCL Researching Computing Platforms Support services, Dr. Jörg Saßmannshausen at UCL Chemistry and of course, the University of Manchester Computational Science Community services, without all of whom the calculations needed for this research would not have been made possible.

And you may ask yourself, “well, how did I get here?”

~ David Byrne

Part I.

Introduction

Theoretical background

Chapter 1. Theoretical background

1.1. Aims and objectives

Computational organoactinide chemistry can be described as the study, using computational chemistry methods, of organoactinide systems in order to describe physical properties such as bonding interactions, bond strength, reaction energies and the electronic structure of such systems. The overall aim of this thesis was to characterise and analyse the electronic structure and bonding of a range of actinide and transition metal complexes incorporating a pyrrolic macrocycle-supported ligand, using a variety of computational methods based on density functional theory (DFT). Some of these complexes have been synthesised and characterised experimentally.

The first objective was to investigate how changing the electronegativity of a second ligand in the macrocycle-metal system affected the bonding and electronic interaction of this metal-ligand bond and the macrocycle-metal bonding. A variety of different bond analysis techniques were used and compared to see how descriptors such as covalency and ionicity were characterised according to the different computational methods, and also how these descriptors related to the bond energies of metal-ligand interactions.

The second objective was to determine reaction energies and thermal stabilities of a range of bimetallic macrocycle-actinide systems synthesised experimentally, and also the reaction and thermal energies of analogous systems having metal centres that have so far eluded experimentalists. The purpose of these studies was to see if potential synthetic targets could be proposed based on the computed reaction energies, and also to determine if computational analysis of the molecular orbitals in these systems can explain the thermal stabilities of certain products found experimentally.

Theoretical background

It is hoped that this study will contribute to the large field of computational actinide chemistry and help add to arguments regarding the bonding nature of such systems.

The rest of this chapter first gives a general introduction to quantum chemistry and the mathematical descriptions of electronic wavefunctions and basis sets, before describing the principles of the main method used in this study – density functional theory. Further to this, a range of different electronic structure and bond analysis techniques used in this research, such as natural bond orbital anaylsis, the quantum theory of atoms in molecules, energy decomposition analysis, and nucleus-independent chemical shift analysis, are described.

Chapter 2 is a literature review describing extensively the current status of the fields of actinide and organoactinide chemistry and computational actinide/organoactinide chemistry, with many of the techniques and methodologies mentioned in this chapter discussed in relation to these fields. Specific methodologies for this thesis are given in chapter 3.

The results are presented and discussed in part II where the results for the first aim are given in chapters 4 and 5, and the results for the second aim given in chapter 6.

1.2. Quantum chemistry

Quantum chemistry attempts to define molecular electronic structure by approximating the electron density in the ground state from the wavefunctions of the electrons by solving the time-independent electronic Schrödinger equation:

Ψ(; ) = ()Ψ(; ) (1.1)

R is the set of fixed locations of the nuclei, Ĥ is the Hamiltonian operator, Ψ is the wavefunction (and eigenfunction of Ĥ) which depends on R and the electronic coordinates r, and E(R) is the total energy of the system (and eigenvalue of Ĥ). Ĥ is a combination of the kinetic and potential energies of the electrons, and in the time-independent electronic Schrödinger equation takes the form below:

Theoretical background

−ħ (1.2) = + () 2

Where ħ is Planck’s constant divided by 2π, me is the mass of the electron, ∇2 is the Laplacian operator and (r) is the potential energy as a function of the position vector of the electron:

1 1 (1.3) () = − + 2

Where the subscripts e and n denote electron and nucleus respectively, rij is the distance between electrons i and j, ZI is the charge of nucleus I and rIi is the distance between nucleus I and electron i. All quantities are in atomic units; energies are in Hartree and distances in Bohr1.

Only the hydrogen (or hydrogenic) atom can be solved analytically; any other system containing more than one electron can be solved only as an approximation due to the calculation becoming a many-bodied problem; each electron is treated as moving in a mean potential field. The overall molecular wavefunction is an antisymmetric product of all the one-electron wavefunctions (molecular orbitals) in the system, which are obtained by taking a linear combination of the atomic orbitals χr (the LCAO approach).

(1.4) =

Where cr is the coefficient of each atomic orbital in each molecular orbital. When the variation principle is applied this gives rise to the equation:

0 = ∑ { − } (1.5)

Where Hrs and Srs are elements of the Hamiltonian and overlap matrix respectively.

= , = ⟨|⟩ (1.6)

Theoretical background

Equations 1.5 is known as a secular equation1 and it is this equation that computational techniques aim to solve. Development of such techniques to solve many-electron systems started in 1927 by D. R. Hartree2 soon after the formulation of the Schrödinger equation the previous year, and was in 1930 refined to take into account the indistinguishability of electrons, independently by both J. C. Slater3 and V. Z. Fock4. That is, as noted above, the overall wavefunction is antisymmetric (it changes sign upon exchange of the coordinates of two electrons – i.e. the Pauli principle)5. These wavefunctions satisfy the Pauli principle by being treated as a collection of electrons with a unique wavefunction (a spin-orbital) χ(x) in a matrix6 where x is the coordinate representing the position and spin of the electron ( = {, }).

() () ⋯ () ( ) ( ) ( ) ( , , … , ) = ⋯ ≡ | , , … , | (1.7) √! ⋮ ⋮ ⋱ ⋮ ⋯ () () ()

The above determinant of the N-electron matrix is known as the Slater determinant, named after J. C. Slater who formulated it. In quantum mechanical calculations, this allows us to satisfy the Pauli principle and retain the one- electron molecular orbital approach, which is very useful for chemists.

The collection of atomic orbital functions used to generate the molecular orbitals is known as a basis set, and the function for each χr is a basis function. The two most common types of basis functions are Slater type orbitals (STOs) and Gaussian type orbitals (GTOs). STOs take the following form in polar coordinates7:

(1.8) = ,(, )

Where N is a normalisation constant, Yl,m are spherical harmonic functions, r is the distance from the nucleus, n is the principal quantum number and ζ is the () Slater exponent given by where Z is the nuclear charge and S is the screening constant. STOs do not have radial nodes and so nodes are instead introduced by taking linear combinations of STOs. For example, when taking a linear combination of two STOs to describe one atomic orbital, this is known as

Theoretical background a “double-zeta” (DZ) STO, the name arising from the two different exponent (ζ) values.

GTOs take the following form and can be written in terms of polar or Cartesian coordinates8:

= ,(, ) (1.9) =

GTOs have radial nodes and the sum of lx, ly and lz gives the type of atomic orbital, i.e. a sum of zero is an s-orbital, one is a p-orbital, two is a d-orbital etc9. The main advantage of GTOs is that the product of two Gaussian functions at different centres is the same as a single Gaussian function located somewhere at a point between the two centres. This is known as the Gaussian product theorem and it allows 4-centre integrals to be described as two-centre integrals which is a major advantage over STOs when regarding computational time. GTOs do have their drawbacks however; e.g. there is no cusp in the wavefunction at r=0 (which is incorrect for a 1s orbital) and the wavefunction decays too rapidly as r increases. The opposite of this is true for STOs when describing the 1s orbitals, and so a way to overcome this problem is by using contracted GTOs (CGTO). A CGTO is a linear combination of each individual GTO with its own ζ value, known as a primitive GTO10. An example of the nomenclature of a CGTO is STO- 3G. This means that the STO is approximated by a fixed linear combination of three primitive Gaussians. As with STOs, improvements can be made by also making GTOs double-zeta. This is done by using Gaussian functions to approximate double-zeta STOs and so a basis set labelled STO-3-21G means each core orbital is represented by a single contraction of three primitive GTOs, with each valence orbital being treated as a double-zeta STO, using two and one Gaussian functions respectively. Further improvements on the minimal basis set (the smallest possible number of basis functions for a given system) take form in triple-zeta (TZ), quadruple-zeta (QZ) and pentuple-zeta (PZ) which as their names suggest are basis sets with three, four and five times as many functions as the minimum basis set respectively9.

Theoretical background

For a lot of systems angular momentum functions, higher than found in the occupied molecular orbitals, are employed and these are known as polarisation functions. For example, when studying a hydrogen atom, which may be described by only s-functions, bonding may be expressed poorly since an s- orbital cannot take into account asymmetric charge distributions, which for hydrogen in most molecular systems is likely the case. Polarisation functions therefore introduce AOs to the basis set that go beyond the valence AOs of a given element, e.g., adding p-functions to hydrogen and d-functions to p-block elements, which effectively polarise the valence AOs in order for bonding to be described more accurately in an asymmetric charge distribution.

The final improvement to GTOs to be mentioned in relation to this work are correlation-consistent CGTOs formulated by Dunning and co-workers11, 12. These attempt to recover the correlation energy of the valence orbitals and are given the general acronym cc-pVXZ (correlation consistent polarised valence X zeta where X is either double, triple, quadruple etc.). These basis sets can also be augmented by adding the acronym aug- and consist of adding an extra GTO for each angular momentum, though with a smaller exponent13.

Two problems arise, however, for elements further down the periodic table, such as the heavier transition metals and the f-block elements. These are (i) the heavier elements have a large number of core electrons, which although do not get involved in any chemistry, are still necessary to be included as functions so as to get a proper description of the valence electrons (and, of course, because all the electrons are integral to the atom) and (ii) relativistic effects become important as the core electrons travel closer to the speed of light and thus gain mass and contract towards the nucleus, affecting the rest of the electronic orbitals. Such a relativistic description of an electron requires a four- rather than three-coordinate system (the fourth coordinate being time) and is instead solved by the Dirac equation – essentially a variation of the Schrödinger equation which takes into account relativity in the Hamiltonian Ĥ. (1.10) = ( ∙ + ) + )

Theoretical background

Where p is the momentum of the electron, m is its mass, c is the speed of light, is the potential energy, and α and β are 4x4 matrices, giving the relativistic wavefunction four components. These are grouped as large and small components describing the electronic and positronic (electron antiparticle) part of the wavefunction respectively9.

Calculating systems in such a way is very costly, and so these problems are typically overcome by using so-called effective core potentials (ECPs) (sometimes called pseudo-potentials (PPs)) instead of explicit all-electron basis sets, which replace the core electrons from an all-electron wavefunction – calculated numerically from ab initio methods – with a function that takes into account both the effective potential of these core electrons and the relativistic properties they exhibit. In this way a non-relativistic Hamiltonian can still be used as only the valence electrons are described explicitly and can be done so using Gaussian functions. This is done by first taking the valence-only model Hamiltonian for an atom with n valence electrons14.

1 1 (1.11) = − + + + 2

Where i and j are electron indices, ∇2 is the Laplacian operator, av is a spin- orbit averaged relativistic ECP and so a spin-orbit term.

= − + exp(− ) (1.12) ,

2 = exp (− ) (1.13) 2 + 1 ,

Where Q is the charge of the core, Pl is the projection operator onto the Hilbert subspace of angular momentum l, and Alk, alk, Blk and blk are free parameters adjusted to produce the valence energies of low-lying electronic states of the neutral atom14.

Theoretical background

Thankfully several sets of ECPs have been generated over the years for most of the periodic table, notably by Dolg and co-workers who have formulated the so- called “Stuttgart/Bonn” PPs and associated explicit valence basis sets15 where reference data for the free parameters in equations 1.12 and 1.13 were taken from previous all-electron Hartree-Fock calculations, and also Dirac-Fock and Wood-Boring derived ECPs.

1.3. Density functional theory

Once a suitable basis set has been selected, there are numerous ways to go about solving the secular equations. The combined work of Hartree and Fock mentioned earlier gave rise to Hartree-Fock Self-Consistent Field Theory (HF- SCF theory), and since then a lot more so-called “post-HF” techniques have been developed to account for the failure of the HF method to account for electron correlation. However, the technique used in this work is an alternative to HF and post-HF theories, known as density functional theory (DFT) developed by Kohn and Sham16. DFT is used to calculate a variety of properties of a many- electron system using functionals based on the electron density (ρ). Early DFT methods did not include orbitals in their models and this approach is known as orbital-free DFT, notable examples of which included the Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models17, 18. It was W. Kohn and L. J. Sham who proposed the introduction of orbitals into DFT16 since orbital-free methods showed poor descriptions of the kinetic energy, and so a method was developed whereby electron densities are estimated by treating electrons as non- interacting in an effective potential. Although the complexity of the electron density increases when including orbitals, Kohn-Sham (KS) theory is still an improvement on TF and TFD models. KS theory is closely related to HF methods, however, in KS theory, the kinetic energy functional is split into two terms: one functional to describe the kinetic energy of the non-interacting electrons exactly – in the form of a Slater determinant, denoted by TS – and a second, small correction term. Since electrons do in fact interact, TS does not describe the total kinetic energy, and the “missing” energy is described in an exchange-correlation term as shown below:

Theoretical background

[] = [] + [] + [] + [] (1.14)

Where EDFT is the total energy calculated from DFT, TS is the kinetic energy from the Slater determinant, Ene is the total nuclear-electron interaction energy, J is the coulomb energy, representing classical electron-electron repulsion and Exc is the total exchange-correlation energy. The exchange-correlation term is made up of both the kinetic energy correction as mentioned above and also an exchange energy-correlation energy term:

[] = ([] − []) + ([] − []) (1.15)

Where T is the total kinetic energy and Eee is the total electron-electron interaction energy. The first parenthesis is the difference between the total kinetic energy and that of the non-interacting electrons (TS), and the second parenthesis is the non-classical part of the electron-electron interaction. A major consideration when calculating exchange and correlation is to assume that the likelihood of finding an electron in the immediate vicinity of another electron is close to zero, and therefore there are said to be “holes” in the electron density around each electron. When considering electrons of opposite spin these are known as Coulomb holes and with the same spin, Fermi holes, which individually integrate to 0 and -1 respectively9. In equation 1.14, the only term that cannot be obtained exactly is EXC, instead it can only be approximated.

In KS many such approximations have been developed over the years. Computationally speaking, when one talks about a particular functional to be used in DFT calculations, it is the exchange-correlation functional in equation 1.15 that one is referring to. The simplest such approximation is known as the local-density approximation (LDA), where only the density at a given spatial coordinate is needed for the functional. The local spin density approximation (LSDA) is similar to LDA but also takes into account electron spin in systems where α and β spin densities are different, and thus for closed-shell systems, there is no difference between the LDA and LSDA approaches9. LDA approaches treat the density at a given point as a uniform electron gas, and so a non- uniform electron gas model approach can also be a better alternative to LDAs. The simplest such methods are generalised gradient approximation (GGA)

Theoretical background functionals which improve on LDA descriptions of the total energy, atomisation energies, energy barriers and structural energy differences19. These take the general form20;

(1.16) [↓, ↑] = (↓, ↑, ∇↓, ∇↑)

Where the exchange-correlation energy is given by EXC = EX + EC which is a functional of the electron spin densities ↑(r) and ↓(r)19. An added variable in GGA functionals is the first-order derivative of the density (i.e. the gradient ∇ρ), whilst also maintaining that the Coulomb and Fermi holes integrate to 0 and -1. One of the first such functionals to be formulated was the B88 functional by A. D. Becke which corrects the LSDA exchange energy21 and later the LYP functional by C. Lee, W. Yang and R. G. Parr, which corrects for the correlation energy22. Put together for both exchange-correlation energy and one obtains the BLYP functional. Other such GGA functionals to describe both exchange and correlation in one were developed by J. P. Perdew and co-workers with PW8623, PW9120 and PBE19.

More sophisticated still than GGA methods are hyper or hybrid-GGA methods. These functionals are essentially a summation of the GGA functional plus a fixed fraction of the exact exchange energy as defined in HF and KS theory24.

[] = ([] − []) + (1.17)

Where a is a fractional parameter which determines by how much the exact exchange energy term is mixed into the specific “flavour” of hybrid-GGA functional. A well-known hybrid exchange functional is B3 developed by A. D. Becke25, and combined with the aforementioned LYP correlation functional gives the widely used B3LYP hybrid functional. The PBE functional has also been developed into a hybrid functional and is known as PBE026. In PBE0 a is set to 0.25.

Being able to accurately describe electronic structure in chemical systems comes down to two fundamental considerations; how one describes electron correlations and the basis set used. It was Pople who first proposed the idea of this ‘model chemistry’ whereby a higher level of theory to describe correlation

Theoretical background and a larger basis set will give results closer to the exact solution of the Schrödinger equation27;

Fig. 1.1. Schematic representation of model chemistries according to Pople27. Image taken from the work of Schreckenbach and Shamov28.

To summarise, a so-called “Jacob’s ladder” of exchange-correlation functionals can be considered where the most “primitive” are LDA functionals, with only ρ as a variable, then the more sophisticated GGA functionals which have both ρ and ∇ρ as variables, and more sophisticated still the hybrid-GGA functionals which have three variables of ρ, ∇ρ and the amount of HF exchange. In this study only GGA, hybrid-GGA, and meta-GGA functionals were employed.

Based on these principles of DFT and molecular quantum mechanics, the potential energy contribution to the molecular Hamiltonian is obtained from the overall interactions of all the electrons and nuclei in a molecule, and not the sum of atomic contributions, and therefore in DFT there can be no unique way to define the individual atoms in a molecule or complex29, 30. However, being able to overcome this problem is useful for obtaining partial atomic charges and other important aspects of bonding such as charge transfer and molecular orbital constitution31.

There have been many ways to tackle this problem, known as decomposition or partition techniques, and out of all the different decomposition techniques that

Theoretical background have been proposed, most can be divided into two categories. Firstly, by basis set-based partitioning, and secondly, by separation of the electron density in real space32.

Throughout this thesis, a variety of these techniques were employed. For basis set-based partition methods, Mulliken population analysis (MPA)33 and natural population analysis (NPA)34 based methods were used, and for methods in which the electron density is separated in real space, Hirshfeld population analysis (HPA)35 and the quantum theory of atoms in molecules (QTAIM)36 were used, with a lot more emphasis on the latter; HPA was used just for investigating partial atomic charges.

The MPA, NPA, HPA and QTAIM methods are here described in more detail.

1.4. Mulliken and Hirshfeld population analyses

MPA aims to analyse the atomic populations and therefore orbital makeup of the Kohn-Sham molecular orbitals (KSMOs) derived from DFT, and so are taken directly from the LCAO method using first-order density functions, which can express the charge density at point r.

(1.18) () = P |()⟩⟨()|

Here, |()⟩ are the basis functions of the molecular orbitals (i.e. basis sets).

Since the atomic population, NA, is the sum of the basis functions on atom A, NA can be written as follows 37:

= (), (1.19) ∈

Where this sum applies only to basis functions found in atom A, denoted by the expression μ ∊ A. The overlap matrix is denoted by S.

From these atomic populations obtained from MPA, atomic charges can be deduced as well as describing the electronic make-up of the KSMOs.

One disadvantage with the MPA is that so-called condensed Fukui (FF) indicators38, 39 – which describe electron density in frontier orbitals, and

Theoretical background expressed in MPA as differences in the atomic populations38, 40 – can give negative values or values that violate the Pauli exclusion principle31.

This shortcoming of MPA has been used to argue the superiority of HPA41-44 over MPA. Conversely, it has been argued for the case of MPA that condensed FF indicators – whilst having to be positive for “normal” molecules – can be negative when indicating the occurrence of redox-induced electron rearrangement39, 45-49.

The HPA scheme differs from the MPA scheme by dividing the so-called “deformation density” between the atoms in a molecule, which is the difference between the “molecular” and “pro-molecular” (un-relaxed) atomic charge densities, in order to define the atomic charges in the system32:

() = () − () = () − ∑ ( − ) (1.20)

Where ρd, ρmol and ρpro are the deformation, molecular and pro-molecular densities at position r respectively, and ρα(r - Rα) is the spherically-averaged electron density of a free atom α in the molecule centered on the atomic nucleus

Rα. From this the effective charge of an atom α (qα) can be determined.

(1.21) = − ()()

Where ωα is the so-called “sharing function”, which measures the amount of contribution from atom α in the overall ρpro of the molecule at position r.

(1.22) () = ( − ) ( − )

Therefore in the HPA scheme, the molecular charge density at each point among the atoms in the molecule is divided in proportion to their respective contributions to ρpro(r). In other words, each atom contributes to local charge in direct proportion to its overall contribution to the molecular charge density32, 35.

Theoretical background

1.5. Natural bond orbital analysis

One of the main analytical approaches used in this study was the natural bond orbital (NBO) analysis, from which natural population analysis (NPA) can be obtained as well. NBO methods describe electronic wavefunctions in ways more akin to the conventional Lewis-structure representations of chemical systems than is typical from HF, post-HF and DFT calculations50. It is an orbital localisation technique, differing from HF or DFT where molecular orbitals are often delocalised and not chemically intuitive. NBO methods are useful in describing hybridisation of bond orbitals, where they agree with Bent’s rule51, and require no simultaneous minimisation of the SCF energy, instead being derived from the first-order density matrix34. Thus in NBO methods, NBOs are divided into two groups; ‘Lewis’ (L type) and ‘non-Lewis’ (NL type) NBOs, where L type NBOs describe each one-centre lone pair and two-centre bond pair in the Lewis structure, and the remaining NL type NBOs describe residual resonance delocalisation effects. NBOs are formulated in terms of natural atomic orbitals (NAOs) – describing the atom-like properties in a complex – which at large inter-atomic distances reduce to the atomic natural orbitals52 (ANOs) of the corresponding atom in isolation. At shorter inter-atomic distances NAOs describe the electronic interactions between the given atoms distinct from their free-atom forms50.

Common atomic orbital basis functions such as CGTOs and STOs often involve overlap of intra- and inter-atomic types, due to a lack of nodal features in both core and valence shells, whereas NAOs maintain intra- and inter-atomic orthonormality50.

To see how NBOs are constructed from NAOs, one can start with a one-electron

Hamiltonian with NAO orbital energies εi(A) as the expectation value of ,

() () ()∗ (1.23) =

From this an effective atomic Hamiltonian of each atom can be constructed.

Theoretical background

() () () () ℎ = (1.24)

This gives a starting point for partitioning a system into intra-atomic (h(A)) and inter-atomic ( int) contributions;

() (1.25) = ℎ +

These NAOs can also help to describe the orbital population (qi(A)) and atomic charge (q(A)) at each atomic centre A. Collectively these properties are known as the natural population (NP)50, 53 and are expressed thus;

() () (1) () = Г (1.26)

() () = − (1.27)

Where Γ(1) is the first-order reduced density operator54 and ZA is the atomic number of atom A. The first-order reduced density operator describes the underlying wavefunction Ψ in the reduced form55, and natural orbitals (NOs) are the eigenorbitals of this:

() Г = (= 1,2, … ) (1.28)

Which have associated eigenvalues to describe occupancy qi:

() = Г (1.29)

Which is limited by the Pauli exclusion principle (0 ≤ qi ≤ 2). In general, these properties allow NOs to be expressed as maximum occupancy NOs, but which need to be distinguished from minimum-energy MOs50.

Based on this, one can search for the best natural Lewis structure description of a system by searching for the highest-occupancy localised one-centre (lone pair) and two-centre (bond pair) regions, since a maximum electron pair occupancy would be qi = 2 in conventional Lewis structure diagrams50.

Theoretical background

1.6. The quantum theory of atoms in molecules

The quantum theory of atoms in molecules (QTAIM)36 was developed by R. F. W. Bader and co-workers and focuses on the topology of the electron density to describe chemical concepts, such as what distinguishes atoms in molecules and crystals as opposed to their free-atom form, and the unambiguous definition of bonding in such environments56. The Hellmann-Feynmann theorem57-60 demonstrates the important role the electron density distribution plays in understanding the forces and bonding within a given molecule, and that the force acting on a nucleus in a molecule can be obtained by electrostatics alone once the electron density distribution of the molecule is known61.

In the QTAIM, this principle is taken further, where rather than using an orbital- based wavefunction approach – as is the case with KS-DFT methods – instead a complex’s electron density distribution is analysed topologically, with no description of molecular or atomic orbitals, but with local maxima at each nuclear position and other so-called critical points (CPs). CPs represent a point at which the first derivatives of the electron density vanish56.

⃗ ⎧ = 0 ( ∞) = + + → (1.30) ⎨ ⎩ ≠ 0⃗ ( ℎ )

Where i, j and k are unit vectors of the gradient operator ∇. The second derivatives (∇2ρ(r)) are useful for distinguishing between local minima, local maxima and saddle points. There are nine such derivatives that form a Hessian matrix, which at a CP is written as:

⎛ ⎞ (1.31) ( ) = ⎜ ⎟ ⎝ ⎠

This matrix can be diagonalised, which is equivalent to the rotation of the coordinate system r(x,y,z)→r(x’,y’,z’) via a unitary transformation, r’ = rU where

Theoretical background

U is a unitary matrix derived from the equations Aui = λiui (i = 1, 2, 3). When this undergoes the similarity transformation U-1AU = Λ, the Hessian is made into its diagonal form56;

0 0 0 0 ⎛ ⎞ = 0 0 = 0 0 (1.32) ⎜ ⎟ 0 0 0 0 ⎝ ⎠

Where the eigenvalues λ1, λ2 and λ3 are the curvatures of the electron density with respect to x’, y’ and z’.

Critical points are described by their ‘rank’ (ω) and ‘signature’ (σ) and are written as (ω,σ). The number of nonzero eigenvalues gives ω, and therefore in a three-dimensional system, CPs have a rank of 3, and so CPs with ω < 3 are considered unstable. σ values are ±1 depending on the sum of the signs of the curvatures (eigenvalues), where a positive curvature corresponds to a maximum in the corresponding eigenvector direction, and a negative curvature corresponds to a minimum in the corresponding eigenvector direction61. This is shown more clearly in figure 1.2.

Theoretical background

Fig.1.2. Classification of all types of critical points possible in 3D space. The arrows represent the electron density gradient paths and their direction. (3,-3) and (3,+3) represent maximum and minimum points respectively, and (3,-1) and (3,+1) represent two types of saddle points.

Thus, CPs are ranked as follows: (3,-3) nuclear critical point – all gradient paths directed towards a maximum; (3,-1) bond critical point – gradient paths directed towards a maximum in two dimensions and a minimum in one dimension; (3,+1) ring critical point – gradient paths directed towards a maximum in one dimension and a minimum in two dimensions; (3,+3) cage critical point – all gradient paths directed towards a minimum56. The number of CPs that can exist in a complex or crystal follows the relationship below.

1 − + − = (1.33) 0

Where n is the number of CPs. A value of 1 is indicative of an isolated complex and a value of 0 is indicative of an infinite crystal lattice. These two equalities are known as the Poincaré-Hopf relationship36 and Morse equation62 respectively. For this project, focus was mostly on QTAIM properties found at the bond critical points (BCPs) of the complexes.

In the QTAIM, a ‘bond path’, is a line of locally maximum density between any two bonded nuclei63. The point along this line at which the electron density is at

Theoretical background a minimum is the BCP, where ∇ρ(r) = 0 (see equation 1.30), and the BCP lies on the boundary between two atoms. BCPs are useful at probing the bond order (BO) of a chemical bond and can be described thus;

= exp [( − )] (1.34)

Where ρ is the electron density at the BCP and A and B are constants. Generally speaking, ρ is greater than 0.2 e bohr-3 in covalent bonding and less than 0.1 e bohr-3 in ionic bonding56. However, these general rules for covalency in the QTAIM were developed using molecules with much lighter atoms, and not with heavier elements such as heavy transition metals and the f-block elements.

Another QTAIM property of interest is the energy density (potential, kinetic and total) at the BCP and these are taken from the one-electron density matrix. The potential energy density (also known as the virial field) Ѵ(r) is always negative and is related to the kinetic energy density and the Laplacian at a stationary point as64, 65.

ħ ∇() = 2() + Ѵ() 4 (1.35)

ħ () = ∇∗ ∙ ∇ 2 (1.36)

Where G(r) is the gradient kinetic energy. This is always greater than zero, and since Ѵ(r) is always negative, a negative ∇2ρ at the BCP indicates a bonding interaction which is dominated by a reduction of the potential energy, with a positive ∇2ρ at the BCP being indicative of the kinetic energy being the dominating force in the bonding interaction. The total energy density H(r) relates the potential and kinetic energies in a simpler form66.

= + Ѵ (1.37) When interactions have a significant sharing of electrons, H is negative, and its magnitude reflects the extent of covalency66.

Theoretical background

Finally, the delocalisation index is a measure of bond order which gives the number of electron pairs shared between two atoms. This is done by integrating the exchange density over each of the two atoms, the magnitude of which is termed the delocalisation index between atoms A and B [δ(A,B)]67.

(, ) = 2| (, )| + 2 (, ) (1.38)

Where F is the Fermi correlation:

(1.39) (, ) = − ()()

Where σ denotes either α or β spin and Sij and Sji are the overlap integrals of two spin orbitals56. The total number of electrons in the complex N can be obtained by taking the sum of the localisation indices λ(A) – that is, performing the double integration in equation 1.35 over just one atom – and half of the sum of all the delocalisation indices.

1 (1.40) () = () + (, ) 2

As shown in equation 1.34, the electron density at a BCP (ρ) is strongly related to the bond order, and since δ(A,B) can also be used to measure bond order at the BCP, it is possible to describe the relationship of ρ to δ(A,B) as68.

(, ) = exp [( − )] (1.41)

For this project, three main QTAIM metrics were analysed; electron density (ρ), energy density (H), and delocalisation index (δ(A,B)).

Further to these partitioning techniques outlined above to study actinide systems, there are other techniques that can be used that do not involve partitioning methods to gain insight into the electronic behaviour of such systems. These other techniques are useful for describing binding energies and electronic phenomena such as aromaticity. These techniques are discussed below.

Theoretical background

1.7. Energy decomposition analysis

The energy decomposition analysis (EDA) approach is a powerful technique for bond energy analysis, where the complex or molecule in question is fragmented about the bond of interest. In the EDA, the total bond energy (EB) is broken down as follows:

= + + (1.43) where EE, EP and EO are the electrostatic interaction, Pauli repulsion, and orbital mixing terms respectively. The EE component is obtained from the superimposed unperturbed fragment electron densities and corresponds to the effects of Coulombic attraction and repulsion. This is mostly dominated by nucleus-electron attractions. The EP component is obtained by ensuring that the Pauli principle is maintained, and this destabilising term is responsible for describing steric repulsion. Finally the EO component is obtained from the relaxation to self-consistency of the molecular system by the mixing of occupied and unoccupied orbitals on each fragment69. What information the EDA provides on covalency is contained within the EO term.

1.8. Nucleus-independent chemical shifts

The nucleus-independent chemical shift (NICS) criterion is an efficient and simple tool to probe aromaticity of π-systems such as benzene and other arene- based systems. The NICS index is taken directly from the inverse of the calculated isotropic magnetic shielding tensors (in ppm) at a non-nuclear point or space within the molecule70, where this point is usually in the centre of the ring in question and also at points out of plane of the ring70-73. These non- nuclear points are obtained by placing a so-called “ghost atom” at the point of interest. Ghost atoms have no charge or basis sets, and therefore do not affect the overall electronic structure of the system. Consequently by using ghost atoms, the isotropic magnetic shielding tensors can be calculated for any chosen point in the system, not just for protons. NICS values at the centre of the ring with values less than zero indicate aromaticity in the ring, and NICS values greater than zero indicate anti-aromaticity70. This centre point is considered to be an indicator of the σ+π-electron delocalisation74. As is convention, NICS

Theoretical background values at the centre of the ring in this thesis will be denoted as NICS(0), and NICS points above the plane of the ring – in this case 1.0 Å above and below – will be denoted as NICS(1), where NICS(1) is the recommended measure of π- electron delocalisation since a point 1.0 Å out of plane of the centre of the ring is considered to have no influences from the σ electrons72, 75, 76.

These methods are discussed in chapter 2 in relation to their relevance in the field of organoactinide chemistry, but first there is required a general introduction to actinide and organoactinide chemistry.

References

1. P. Atkins and R. Friedman, Molecular Quantum Mechanics, Oxford University Press, New York, 2011, p.295. 2. D. R. Hartree, Proc. Camb. Philos. Soc., 1927, 24, 89. 3. J. C. Slater, Phys. Rev., 1930, 35, 210. 4. V. Z. Fock, Phys., 1930, 61, 126. 5. P. Echenique and J. L. Alonso, Mol. Phys., 2007, 105, 3057. 6. J. C. Slater, Phys. Rev., 1929, 34, 1293. 7. J. C. Slater, Phys. Rev., 1930, 36, 57. 8. S. F. Boys, Proc. R. Soc. (London) A, 1950, 200, 542. 9. F. Jensen, Introduction to Computational Chemistry, Wiley, Chichester, 2nd edn., 2007. 10. E. R. Davidson and D. Feller, Chem. Rev., 1986, 86, 681. 11. T. H. Dunning Jr., J. Chem. Phys., 1989, 90, 1007. 12. A. K. Wilson, T. van Mourik and T. H. Dunning Jr., J. Mol. Struct., 1996, 388, 339. 13. R. A. Kendall, T. H. Dunning Jr. and R. J. Harrison, J. Chem. Phys., 1992, 96, 6796. 14. X. Cao and M. Dolg, J. Molec. Struct. (Theochem), 2004, 673, 203. 15. W. Küchle, M. Dolg, H. Stoll and H. Preuss, J. Chem. Phys., 1994, 100, 7535. 16. W. Kohn and L. J. Sham, Phys. Rev., 1965, 140, 1133. 17. F. Bloch, Z. Physik, 1929, 57, 545. 18. P. A. M. Dirac, Proc. Camb. Philos. Soc., 1930, 26, 376. 19. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865. 20. J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, Phys. Rev. B, 1992, 46, 6671. 21. A. D. Becke, Phys. Rev. A, 1988, 38, 3098. 22. C. Lee, W. Wang and R. G. Parr, Phys. Rev. B, 1988, 37, 785. 23. J. P. Perdew and Y. Wang, Phys. Rev. B, 1986, 33, 8800. 24. K. Burke and L. O. Wagner, Int. J. Quantum Chem., 2013, 113, 96.

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74. G. V. Baryshnikov, B. F. Minaev, M. Pittelkow, C. B. Nielsen and R. Salcedo, J. Mol. Model., 2013, 19, 847. 75. P. v. R. Schleyer, H. Jiao, N. J. R. v. E. Hommes, V. G. Malkin and O. L. Malkina, J. Am. Chem. Soc., 1997, 119, 12669. 76. A. Stanger, J. Org. Chem., 2006, 71, 883.

Organometallic chemistry of the f-elements

Chapter 2. Organometallic chemistry of the f-elements

The first part of this chapter provides an overview of the organometallic chemistry of the f-elements. This is followed by a literature review of the computational techniques which are applied to computational organoactinide chemistry. Finally, the specific pyrrolic macrocycle-supported complexes which were studied in this thesis are presented and described.

2.1. Background and chemistry of organoactinides

Research in the organometallic chemistry of the early actinides has seen a significant amount of interest in recent years1-11. However, the history of actinides being used in the context of organometallics can be traced back to the middle of the 20th century, both during and after the Manhattan Project12. The attempted syntheses of tetramethyl- and tetraethyl-uranium for uranium isotope separation were unsuccessful or were thought to lead to highly unstable products13. Subsequent work in 1974 by Marks and Seyam continued to show that tetra alkyls of uranium(IV) readily decomposed at room temperature14 but the first successful synthesis of a peralkyl complex of an actinide element was tetrabenzyl-thorium in the same year15.

Carbocyclic organometallic complexes involving the actinide series were discovered earlier than 1974 in the decades immediately following the second world war16-18. Notably, 1956 saw the synthesis of U(Cp)3Cl and similar thorium derivatives19 and over the next few decades complexes analogous to these were synthesised for actinides across the series ranging from thorium to californium20-23. 1968 saw the synthesis of uranocene24; a uranium compound where the uranium is bonded to two cyclooctatetraenyl rings in the bis-η8 fashion, where the Greek letter ‘η’ (eta) denotes the degree of hapticity – i.e. uranium bonded to all eight carbon bonds in the cyclooctatetraenyl ring. This is

Organometallic chemistry of the f-elements of interest as it is an example of a so-called “sandwich” complex; a family of organometallic complexes where two aromatic rings coordinate to metal centres with high hapticity. Research into sandwich complexes gained ground in the 1950s and ‘60s after Miller et al. accidentally synthesised ferrocene, or bis(η5-cyclopentadienyl)iron, in 1951. This was from trying to oxidatively couple cyclopentadienyl25. The structure of ferrocene was determined independently by two separate groups a year later by Wilkinson et al.26 and Fischer et al.27, both of whom shared the Nobel Prize for Chemistry in 1973 for their work.

The interest in organoactinide complexes was due in part to the unique presence of 5f-orbitals in actinides, which are at a high enough energy to take part in bonding. This is in contrast to the lanthanides where the 4f-orbitals are more core-like, shielded by the 5d and 6s orbitals. Therefore, the early actinides can adopt a wide range of oxidation states. Since the 5f-orbitals become increasingly core-like as one progresses further across the periodic table, the later actinides become increasingly lanthanide-like. Furthermore, by using the same ligands found for transition metal sandwich complexes it was suggested that complexes with higher coordination numbers to actinide centres may exist due to the availability of more symmetry-allowed combinations of metal orbitals28. This is especially true for uranocene and other actinocenes, where there are a number of symmetry-allowed orbital combinations, which are not found in the transition metals, between the 5f-orbitals from uranium and the p- orbitals of the eight carbons, as shown in figure 2.1.

Organometallic chemistry of the f-elements

Fig.2.1. Representations of the 5f- (red) and 6d-bonding (blue) interactions in actinocenes. Image taken and edited from the work of Minasian and co-workers29.

As with the transition metals, the actinides can also form sandwich complexes with five and six-membered aromatic rings, except due to the presence of the f- orbitals, there are more symmetry-allowed combinations of the C6H6 and C5H5 π-orbitals to the actinide centres, giving rise to δ- and φ-bonding interactions, as shown in figure 2.2.

Organometallic chemistry of the f-elements

Fig.2.2. Representations of the 5f- (red) and 6d-antibonding (blue) interactions in bis-arene (top) and bis-C5H5 (bottom).

The research in this thesis is concerned with actinide complexes that exhibit sandwich interactions as shown in figure 2.2, and examples of the computational study of other such complexes are discussed later in this chapter.

Recognition that the f-orbitals may play an important role in such haptic bonding dates back to the work of Wilkinson and Reynolds19. However,

Organometallic chemistry of the f-elements covalency in the early actinides involving the 5f-orbitals has been a subject of debate, both experimentally and theoretically28, 30, 31, ever since various spectroscopic techniques were employed to probe their bonding28. As such, much care needs to be taken when defining exactly the type of bonding that arises in these systems30. Whilst traditionally it is thought that transition metals and early actinides may have significant covalency characteristics, and the lanthanides exhibit more ionic character32, these descriptions are constantly being reassessed33 as new f-block systems are synthesised and characterised34- 37, whilst the nature of covalency itself (overlap-drive vs energy-driven) has also recently been scrutinised closely30, 38, 39.

2.2. Computational organometallic chemistry of the f-elements

Computational methods are of particular importance to actinide and organoactinide chemistry. Experimentally, the majority of actinide systems only feature thorium or uranium, owing to these elements’ relatively lower radioactivity compared to the other actinide elements, which allows them to be handled outside of specialist laboratory facilities. For actinium and protactinium, and the rest of the transuranic elements, specialist equipment and laboratories are required as these actinides become increasingly more radioactive and difficult to handle. As such, the ability to study transuranic complexes computationally is very helpful in inspecting the electronic structures of these systems that may be either extremely difficult to synthesise or handle experimentally. Of course, one needs to be confident that the computational results are reliable in the absence of experimental data, usually through bench-marking of simpler systems that can be directly compared to experiment.

However, computational studies of the f-elements are not without problems. The understanding of electronic structure and bonding is not as straightforward for the lanthanides and actinides as it is with complexes with lighter atoms. This is due to the more complex electronic structures in f-elements arising from the many possible electronic configurations of the f-orbitals, electron correlation effects, and relativistic effects seen largely with the heavier elements40, 41. Therefore, one of the main concerns with actinide-based systems is that

Organometallic chemistry of the f-elements different computational approaches can yield different descriptions of their bonding41, and so choosing the right technique is often difficult and requires care.

In most cases density functional theory (DFT) is one of the most practical methods in treating the correlation for actinide systems42, 43, and there are many reviews about the use of DFT in inorganic and organometallic chemistry44-46. Even in the context of f-element chemistry, there is not one method of DFT which can guarantee correct results for descriptions of ionicity, covalency, partial atomic charges, spin densities and electron densities - different types of DFT need to be used and compared41. The lack of consistency found in DFT between functionals in describing bonds even across the s-, p- and d-blocks are discussed by Kepp45.

Despite these shortcomings, computational chemistry can still complement experimental research aiming to investigate the nature of such systems. For example, early studies found evidence for [bis(η6-benzene)An]+ from mass spectrometry data, where An is either thorium or uranium47, 48. Driven by this, computational studies showed that the neutral form of bis(η6-benzene)U is thermodynamically stable and therefore a possible synthetic target49, 50. This has yet eluded synthetic chemists. A recent study found that it is possible to synthesise the neutral single benzene complex An(C6H6) (where An = Th or U) but that no experimental evidence for the analogous sandwich complexes in the neutral form were found51.

2.2.1. DFT and orbital-based partition methods

One common orbital-based partition method is Mulliken population analysis (MPA) which is useful for describing the bonding in organoactinide systems.

There are a number of studies using MPA analysis to describe the bonding in carbocyclic actinide complexes. As has been demonstrated by figure 2.2, the ability of these rings to bind with high hapticity to an actinide centre owes itself to the range of symmetry-allowed orbital combinations of the actinide d- and f- orbitals with the p-orbitals of the carbon rings. The opportunity to study the bonding in these unique systems from a computational perspective is therefore

Organometallic chemistry of the f-elements far-reaching. One such study30, (again using the MPA), sets out to investigate whether covalency increases across the actinide series for a set of AnCp3 and

AnCp4 complexes (An = Th – Cm).

The study showed that on the basis of orbital mixing from DFT and MPA, the actinide-carbon bonds from the Cp rings increased in covalency across the series. However, the CmCp4 broke the expected trend of a progressive shortening of the actinide to ligand bond, with a slightly increased Cm-Cp centroid distance observed52. In this particular study, lengthening of the Cm-Cp separation was further rationalised by the conclusion that the Cm(IV) ion, which is formally 5f6, undergoes ligand to metal charge transfer, due to the stability of the 5f orbitals this far in to the actinide series52, resulting in a Cm(III) f7 centre.

Although not an organoactinide system, similar observations as highlighted above have been found in another very widely-studied system; the dioxo actinyl unit (Oyl-An-Oyl)n+ (or simply AnO22+), which is very common in uranium chemistry. This exists experimentally within compounds and organoactinide frameworks. A previous study53 of AnO2 (An = Th – Es) systems in isolation showed that covalency of the An-Oyl bonds increased across the actinide series based on spin densities of actinide 5f orbitals and oxygen 2p orbitals obtained from DFT. Building on this finding in the context of organoactinide chemistry, a later study54 of [(AnO2)(CO3)3]4- (An = U – Cm), in relation to their bonding orbitals, was carried out to investigate why the Cm(VI) system of this complex has so far eluded synthetic chemists. It was concluded that as the actinide centre becomes progressively heavier past uranium, the 5f orbitals – which for Ac-Pa are too high in energy to take part in bonding – contract enough to take part in bonding, before contracting so much and falling so low in energy that they are no longer able to overlap with the ligand orbitals. From this the expected trend of a shortening of the An-Oyl across the actinide series was broken, as was found with the AnCp4 series52, with instead a slight lengthening of this bond observed for Am and Cm54. There are other studies employing computational methods to probe the behaviour of actinide bonding in these

Organometallic chemistry of the f-elements actinyl units55, 56. However, as these studies are not in the context of organoactinide chemistry, they are not discussed here.

Returning to the work by Tassell and Kaltsoyannis on the Cp-based systems, this study also employed the use of NBO analysis – another orbital-based partitioning scheme – and for the 6d orbitals was in agreement with the MPA52. Like the MPA, NBO analysis has been used extensively when studying f-element complexes, with the earliest such study being on lanthanide(II) metallocenes in 1992 by Kaupp and co-workers57. However, the older versions of the NBO code available at the time of this study conformed strictly to the Aufbau principle, which would force some f-block metals to be analysed as if in their excited state electronic configurations, which can affect the NPA charges of the lanthanides and actinides58.

This issue was first raised by Maseras and Morokuma who argued whether or not the addition of empty p-orbitals to the valence space of the NPA in transition metals should be considered59. All recent NBO versions now take such orbitals into account, including for the f-block metals60. However there is still contention in the theoretical community as to the best method to employ for electronic structure analysis, with a recent review by Dognon comparing a range of techniques – including NBO analysis – when applied to systems of

[(R)UO2(O2C-R)2]- (R = CH3)41. For this study by Dognon41, as well as employing a variety of partition methods to assess the uranium charges in this complex, increasingly large all-electron double, triple and quadruple zeta basis sets were also used to see how this affected the results. Whilst the charges changed little as a function of basis set within each partition method, each method yielded very different results for the uranium charges when compared, where this charge ranged from 0.58 to 2.99. The NPA method underestimated the uranium charge, and the MPA method showed a larger charge by comparison41.

Nevertheless, a myriad of recent studies have proven NBO and associated NPA analyses to be reliable tools when analysing electronic structure and covalent bonding in the f-elements52, 61-65. The joint experimental and computational study by Arnold et al63 found that for the dinuclear uranium complex [UN’’2]2(μ-

C6H6) (N’’ = N(SiMe3)2) shown in figure 2.3, increasing the pressure of the

Organometallic chemistry of the f-elements system resulted in the evolution of an agostic bond – a three-centre two- electron interaction – between the metal-to-hydrocarbyl C-H interaction which was supported by NBO analysis63.

Fig.2.3. [N’’2U]2(C6H6), labelled as ‘1’ by Arnold et al. Image reproduced from reference 63.

Organoactinide systems that do not feature haptic bonding (ηn cf. start of this chapter) with aromatic ring systems have also been studied. Narbutt et al64 used NBO and NPA analysis to investigate bonding in europium and americium to the ligand N,N,N’,N’-tetraoctyl-diglycolamide (TODGA) (figure 2.4) to try to rationalise the lack of actinide selectivity by this particular ligand, which has also been known to favour bonding with lanthanides over actinides66.

Fig.2.4. Chemical structure of TODGA (n-Oct = n-octanol). Image reproduced from Wang and co- workers67.

NBO analysis found a slightly greater degree of covalency in the Am-O bonds than in the Eu-O bonds, which corresponded to a greater formation energy of

[M(TODGA)3]3+ in water, but not in the gas phase. This difference in formation energy between phases led the authors to conclude that NBO analysis was better suited for analysing covalency rather than for estimating total bond strength64.

Organometallic chemistry of the f-elements

A similar study by Wu et al65 set out to investigate the selectivity of four 1,10- phenanthroline-derived ligands for the separation of trivalent actinides and lanthanides. It was found through NPA and NBO analyses that the 5d and 6d orbitals of Eu and Am respectively accept more electron density than other orbitals, but that the d orbitals with more accepted electrons contributed little to the overall metal-ligand bond65. Moreover, the natural charges of the metal and ligating atoms suggested a higher degree of charge transfer and therefore a bond dominated by electrostatic interactions.

NBO analysis has also been used to complement experimental research in a joint electrospray ionisation mass spectrometry (ESI-MS) and DFT study of europium, uranyl and thorium-phenanthroline amide complexes which showed evidence of covalency in the metal-ligand interactions68.

There are new orbital-based partition methods under development. For example, work to overcome the basis set sensitivity of a range of methods highlighted by Dognan41 has been carried out through a relatively recent approach by Gagliardi and co-workers known as “LoProp”69, and has shown promising results with non-actinide systems69-71. This method is of interest to actinides since, as well as DFT, it can also be used at the complete active space self-consistent field (CASSCF)72, 73 level of theory74. Although not used in this thesis, CASSCF is nevertheless an important computational method used in actinide chemistry, and it is worth describing in brief. CASSCF works by dividing orbitals into active and inactive orbitals and then performing a full configuration interaction (FCI)75 within the CAS76. CASSCF is therefore a very robust method for describing excited states in the 5f series, where the many different possibilities for the electron configurations beget complex electronic structures.

This is not to say that CASSCF is universally superior to DFT; DFT studies can still give reliable results for describing electronic structure and bonding in the actinides, particularly for probing the bond strengths and energies of actinide- based complexes77, 78.

Organometallic chemistry of the f-elements

The majority of the orbital-based partition method studies highlighted in this section did not employ only MPA and NPA analyses, as has been pointed out at least for Dognon’s work41. Partition methods based on the electron density of the systems – predominantly the QTAIM analysis – were also used extensively, as well as in this thesis. The next section discusses how these different types of partition methods affect the results in the complexes discussed in section 2.2.1, and therefore highlights the care and considerations needed when selecting a particular partition method for bonding and electronic structure analyses in actinide organometallics.

2.2.2. QTAIM analysis of organometallics of the f-block elements

In computational organometallic chemistry, the QTAIM has been employed extensively for studying transition metal complexes79-81. However, the application of the QTAIM to actinide complexes occurred only as recently as 2006 in a limited study by Petit et al.82 Since then, the QTAIM has made important contributions to the discussion of covalency and ionicity in actinide bonding30.

Studies on the AnCp3 and AnCp4 systems outlined in section 2.2.1, which showed increasing covalency across the actinide series with NPA analysis, actually showed the exact opposite trend when analysed by the QTAIM i.e. according to the QTAIM, the An-Cp interactions became more ionic across the actinide series30. This contradiction between the two methods is not necessarily universal, however. E.g. the QTAIM analysis on the [M(TODGA)3]3+ complexes showed a larger degree of covalency for the Am-O bond compared with the Eu- O bond, which agreed with the orbital-based partitioning approach of NBO analysis64. Furthermore, QTAIM bond analysis of Eu and Am to 1,10- phenanthroline-derived ligands carried out by Wu et al65 agreed with the observation from NPA and NBO analysis suggesting a more ionic interaction, based on the QTAIM electron density at the BCP.

As with the orbital-based partition methods, the QTAIM has also played a key role in complementing both experimental data and other computational methods for a range of f-block organometallics83-86. Key studies in conjunction

Organometallic chemistry of the f-elements with experiment were carried out by Zhurov and co-workers, in which

Th(S2PMe2)487 and Cs2UO2Cl4 were the first actinide complexes to be studied by the QTAIM using electron density obtained from experimental data88, 89. The data from Zhurov and co-workers was recently compared to computationally- derived QTAIM data for the same complexes by Wellington and co-workers90. It was found that the differences between the experimentally and computationally-determined electron densities may have arisen from the experimental approach rather than the computational approach.

The QTAIM has also been used recently to study more actinide systems which continue to show different descriptions of bonding in terms of whether they are covalent or ionic. Studies on U-Cl bonds in [Li(THF)4][UCl5(THF)]91; Th-Th interactions in (C5H5)2Th2(CO)3 and (C5H5)2Th2(CO)492; and U-X bonds (X = F-,

Cl-, OH-, CO22-, and O22-) in uranyl(VI) complexes93 all showed significant ionic characteristics in the actinides, whereas a study of U-OAr2 and U-SAr2 bonds in the U-S interactions compared with U-O94; and U-N bonds in BTP and isoamethryn95 showed covalent characteristics.

Furthermore, the QTAIM has also been shown to predict and model the strengths of actinide bonds in a variety of complexes96-98, and this particular use of the QTAIM for this thesis is revisited in chapter 5.

2.2.3. Non-partition-based methods – EDA and NICS analyses

Other approaches that are not partition-based methods have been used in relation to actinide chemistry, for example, to study bonding energies. As outlined in chapter 1, a very common approach is the EDA method. This has been found to be useful in the context of computational organometallic chemistry of transition metals and actinides. Furthermore, the standard EDA scheme to determine bond energies has been found to compare well with partition methods used to describe covalency or ionicity mentioned in section 2.2.2.

In non-metallic systems, linear relationships were found between the hydrogen bond energies in hydrogen fluoride and nitrile complexes and ρ at the BCP from the QTAIM99, 100. Since then studies on dimeric M2X6 systems (M = Mo, W, U; X =

Organometallic chemistry of the f-elements

Cl, F, OH, NH2, CH3) showed correlations between the QTAIM metrics at the bond critical points of the M-M bonds with the M-M bond energies obtained from EDA96. In this same study, the EDA and QTAIM metrics were also correlated for M-ligand bonds in (CO)5M- units bonded to three different tautomers of imidazole (where M = Cr, Mo, W)96. These correlations, however, were found only when the electrostatic and Pauli energies in the EDA summed approximately to zero, meaning that the vast majority of the total bond energy arose from the orbital mixing term, and therefore the QTAIM metrics for covalency could be directly compared to the orbital mixing energies obtained from the EDA101, 102.

More recent approaches to the EDA scheme have been developed specifically for open-shell systems, such as the absolutely localised molecular orbital-EDA (ALMO-EDA)103 scheme, used to study alkyl radicals and benzene radical cation complexes104. More applicable to the f-elements is the constrained space orbital variation (CSOV) method105 for both open and closed shell f-block mono aqua complexes. This has proved useful for obtaining bond energies for open shell systems, where a polarisation contribution Epol is included in the CSOV EDA method, 10% of which is made up from the polarisation energy of the unpaired electrons106. Although the ALMO-EDA and CSOV methods of the EDA can be more useful for analysing the f-elements due to such complexes usually being open-shell, the standard EDA scheme is still a reliable approach.

Another non-partition-based method useful for inferring key physical characteristics of bonding in the organometallic chemistry of the f-elements is NICS analysis. As discussed in section 1.8, NICS analysis is a useful way of measuring aromaticity, which is of particular use for organoactinide complexes exhibiting haptic bonding with CnHn rings. A recent study107 of An(COT)2 (An = Th, Pa, U; COT = 1,3,5,7-cyclooctatetraene) used NICS to conclude that in these complexes, the delocalisation of the 5f orbitals on the actinide centres contributes to increased π-aromaticity in the COT rings when compared to the isolated COT2- rings. This phenomenon of electron delocalisation as a result of metal centre-ring interaction has been described by some authors as spatial aromaticity108.

Organometallic chemistry of the f-elements

Another study has successfully characterised the extent of aromaticity in the uranium metallacycles cyclo-UnXn (n = 3, 4; X = O, NH) and cyclo-Un(µ2-X)n (n = 3, 4; X = C, CH, NH) clusters109 which showed very large and negative NICS values compared to the much smaller NICS values found in similar metallacycles of ruthenium110 and three-membered Mg3n- (n = 0, 1, 2) rings111, 112. This finding builds on the evidence of the higher extent of radial distribution found in the frontier orbitals of the actinides and how this can have a direct effect on the electron delocalisation of such organoactinide systems.

NICS can also be compared to the QTAIM, since a study by Bader et al.113 on benzene showed how measuring the delocalisation index between two para- carbons in a benzene ring can be an indirect measure of aromaticity. Chapter 4 of this thesis shows how this QTAIM measure of aromaticity has been applied to some of the model systems studied in the rest of this thesis, and how this can be directly compared to the NICS analysis of the same complexes.

2.3. Recent developments in carbocyclic organoactinide chemistry

The recent synthesis of uranium-arene complexes [(X2)U(µ-C6H5R)], where X and R are various ligands and organic groups respectively7, has prompted more computational studies of the bonding of actinide-arene systems, recognising that the d- and f-orbitals in the actinide – back-donating to the π-orbitals in the arene rings – as being an important component in the bonding of such complexes114-116.

These complexes where actinides are bonded to large, delocalised π-systems have been the key to finding f-element complexes where extensive metal-to- ligand electron-transfers enable the high reactivity required for dinitrogen cleavage117, and nitride and dinitrogen partial hydrogenation118-121. Therefore, the need for a theoretical understanding of the electronic properties of these systems is imperative. Using pyrrolide-based ligands has also been of interest to actinide chemists since the turn of this century121-126, owing to their similarity with cyclopentadienyl anions and their ability to enhance the reactivity of low- valent samarium121, 122 and stabilise low oxidation states of thorium121, an actinide not well-known for low oxidation states127-129. The presence of a single

Organometallic chemistry of the f-elements arene ring as a link between two pyrrolide anions stabilises this rare thorium species121. However, this particular ligand could lead to ring opening and therefore the destruction of the desired bonding motif130. As such, a further investigation into obtaining a more stable aromatic ligand to moderate the reactivity of the f-element complex employed a system whereby the pyrrolide anions are linked by two arene rings instead of one121. Such a ligand was found with the trans-calix[2]benzene[2]pyrrolide ligand first synthesised by Sessler et al131.

2.3.1. The trans-calix[2]benzene[2]pyrrolide ligand

Bis-arene complexes of thorium and uranium are the main target of this thesis, specific examples of which have been recently synthesised and studied by P. L. Arnold et al3, 11, 132. These unique complexes adopt the bis-arene motif present in the trans-calix[2]benzene[2]pyrrolide (L), the neutral form of which is shown in figure 2.5.

Fig. 2.5. Neutral form of trans-calix[2]benzene[2]pyrrolide with hydrogens on the nitrogens. Image taken from the work of Arnold and co-workers3.

Due to the alternating system of aromatic rings in arene and pyrrole and the interrupted conjugation of these rings by dimethyl linkers, this complex is able to adopt a variety of conformations when ligated to various metal centres. For f- element complexes of this ligand , the loss of hydrogen on the pyrrole nitrogens (L2-) can allow these nitrogen atoms to bond with the actinides in a κ1:κ1 (analogous to η1:η1 but where κ1 indicates a bond to the nitrogen, not a carbon,

Organometallic chemistry of the f-elements in the pyrrole ring) fashion whilst the benzene rings are able to bond in an η6:η6 fashion with the actinide centre131. This bonding mode was first found in samarium(III) complexes121 but has since also been seen in uranium(III), uranium(IV) and thorium(IV) complexes, the latter two also being able to exhibit κ5:κ5 bonding on the pyrrole rings instead of κ1:κ1 bonding11. Furthermore, this ligand has been shown to accommodate two uranium centres: one uranium resides in the bis-arene pocket (η6:η6); and the other in the bis-pyrrole pocket (κ5:κ5)11. Alkali metal cations are also accommodated in the bis-arene pocket following further deprotonation of L2- whereby protons are lost from the arene rings (L4-), allowing κ5:η1:κ5:η1 bonding to the actinide centre132. All of these different bonding motifs are presented in figure 2.6.

Fig. 2.6. Different bonding motifs of L2- and L4- with various metal centres. Clockwise from top left: LAnX2 κ5:κ5; LUIIIX η6:κ1:η6:κ1; LU2I4 κ5:κ5 and η6:η6; and M[LAnR] κ5:η1:κ5:η1. An = Th, U; X =

Cl, I; M = Li, K; R = CH2Ph, CH(SiMe3)2, Me, CH2SiMe3. Images taken from references 11 and 132.

Organometallic chemistry of the f-elements

Recent research by Arnold et al. has involved the synthesis of more complexes analogous to LUIIIX in figure 2.6, with the L2- ligand in the η6:κ1:η6:κ1 bonding mode. These take the general form of [LAnX]n+ (An = UIII, ThIV; n = 0, 1) and are

LUN(TMS)211 (where TMS is tetramethylsilane), LUBH411, 133, LUDTBP11 (where

DTBP = 2,6-di-tert-butylphenoxide) [LThN(TMS)2]+134 and bi-metallic complexes incorporating L2-/L4- with alkynyl X ligands and an alkaline or transition metal as well as the presence of an actinide centre132. There is also ongoing work to generate an alkyl form of [LAnX]n+ wherein a methyl group coordinates in place of N(TMS)2, BH4 and DTBP. This family of complexes provides an excellent opportunity to computationally probe the bonding of the actinides to the X-type ligand where the ligating atom in X becomes progressively more electronegative from boron to oxygen, and by extension, to investigate how changing this ligand affects the rest of the bonding between the actinide centre and the L2- ligand.

The next chapter introduces the model complexes studied in this thesis which incorporate the L2-/4- ligand, and a description of the computational methodology used.

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Methodology

Chapter 3. Methodology

3.1. Model complexes

A systematic computational study of the bonding and electronic structure of [LAnX]n+ (An = UIII, ThIII, ThIV; n = 0, 1) complexes in which L2- adopts the η6:κ1:η6:κ1 bonding mode was carried out. Particular attention was given to the actinide-X, actinide-nitrogen and actinide-arene bonds with respect to their electronic structure and bonding properties. The X ligands were units where the ligating atom covered the first row p-block series from boron to oxygen, in the form of BH4, CH3 and ligands based on the experimentally-characterised complexes of LUN(TMS)2, LUDTBP, [LThN(TMS)2]+ plus a second boron-based ligand based on pinacolato boron.

For these [LAnX]n+ systems, the largest model complexes were simplified so that the methyl groups in L2- were replaced with hydrogen atoms, and any methyl groups in the X ligands which were thought not to be directly involved in bonding were also replaced with hydrogen atoms, i.e. pinacolato boron became BO2C2H4, N(TMS)2 became N(SiH3)2 and DTBP became OPh. Therefore fifteen [LAnX]n+ complexes were initially studied, where An = ThIV, ThIII or UIII and X = BH4, BO2C2H4, CH3, N(SiH3)2 and OPh, as shown in figure 3.1 for the simplified ligands.

Fig.3.1. The simplified X-ligands: (a) BO2C2H4; (b) N(SiH3)2; (c) OPh

The [LAnX]n+ complex therefore adopted the following conformation in figure 3.2.

Methodology

Fig.3.2. [LAnX]n+ complex (An = UIII, ThIII, ThIV; n = 0, 1) with labelled arene rings and pyrrole nitrogens.

In chapter 4, these [LAnX]n+ complexes were first optimised with the PBE and PBE0 functionals, to determine which functional was best suited for matching geometric data with experiment. Partial charge analyses of the actinide centres and X ligands using MPA, HPA, NPA and QTAIM were then carried out with the preferred functional, before analysing the bonding properties of the An-X interaction using the QTAIM and NBO analyses. As well as these actinide-based complexes, analogous complexes with transition metals were studied to compare how the NBO and QTAIM descriptions of bonding differed between the d- and f-block elements. The transition metals employed for this were hafnium(IV) and tungsten(III), thus giving an additional ten [LMX]n+ complexes. Returning to the actinide [LAnX]n+ complexes, the Kohn-Sham molecular orbitals (KS-MOs) of the An-X bonds obtained from DFT were compared to the QTAIM data to investigate how the KS-MO descriptions differed from the NBO analysis. Finally, NICS analysis on the [LThIVX]+ complexes was carried out to study the aromaticity of the arene rings in L2- and to compare these findings with the QTAIM metrics of these rings, as well as to see if the QTAIM metrics of the Th-X bond showed any correlations with the NICS results of the arene rings in each [LThX]+ complex. Finally, the NICS data was compared with the KS-MOs of the Th-Ar interactions to see if indirect evidence of aromaticity from KS-MO analysis could be inferred.

Methodology

Chapter 5 focuses on the bond energies of the An-X bonds in the fifteen [LAnX]n+ complexes based on their SCF energies and thermal corrections. These bond energies were calculated both as heterolytic and homolytic separations, with these energies compared against the QTAIM An-X bond metrics calculated in chapter 4. The EDA was further used to compare the different components of the total bond energy with the QTAIM metrics. Furthermore, with the QTAIM vs EDA analysis, the set of [LAnX]n+ was expanded to include simplified X-type ligands where the chemical environment of each X-type ligand was kept the same. Therefore the expanded set of X-type ligands in this part of chapter 5 were as follows:

 X ligands; BH4, BO2C2H4, CH3, N(SiH3)2 and OPh.

 X’ ligands; CH3, NH2, OH and F.

 X’’ ligands; CH2Ph, NHPh and OPh.

 X* ligands; SiH3, PH2, SH and Cl.

 X** ligands; SiH2Ph, PHPh and SPh.

 X† ligands; CPh3, SiPh3, NPh2, PPh2, OPh and SPh.

Finally, in chapter 6, M[LAnR] and LAnR’2 (M = Li-Cs; An = Th; R = CH2Ph,

CH(SiMe3)2, Me; R’ = CCSiH3, CCSiMe3, CCSiiPr3) complexes were investigated for their thermal stabilities when looking at their reaction pathways of M[LAnR]

→ LAnR’2. These complexes are shown in figure 3.3.

Fig.3.3. Schematic of, left; the M[LThR] complexes (M = Li, Na, K, Cs and Rb; R = Me, CH2Ph) and right; the LTh(CCR’)2 complexes (R’ = SiH3, SiMe3 and SiiPr3). Image taken from reference 1.

Methodology

Further to these complexes, the KS-MOs of much larger systems – involving a secondary transition metal centre of either Ni(0) or Pt(0) – were investigated in order to understand the reasons behind the relative thermal stabilities of these complexes’ two different binding modes (denoted ‘a’ and ‘b’) of L2- to the An(IV) centre. These complexes were studied with An(IV) centres ranging from Th-Am, and an example of the Th(IV) with Ni(0) version of this complex, with its different binding modes, is shown in figure 3.4.

Fig.3.4. Schematic of the [LTh(CCSiMe3)2][NiPR3] complexes (R = Cy, Ph) in the a form (left) and b form (right). Image taken from reference 1.

3.2. Computational methodology

The software and input parameters for this study are discussed here. Unless stated otherwise, all geometry optimisation calculations, frequencies calculations, single point calculations and orbital population analyses (chapters 4 and 6) were carried out using KS-DFT in the Gaussian 09 code (revision D.01)2, using GGA in the form of the PBE functional and also the hybrid functional PBE0. Dunning’s correlation consistent polarised valence triple-ζ (cc- pVTZ) and polarised valence double-ζ (cc-pVDZ) quality basis sets3, 4 were used for light atoms and Stuttgart/Bonn quasi-relativistic 60 core-electron pseudopotentials and associated valence basis sets were used for thorium to americium5-7, and a quasi-relativistic 48 core-electron PP for cerium8, 9. For the transition metals, Stuttgart/Bonn fully-relativistic 10 and 60 core-electron PPs and their associated valence basis sets were used for nickel10, 11 and platinum12 respectively, and quasi-relativistic 60 core-electron PP and associated basis set was used for hafnium and tungsten11, 13. Finally, potassium, rubidium and

Methodology

caesium also required the use of PPs which were quasi-relativistic 10, 28 and 46 core-electron PPs with their associated valence basis sets respectively14.

The ultra-fine integration grid was used. Frequencies calculations were used to determine if all stationary points are true minima, and to obtain thermodynamic corrections to the self-consistent field (SCF) energies, which are useful when calculating bond dissociation energies. The number of SCF cycles permitted for SCF convergence was set to 512.

NBO calculations were carried out using the NBO6.0 software package15. The QTAIM calculations were carried out using AIMQB (Version 14.11.23, Professional) and their results analysed in AIMStudio (Version 14.11.23, Professional) from the AIMAll software package16.

For chapter 5, the Amsterdam Density Functional (ADF) software package17-19 was used for the EDA analysis and for these calculations the PBE functional was used in single point calculations at the optimised geometries of the PBE0-based full complexes and ionic fragments carried out in Gaussian09. This was due to the PBE0 functional consistently failing to converge the SCF energy in ADF. All light atoms in ADF were treated with triple-ζ quality Slater type orbital basis sets with one set of polarisation functions (TZP) and for the actinides with all- electron quadruple-ζ basis sets with four polarisation functions (QZ4P). Scalar- relativistic effects were incorporated by means of the zeroth-order regular approximation (ZORA)20-22. The SCF cycle was limited to 500 iterations with the default convergence criterion of 10-6 Hartrees. The Veronoi integration grid23, 24 was used with a precision parameter of 6.0 and a pair-fit density fitting scheme with a symmetric fit approximation set at the default 10.0 Å19.

For open-shell ionic fragments, a spin restricted single point calculation on the fragment was first needed, followed by an unrestricted single point calculation at the same fragment geometry with an accompanying EDA calculation. This produced a correction energy term which was subtracted from the EO and EB energies obtained in the EDA calculation of the full open-shell complex, which was performed spin restricted, as per the conventional method for open shell fragments25.

References

1. M. Suvova, K. T. P. O'Brien, J. H. Farnaby, N. Kaltsoyannis and P. L. Arnold, Organometallics, 2017, 36, 4669. 2. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. 3. T. H. Dunning Jr., J. Chem. Phys., 1989, 90, 1007. 4. R. A. Kendall, T. H. Dunning Jr. and R. J. Harrison, J. Chem. Phys., 1992, 96, 6796. 5. W. Küchle, M. Dolg, H. Stoll and H. Preuss, J. Chem. Phys., 1994, 100, 7535. 6. X. Cao, M. Dolg and H. Stoll, J. Chem. Phys., 2003, 118, 487. 7. X. Cao and M. Dolg, J. Molec. Struct. (Theochem), 2004, 673, 203. 8. M. Dolg, H. Stoll, A. Savin, H. Preuss, Theor. Chim. Acta., 1989, 75, 173. 9. M. Dolg, H. Stoll, A. Savin, H. Preuss, Theor. Chim. Acta., 1993, 85, 441. 10. M. Dolg, U. Wedig, H. Stoll and H. Preuss, J. Chem. Phys., 1987, 86, 866. 11. J. M. L. Martin and A. Sundermann, J. Chem. Phys., 2001, 114, 3408. 12. D. Figgen, K. A. Peterson, M. Dolg and H. Stoll, J. Chem. Phys., 2009, 130, 164108.

References

13. D. Andrae, U. Haeussermann, M. Dolg, H. Stoll, H. Preuss, Theor. Chim. Acta., 1990, 77, 123. 14. T. Leininger, A. Nicklass, W. Küchle, H. Stoll, M. Dolg and A. Bergner, Chem. Phys. Lett., 1996, 255, 274. 15. E. D. Glendening, J. K. Badenhoop, A. E. Reed, J. E. Carpenter, J. A. Bohnmann, C. M. Morales, C. R. Landis and F. Weinhold, in Theoretical Chemistry Institute, University of Wisconsin, Madison, 2013. 16. T. A. Keith, AIMAll (Version 14.11.23), TK Gristmill Software, Overland Park KS, USA. (aim.tkgristmill.com) 17. G. te Velde, F. M. Bickelhaupt, S. J. A. van Gisbergen, C. Fonseca Guerra, E. J. Baerends, J. G. Snijders and T. Ziegler, J. Comput. Chem., 2001, 22, 931. 18. C. Fonseca Guerra, J. G. Snijders, G. te Velde and E. J. Baerends, Theor. Chem. Acc., 1998, 99, 391. 19. SCM. ADF2013, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com, 2013. 20. E. van Lenthe, E. J. Baerends and J. G. Snijders, J. Chem. Phys., 1993, 99, 4597. 21. E. van Lenthe, E. J. Baerends and J. G. Snijders, J. Chem. Phys., 1994, 101, 9783. 22. E. van Lenthe, A. Ehlers and E. J. Baerends, J. Chem. Phys., 1999, 110, 8943. 23. P. M. Boerrigter, G. te Velde and E. J. Baerends, Int. J. Quantum Chem., 1988, 33, 87. 24. G. te Velde and E. J. Baerends, J. Comp. Phys., 1992, 99, 84. 25. SCM. ADF2013, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, https://www.scm.com/doc/ADF/Examples/PCCP_Unr_BondEnergy.htm l. 2013.

Part II.

Results and Discussion

Geometry optimisations

Chapter 4. Geometry optimisations and electronic structures

In this chapter, the geometry optimisations for fifteen [LAnX]n+ complexes (n =

1 for Th(IV), 0 for U(III) and Th(III); X = BH4, BO2C2H4, CH3, N(SiH3)2, OPh) for both PBE and PBE0 were analysed with a view to establishing the best form of DFT to employ when studying these systems based on available experimental crystal structure data.

Once this was established, an array of methods to study the electronic structures of these complexes was employed. Firstly, various partition methods (MPA, HPA, NBO and QTAIM) were used to compare partial charge analyses of the actinide centres and X ligands. Next, QTAIM and NBO data for the An-X bonds were analysed and then compared to determine the nature of these interactions in terms of their relative covalency and ionicity. These QTAIM and NBO analyses were then carried out for a further set of ten transition metal

[LMX]n+ complexes (n = 1 for Hf(IV), 0 for W(III); X = BH4, BO2C2H4, CH3,

N(SiH3)2, OPh) to see if the conclusions from the QTAIM and NBO data for the actinide systems still held true for analogous transition metal systems.

Finally, NICS analysis was carried out on [LThIVX]+ to study the aromaticity of the arene rings in the L2- as a function of X ligand, and to therefore indirectly measure any interaction between the arene rings and Th(IV) centre. Further to this, MPA was used to study the orbital interactions of all three of the Th(IV), Th(III) and U(III) centres to the L2- ligand and the X ligands, and how the orbital energies for these interactions differ when going across the X-ligand series, and in particular, how these orbitals for the Th(IV) complexes compared to the NICS analysis.

Geometry optimisations

4.1. Geometry optimisations of Th(IV) complexes

Initial geometry optimisations were performed for the Th(IV) complexes for PBE and PBE0 and key bond lengths and angles are presented in tables 4.1 and 4.2, which also gives comparisons with available crystallographic data. The column headings mentioning N1/2 and Ar1/2 refer to the centroids of the arene rings and pyrrole nitrogen atoms indicated in figure 3.2 of the previous chapter.

There is not a direct bond between the actinide and boron atoms in the

[LAnBH4]n+ systems, although the values presented here are the distances from actinide centres to boron. X-ray data of the uranium analogue suggests the BH4 group is bonded to the actinide centre via the hydrogen atoms in either a (µ-

H)2BH2 or (µ-H)3BH fashion1. Initially these BH4 systems were modelled in the

(µ-H)3BH bonding mode, but for LUBH4, there was a U-B separation difference of almost half an Ångstrom between the experimental value of 2.927 Å and the

PBE and PBE0 values of 2.533 and 2.549 Å respectively. For all the [LAnBH4]n+ complexes where BH4 was bonded to the actinide centre in the (µ-H)2BH2 bonding regime, the plane of the bridging hydrogen atoms was modelled to be approximately parallel with the plane of the arene rings, as a perpendicular arrangement of these bridging bonds with respect to the arene rings yielded optimised geometries in which the BH4 reverted back to the An-(µ-H)3BH bonding regime. The SCF energy for [LAnBH4]n+ complexes in the (µ-H)2BH2 bonding regime were found to be the more stable compared to complexes with

(µ-H)BH3, with the SCF energies for the latter being 7.9 kJ mol-1 more positive for the Th(IV) complex and 9.1 kJ mol-1 more positive for the U(III) complex.

Table 4.1 shows An-BH4 distances when bonded in the (µ-H)2BH2 fashion, and for LUBH4 this agrees more with experiment. Indeed, experimentally, Arnold and co-workers based their conclusion of a possible (µ-H)2BH2 bonding mode on the longer U-B separation of other uranium(III) borohydrides2. Based on these considerations, all data in tables 4.1 and 4.2 and onwards are for

[LAnBH4]+ complexes in which BH4 adopts the (µ-H)2BH2 bonding regime only.

As can be seen in table 4.1, bond distances between thorium and the centroids of the arene rings vary greatly between the functionals, whereas there is much

Geometry optimisations less variation between thorium and the pyrrole nitrogen atoms. The bonds that show a strong trend are the thorium to X ligand, which are seen to decrease from boron to oxygen. This might be expected due to the increasing electronegativity of the X atoms as one progresses further right across the periodic table, creating a greater charge difference between thorium and the X ligand and thus higher ionicity. Another trend that can be seen is the slight increase in the average bond length between thorium and the two pyrrole nitrogen atoms, which seems to correlate with the decrease in bond length of Th-X, although clearly the change of the Th-N(av) bond is much less dramatic than that in Th-X. This is highlighted in figure 4.1.

Geometry optimisations and

2 ) 3 d - - - - - U-X T h-X an

2.927(7) 2.364(3) 2 2.275(13) 2.242(17) ) 3 a, N(SiH - - - - - U-N 1 T h-N 1 2.464(6) 2.452(4) 2.532(5) 2.537(19) - - - - - 6(19) -N 2 82(6) 76(4) 45(5) U T h-N 2 2.4 2.4 2.5 2.49 Experimental ------Ar2 t for experimental dat 2.692 U-Ar2 2.580 2.642 2.745 T h - - - - - 2.687 2.601 2.814 2.618 U-Ar1 T h-Ar1 *Note that for experimental data, N(SiH U-X T h-X 2.837 2.700 2.475 2.272 2.106 2.855 2.677 2.519 2.359 2.159 ------N-U-N N-Th-N 116.9(6) 115.5(19) 118.9(14) 114.6(16) U-N 1 2.394 2.405 2.413 2.426 2.422 2.460 2.467 2.484 2.473 2.486 T h-N 1 s (Å) ------21.3 14.4 19.5 17.3 Interplanar PBE 0 U-N 2 2.394 2.405 2.405 2.418 2.422 2.460 2.467 2.468 2.470 2.486 T h-N 2 Interplanar Experimental -Ar .4 .7 Bond distance ------169 174 176.0 174.2 Ar-U-Ar Ar-Th 2.615 2.581 2.645 2.690 2.651 2.575 2.508 2.564 2.596 2.620 U-Ar2 T h-Ar2 mplexes and experimental data where available. *Note tha 119.9 123.7 121.2 117.0 119.3 119.5 121.7 121.2 118.7 119.4 N-U-N Ar1 615 581 641 689 651 575 508 615 724 620 N-Th-N ) o 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. U- T h-Ar1 r r 9.2 4.0 9.2 3.3 -X 12.6 16.8 10.8 11.6 16.8 10.6 PBE0

U-X T h 2.843 2.705 2.485 2.280 2.120 2.840 2.650 2.518 2.267 2.148 Interplana Interplana Bond anglesBond (

179.3 177.1 177.8 174.2 177.6 177.9 177.6 177.3 175.4 176.0 Ar-U-Ar Ar-Th-Ar U-N 1 2.404 2.420 2.425 2.431 2.438 2.448 2.466 2.479 2.412 2.494 T h-N 1 orium and uranium complexes and experimental data where available. espectively. 120.5 124.6 121.6 117.1 119.2 121.4 124.5 122.1 123.1 119.7 N-Th-N PBE U-N 2 2.404 2.420 2.417 2.443 2.438 2.448 2.466 2.463 2.428 2.494 T h-N 2 N-U-N and DTBP respectively.

2 r 2.3 9.2 0.9 8.9 and DTBP r PBE 10.2 13.0 17.2 10.8 10.1 34.4

2 2.623 2.585 2.667 2.710 2.669 2.561 2.462 2.516 2.371 2.584 U-Ar2 T h-Ar2 Interplana Interplana r Key bond lengthsKey bond for the thorium and uranium co

179.5 175.6 178.1 174.2 177.5 179.5 175.1 174.8 179.0 175.9 2.623 2.585 2.620 2.713 2.669 2.561 2.462 2.589 3.415 2.584 U-Ar1 T h-Ar1 Ar-Th-Ar Ar-U-Ar Key bond angles for the th are instead N(TMS)

* * 4 4 * * 4 4 2 2 2 2 ) ) H H ) ) H H Ph able 4.1. 4.1. able 4 3 4 3 2 2 4 3 4 3 2 2 C C T O

C C 2 2 Me Me 2 2 are instead N(TMS) BH BH M e M e OPh BH BH

ligand O Ph OPh* O Ph* X ligand X X BO BO BO BO N(SiH N(SiH N (SiH N (SiH Table 4.2. OPh

Geometry optimisations

Fig.4.1. The average bond length of the two Th-N(py) bonds vs the Th-X bonds for PBE (dashed lines) and PBE0 (solid lines) for [LThIVX]+ complexes. Th-BH4 distance is from thorium to boron, although there is no direct bond between the two.

This is very slightly more prominent with the PBE functional where the Th- N(py) bond ranges from 2.404 to 2.438 Å – compared to a range of 2.394 to 2.422 Å for PBE0. It may be significant as it appears to suggest that the effect of a more electronegative X atom is the weakening of the bond between thorium and the N(py) as electron density is drawn more from the thorium centre and into the X ligand. As mentioned regarding the data in table 4.1, figure 4.1 shows strong trends with the Th-X bond length as a function of X ligand.

Table 4.2 shows a lot of variation of the interplanar angles – that is the angle formed by the two planes of the arene rings; a perfectly parallel sandwich complex having an interplanar angle of 0o – with X, and also a small variation of the N(py)-Th-N(py) angle with a range of 7.51o for PBE and 5.79o for PBE0. The angle between the centroid of the arene rings and the thorium centre (Ar-Th-Ar in table 4.2) changes the least with a range of 5.30 and 5.10o for PBE and PBE0 respectively, which suggests that the interplanar and Ar-Th-Ar angles are independent of each other.

Geometry optimisations

Fig.4.2. Bond angles for N(py)-Th-N(py) and Ar-Th-Ar against X ligand for PBE (dashed lines) and PBE0 (solid lines) for [LThIVX]+ complexes.

From figure 4.2, there is no clear trend of the bond angles as a function of X ligand; both the N-Th-N and Ar-Th-Ar remain around 120o and 180o respectively regardless of the X ligand present, with [LThN(SiH3)2]+ showing the largest deviation from 120o for the N-Th-N angle, at 117.1 and 117.0o for PBE and PBE0 respectively.

Fig.4.3. Interplanar bond angles against X ligand for PBE and PBE0 for [LThIVX]+ complexes

Figure 4.3 shows the trend in the interplanar angles between the arene rings for both functionals as the X ligand is changed. The two largest angles are found

Geometry optimisations

with [LThN(SiH3)2]+. The only significant differences between [LThN(SiH3)2]+ for both functionals and experiment (tables 4.1 and 4.2) are the bond lengths between the thorium centre and the nitrogens on the pyrrole rings (both being longer according to experiment), and also the interplanar angles, which are smaller computationally than by experiment, though the PBE functional gives a result more in accordance with experiment. This angle could be affected by steric hindrance, as mentioned above, and as this model compound has had the methyl groups on the X-ligand omitted for computational cost, it may be unwise at this stage to suggest that this is the reason for the angle discrepancy (see figure 4.4 for a visual comparison of the synthesised and calculated complex).

Fig.4.4. [LThN(TMS)2]+ structure from X-ray data (left) and [LThN(SiH3)2]+ from geometry optimisation at PBE level (right). Hydrogen atoms have been omitted for clarity.

4.2. Geometry optimisations of U(III) complexes

Geometry optimisations were performed for the U(III) complexes, also with the PBE and PBE0 functionals, and the key bond lengths and angles are again found in tables 4.1 and 4.2. As with the thorium complexes, bond distances from uranium to the arene centroids show wide variety over both functionals, while the bond lengths between uranium and the pyrrole nitrogen atoms show less difference for both PBE and PBE0. As with the thorium complexes, there is a tendency for the U-X bond to shorten as the X ligand increases in electronegativity, seen in figure 4.5:

Geometry optimisations

Fig.4.5. The average bond length of the two U-N(py) bonds vs the U-X bonds for PBE (dashed lines) and PBE0 (solid lines) for LUIIIX complexes.

Unlike with the thorium complexes however, the U-N(av) distances in figure 4.5 do not show the trend of increasing bond length as the U-X bond decreases in length. In fact the pattern is different for both functionals, with PBE showing LUOPh to have the largest U-N(av) bond separation, whereas PBE0 shows this same compound to have the lowest U-N(av) bond separation.

Of the uranium complexes, LUBH4, LUN(TMS)2 and LUDTBP have been synthesised, and the corresponding X-ray data thus provide an excellent opportunity to compare computational with experimental geometries. Of the experimental data, key bond distances for these three synthesised uranium complexes are taken from references 1 and 3.

LUN(TMS)2 shows a difference in the two uranium-arene distances. From the distances in table 4.1, U-Ar(1) is 2.371 Å and U-Ar(2) is 3.415 Å for PBE, whereas these same bonds are 2.596 and 2.724 Å respectively for PBE0. For comparison, from X-ray data these distances are 2.814 and 2.642 Å for U-Ar(1) and U-Ar(2) respectively. Due to this large difference between PBE and PBE0 for this compound it seems PBE0 gives a more sensible optimised geometry. This is true also for bond angles, where N-U-N is 123.1 and 118.7o for PBE and PBE0 respectively (114.6o from experiment), and the interplanar angle is 34.4 and 16.8o for PBE and PBE0 respectively (19.5o from experiment).

Geometry optimisations

PBE and PBE0 give similar results for the LUOPh complex, but they differ significantly from the experimentally determined structure of LUDTBP. Notably, the much shorter bond distance between uranium and oxygen found by both functionals, in comparison with experiment. This difference may again arise from the simplification of the calculated complex, where the tert-butyl groups on the phenyl ring of the X ligand have been omitted. There is also a difference in the U-O-Ph bond angle; experimental data show that the U-O-DTBP is bent (144.69o) whereas in the model system both PBE and PBE0 find this angle to be exactly linear, even though symmetry constraints were not used. This is shown in figure 4.6 for the PBE0 functional.

Fig.4.6. Comparison of LUDTBP from X-ray data (left) and the LUOPh structure using the PBE0 functional (right). Hydrogen atoms have been omitted for clarity.

Since both tert-butyl groups are in the ortho position on the phenyl ring these may play a significant role in determining the molecular structure, insofar as steric hindrance may override electronic preference for the bonding, as a linear U-O-DTBP bond may bring the butyl groups too close to the L2- ligand. Bending this angle will move these butyl groups away from the L2- ligand, but since the arene ring on the DTBP ligand would then be closer to one of the arene rings on the L2- ligand (as seen in figure 4.6), this arene ring must be further away from the X ligand, which explains the difference between the two U-Ar bond distances and interplanar angle seen from experiment. It cannot be firmly concluded, however, that the linearity of U-O-Ph found computationally is due to the omission of the butyl rings, since this compound relaxed to C2 symmetry

Geometry optimisations in the optimisation process. This is why both U-Ar bond lengths are identical, and indeed may be the reason why U-O-Ph is found to be linear. All the complexes in table 4.1 were calculated in C1 symmetry, although some –

[LAnBH4]n+, [LAnBC2O2H4]n+ and [LAnOPh]n+ – relaxed to C2 symmetry in the optimisation.

Fig.4.7. Bond angles for N-U-N and Ar-U-Ar against X ligand for PBE (dashed lines) and PBE0 (solid lines) for LUIIIX complexes.

The U-X bonds for LUN(TMS)2 and LUDTBP are identical according to the X-ray data (2.364 Å) and a decrease in the average U-N(py) bond length is seen going from N(TMS)2 to DTBP. The opposite is seen in the computational data for PBE, where the average U-N(py) bond length increases from N(SiH3)2 to OPh, accompanied by a marked decrease in the U-X bond length. PBE0 also finds a decrease in the U-X bond length across these two ligands, and the U-N(av) decreases in length also.

As with the thorium complexes, there is not much variation in the Ar-U-Ar angles, the largest being seen for LUBH4, which is also found to be the largest out of both sets of thorium and uranium complexes over both functionals. Also as with the thorium complexes, there is less variation in the N(py)-U-N(py) bond angles, with a range of only 4.8o for PBE and 3.0o for PBE0. Figure 4.7 shows the comparison of these two angles as the X ligand is changed.

Geometry optimisations

As in figure 4.5, there is some difference between the functionals, with the Ar-U-

Ar angle not changing much for PBE, apart from a small jump for LUN(SiH3)2, although the angles again deviate only slightly as a function of X ligand from 120o and 180o for the N(py)-U-N(py) and Ar-U-Ar bond angles respectively.

When comparing the interplanar angles for both functionals, it is found that the

LUN(SiH3)2 complex exhibits the largest differences, see figure 4.8.

Fig.4.8. Interplanar bond angles against X ligand for PBE and PBE0 for LUX complexes

In fact the PBE interplanar angle for this complex is more than double than that found with PBE0. This strong difference in the interplanar angle is not the only geometry parameter that differs significantly between the two functionals for

LUN(SiH3)2; for PBE this is found to be 2.267 Å and for PBE0 2.359 Å, which is more in agreement with experiment (see table 4.1), whereas for the rest of the complexes the differences in U-X bond lengths are not that great between the two functionals, and this is true for the interplanar angles as seen in figure 4.8. Such a shorter bond length would explain a larger interplanar angle if one considers that same steric effects mentioned for [LThN(SiH3)2]+ are playing a role here; if the bulky nitrogen group is brought closer to the metal centre then the arene rings would bend back.

The above discussion suggests that PBE0 provides more reliable geometrical data when compared with experimental data. To quantify this further, mean absolute deviation (MAD) analysis between theory and experiment is provided

Geometry optimisations for key geometric variables in tables 4.3 – 4.9. For each of these tables, a separate MAD analysis has been carried out without the LUDTBP/Ph data, since as discussed (figure 4.6), the LUOPh geometry relaxed into C2 symmetry, even without imposing such constraints, and so led to a large difference in the U-O- Ph angles when compared to experiment. Therefore it was useful to see how including or excluding the LUDTBP/Ph data affected the overall MAD analyses.

Table 4.3. MAD analysis for PBE and PBE0 when compared to experimental average bond lengths of the actinide to pyrrole nitrogens.

Average An-N(py) bond distance (Å)

Table 4.4. MAD analysis for PBE and PBE0 when compared to experimental bond lengths of the actinide to arene(1) centroid.

An-Ar(1) bond distance (Å)

Geometry optimisations

Table 4.5. MAD analysis for PBE and PBE0 when compared to experimental bond lengths of the actinide to arene(2) centroid.

An-Ar(2) bond distance (Å)

Table 4.6. MAD analysis for PBE and PBE0 when compared to experimental bond lengths of the actinide to X ligand.

An-X bond distance (Å)

Table 4.7. MAD analysis for PBE and PBE0 when compared to experimental bond angles between arene(1) centroid to actinide to arene(2) centroid.

Ar-An-Ar bond angle (o)

Geometry optimisations

Table 4.8. MAD analysis for PBE and PBE0 when compared to experimental bond angles between pyrrole nitrogen(1) to actinide to pyrrole nitrogen(2).

N(py)-An-N(py) bond angle (o)

Table 4.9. MAD analysis for PBE and PBE0 when compared to experimental interplanar bond angles.

Interplanar bond angle (o)

As can be seen, the MAD values from experimental data for PBE0 are consistently lower than for PBE. These results suggest, therefore, that it would be best to focus further analysis on structures optimised using PBE0.

4.3. Geometry optimisations of Th(III) complexes

Th(III) complexes with the same X ligands were modelled with PBE0 to provide comparison with the U(III) complexes, to see how these systems differ with different actinides in the same oxidation state, and also to see how they compare to Th(IV). No LThIIIX complexes with the ligand systems presented in this report are known experimentally.

Geometry optimisations

Table 4.10. Bond distance and bond angle parameters for Th(III) complexes using PBE0.

Bond distances (Å) Bond angles (o)

X ligand Th-Ar1 Th-Ar2 Th-N1 Th-N2 Th-X Ar-Th-Ar Interplanar N-Th-N

BH4 2.775 2.385 2.469 2.480 2.888 176.8 9.6 115.7

BO2C2H4 2.482 2.482 2.482 2.482 2.652 171.1 6.3 126.5

Me 2.411 2.831 2.476 2.495 2.525 177.3 12.4 118.2

N(SiH3)2 2.401 3.055 2.492 2.459 2.341 175.7 21.7 116.3

OPh 2.576 2.576 2.487 2.487 2.168 178.3 7.9 120.1

When comparing the An-X distances together in figure 4.9, it is found that the longest An-X bond distance is that of Th(III)-BH4 and the shortest that of Th(IV)-OPh. The Th(III) and U(III) are the most similar in value for the An-X bond lengths – especially for An-Me – which is perhaps unsurprising as they are in the same oxidation state, whereas the Th(IV)-X bond distances are all shorter than the Th(III) and U(III) counterparts, except for the BO2C2H4 ligand, where the Th(IV) is the longest of the three.

Fig.4.9. An-X bond distances for Th(IV), Th(III) and U(III) complexes. All values optimised at PBE0 level.

Geometry optimisations

There is a clear trend of a shortening of An-X bond distance with an increasingly electronegative ligating X atom for all three actinide centres of Th(IV), Th(III) and U(III).

The ionic radius of U(III) is 1.18 Å4 and for Th(IV) is 0.94 Å5, giving a difference of 0.24 Å. The smaller radius in Th(IV) correlates with the generally smaller Th- X separation when compared to that of U-X, but these differences are not as large as the difference in ionic radii, with the largest difference being for the An-

N(SiH3)2 bond with 0.087 Å found computationally, and 0.089 Å found experimentally. Looking at the actinide-pyrrole bond separations, it is apparent the radii difference is averaged out across the other bonds, by looking at the An- N(py) separations and An-Ar separations. From table 4.1, the distances between An-N(py) are longer for the U(III) complexes than for the Th(IV) complexes, however the Th(IV) show longer separations for the An-Ar distances. When adding these An-N(py) separation differences to those of An-X, the differences become closer to that of the ionic radii difference between U(III) and Th(IV).

Table 4.11. Differences of selected bond parameters between LUIIIX and [LThIVX]+ in Ångstroms

ΔAn-X ΔAn-N(py)1 ΔAn-N(py)2 Sum

[LAnBH4]n+ 0.018 0.066 0.066 0.150

[LAnBO2C2H4]n+ 0.021 0.062 0.062 0.145

[LAnMe]n+ 0.044 0.071 0.063 0.178

[LAnN(SiH3)2]n+ 0.087 0.047 0.052 0.186

[LAnOPh]n+ 0.014 0.064 0.064 0.142

The sum of these differences show values closer to 0.24 Å (the difference between the aforementioned U(III) and Th(IV) ionic radii), with the closest being with the [LAnN(SiH3)2]n+ complexes. The distances between the actinide centre and the arene rings were however found to be shorter for the U(III) complexes and longer for the Th(IV) complexes, which might be more to do with the L ligand distortion with the stretching of the U-N(py) bonds rather

100

Geometry optimisations than ionic radii, since keeping with the ionic radii differences, one would expect the U-Ar distances to be longer than the Th-Ar distances as well.

4.4. Partial charge analyses of Th(IV), U(III) and Th(III) complexes

Tables 4.12 to 4.14 show the partial charges of the actinide metal centre, the atom bonded to the metal centre from the X ligand and the average partial charges of the two pyrrole nitrogens, using Hirshfeld, Mulliken, Natural and QTAIM charge data, obtained at the PBE0//PBE0 level.

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s. -1.297 -1.243 -1.297 -1.298 -1.295 -1.315 -1.305 -1.317 -1.318 -1.314 -1.320 -1.168 -1.170 -1.168 -1.170 QTAIM QTAIM QTAIM rge al -0.646 -0.630 -0.612 -0.651 -0.653 -0.683 -0.631 -0.658 -0.663 -0.692 -0.737 -0.726 -0.734 -0.721 -0.739 Natural Natur Natural optimised geometrie - optimised geometries. optimised geometries. - - an 1 0 3 e N(py) charge PBE0 PBE0 -0.351 -0.327 -0.341 -0.333 -0.341 -0.330 -0.355 -0.318 -0.326 -0.327 -0.36 -0.34 -0.34 -0.346 -0.359 Mullikan Mullikan Mullik Average N(py) charge Average N(py) cha Averag 02 04 hfeld 244 242 244 ligand from PBE0 -0. -0. -0. -0.245 -0.246 -0.196 -0.196 -0.197 -0.197 -0.198 -0.200 -0.200 -0.202 -0.2 -0.2 Hirs Hirshfeld Hirshfeld AIM .706 1.710 1.224 1.709 1.198 1 1.198 -0.456 -2.265 -1.300 -0.494 -2.253 -1.304 -0.503 -2.126 -1.196 QTAIM QTAIM QT 0.684 0.604 0.736 -0.600 -1.212 -1.678 -0.784 -0.602 -1.274 -1.657 -0.877 -0.548 -1.243 -1.639 -0.840 Natural Natural Natural X atom charge X atom charge X atom charge ullikan -0.093 -0.106 -0.326 -0.547 -0.552 -0.050 -0.042 -0.217 -0.556 -0.500 -0.059 -0.021 -0.254 -0.539 -0.500 Mullikan M Mullikan orium) and average N(py) with each different X ligand from orium) and average N(py) with each different X ligand from 0.012 0.080 0.091 -0.116 -0.343 -0.510 -0.310 -0.047 -0.272 -0.444 -0.240 -0.075 -0.288 -0.478 -0.244 Hirshfeld Hirshfeld Hirshfeld (bonded to th 2.064 1.983 2.043 2.097 2.111 2.527 2.253 2.372 2.424 2.474 2.420 2.309 2.421 2.475 2.206 QTAIM QTAIM QTAIM 1.071 0.949 1.039 1.264 1.375 1.513 1.433 1.681 1.386 1.921 1.349 0.970 1.384 1.164 1.684 Natural Natural Natural ), X ligand atom (bonded to thorium) and average N(py) with each different X n um charge 0.853 0.778 0.930 0.971 1.067 0.953 0.844 0.896 1.023 1.245 0.964 0.851 0.965 1.079 1.188 Thorium charge Thori Uranium charge Mullikan Mullikan Mullika 2 7 eld 0.554 0.463 0.524 0.531 0.511 0.31 0.223 0.31 0.266 0.320 0.227 0.120 0.237 0.211 0.219 Partial charges for U(III), X ligand atom (bonded to th Hirshf Hirshfeld Partial charges for Th(III Hirshfeld

Partial charges for Th(IV), X ligand atom .

2 2 2 4 4 4 ) ) ) .12. H 3 H 3 3 H 4 3 4 3 4 3 2 h 2 nd 2 H C C C 2 2 2 CH CH CH BH BH BH OPh OP OPh Ligand Liga Ligand Table 4.13 Table

BO N(Si BO N(SiH BO N(SiH Table 4.14. 4.14. Table

Table 4 Table

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Geometry optimisations

As seen from the data in table 4.12, and presented in figures 4.10 and 4.11, there is a trend in the partial charge on thorium and the partial charge of the atom in the X ligand it is bonded to. Generally, it appears thorium becomes more positive after BH4, except the natural charge analysis and Hirshfeld analysis shows a break in this trend with N(SiH3)2. Conversely, the X atom bonded to thorium becomes more negative generally, though becomes more positive after N(SiH3)2, this being very pronounced for the natural and QTAIM charge analyses.

Fig.4.10. Partial charges of Th(IV) as a function of X ligand using Hirshfeld, Mulliken, Natural and QTAIM charge analyses.

Fig.4.11. Partial charges of X atom bonded to Th(IV) for each X ligand using Hirshfeld, Mulliken, Natural and QTAIM charge analyses.

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Geometry optimisations

For the uranium complexes, the QTAIM charge (see table 4.12) is similar in trend to that of the thorium complexes in that the actinide charge tends to increase from boron-based X ligands to the oxygen based X ligand, but the NBO and Hirshfeld charges show slight differences. Most notably the peak in the trend for [LThMe]+ in figure 4.10, and the increase for [LThOPh]+, whereas the uranium counterparts do not show this LUMe peak and there is a decrease in actinide charge for LUOPh. Another difference is that for the uranium complexes, the U(III) partial charge is lower than the Th(IV) for each corresponding X ligand in all the analyses, except for the Hirshfeld partial charges, where the U(III) is higher than the Th(IV). This would be expected as Th(IV) is of course in a higher oxidation state, however it is counter-intuitive that the lower oxidation state of U(III) should have a higher partial charge according to Hirshfeld analysis.

The data in table 4.13 for the partial charges of the ligating atom on the X ligand are similar to table 4.12. Generally, the partial charges of the X ligand atom bonded to the actinide centre remains largely unchanged between Th(IV) and U(III). This is perhaps expected, since the ligands remain the same for the thorium and uranium groups of complexes, but it also suggests that charge is localised rather than distributed between the ligating atom and actinide centre, indicating more ionic rather than covalent bonding character.

Finally, the partial charge analyses are presented for the Th(III) complexes and similar trends are seen here as with the Th(IV) and U(III) analogues, in table 4.14. Again, the charge on the ligating atom of the X ligand is largely unchanged and shows the same trends seen for Th(IV) and U(III), however, the X atom charge for Th(III) match more closely the trends found for U(III) than those of Th(IV).

The next set of analyses focusses on the partial charge differences between the actinide centres and ligating atoms in the X ligands.

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Geometry optimisations

Fig.4.12. Partial Hirshfeld charge difference between An and ligating X atom against An-X bond distance. Blue for Th(IV), orange for Th(III) and green for U(III) complexes.

Fig.4.13. Partial Mulliken charge difference between An and ligating X atom against An-X bond distance. Blue for Th(IV), orange for Th(III) and green for U(III) complexes.

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Geometry optimisations

Fig.4.14. Partial Natural charge difference between An and ligating X atom against An-X bond distance. Blue for Th(IV), orange for Th(III) and green for U(III) complexes.

Fig.4.15. Partial QTAIM charge difference between An and ligating X atom against An-X bond distance. Blue for Th(IV), orange for Th(III) and green for U(III) complexes.

Figures 4.12 to 4.15 show that for all the actinide complexes, the charge differences between An and N on N(SiH3)2 are the greatest when compared to the other An-X charge differences, except for the Mulliken charges (figure 4.13) where the greatest charge difference is between An and O in the OPh ligand. All charge analyses apart from the QTAIM shows that the charge difference is the lowest between An and B in the BO2C2H4 ligand, and this is true for all the actinides.

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Geometry optimisations

These analyses – with the exception of MPA – indicate that the charge separation between the actinide centre and ligating X-atom is largest with N in

N(SiH3)2, which is perhaps surprising given that oxygen is more electronegative than nitrogen. The reasons behind this apparent anomaly with the

N(SiH3)2 will be explored later, as the QTAIM metrics obtained from the QTAIM analysis of the An-X are discussed.

4.5. QTAIM analysis

It was found in the previous section there are strong trends in the QTAIM partial charges as a function of the X ligand. The QTAIM parameters δ(A,B), ρ and H mentioned in chapter 1.6 are presented here.

Table 4.15. Electron density (ρ) and energy density (H) at An-X BCP and An-X delocalisation indices (δ) from QTAIM analysis. Non-italics are for Th(IV), italics for U(III) and parentheses for Th(III) complexes.

X ligand δ(An,X) ρ (e bohr-3) H (Hartrees bohr-3)

BH4 0.527 0.480 (0.465) 0.042 0.037 (0.037) -0.021 -0.012 (-0.015)

BO2C2H4 0.561 0.570 (0.515) 0.068 0.067 (0.071) -0.021 -0.021 (-0.023)

Me 0.679 0.593 (0.605) 0.088 0.076 (0.081) -0.031 -0.024 (-0.028)

N(SiH3)2 0.807 0.599 (0.653) 0.104 0.082 (0.090) -0.039 -0.023 (-0.029)

OPh 0.857 0.673 (0.670) 0.116 0.105 (0.121) -0.042 -0.030 (-0.031)

Table 4.15 shows the aforementioned QTAIM parameters for the [LAnX]n+ complexes. As can be seen, the magnitude of δ(An,X), ρ and H increases as a function of X ligand for all the actinide complexes.

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Geometry optimisations

Fig.4.16. Delocalisation index between An-X bond as a function of An-X bond length. Orange is for Th(IV) (R2=0.986), blue is for Th(III) (R2=0.932) and grey for U(III) (R2=0.912). R2 values from linear fits.

Fig.4.17. ρ values at the BCP between An-X bond as a function of An-X bond length. Orange is for Th(IV) (R2=0.989) , blue for Th(III) (R2=0.963) and grey for U(III) (R2=0.958). R2 values from linear fits.

From figures 4.16 and 4.17, there is found to be very good correlation for both δ(An,X) and ρ respectively with the An-X bond length. The delocalisation index for An-(µ-H)2BH2 is the summation of each individual An-H δ value, and the electron density of the same bond is taken from the average of the two different An-H ρ values at each bond critical point. Figures 4.16 and 4.17 show that the

108

Geometry optimisations

δ(An,X) and ρ data are similar for Th(IV) and U(III) for both of the boron X ligands (that is the longest two bond lengths on both x-axes), but then the data diverge slightly with the methyl ligand and beyond. All ρ values, seen in detail in table 4.10, are well below 0.2, indicating that the An-X bonds are not very covalent in character, which matches the ionic character suggested by the localised charges of the ligating atoms for the X ligands in tables 4.12 to 4.14, and also with other studies of actinide bonding of uranium to nitrogen and uranium to oxygen6, and also of uranium to carbon7.

Fig.4.18. H values at the BCP between An-X bond as a function of An-X bond length. Orange is for Th(IV) (R2=0.961) , blue for Th(III) (R2=0.886) and grey for U(III) (R2=0.862). R2 values from linear fits.

Figure 4.18 shows the correlation for the An-X bonds with the energy densities at the BCP. The H values are all negative, indicating an An-X interaction dominated by the potential rather kinetic energy of the bond, with sharing of electrons, as mentioned in chapter 1.6. Also, since for H the magnitude indicates the extent of covalency, it is again found that the An-X bond becomes progressively more covalent from boron to oxygen.

For all three QTAIM metrics, the Th(IV) complexes give the best correlation with the An-X bond lengths, with the highest R2 value being 0.989 for the ρ values. In fact this metric gives the best correlations for all three actinides. U(III) gives the poorest correlations for all three metrics, but nevertheless

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Geometry optimisations correlates well with the QTAIM data, with the lowest R2 value for the U(III) complexes being for the H metric, 0.862.

Next, the delocalisation indices, electron densities and energy densities at the An-X bond critical point were compared with the charge difference between the An and ligating X atom ions as shown in figures 4.19 to 4.21 below.

Fig.4.19. QTAIM (An-X) charge difference against An-X BCP electron density for Th(III) (circles),

Th(IV) (triangles) and U(III) complexes (squares) for each X ligand; Blue = BH4, orange =

BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

Fig.4.20. QTAIM (An-X) charge difference against An-X delocalisation indices for Th(III)

(circles), Th(IV) (triangles) and U(III) complexes (squares) for each X ligand; Blue = BH4, orange

= BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

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Geometry optimisations

Fig.4.21. QTAIM (An-X) charge difference against An-X energy density for Th(III) (circles),

Th(IV) (triangles) and U(III) complexes (squares) for each X ligand; Blue = BH4, orange =

BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

The figures indicate that although the An-OPh bond has both the highest

δ(An,X) and ρ values for each different actinide in the complexes, and H having the largest value for the An-OPh bond, these don’t match with the highest charge difference, which is found for all three actinide centres to be with the An and N bond in [LAnN(SiH3)2]n+, indicated in purple (see also section 4.4). Below are the R2 values for correlation of the data in figures 4.19 to 4.21.

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Geometry optimisations

Table 4.16. R2 values from trends in figures 4.19, 4.20 and 4.21 for all three actinide complexes.

For ρ vs Δq

[LAnX]n+ complexes With N(SiH3)2 Without N(SiH3)2

Th(IV) 0.850 0.928

Th(III) 0.617 0.848

U(III) 0.633 0.860

For δ(An,X) vs Δq

[LAnX]n+ complexes With N(SiH3)2 Without N(SiH3)2

Th(IV) 0.888 0.925

Th(III) 0.922 0.990

U(III) 0.564 0.831

For H vs Δq

[LAnX]n+ complexes With N(SiH3)2 Without N(SiH3)2

Th(IV) 0.915 0.970

Th(III) 0.767 0.850

U(III) 0.510 0.841

As with the other QTAIM metrics, the Th(IV) complexes give the best fits with R2 values of 0.850, 0.888 and 0.915 for figures 4.19 to 4.21 respectively. Since all three [LAnN(SiH3)2]n+ complexes have the highest An-X charge difference, and yet not the highest H, ρ and δ(An,X) values, the trends were analysed further without the N-ligand complexes. As can be seen from table 4.16, this gives a stronger linear correlation for all three actinide complexes, again, with Th(IV) showing the strongest trend for ρ vs Δq and H vs Δq, and Th(III) showing the strongest trend for δ(An,X) vs Δq.

It has been seen in figures 4.12, 4.13 and 4.15, that the N(SiH3)2 complexes do not fit the overall trend of an increase in An-X charge difference when changing from boron through to oxygen-based ligands, and it is seen again in figures 4.19

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Geometry optimisations

to 4.21 that this An-N(SiH3)2 bond does not fit with the rest of the trends seen in the X ligand series, this time with respect to the An-X QTAIM charge difference and the An-X QTAIM metrics. This discrepancy in partial charge and QTAIM analyses with the N(SiH3)2 complexes was thought to be due to this particular X ligand being the only one in the series with the presence of second row p-block atoms (Si) making up the rest of the ligand. Therefore, the presence of these silane groups on N(SiH3)2 could be affecting the nitrogen charge in a way that causes it to be more electronegative relative to oxygen. As such, N(SiH3)2 was replaced with NH2 to see if the removal of a second row p-block X ligand shows a better trend with the rest of the X ligand series for QTAIM metrics and An-X charge difference. The [LAnNH2]n+ complexed were optimised at PBE0 with their QTAIM metrics taken from a single point at this optimised geometry. These QTAIM metrics are shown in table 4.17 and the new QTAIM metric correlations with An-X charge difference in figures 4.22 to 4.24.

Table 4.17. Electron density and energy density at An-N BCP, An-N delocalisation indices and An-N charge difference from QTAIM analysis.

Complex δ(An,N) ρ (e bohr-3) H (Hartrees bohr-3) An-N charge

difference (Δq)

[LThNH2]+ 0.818 0.116 -0.045 4.000

LThNH2 0.750 0.101 -0.037 3.915

LUNH2 0.747 0.097 -0.030 3.488

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Geometry optimisations

Fig.4.22. New QTAIM (An-X) charge difference against An-X BCP electron density with NH2 replacing N(SiH3)2 for Th(III) (circles), Th(IV) (triangles) and U(III) complexes (squares) for each X ligand; Blue = BH4, orange = BO2C2H4, green = Me, purple = NH2 and red = OPh.

Fig.4.23. New QTAIM (An-X) charge difference against An-X delocalisation index with NH2 replacing N(SiH3)2 for Th(III) (circles), Th(IV) (triangles) and U(III) complexes (squares) for each X ligand; Blue = BH4, orange = BO2C2H4, green = Me, purple = NH2 and red = OPh.

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Fig.4.24. New QTAIM (An-X) charge difference against An-X BCP energy density with NH2 replacing N(SiH3)2 for Th(III) (circles), Th(IV) (triangles) and U(III) complexes (squares) for each X ligand; Blue = BH4, orange = BO2C2H4, green = Me, purple = NH2 and red = OPh.

From figures 4.22 to 4.24, it is seen that the replacement of N(SiH3)2 with NH2 gives a more linear trend compared with figures 4.19 to 4.21. The R2 from figures 4.22 to 4.24 are presented in table 4.18.

Table 4.18. R2 values from trends in figures 4.22, 4.23 and 4.24 for all three actinide complexes.

[LAnX]n+ complexes For ρ vs Δq

Th(IV) 0.938

Th(III) 0.836

U(III) 0.882

[LAnX]n+ complexes For δ(An,X) vs Δq

Th(IV) 0.936

Th(III) 0.933

U(III) 0.832

[LAnX]n+ complexes For H vs Δq

Th(IV) 0.978

Th(III) 0.863

U(III) 0.898

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From table 4.18, the R2 values increase significantly compared to those in table

4.16 (for values with N(SiH3)2), particularly for the U(III) complexes. The ρ vs Δq correlation is also greatly improved for the Th(III) complexes, with R2 values changing from 0.617 with N(SiH3)2 to 0.836 with NH2.

In summary, it was found that the Th(IV) complexes exhibit mostly the highest An-X QTAIM metrics when compared with the Th(III) and U(III) counterparts. On the other hand, the Th(III) charge differences from QTAIM analyses (indicated by the circle points on figures 4.19 to 4.21) are higher than the charge differences for the Th(IV) and U(III) complexes except for LThIIIBH4 and LThIIIOPh where the Th(IV) counterpart shows the highest charge difference. There is definite correlation between QTAIM metrics and An-X bond distance. However, when it comes to charge differences, although there is a general trend of an increasing difference coinciding with an increasing δ(An,X) value and ρ value, this trend is broken with [LAnN(SiH3)2]n+ and [LAnOPh]n+, where the nitrogen-based ligand gives a larger charge difference than the oxygen-based ligand, but the former group of complexes still show lower δ(An,X) values and ρ values than the latter. This is expressed with the R2 values in table 4.16 where the exclusion of the [LAnN(SiH3)2]n+ complexes gives a better linear correlation for all three actinides and for all QTAIM metrics. However, instead of omitting these data points, replacing [LAnN(SiH3)2]n+ with [LAnNH2]n+ improved the correlations, as seen in figures 4.22 to 4.24 and table 4.18. This lattermost data is more reliable for showing how the [LAnN(SiH3)2]n+ complexes can affect the linear trend across the X ligand series for two reasons; firstly, there is still a direct comparison with figures 4.19 to 4.21 because there is still a nitrogen- based ligand in a series of ligands ranging from boron to oxygen-based; and secondly, there are still the same amount of data points in figures 4.22 to 4.24 as there are in figures 4.19 to 4.21, and so the R2 values in table 4.18 are a much better comparison to those including the N(SiH3)2 ligand in table 4.16 than the R2 values excluding these data in the same table.

4.6. NBO analysis

The orbital structure of the An-X bonds and how these change with actinide centre and X ligand have been probed. NBO analysis for Th(IV) and U(III)

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Geometry optimisations complexes have found interesting trends in the covalency and ionicity of these bonds, as is now discussed. NBO calculations on the Th(III) systems proved unsuccessful in finding an NBO for all the ThIII-X bonds, with only LThIIIN(SiH3)2 and LThIIIOPh finding such NBOs. Hence, no NBO data are given for these Th(III) complexes due to such a small data set.

Table 4.19. Overall orbital contributions to An-X NBOs from actinide centre and X atom (X atom=B, C, N or O) as a percentage, with breakdown of AOs which make up these contributions.

Complex Th(IV) X atom U(III) X atom

[LAnBO2C2H4]n+ 34.6 65.4 36.5 63.5

(13.3 f, 73.3 d) (45.4 s, 54.1 p) (17.9 f, 86.5 d) (47.2 s, 52.3 p)

[LAnMe]n+ 18.8 81.2 21.3 78.7

(13.6 f, 76.4 d) (33.4 s, 66.7 p) (16.9 f, 64.6 d) (33.4 s, 66.5 p)

[LAnN(SiH3)2]n+ 10.1 89.9 10.3 89.7

(22.0 f, 71.3 d) (47.9 s, 52.0 p) (32.6 f, 60.4 d) (32.2 s, 67.8 p)

[LAnOPh]n+ 6.8 93.2 7.5 92.5

(20.0 f, 70.7 d) (65.2 s, 34.8 p) (13.1 f, 72.4 d) (64.8 s, 35.9 p)

Table 4.19 shows that as the X atom changes from boron to oxygen, the overall contribution of orbitals from the actinide centre drops progressively (note there are no data for [LAnBH4]n+ since no bonds were found between An and

BH4 in the NBO analysis), hinting at more ionicity as the electronegativity of the X ligand increases.

The An-X NBOs for [LThBO2C2H4]+, LUBO2C2H4, [LThOPh]+ and LUOPh are shown in figure 4.25 to illustrate the decrease in An orbital contribution when changing the X ligand from the boron-based to oxygen-based ligand.

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Fig.4.25. Visual representations of NBOs from table 4.17 for [LAnBO2C2H4]n+ (left) and [LAnOPh]n+ (right) for the Th(IV) (top) and U(III) (bottom) complexes. Hydrogen atoms are omitted for clarity. Isovalue = 0.025.

As the breakdown of the NBOs in table 4.19 show, the An orbitals in figure 4.25 are predominantly d-orbital in character, creating a σ bond with the p-orbitals of boron and oxygen. It can also be seen that the An orbitals have smaller radial distribution for [LAnOPh]n+ compared to [LAnBO2C2H4]n+ which fits with the values in table 4.19 with regards to the complexes’ respective An contributions.

These NBOs in table 4.19 were next compared to the QTAIM data obtained for the An-X bonds. Plotting the QTAIM and natural An-X charge difference against orbital contribution of the actinide centre shows an interesting trend.

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Fig.4.26. An-X charge difference (solid line = natural charge, dotted line = QTAIM charge) against orbital contribution for An-X bond from the actinide (blue = Th(IV), orange = U(III)).

Table 4.20. R2 values for trends in figure 4.26. Natural charge from the solid lines and QTAIM charge from the dotted lines.

Natural charge QTAIM charge

Th(IV) 0.799 0.882

U(III) 0.774 0.888

From figure 4.26 and table 4.20 there is a reasonable trend for both the Th(IV) and U(III) complexes with regards to their charge differences and orbital contribution to the An-X bond from the actinide centre. However, as has been the case with other analyses so far, the outliers in figure 4.26 are with the An-

N(SiH3)2 bonds, which although fit with a steady decrease in total actinide contribution to the NBO as a function of X ligand, its natural and QTAIM An-N charge difference is larger than that of An-O, which gives rise to the patterns shown in figure 4.26. Having said that, using the QTAIM charge difference gives better R2 values, with the best fit being for the U(III) complexes with an R2 value of 0.888. As with figures 4.22 to 4.24, the N(SiH3)2 ligand was replaced with NH2 to see if a better correlation is found. The pattern found in figure 4.26 however did not change with this replacement N-based ligand, as shown in figure 4.27.

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Fig.4.27. An-X charge difference (solid line = natural charge, dotted line = QTAIM charge) against orbital contribution for An-X bond from the actinide (blue = Th(IV), orange = U(III)).

N(SiH3)2 replaced with NH2.

Table 4.21. R2 values for trends in figure 4.27. Natural charge from the solid lines and QTAIM charge from the dotted lines. N(SiH3)2 replaced with NH2.

Natural charge QTAIM charge

Th(IV) 0.798 0.947

U(III) 0.753 0.958

From table 4.21, whilst the R2 values for the natural charge vs the actinide orbital contribution does not change much from table 4.20, the R2 values for the QTAIM charge vs actinide orbital contribution does, with an improved value. Nevertheless simplifying the N-based X ligand in this case does not yield significant insights into this analysis than was found for figures 4.22 to 4.24 with QTAIM covalency metrics.

As stated earlier, an increase in charge difference would correlate with an increase in ionic character, which is largely the case based on the orbital contributions presented here. However, these contributions correlate with charge difference in the same way as with the ρ, δ(An-X) and H values found with the QTAIM analysis. I.e. as these QTAIM measures of covalency increase, so

120

Geometry optimisations does the measure of apparent ionic character from the NBOs (based on decreasing An orbital contribution), as shown below in figures 4.28 to 4.30.

Fig.4.28. An-X BCP electron density against total actinide orbital contribution for An-X NBO (blue = Th(IV), orange = U(III)).

Fig.4.29. An-X delocalisation index against total actinide orbital contribution for An-X NBO (blue = Th(IV), orange = U(III)).

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Fig.4.30. An-X BCP energy density against total actinide orbital contribution for An-X NBO (blue = Th(IV), orange = U(III)).

Table 4.22. R2 values for trends in figures 4.28 to 4.30.

Figure 4.28 Figure 4.29 Figure 4.30

Th(IV) 0.969 0.966 0.994

U(III) 0.715 0.605 0.512

From table 4.22 it is clear that the Th(IV) complexes give a much stronger correlation with these QTAIM metrics and An orbital contribution, with the strongest found with the energy density against orbital contribution. U(III) complexes show a weaker correlation than Th(IV) for all of these metrics, with the lowest being with the energy density.

This observation of NBO data and QTAIM metrics showing different interpretations of bond covalency and ionicity has been seen before in AnCp3 and AnCp4 systems (An = Th-Cm) where MPA and NBO data suggested the An-C interactions were covalent, but QTAIM data suggested the same bonds were highly ionic, particularly with the early actinides7, 8. However, a more recent study9 found that An-Oyl bonds in AnO2(H2O)+ (An = Pa – Pu) increased in covalency across the actinide series according to both NBO and QTAIM analysis.

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Due to the apparent contradiction between QTAIM and NBO metrics found in this study, it was decided to probe these effects at a fixed An-X distance. The chosen bond length was one midway between the An-Me and the An-N(SiH3) bonds, which for the ThIV complexes was 2.375 Å and for UIII complexes 2.440 Å. The L2- ligand structure was kept in the relaxed geometries for each of the [LAnX]n+ complexes in this case. The results are shown in figure 4.31.

Fig.4.31. An-X BCP electron density against the orbital actinide contribution for An-X NBO (blue = Th(IV) R2 = 0.816, orange = U(III) R2 = 0.823) for a fixed An-X bond length.

From figure 4.31 it is seen that the total actinide orbital contribution to the An-X NBOs does not differ much from the complexes that underwent geometry optimisation (from table 4.19). However, what does change significantly is the electron density from the QTAIM analysis, which shows an opposite trend from before; electron density at the An-X BCP is here found to decrease when going from the boron to the oxygen-based X ligands. Looking at the other QTAIM metrics against NBO orbital contributions shows similar trends, shown in figures 4.32 and 4.33.

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Fig.4.32. An-X delocalisation index against the orbital actinide contribution for An-X NBO (blue = Th(IV) R2 = 0.272, orange = U(III) R2 = 0.863) for a fixed An-X bond length.

Fig.4.33. An-X BCP energy density against the orbital actinide contribution for An-X NBO (blue = Th(IV) R2 = 0.855, orange = U(III) R2 = 0.855) for a fixed An-X bond length.

As can be seen from figures 4.31, 4.32 and 4.33, all orbital contributions share a reasonable linear relationship the QTAIM metrics, with the exception of δ(An,X) for the Th(IV) having the poorest correlation (R2 value of 0.272). As for the rest of the trends across both sets of actinide complexes, the R2 values are no less than 0.816 (see figure 4.31), which suggests a strong relationship. These R2 are summarised in table 4.23 below. What is clear, when comparing figures 4.28 – 4.30 and 4.31 – 4.33, is that the direction of the correlation (positive or

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Geometry optimisations negative) between the QTAIM metrics and the NBO actinide orbital contributions is dependent on the distance of the An-X bond.

Table 4.23. R2 values from QTAIM metrics against actinide orbital contributions (%).

Figure 4.31 Figure 4.32 Figure 4.33

Th(IV) 0.816 0.272 0.855

U(III) 0.823 0.863 0.855

What is more, it is clear that the QTAIM metrics are far more sensitive to the An-X bond distances than are the NBO contributions, and therefore it is arguable that NBO analysis may be a better approach when studying systems with significantly different bond lengths. Whilst in this study the variable in the systems was the ligand to which the An centres are bonded to, in the work of

Kaltsoyannis9 the variable in the AnO2(H2O)+ complexes was the An centre, whilst the ligand (Oyl) remained the same. In this latter study it was the NBO metal contributions which were sensitive to bond length – An-Oyl decreased in length across Pa – Pu whilst the An NBO contribution increased – whereas as was seen in figures 4.31 to 4.33, here it is the QTAIM metrics which were sensitive to bond length rather than An NBO contributions. Indeed, although only two An centres – Th(IV) and U(III) – were presented in this study, table 4.19 shows that the An NBO contribution increases across the two actinide centres when compared with the same X ligand, in agreement with the An-Oyl study. Nevertheless, both this study and that of the AnO2(H2O)+ complexes suggest that NBO analysis is more robust for analysing similar systems with varying lengths of the bonds of interest.

4.6.1. Transition metal complexes

In an attempt to understand the trends observed with the actinide complexes with regards to the An-X bond, analogous complexes with d-block rather than f- block metals were modelled. It was thought that for the actinide complexes, the actinide 5f-orbitals in the An-X bond may be at similar energies to the X ligand MOs, which as a population analysis method, NBO interprets accordingly by finding the actinide orbital contributions presented in table 4.19. However, 125

Geometry optimisations although there may be orbital energy overlap in the An-X bond, the small radial distribution of the 5f-orbitals may mean there is little orbital spatial overlap, which would explain the decreasing ρ from QTAIM at the BCP on the one hand, but apparent increase in actinide orbital contribution from NBO analysis on the other. This debate over energy-driven and overlap-driven covalency has been discussed before in the literature7-10, and perhaps the same contradictory conclusions from the two descriptions were found in this study.

As such, by placing third row transition metals instead of actinides at the metal centre, it was thought that, since the 5d-orbitals are more diffuse, there would be increased metal-ligand orbital spatial overlap. The [LThIVX]+ complexes were compared with [LHfIVX]+ complexes, and the LUIIIX complexes with LWIIIX complexes, since hafnium and tungsten have group valences of 4 and 6 respectively, as do Th and U. Initial geometry optimisations yielded structures with large interplanar and N-M-N angles, with the metal centres lying far closer to one arene ring than the other, in a lot of cases having a difference of more than 1.0 Å. In other words, they were not adopting the bis-arene motif found with the [LAnX]n+ structures. As such, these geometries were more reminiscent of the structure of (benzene)chromium tricarbonyl11 [Cr(C6H6)(CO)3], where the arene ring bonds to the metal in an η6 fashion, and then as a single bond to each nitrogen on the pyrrole rings and to the X ligand; these latter three bonds being analogous to the three CO ligands in Cr(C6H6)(CO)3.

Due to these significant differences in the L2- ligand geometry compared to the actinide complexes, it was thought that comparing the M-X bonds for the transition metal complexes with the An-X bonds in the actinide complexes would not be a direct comparison of the X ligand interaction over both sets of systems, and as such, the geometry of the L2- ligand in the transition metal complexes was fixed to match those in the actinide complexes, and only the X ligand was allowed to relax during the geometry optimisation calculation. For consistency, the L2- ligand geometry for the Hf(IV) complexes was fixed to match that of the relaxed L2- ligand geometry in the [LThIVX]+ complexes, and likewise the L2- ligand geometry in the W(III) complexes was matched to that of

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Geometry optimisations the relaxed L2- ligand geometry in the LUX complexes. These M-X bond lengths are shown below.

Table 4.24. M-X bond lengths (Å) after fixing the L2- ligand geometry to that in the [LAnX]n+ analogues.

BH4 BO2C2H4 Me N(SiH3)2 OPh

[LHfX]+ 2.486 2.427 2.225 2.000 1.877

LWX 2.372 2.204 2.146 1.936 1.852

Partial charge analyses of the bonds quoted in table 4.24 yielded the following results.

Fig.4.34. Partial charge difference between Hf(IV) and its ligating X-atom.

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Fig.4.35. Partial charge difference between W(III) and its ligating X-atom.

As can be seen from figure 4.34, the HfIV-X partial charge differences follows the same trends with those seen for the ThIV-X partial charge differences presented in figures 4.12 to 4.15 in section 4.4, where the difference is largest between the metal and nitrogen of the N(SiH3)2 ligand for all methods except the Mulliken analysis, where the largest difference is between the metal and oxygen of the OPh ligand. Likewise, the smallest partial charge difference is found with the metal and boron in BO2C2H4 for Hirshfeld and Natural analyses, but not from QTAIM analysis, where the smallest difference is that between the metal and boron in BH4. Mulliken analysis, however, finds the smallest charge difference to be between Hf(IV) and the carbon in the methyl ligand, and also the Hf(IV) and BO2C2H4 boron charge difference is larger than that of the Hf(IV) and BH4 boron, whereas for the Th(IV) complexes the charge difference for the BH4 is the largest of the two boron-based ligands. The W(III) complexes follow the same trends as the Hf(IV) complexes with regards to the magnitudes of these M- X partial charge differences, except for the QTAIM partial charge where the smallest difference is between W(III) and the BO2C2H4 boron. This is also different from the trend found with the actinide complexes for the QTAIM partial charge difference.

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QTAIM analyses were carried out on the geometries with the fixed L2- ligand and the data are presented in table 4.25 and plotted against M-X bond length in figures 4.36 to 4.38.

Table 4.25. Electron density and energy density at M-X BCP and M-X delocalisation indices of the [LMX]n+ geometries with a fixed L ligand. Non-italics are for Hf(IV) and italics for W(III). ρ and H in atomic units.

X ligand δ(M,X) ρ (e bohr-3) H (Hartrees bohr-3)

BH4 0.628 1.107 0.068 0.120 -0.019 -0.032

BO2C2H4 0.640 0.860 0.088 0.147 -0.034 -0.081

Me 0.720 1.018 0.111 0.168 -0.048 -0.063

N(SiH3)2 0.881 0.929 0.143 0.138 -0.064 -0.036

OPh 0.840 1.136 0.156 0.249 -0.061 -0.085

Fig.4.36. ρ values between M-X bond for each M-X bond length. Blue is for Hf(IV) (R2 = 0.986), and orange for W(III) (R2 = 0.667).

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Fig.4.37. Delocalisation index between M-X bond for each M-X bond length. Blue is for Hf(IV) (R2 = 0.912), and orange for W(III) (R2 = 0.005).

Fig.4.38. H values between M-X bond for each M-X bond length. Blue is for Hf(IV) (R2=0.901), and orange for W(III) (R2 = 0.138).

From the values in table 4.25 and figures 4.36 to 4.38, it is clear there is little correlation between the QTAIM metrics and the M-X bond length for the W(III) complexes, whereas there are clearer trends for the Hf(IV), with the best correlation being found for the electron densities at the BCP, with an R2 value of 0.986. This is the same observation found with the Th(IV) analogues, where the best fit from the three QTAIM metrics was also found to be with electron densities at the BCP, with an R2 value of 0.989 (see figure 4.17 in section 4.5).

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As with the actinide complexes, the transition metal complexes’ QTAIM metrics for the M-X BCPs were compared against their QTAIM partial charge difference between the metal and X-ligand atom centres. The trendlines and associated R2 values in figures 4.39 to 4.41 are for the [LHfX]+ data only. R2 values for the LWX data are presented in the figure captions.

Fig.4.39. M-X electron density against QTAIM (M-X) charge difference for the Hf(IV) (circles, R2

= 0.876) and W(III) (squares, R2 = 0.339) complexes for each X ligand; Blue = BH4, orange =

BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

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Fig.4.40. M-X delocalisation indices against QTAIM (M-X) charge difference for the Hf(IV)

(circles, R2 = 0.953) and W(III) (squares, R2 = 0.022) complexes for each X ligand; Blue = BH4, orange = BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

Fig.4.41. M-X energy density against QTAIM (M-X) charge difference for the Hf(IV) (circles, R2 =

0.930) and W(III) (squares, R2 = 0.000) complexes for each X ligand; Blue = BH4, orange =

BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

As with the actinides (see figures 4.19 to 4.21), figures 4.39 to 4.41 show that although the M-OPh bond shows the highest absolute QTAIM metrics, this does not match with the highest charge difference, which, as with the actinides, is found for the M-N bond on the N(SiH3)2 ligand. There is one difference however to this observation, and that is for the Hf(IV) complexes, the highest δ(M,X)

132

Geometry optimisations value (see figure 4.40) does correspond to the highest charge difference. As can be seen in figure 4.40, the best correlation against the Hf-X charge difference was found for the δ(Hf,X) QTAIM metric, with an R2 value of 0.953, whereas for the Th(IV) complexes the best correlation was found for the H metric, with an R2 value of 0.915 (see table 4.16).

NBO analysis of these complexes gave the results shown in table 4.26. As with the actinide complexes, no NBOs were found for the [LMBH4]n+ complexes.

Table 4.26. Overall orbital contributions to M-X NBOs from metal centre and X atom (X atom=B, C, N or O) as a percentage, from the complexes with fixed L geometry, with breakdowns of the main AOs which make up these contributions.

Complex Hf(IV) X atom W(III) X atom

[LMBO2C2H4]n+ 33.4 66.6 45.3 54.7

(84.8 d, 14.8 s) (56.0 p, 43.7 s) (89.3 d, 10.6 s) (56.8 p, 43.0 s)

[LMMe]n+ 18.6 81.4 27.2 72.8

(84.5 d, 15.1 s) (71.1 p, 28.7 s) (88.4 d, 11.5 s) (71.7 p, 28.1 s)

[LMN(SiH3)2]n+ 9.3 90.7 10.8 89.2

(95.0 d, 1.2 p, 3.2 s) (64.6 p, 35.4 s) (88.2 d, 11.1 s) (77.2 p, 22.8 s)

[LMOPh]n+ 6.4 93.6 9.3 90.7

(89.8 d, 9.1 s) (40.8 p, 59.2 s) (99.1 d) (100 p)

Unlike with the QTAIM metrics, the NBO analysis gave a trend for the W(III) complexes with respect to their X ligands, where, as with the Hf(IV) complexes, the total metal orbital contribution decreases across the M-X bond from boron through to oxygen. All of the X atom orbital contributions are sp or sp2 hybridised – or at least somewhere between the two (pure sp being 50:50 s and p, and pure sp2 being 25:75 s and p) – except for LWOPh, where the X atom at the W-O NBO is 100% p-orbital in character, and the WIII atom is almost 100% d-orbital in character.

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Fig.4.42. M-X BCP electron density against total metal orbital contribution for the M-X NBOs. Blue = Hf(IV) (R2 = 0.956), orange = W(III) (R2 = 0.229).

Fig.4.43. M-X delocalisation index against total metal orbital contribution for the M-X NBOs. Blue = Hf(IV) (R2 = 0.894), orange = W(III) (R2 = 0.449).

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Fig.4.44. M-X BCP energy density against total metal orbital contribution for the M-X NBOs. Blue = Hf(IV) (R2 = 0.958), orange = W(III) (R2 = 0.144).

Figures 4.42 to 4.44 show the QTAIM metrics plotted against the NBO data and, as with the actinide complexes (see figures 4.28 to 4.30), there is a general negative correlation for the Hf(IV) complexes. As with other QTAIM investigations in this section, there is no clear trend found with the W(III) complexes. Due to this similarity in the Hf(IV) trend with those found with the actinide complexes, and for a more complete comparison with the QTAIM and NBO data, these transition metal complexes were next studied with a fixed M-X bond length, whilst also keeping the fixed L2- ligand geometries used for the complexes discussed up to this point. The M-X bond lengths for the Hf(IV) complexes were fixed at 2.113 Å, and for the W(III) complexes at 2.035 Å. The QTAIM metrics were then compared with the corresponding NBOs for these bonds. Unfortunately, there was no NBO found for the Hf-O bond in these fixed geometries, therefore there are only three data points for the [LHfX]+ complexes. The results are shown below.

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Fig.4.45. M-X BCP electron density against the total metal orbital contribution for the M-X NBO (blue = Hf(IV), orange = W(III)) for a fixed M-X bond length (2.113 Å for Hf, 2.035 Å for W).

Fig.4.46. M-X delocalisation index against the total metal orbital contribution for the M-X NBO (blue = Hf(IV), orange = W(III)) for a fixed M-X bond length. (2.113 Å for Hf, 2.035 Å for W).

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Fig.4.47. M-X BCP energy density against the total metal orbital contribution for the M-X NBO (blue = Hf(IV), orange = W(III)) for a fixed M-X bond length. (2.113 Å for Hf, 2.035 Å for W).

Firstly, figure 4.45 shows a very poor trend for the W(III) complexes with the electron density as was found with the relaxed W-X bond lengths in figure 4.42, with an R2 value of 0.156. The Hf(IV) complexes on the other hand showed a good fit with an R2 value of 0.867, but note that the data set is small. It is, however, a positive correlation, whereas for the relaxed Hf-X bonds this was negative. For the delocalisation index (figure 4.46), fixing the M-X bond length does not alter the direction of the correlation for the Hf(IV) complexes. Unlike with the actinide complexes, where fixing the An-X bond length made this correlation positive (see figure 4.32), here in figure 4.46, the correlation remains negative, although with an improved R2 value of 0.995. The W(III) complexes continue to show a very poor correlation. Finally, the H values in figure 4.47 show modest correlation for both sets of metal complexes.

In summary, by fixing the M-X bond length, the QTAIM metrics for the LWX complexes continued to show a poor correlation with the NBO data. Unlike the actinide complexes, the correlation remained negative for the delocalisation index. As for the Hf(IV) complexes, the lack of an NBO at the Hf-O bond in [LHfOPh]+ made for unreliable correlations for these QTAIM metrics against the NBO data.

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Hence, by changing the complexes from 5f to 5d systems, the anti-correlation found between the NBO and QTAIM data in the actinide complexes still holds. The theory that the larger radial distribution of the 5d-orbitals gives rise to better metal-ligand orbital and spatial overlap and hence improved correlation with the QTAIM metrics, would therefore appear not to hold. That said, the fact that the transition metal complexes were analysed in a geometry that was not a relaxed structure (the L2- geometry was taken from the [LThX]+ and LUX structures) may be the underlying cause for this anti-correlation.

Returning to the actinide systems, the next analyses focussed on the Mulliken population data and comparing that with the QTAIM data.

4.7. Mulliken population analysis of the An-X interaction

Mulliken population analysis was carried out on all three sets of the [LAnX]n+ actinide complexes at their relaxed geometries to probe the molecular orbital make-up of the An-X bond and, as with the NBO data in table 4.19, were then compared to the QTAIM metrics in table 4.15. Firstly, the Kohn-Sham MOs (KS- MOs) of the An-X bonds and the contribution from the actinide centres and X- atom are presented in tables 4.27 and 4.28 respectively.

Table 4.27. Overall orbital contributions to An-X KS-MOs from actinide centre (%, Mulliken), with breakdown of AOs which make up these contributions.

Complex Th(IV) Th(III) U(III)

[LAnBH4]n+ 11 (2f, 7d, 2p) 4 (4d) 7 (7d)

[LAnBO2C2H4]n+ 24 (20d, 4s) 20 (3f, 14d, 3s) 14 (14d)

[LAnMe]n+ 21 (19d, 2f) 16 (16d) 14 (14d)

[LAnN(SiH3)2]n+ 8 (3f, 5d) 3 (3f) 8 (6f)

[LAnOPh]n+ 3 (3d) 9 (9d) 2 (2f)

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Table 4.28. Overall orbital contributions to An-X KS-MOs from X atom (X atom=B, C, N or O) (%, Mulliken), with breakdown of AOs which make up these contributions.

Complex Th(IV) Th(III) U(III)

[LAnBH4]n+ 40 (26p, 14s) 41 (15p, 25s) 42 (15p, 27s)

[LAnBO2C2H4]n+ 15 (11p, 4s) 9 (7p, 2s) 11 (7p, 4s)

[LAnMe]n+ 45 (45p) 41 (37p, 4s) 34 (30p, 4s)

[LAnN(SiH3)2]n+ 18 (14p, 4s) 47 (47p) 50 (50p)

[LAnOPh]n+ 65 (65p) 21 (21p) 71 (71p)

As is seen from table 4.27, the actinide contributions to the An-X MO qualitatively match those found for the An-X NBOs in table 4.19, in that, with the exception of the An-BH4 bonds, the actinide contribution decreases as a function of X ligand. Table 4.28 also matches the NBO data in table 4.19 with the X ligand increasing in MO contribution as a function of X ligand with the exceptions of

N(SiH3)2 in the Th(IV)-N(SiH3)2 bond and OPh in the Th(III)-OPh bond, where these contributions decrease when compared to the preceding X ligand. The X atom contributions are also less than those found with the X atom contributions in the NBOs, which is explained by all these An-X MOs being more delocalised than their analogous NBOs, as shown in figure 4.48.

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Fig.4.48. Visual representations of MOs from table 4.27 and 4.28 for [LAnBO2C2H4]n+ (left) and [LAnOPh]n+ (right) for the Th(IV) (top), Th(III) (middle) and U(III) (bottom) complexes. Hydrogens are omitted for clarity. Isovalue = 0.025.

As can be seen, a significant amount of MO contribution in figure 4.48 comes from the pyrrole and arene rings as well as the An centres and X atoms. Whilst the An-B interactions look similar to those found in the NBOs (figure 4.25), the MOs in figure 4.48 show a π rather than σ-interaction between the An centres and OPh group. Furthermore, this π-interaction is also at different spatial orientations for each [LAnOPh]n+ complex. The fact that these orbitals are more delocalised when compared to the NBOs is no surprise considering that the very point of NBO analysis is to localise two electrons around one particular bond as much as possible, however, given that there is a difference between the KS-MOs

140

Geometry optimisations and NBOs with respect to the type of interaction at the An-OPh bonds makes it more difficult to see any evidence of actinide orbital contraction from one end of the X ligand series to the other, something which was easy to see in the NBOs in figure 4.25.

Nevertheless, the MOs in tables 4.27 and 4.28 were compared to the QTAIM metrics in table 4.15, albeit without the An-BH4 data so that the results can be directly compared to the QTAIM vs NBO data in figures 4.28 to 4.30.

Fig.4.49. An-X BCP electron density against total actinide orbital contribution for An-X KS-MOs (blue = Th(IV), green =Th(III) orange = U(III)).

Fig.4.50. An-X BCP delocalisation index against total actinide orbital contribution for An-X KS- MOs (blue = Th(IV), green =Th(III) orange = U(III)). 141

Geometry optimisations

Fig.4.51. An-X BCP energy density against total actinide orbital contribution for An-X KS-MOs (blue = Th(IV), green =Th(III) orange = U(III)).

The same anti-correlation of increasing QTAIM covalency metrics but decreasing actinide orbital contribution as was found with the NBOs, is also found in figures 4.49 to 4.51 for the Mulliken analysis. The R2 values from figures 4.49 to 4.51 are presented in table 4.29, where there are also comparisons with the R2 values of the QTAIM vs NBO data in table 4.22.

Table 4.29. R2 values for trends in figures 4.49 to 4.51. Red numbers are QTAIM vs NBO R2 values from table 4.22.

Figure 4.49 Figure 4.50 Figure 4.51

Th(IV) 0.918 0.969 0.939 0.966 0.875 0.994

Th(III) 0.332 - 0.736 - 0.569 -

U(III) 0.915 0.715 0.862 0.605 0.686 0.512

Table 4.29 shows that for the Th(IV) complexes, the QTAIM data correlate best with the NBO data, whereas for the U(III) complexes, the QTAIM data correlate best with the Mulliken population data. With the exception of the U(III) H values, the QTAIM data nevertheless show good correlations for both NBO and Mulliken data, and so with anti-correlations found again in figures 4.49 to 4.51, it is reasonable to suggest that these would become positive correlations if the

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Geometry optimisations

An-X separation was fixed, as was done for NBO analysis (figures 4.31 to 4.33). Unfortunately, due to time constraints, this method of fixing the An-X separation was not carried out further for Mulliken analysis. However, the fact that both NBO and MPA agree with an increase in ionicity across the X ligand series, whereas QTAIM shows the opposite case, agrees with observations in the literature mentioned earlier where both MPA and NBO data suggested the An-C interactions in AnCp3 and AnCp4 systems (An = Th-Cm) were covalent, but the QTAIM data suggested the same bonds were highly ionic7, 8.

MPA data from the [LAnX]n+ complexes will be revisited later in section 4.9 where the An-arene interactions were investigated and compared to the NICS analysis for these arene rings’ aromaticity, which is discussed in the next section.

4.8. Nucleus-independent chemical shift analysis

For NICS analysis, the “NMR” keyword available in Gaussian09 was used along with the addition of “ghost atoms”, explained in chapter 1.8. Given the difficulties associated with the calculation of NMR shifts in paramagnetic molecules12, the NMR shielding was only calculated for the closed-shell [LThIVX]+ systems. Although there are some recent developments13, 14 to overcome this problem with open-shell, paramagnetic systems in NMR – known as pNMR – for an initial study of NICS analysis on these systems, it was considered less problematic to just study the more straightforwardly-obtained isotropic values of the closed-shell systems.

As was done in the work of Baryshnikov et al15, the NICS(0) value was obtained from the coordinates of the ring critical points of each arene ring from the QTAIM analysis. This was thought to be a better method than taking the geometric centre of the arene rings, where the electron density may not be at a minimum within the π-electron system if the ring is not in D6h symmetry. The advantage of using QTAIM analysis to find the NICS(0) point, is that QTAIM can also be used to probe aromaticity by taking the δ(A,B) value for two para- related carbons on the arene rings, which has been found to show significant electron delocalisation16. Two more points, NICS(1) and NICS(2), were obtained

143

Geometry optimisations by placing a “ghost atom” 1.0 Å above the NICS(0) point above the plane of the arene ring (NICS(1)) and another below the NICS(0) point between the Th(IV) centre and plane of the arene ring (NICS(2)). This is shown in figure 4.52 for [LThMe]+.

Fig.4.52. NICS(0), NICS(1) and NICS(2) points (pink “ghost atoms”) for arene 1 and 2 in

[LThMe]+. Red circles indicate carbons taken for δ(C,C)p. Hydrogen atoms omitted for clarity.

By comparing the NICS data in conjunction with the QTAIM analysis of the arene rings in the [LThIVX]+ complexes it was hoped to produce insight into the effect of the magnitude of the arene ring aromaticity as a function of X ligand, and therefore give insight into interactions between the arene rings and actinide metal centre.

The results of the NICS analysis and QTAIM delocalisation indices for two para carbons in the arene rings (here denoted as δ(C,C)p) and δ(Th,X) are presented in table 4.30.

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Geometry optimisations

Table 4.30. NICS(0), NICS(1) and NICS(2) isotropic values (ppm) for both arene rings in

[LThX]+ as well as δ(C,C)p) and δ(Th,X) values.

Arene 1 Arene 2

X NICS(0) NICS(1) NICS(2) δ(C,C)p NICS(0) NICS(1) NICS(2) δ(C,C)p δ(Th,X)

BH4 -9.38 -9.14 -14.79 0.079 -9.37 -9.13 -14.79 0.079 0.527

BO2C2H4 -9.02 -8.77 -13.14 0.077 -9.02 -8.77 -13.14 0.077 0.561

Me -8.95 -8.93 -13.53 0.081 -8.94 -8.86 -13.55 0.081 0.679

N(SiH3)2 -8.25 -8.66 -13.24 0.083 -8.30 -8.70 -13.14 0.083 0.807 OPh -8.36 -8.78 -13.03 0.083 -8.36 -8.78 -13.03 0.083 0.857

From table 4.30, it is seen that as a function of X ligand, there is no obvious trend with regards to the NICS isotropic values. Since this QTAIM metric was taken at the ring critical point of the arene rings, this can only be compared directly with NICS(0) which is, as mentioned above, taken at the same point in space. Also, since the NICS(0) values change very little between the two arene rings, only the values from Ar1 are taken into account. This comparison is shown in figure 4.53.

0.084 OPh 0.083 N(SiH3)2 0.082 R² = 0.663

p 0.081 Me (C,C)

δ 0.080

0.079 BH4 0.078 BO2C2H4 0.077 -9.60 -9.40 -9.20 -9.00 -8.80 -8.60 -8.40 -8.20 -8.00 NICS(0) isotropic (ppm)

Fig.4.53. δ(C,C)p values against NICS(0) isotropic values for [LThX]+ complexes on Ar1.

There is only a modest trend with an R2 value of 0.663, with [LThBO2C2H4]+ appearing to be responsible for breaking the overall trend. When removing this one data point, the trend improves significantly, with an R2 value of 0.929.

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Figure 4.54 shows all the NICS points compared with the δ(Th,X) values.

Fig.4.54. δ(Th,X) values against NICS(0) (top), NICS(1) (middle) and NICS(2) (bottom) isotropic values for [LThX]+ complexes on Ar1.

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Geometry optimisations

From figure 4.54, there is a very strong trend between the δ(Th,X) values and NICS(0) isotropy, with an R2 value of 0.900, whereas there are poor correlations with the rest of the NICS values.

Although the two different measures of aromaticity – NICS(0) and δ(C,C)p – did not correlate well with one another (see figure 4.53), the fact that δ(Th,X) correlated very well with NICS(0) suggests a comparison between δ(Th,X) and

δ(C,C)p; this is presented in figure 4.55.

Fig.4.55. δ(Th,X) values against δ(C,C)p values for [LThX]+ complexes on Ar1.

As can be seen, these two different delocalisation indices correlate well together, with an R2 value of 0.861. This suggests that an increase in delocalisation index across the Th-X bond increases the aromaticity of the arene rings. This is also true if one takes the NICS(0) values as measures of aromaticity. However, the more standard measurements for aromaticity with NICS analysis – NICS(1) and NICS(2) – do not correlate well with this QTAIM metric (figure 4.54). On the other hand, from figure 4.54, this appears to be down to [LThBO2C2H4]+ again, and removing these data points gives R2 values for δ(Th,X) vs NICS(0), NICS(1) and NICS(2) of 0.860 and 0.924 respectively, as shown in figure 4.56.

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Geometry optimisations

Fig.4.56. δ(Th,X) values against NICS(1) (top) and NICS(2) (bottom) isotropic values for

[LThX]+ complexes on Ar1. [LThBO2C2H4]+ omitted from data set.

The higher R2 values when the [LThBO2C2H4]+ data was omitted in figure 4.56 therefore contradicts the findings in figure 4.55, in that rather than an increase in δ(Th,X) correlating with an increase in Ar1 aromaticity, an increase in δ(Th,X) in fact correlates with a decrease in Ar1 aromaticity. This can be rationalised by taking into account the isotropic values of the NICS(2) points. One would expect these to be areas of high aromaticity because the π-orbitals of the arene rings are mixing with the d-orbitals of the Th(IV) centre, and therefore becoming much more delocalised. This is the spatial aromaticity introduced by Jutzi and Burnford17 at the end of chapter 1. Indeed, evidence of this spatial aromaticity is supported by the much larger isotropic values of

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Geometry optimisations

NICS(2) when compared to NICS(0) and NICS(1) (see table 4.30). As the X ligand changes from boron-based to oxygen-based ligands however, the steady increase of δ(Th,X) across the Th-X bond could be drawing electron density away from the space between the Th(IV) centre and arene rings, i.e. the points at NICS(2). This decrease in electron density here would therefore reduce the amount of arene π-orbital and Th(IV) d-orbital mixing, and therefore reduce the extent of spatial aromaticity. Again, this is supported by figure 4.56 (with

[LThBO2C2H4]+ data omitted) where an increase in δ(Th,X) directly correlates with a decrease in NICS(2). This rationale also could explain why NICS(0) increases along with an increasing δ(Th,X), as the more localised the π-orbitals of the arene rings become (a decrease in NICS(2)) this in turn increases their localisation closer to the centre of the arene rings (NICS(0)). The contradiction mentioned above between figure 4.54 and 4.55 with respect to these NICS(0) is only contradictory if one takes NICS(0) to be a direct measure of aromaticity. However, as has been mentioned in chapter 1, NICS(0) is not often recommended due to contribution from σ-orbitals in the arene ring as well17, 18 and so if, on the other hand, one does not take NICS(0) to be a measure of aromaticity – instead using NICS(2) and NICS(1) as this measure – then the observations for NICS(0) with a changing X ligand appear to fit with the decrease of spatial aromaticity between the Th(IV) and arene rings.

These data therefore suggest that a greater electronic interaction between the arene rings and Th(IV) centre requires an X ligand that pushes rather than withdraws electron density from the Th(IV) centre.

4.9. Mulliken population analysis of the An-arene interaction

The Mulliken population analysis carried out and mentioned in section 4.7 for analysing the An-X MOs also yielded information to probe the molecular orbital make-up of the actinide to arene ring interactions, which provides a good opportunity to compare with the NICS data presented in the previous section. All such interactions were found to be π interactions from the actinide d- orbitals to the arene p-orbitals, except with the Th(III) complexes, where δ interactions were also found from the thorium f- and d-orbitals, shown in the table below.

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Geometry optimisations

Table 4.31. Total actinide atomic orbital contribution (%, Mulliken analysis) to An(Ar)2 molecular orbitals for each [LAnX]n+ complex.

MO type BH4 BO2C2H4 Me N(SiH3)2 OPh

ThIV-Ar π 13 (3f, 10d) 8d 9d 9d 9d

ThIII-Ar π 9 (3f, 6d) 17 (4f, 13d) 9d 15 (12d, 3p) 11 (4f, 7d)

ThIII-Ar δ 27 (17f, 10d) 23f 26 (19f, 7d) 27 (18f, 9d) 30f

UIII-Ar π 13 (10f, 3d) 8d 8d 10 (2f, 8d) 8d

Table 4.31 shows that for the Th(IV) and U(III) complexes, there is not much difference between the two with regards to the actinide orbital contribution for the π-bonds to the arene rings, whereas Th(III) shows the most actinide orbital contribution for these π-bonds, except for LThIIIMe, where the d-orbital contribution is the same as that for its Th(IV) analogue at 9%, and for LThIIIBH4, where it is again at 9% and lower than both its Th(IV) and U(III) analogues.

The Th(IV) data in table 4.31 was compared with the NICS analysis in the previous section.

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Geometry optimisations

Fig.4.57. Total Th(IV) orbital contribution to the Th-Ar MO against NICS(1) (top) and NICS(2) (bottom) isotropric.

Although [LThMe]+, [LThN(SiH3)2]+ and [LThOPh]+ show the same amount of Th(IV) orbital contribution to this MO, figure 4.57 nevertheless shows positive correlations between these MOs and the NICS values from table 4.30. The much larger Th(IV) orbital contribution seen with [LThBH4]+ corresponds to the larger NICS(1) and NICS(2) values in the same complex. Figure 4.57 therefore shows evidence to support that the more the actinide centre contributes to the

MOs in the An-(Ar)2 interactions, the more there is spatial aromaticity between the An and arene centres. This is perhaps intuitive anyway, however, the fact these data match could therefore suggest that the An contributions to the MOs in the rest of table 4.31 can be used as indirect measurements of spatial

151

Geometry optimisations aromaticity in the Th(III) and U(III) complexes where NICS data are more difficult to obtain due to these complexes being open shell.

Focussing on the Mulliken populations of the rest of these MOs, it is seen that the δ-bonding found in all five of the Th(III) complexes is in the HOMO, where the unpaired electron in the 5f-based orbital (and in some cases the d-electrons as well, in an apparent df hybrid) interacts with the empty π* orbitals of the arene rings. These interactions were seen most clearly in LThIIIBO2C2H4 and LThIIIOPh as shown in figure 4.58.

Fig.4.58. HOMO of LThIIIBO2CcH4 (left) and LThIIIOPh (right), showing δ-bonding from the thorium centre to both arene rings at an Isovalue of 0.02. Hydrogens omitted for clarity.

From table 4.31, there is also no apparent effect on the total actinide orbital contribution to the An-(Ar)2 π-bonds when changing the X ligand. However, when ignoring the complex with the BH4 ligand, the Th(III) complexes seem to show some trend for the δ-bonding with respect to the total actinide orbital contribution. As the X ligand changes from the boron (except BH4) to the oxygen based ligands, the f-character of this δ interaction increases.

A reason for this δ interaction being found in the Th(III) complexes but not the Th(IV) or U(III) could be down to energetics of the HOMOs of all the complexes.

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Geometry optimisations

Table 4.32. Energies (eV) of the HOMO of the [LAnX]n+ complexes.

BH4 BO2C2H4 Me N(SiH3)2 OPh

[LThIVX]+ -8.708 -8.354 -8.490 -8.381 -8.354

LThIIIX -4.054 -3.592 -3.701 -3.918 -3.075

LUIIIX -5.061 -4.572 -4.572 -4.680 -4.517

Where the HOMOs of the Th(IV) complexes are the π orbitals of the pyrrole rings in the L ligand, the HOMOs of the Th(III) complexes are the δ-bonds between thorium and the arene rings, as mentioned previously, and the HOMOs of the U(III) complexes are largely uranium f-orbitals. The energies of these lattermost HOMOs are in agreement with the energies found in other work where the HOMO of [UIII(L)I(THF)] – essentially a variant of this study’s LUX compound where an iodine atom and THF complex are ligated to uranium in place of a single X ligand – are around about -5 eV and are also purely uranium f-orbital in character19. It is clear from table 4.32 that the LThIIIX complexes have the HOMOs of the highest energy, and that occupied f-orbitals at this energy level are at a suitable energy to interact with the high energy π* orbitals of the arene rings.

4.10. Conclusions and future work

In summary – with PBE0 used as the most reliable functional based on experimental data – various orbital- and electron density-based partition method analyses and NICS analysis yielded some insightful results.

Partial charge analyses showed a range of charge differences between the An centres and ligating X-atoms, depending on the analysis technique used. They did, however, all agree with the general trend of the [LAnX]n+ complexes with a boron-based X ligand showing the lowest An-X charge difference, and the more electro-negative nitrogen and oxygen-based X ligands showing the largest An-X charge difference. The QTAIM An-X charge difference also showed appreciable positive correlations against the QTAIM metrics δ(An,X), ρ and H, where a greater charge difference coincided with a greater degree of covalency

153

Geometry optimisations

(according to the QTAIM definitions). This was also the case for the [LHfIVX]+ analogues, whereas the LWIIIX analogues showed no such correlation. Conversely, the An-X charge difference showed a negative correlation with the total actinide orbital contribution to the An-X bond from NBO analysis, for the Th(IV) and U(III) complexes, indicating that these bonds may be more ionic as the X ligand changes from boron to oxygen-based. Hence, the QTAIM data and NBO data seemed to contradict each other, since as the QTAIM covalency metrics increased in magnitudes, one would expect the NBO actinide orbital contributions to increase also. Fixing the An-X bond at a given bond length corrected this apparent contradiction, by showing a positive but non-linear trend between the QTAIM and NBO data. It was the QTAIM data which changed however, when fixing the An-X bond length, suggesting that the QTAIM metrics are more sensitive to bond length than NBO analysis, and so when probing systems with a diverse range of bond lengths, NBO analysis may be a more robust and reliable approach to infer bonding character. This has added to the evidence of different covalency descriptors – energy-driven vs overlap-driven – often resulting in conflicting conclusions, and that these analyses can be sensitive to bond length, already found in the literature7-10.

Similar, albeit weaker, trends were found for the transition metal complexes of [LMX]n+. The QTAIM metrics therefore appeared to be sensitive to not only An-X separations, but also to whether the metal centre was an actinide or transition metal. The NBO data on the other hand were not as sensitive to such variables, with the transition metal complexes still showing a decrease of metal orbital contribution across the M-X bond, just like their actinide analogues.

The MPA results to study the actinide and X ligand contribution to the KS-MOs also showed similar trends against the QTAIM metrics as was found with the NBO data. As expected, these MOs were a lot more delocalised throughout the whole [LAnX]n+ complexes and so the X ligand MO contributions were less than those found with the NBO analysis. Unlike with the NBO data however, the MPA was not studied for the fixed bond lengths of An-X, where for the QTAIM vs NBO data this was seen to reverse the negative correlation as has been discussed. It would be interesting therefore for future work to see if the MPA data will also

154

Geometry optimisations agree with the NBO data when fixing the An-X bond distances, and how this will compare with the [LMX]n+ complexes as well.

The NICS analysis showed interesting trends with regards to the spatial aromaticity between the Th(IV) centres and arene rings. The NICS(0) data showed a negative correlation with the QTAIM δ(C,C)p values, and these δ(C,C)p values showed a positive correlation with the δ(Th,X) values. I.e. according to QTAIM, the aromaticity of the arene ring increased as a function of increasing electron delocalisation across the Th-X bond. However, this increasing of electron delocalisation showed a negative correlation with the NICS(1) and NICS(2) values, which, being points out of plane of the arene rings, are the more standard measures of aromaticity. The latter values, NICS(2), showed that spatial aromaticity between the Th(IV) centre and arene rings decreased when the δ(Th,X) values increased, and therefore a more electronegative X ligand appeared to reduce the spatial aromaticity found at NICS(2).

As was mentioned in section 4.9 there are difficulties when calculating the NMR shifts in paramagnetic molecules12 – chemical shifts which are intrinsic to obtaining NICS data. As NICS analysis was carried out only on the closed-shell [LThIVX]+ systems, a scope for future work would be to apply this analysis to the open-shell LThIIIX and LUIIIX complexes to see if similar trends can be found. pNMR calculation methods are still under development however, with only a few recent examples in the literature13, 14. A most recent study by Moylan and McDouall20 focussed on calculating the g tensors – important values needed for describing the effect of a magnetic field on electron spin – for open-shell U(V) complexes bonded to five, seven and eight-membered aromatic rings using the method of Bolvin21. Although this study focussed on calculating the g tensors for electron paramagnetic resonance (EPR) data for the open-shell U(V) systems, obtaining the g tensor can also be applied to pNMR20. However, this method was shown to work best with CASSCF, and DFT calculations at the PBE0 level showed poorer results20.

MPA showed actinide interaction with the arene rings as predominantly π- bonding from the actinide d-orbitals to the arene p-orbitals, however, significant δ-bonding was also observed for the LThIIIX complexes in the

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Geometry optimisations

HOMOs, arising from f-orbitals interacting with the LUMO of the arene rings. These actinide orbital contributions varied in percentages and orbital make-up in some cases, depending on which X ligand was present, though no clear correlation was found.

However, for the [LThX]+ complexes, these An-arene interactions correlated well with the NICS(2) data, where an increase in Th(IV) MO contribution to the arene rings corresponded to an increase in this spatial aromaticity.

The next chapter focusses how these QTAIM data can also be used to interpret the effect the X ligand has on the bonding energy of the An-X bonds.

156

References

1. P. L. Arnold, C. J. Stevens, J. H. Farnaby, M. G. Gardiner, G. S. Nichol and J. B. Love, J. Am. Chem. Soc., 2014, 136, 10218-10221. 2. N. Edelstein, Inorg. Chem., 1981, 20, 297. 3. P. L. Arnold, J. H. Farnaby, M. G. Gardiner and J. B. Love, Organometallics, 2015, 34, 2114. 4. P. D'Angelo, F. Martelli, R. Spezia, A. Filipponi and M. A. Denecke, Inorg. Chem., 2013, 52, 10318. 5. Database of Ionic Radii, http://abulafia.mt.ic.ac.uk/shannon/radius.php?Element=Th, Accessed 23/07/2015. 6. A. R. E. Mountain and N. Kaltsoyannis, Dalton Trans., 2013, 42, 13477. 7. M. J. Tassell and N. Kaltsoyannis, Dalton Trans., 2010, 39, 6719. 8. I. Kirker and N. Kaltsoyannis, Dalton Trans., 2011, 40, 124. 9. N. Kaltsoyannis, Dalton Trans., 2016, 45, 3158. 10. I. D. Prodan, G. E. Scuseria and R. L. Martin, Phys. Rev. B, 2007, 76, 033101. 11. P. Corradini and G. Allegra, J. Am. Chem. Soc., 1959, 81, 2271-2272. 12. J. Vaara, in Science and Technology of Atomic, Molecular, Condensed Matter & Biological Systems, ed. R. H. Contreras, Elsevier, 2013, vol. 3, ch. Chapter 3 - Chemical Shift in Paramagnetic Systems, p. 41. 13. F. Gendron, K. Sharkas and J. Autschbach J. Phys. Chem. Lett., 2015, 6, 2183. 14. J. Autschbach, Ann. Rep. Comput. Chem., 2015, 11. 15. G. V. Baryshnikov, B. F. Minaev, M. Pittelkow, C. B. Nielsen and R. Salcedo, J. Mol. Model., 2013, 19, 847. 16. R. F. W. Bader, A. Streitwieser, A. Neuhaus, K. E. Laidig and P. Speers, J. Am. Chem. Soc., 1996, 118, 4959.

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17. P. Jutzi N. Burnford, in Metallocenes: Synthesis, Reactivity, Applications, ed. A. Togni and R. Halterman, Wiley-VCH Verlag GmbH, Weinheim, Germany, 1998, ch. 1. 18. P. v. R. Schleyer, M. Manoharan, Z-X, Wang, B. Kiran, H. Jiao, R. Puchta and N. J. R. v. E. Hommes, Org. Lett., 2001, 3, 2465. 19. P. L. Arnold, J. H. Farnaby, R. C. White, N. Kaltsoyannis, M. G. Gardiner and J. B. Love, Chem. Sci., 2014, 5, 756. 20. H. M. Moylan and J. J. W. McDouall, Chem. Eur. J., 2017, 23, 7798. 21. H. Bolvin, Chem. Phys. Chem., 2006, 7, 1575.

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The strength of the An-X interactions

Chapter 5. The strength of the An-X interactions

5.1. Introduction

This chapter reports a systematic computational study of [LAnX]n+ complexes, with focus on the QTAIM analysis of the An-X bond and possible correlations of these QTAIM data with the An-X bond strength and its decomposition. As mentioned in chapter 2.2.3, linear relationships between EDA bond energies and QTAIM metrics have been found with hydrogen fluoride, nitrile complexes, transition metal and uranium dimers, and a range of organometallic complexes1-3, although analysis of the EDA showed the total bond energies were dominated by orbital mixing energies4, 5.

In addition to the intrinsic interest in understanding the relationships between these two rather different approaches for analysing molecular electronic structure and bonding, it should be noted that QTAIM calculations are typically more straightforward to perform than bond energy calculations and decompositions, particularly for systems with several unpaired electrons. Thus, if clear links between QTAIM properties and bond energy terms can be further established, a situation may be arrived at in which one need only calculate QTAIM metrics to gain insight into actinide–ligand bond strengths and covalency. The results in sections 5.7 to 5.13 of this chapter have been published by the author and Kaltsoyannis in Dalton Transactions6.

5.2. Methodologies

Frequency calculations were carried out on the optimised geometries of the complexes from tables 4.1 to 4.3 in chapter 4 (PBE0 level only) in order to calculate the zero point and enthalpy corrections to the SCF energy. These data

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The strength of the An-X interactions

are shown again in tables 5.1 and 5.2. This process was repeated for optimised geometries of the LAnn+ (n = 1 for U(III) and Th(III), 2 for Th(IV)) and X- fragments. Similar calculations were then carried out for radical rather than ionic fragments.

Subsequent QTAIM and EDA calculations were carried out where the X ligand series was modified such that only the ligating atom changed across the p-block in the first and second row, with its chemical environment being hydrogen based, phenyl based, or a mixture of the two, as shown in the list of all the X- type ligands studied below:

 X ligands; BH4, BO2C2H4, CH3, N(SiH3)2 and OPh.

 X’ ligands; CH3, NH2, OH and F.

 X’’ ligands; CH2Ph, NHPh and OPh.

 X* ligands; SiH3, PH2, SH and Cl.

 X** ligands; SiH2Ph, PHPh and SPh.

 X† ligands; CPh3, SiPh3, NPh2, PPh2, OPh and SPh.

This further set of complexes still retained the general structure shown in figure 3.2 in chapter 3.

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The strength of the An-X interactions

U-X 2.855 2.677 2.519 2.359 2.159 U-N1 2.460 2.467 2.484 2.473 2.486

LUX U-N2 2.460 2.467 2.468 2.470 2.486 e arene rings. 2.575 2.508 2.564 2.596 2.620 U-Ar2 2.575 2.508 2.615 2.724 2.620 U-Ar1 119.5 121.7 121.2 118.7 119.4 N-U-N Th-X 2.888 2.652 2.525 2.341 2.168 9.2 3.3 LUX 11.6 16.8 10.6 1 Interplanar 2.480 2.482 2.495 2.459 2.487 Th-N 177.9 177.6 177.3 175.4 176.0 Ar-U-Ar

LThX 2.469 2.482 2.476 2.492 2.487 Th-N2 Bond distances (Å) 115.7 126.5 118.2 116.3 120.1 N-Th-N 2.385 2.482 2.831 3.055 2.576 ) Th-Ar2 o ( sed geometries. Ar1 and Ar2 refer to centroids of respectiv -Ar1 775 411 401 576 9.6 6.3 7.9 12.4 21.7 LThX 2. 2.482 2. 2. 2. optimi Th - optimised geometries. - Interplanar Bond angles Th-X 2.837 2.700 2.475 2.272 2.106 176.8 171.1 177.3 175.7 178.3 Ar-Th-Ar 2.394 2.405 2.413 2.426 2.422 Th-N1 complexes for PBE0

complexes for PBE0

+ n + 119.9 123.7 121.2 117.0 119.3 n N-Th-N + 2.394 2.405 2.405 2.418 2.422 Th-N2 + [LThX] 9.2 4.0 12.6 16.8 10.8 [LThX] Interplanar 2.615 2.581 2.645 2.690 2.651 Th-Ar2 179.3 177.1 177.8 174.2 177.6 2.615 2.581 2.641 2.689 2.651 Ar-Th-Ar Th-Ar1 Key bond lengthsKey bond for [LAnX] Key bond anglesKey bond for [LAnX]

4 2 4 2 ) ) H 3 H 4 3 2 4 2 C C 2 Me 2 Me BH OPh BH OPh X ligand X X ligand X BO N(SiH BO N(SiH Table 5.1. 5.1. Table

Table 5.2. 5.2. Table

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The strength of the An-X interactions

5.3. Results

The list of the full [LAnX]n+ complexes and their energies as well as the energies for the ionic fragments (for heterolytic bond cleavage) are given in tables 5.3 to

5.6, where terms E, EZPE, H298 and G298 are SCF energies, SCF + ZPE energies, enthalpies and Gibbs energies respectively.

Table 5.3. SCF energies, ZPE and thermal corrections for the [LThIVX]+ complexes. All values in Hartree.

Complex E EZPE H298 G298

[LThBH4]+ -1469.9614 -1469.5420 -1469.5177 -1469.5937

[LThBO2C2H4]+ -1696.5321 -1696.0826 -1696.0552 -1696.1391

[LThMe]+ -1482.6041 -1482.1902 -1482.1658 -1482.2413

[LThN(SiH3)2]+ -2079.8878 -2079.4521 -2079.4243 -2079.5069

[LThOPh]+ -1749.4325 -1748.9585 -1748.9300 -1749.0175

Table 5.4. SCF energies and thermal corrections for the LThIIIX complexes. All values in Hartree.

Complex E EZPE H298 G298

LThBH4 -1470.1339 -1469.7181 -1469.6935 -1469.7959

LThBO2C2H4 -1696.6951 -1696.2495 -1696.2220 -1696.3058

LThMe -1482.7633 -1482.3538 -1482.3287 -1482.4067

LThN(SiH3)2 -2080.0493 -2079.6176 -2079.5885 -2079.6771

LThOPh -1749.5797 -1749.1118 -1749.0833 -1749.1721

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The strength of the An-X interactions

Table 5.5. SCF energies and thermal corrections for the LUIIIX complexes. All values in Hartree.

Complex E EZPE H298 G298

LUBH4 -1539.3910 -1538.9731 -1538.9486 -1539.0253

LUBO2C2H4 -1765.9454 -1765.4982 -1765.4705 -1765.5563

LUMe -1552.0161 -1551.6040 -1551.5793 -1551.6568

LUN(SiH3)2 -2149.2979 -2148.8642 -2148.8350 -2148.9245

LUOPh -1818.8380 -1818.3628 -1818.3370 -1818.4270

Table 5.6. Energies of molecular ionic fragments with ZPE and thermal corrections. All values in Hartree.

Fragment E EZPE H298 G298

BH4- -27.2084 -27.1748 -27.1709 -27.1948

BO2C2H4- -253.7185 -253.6534 -253.6479 -253.6804

Me- -39.7700 -39.7418 -39.7380 -39.7610

N(SiH3)2- -637.1149 -637.0626 -637.0565 -637.0913

OPh- -306.6365 -306.5458 -306.5396 -306.5740

LTh2+ -1442.4102 -1442.0308 -1442.0092 -1442.0800

LTh+ -1442.7257 -1442.3479 -1442.3262 -1442.3970

LU+ -1511.9751 -1511.5963 -1511.5746 -1511.6464

The sum of the values of the energies in table 5.6 and their respective values for each X ligand were subtracted from the overall energies of the complexes from the values of the energies in tables 5.3 to 5.5 to give the bond energies between [LAn]n+ and X- according to:

163

The strength of the An-X interactions

∆ = [] − + (5.1)

[] ∆ = − + (5.2)

[] ∆ = − + (5.3)

[] ∆ = − + (5.4)

The bond energies for homolytic cleavage were determined in the same way as for the heterolytic model, only the values for each fragment were taken from table 5.7.

Table 5.7. Energies of molecular radical fragments with ZPE and thermal corrections. All values in Hartree.

Fragment E EZPE H298 G298

BH4 ̇ -27.1017 -27.0687 -27.0646 -27.0892

BO2C2H4 ̇ -253.7138 253.6456 -253.6402 -253.6740

Me ̇ -39.7930 -39.7634 -39.7594 -39.7832

N(SiH3)2 ̇ -637.0174 -636.9647 -636.9592 -636.9929

OPh ̇ -306.5649 -306.4733 -306.4671 -306.5021

LTh+ ̇ -1442.7064 -1442.3311 -1442.3105 -1442.3780

LTh ̇ -1442.9009 -1442.5267 -1442.5049 -1442.5760

LU ̇ -1512.1507 -1511.7751 -1511.7532 -1511.8262

The energies of the homolytic bond breakings were calculated from reactions 5.5 to 5.8.

• • ∆ = [] − + (5.5)

[] • • (5.6) ∆ = − +

[] • • ∆ = − + (5.7)

[] • • ∆ = − + (5.8)

164

The strength of the An-X interactions

5.4. Heterolytic reactions

The results from equations 5.1 to 5.4 using the data from tables 5.3 to 5.6 are presented in tables 5.8 to 5.10 below.

Table 5.8. Th-X bond enthalpies and Gibbs free energies (eV) for the [LThIVX]+ complexes from ion fragments.

Th-X bond ΔE ΔE + ZPE ΔH298 ΔG298

Th-(µ-H2)BH2 -9.33 -9.15 -9.16 -8.74

Th-BO2C2H4 -10.98 -10.84 -10.81 -10.30

Th-Me -11.54 -11.36 -11.39 -10.89

Th-N(SiH3)2 -9.87 -9.76 -9.76 -9.13

Th-OPh -10.50 -10.39 -10.37 -9.89

Table 5.9. Th-X bond enthalpies and Gibbs free energies (eV) for the LThIIIX complexes from ion fragments.

Th-X bond ΔE ΔE + ZPE ΔH298 ΔG298

Th-(µ-H2)BH2 -5.44 -5.32 -5.34 -4.84

Th-BO2C2H4 -6.83 -6.76 -6.75 -6.21

Th-Me -7.28 -7.19 -7.20 -6.35

Th-N(SiH3)2 -5.68 -5.64 -5.60 -5.14

Th-OPh -5.92 -5.94 -5.92 -5.47

165

The strength of the An-X interactions

Table 5.10. U-X bond enthalpies and Gibbs free energies of reaction (eV) for the LUIIIX complexes from ion fragments.

U-X bond ΔE ΔE + ZPE ΔH298 ΔG298

U-(µ-H2)BH2 -5.64 -5.50 -5.53 -5.01

U-BO2C2H4 -6.85 -6.76 -6.75 -6.24

U-Me -7.37 -7.23 -7.26 -6.79

U-N(SiH3)2 -5.66 -5.59 -5.55 -5.08

U-OPh -6.16 -6.01 -6.06 -5.62

Based on the ΔG298 values, the most spontaneous reactions are those between LAn+ and Me- and the least spontaneous are for LAn2+ and BH-. All of them however show a favourable reaction, with very strong bonds – based on the

ΔH298 values – although the strongest bond out of all of the actinide complexes is between the Th-C in [LThIVMe]+ at -11.39 eV, instead of the Th-O bond in [LThIVOPh]+ (-10.37 eV), which was expected to be the strongest based on the bond lengths and partial charge and QTAIM analyses presented previously. The An-C bond is also the strongest for the Th(III) and U(III) complexes at -7.20 and

-7.26 eV respectively. As expected though, the An-(µ-H)2B2 bond is found to be the weakest. Also of note is that the bond energies for the Th(III) and U(III) complexes are more similar than the bond energies for the Th(III) and Th(IV) complexes. This could suggest that the stability of these [LAnX]n+ complexes may rely more on the oxidation state of the actinide rather than which specific actinide is used. However, given the limited data set for a range of actinides and oxidation states, it is by no means conclusive here that this is the case.

For purposes of discussion, all hitherto mentions of bond energies refers to both

ΔH298 and ΔG298 values. These bond energies were compared with bond lengths and with the QTAIM metrics presented in chapter 4. The bond energies in tables 5.8 to 5.10 were plotted against the An-X bond lengths in figure 5.1:

166

The strength of the An-X interactions

Fig.5.1. An-X bond enthalpies from equation 5.3 (solid points) and Gibbs free energies from equation 5.4 (hollow points) against An-X bond length. For the different actinides, circles =

[LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue = BH4, orange

= BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

There is a common trend between the bond lengths of An-X and their associated bond energies; an increasing energy from the X = BH4 to X = Me, then a reduction to X = N(SiH3)2 before increasing again for OPh. If indeed both bond length and bond enthalpies are indicators of bond strength, one would expect that the N(SiH3)2 and OPh data points to be higher in energy than the Me data points, thus forming a linear relationship from the boron to oxygen based ligands. This non-linear pattern is seen again for the δ(An,X) values in figure 5.2.

167

The strength of the An-X interactions

Fig.5.2. An-X bond enthalpies from equation 5.3 (solid points) and Gibbs free energies from equation 5.4 (hollow points) against An-X delocalisation indices. For the different actinides, circles = [LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue =

BH4, orange = BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

Fig.5.3. An-X bond enthalpies from equation 5.3 (solid points) and Gibbs free energies from equation 5.4 (hollow points) against An-X QTAIM charge differences. For the different actinides, circles = [LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue =

BH4, orange = BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

These bond energies are plotted against An-X charge difference in figure 5.3. The lowest charge difference coincides with the lowest bond energies, which makes sense if all the An-X bonds are thought to be ionic. However by this logic, the [LAnN(SiH3)2]n+ complexes would exhibit the most negative bond energies,

168

The strength of the An-X interactions

given the charge An-X charge difference for these complexes are the largest, yet they do not.

Fig.5.4. An-X bond enthalpies from equation 5.3 (solid points) and Gibbs free energies from equation 5.4 (hollow points) against An-X BCP electron density. For the different actinides, circles = [LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue =

BH4, orange = BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

Figure 5.4 shows that for all three sets of actinide complexes, the electron densities at the BCP follow the same trend found with the An-X bond lengths and the An-X delocalisation indices, in that there seems to be a linear relationship with bond energies from the boron to carbon-based ligands, but then the trend diverges from this relationship when changing the X ligand to the nitrogen and oxygen based ligands. A similar trend is also found with the energy densities at the BCP, but also what differs with this H metric is that the thorium- based complexes are much closer together in H values than the uranium-based complexes, which also show the largest magnitude of H, coinciding with a larger reaction enthalpy and Gibbs free energy, as seen in figure 5.5.

169

The strength of the An-X interactions

Fig.5.5. An-X bond enthalpies from equation 5.3 (solid points) and Gibbs free energies from equation 5.4 (hollow points) against An-X BCP energy density. For the different actinides, circles

= [LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue = BH4, orange = BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

In previous work a linear correlation was found between QTAIM metrics at the metal-ligand BCP and the metal-ligand binding energy in (CO)5M- units bonded to three different tautomers of imidazole (where M = Cr, Mo, W)3. The present data show only very poor linear correlations between the bond energies and the

QTAIM metrics – with R2 values for ΔH298 against the QTAIM metrics for all [LAnX]n+ complexes of 0.218, 0.031 and 0.310 for δ(An,X), ρ and H respectively – indicating that the correlations found previously by Mountain and Kaltsoyannis3 are by no means general.

5.5. Homolytic reactions

The energies in the previous section are large because as mentioned, separation is to heterolytic fragments. The same type of calculation was carried out for the fragments but with homolytic separation, so as to produce neutral (except for the [LThIV]+ fragment, which had a +1 charge) fragments of radicals. The results from equations 5.5 to 5.8 using the data from tables 5.3 to 5.5 and table 5.7 are presented below.

170

The strength of the An-X interactions

Table 5.11. Th-X bond enthalpies and Gibbs free energies of reaction for the [LThIVX]+ complexes from radical fragments.

Th-X bond ΔE ΔE + ZPE ΔH298 ΔG298

Th-(µ-H2)BH2 -4.17 -3.87 -3.88 -3.41

Th-BO2C2H4 -3.04 -2.88 -2.84 -2.37

Th-Me -2.85 -2.60 -2.61 -2.18

Th-N(SiH3)2 -4.46 -4.25 -4.21 -3.70

Th-OPh -4.38 -4.20 -4.15 -3.74

Table 5.12. Th-X bond enthalpies and Gibbs free energies of reaction (eV) for the LThIIIX complexes from radical fragments.

Th-X bond ΔE ΔE + ZPE ΔH298 ΔG298

Th-(µ-H2)BH2 -3.57 -3.34 -3.37 -2.84

Th-BO2C2H4 -2.19 -2.10 -2.09 -1.52

Th-Me -1.87 -1.73 -1.75 -1.29

Th-N(SiH3)2 -3.56 -3.43 -3.38 -2.95

Th-OPh -3.10 -3.04 -2.03 -2.56

Table 5.13. U-X bond enthalpies and Gibbs free energies of reaction (eV) for the LUIIIX complexes from radical fragments.

U-X bond ΔE ΔE + ZPE ΔH298 ΔG298

U-(µ-H2)BH2 -3.77 -3.53 -3.57 -3.02

U-BO2C2H4 -2.20 -2.11 -2.10 -1.52

U-Me -1.97 -1.78 -1.81 -1.29

U-N(SiH3)2 -3.53 -3.38 -3.34 -2.87

U-OPh -1.37 -1.70 -1.65 -1.19

171

The strength of the An-X interactions

As expected, the energies are smaller, in an absolute sense, in tables 5.11 to 5.13 when compared to tables 5.8 to 5.10, and, unlike the results for the heterolytic reactions, the homolytic reaction suggests that the reaction between the LTh+⦁ and OPh⦁ fragments is the most spontaneous, with a Gibbs free energy of reaction of -3.74 eV, whereas the Th-N(SiH3)2 bond appears to be the strongest with an enthalpy at 298.15 K of -4.21 eV. From table 5.11, for both ΔH and ΔG, the Th-Me bond is the weakest and least spontaneous out of the five complexes; the opposite of the results found for the heterolytic reactions (see table 5.8). On the other hand, from table 5.12, the Th(III) complexes show that the Th-

N(SiH3)2 is the strongest and that the reaction between LTh⦁ and ⦁N(SiH3)2 is the most spontaneous of the five reactions. The U(III) complexes also show that the

U-BH4 bond is the most stable of the five U(III) complexes and the most stable of these reactions. The U(III) bond energies are very similar to the Th(III) bond energies, except in the case of An-OPh where, perhaps surprisingly the U-OPh is the least stable, whereas for Th(III) and Th(IV) complexes in both the homolytic and heterolytic reactions – and indeed for the U(III) complexes in the heterolytic reactions – this An-OPh has been amongst the most stable of the An- X bonds.

Fig.5.6. An-X bond enthalpies from equation 5.7 (solid points) and Gibbs free energies from equation 5.8 (hollow points) against An-X bond length. For the different actinides, circles =

[LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue = BH4, orange

= BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

172

The strength of the An-X interactions

From figure 5.6, as with the energies of the heterolytic reactions, there is no clear correlation between bond energies and An-X bond length. The above figures also show a reverse in trends than those found in figure 5.1 in regards to the bond energies for the complexes. What is also perhaps most noticeable is that unlike the energies for the heterolytic reactions, there is no distinct differences in the bond energies between the Th(IV) complexes and the U(III) or Th(III) complexes, except for where X = OPh. All three sets of actinide complexes are more closely grouped together in terms of these bond energies suggesting that, with the exception of the OPh ligands, all these LAn⦁ and X⦁ reactions are quite similar for their An-X bond stabilities, regardless of the actinide centre.

Fig.5.7. An-X bond enthalpies from equation 5.7 (solid points) and Gibbs free energies from equation 5.8 (hollow points) against An-X charge difference. For the different actinides, circles =

[LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue = BH4, orange

= BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

The trends for the QTAIM charge difference in figure 5.7 also repeats what was found with the bond lengths. As with the heterolytic reactions the least stable energies coincide generally with the smallest charge difference. If the An-X bonds are ionic in character, this would make sense, and since the QTAIM metrics for the Th(III) complexes were not able to be compared with any NBO data for the ThIII-X bond (see chapter 4) – the purpose of which was to ascertain the ionic or covalent character of these bonds – the results from figure 5.7 may

173

The strength of the An-X interactions

show that the ThIII-X are more ionic rather than covalent in character, and become more so with a more electronegative X ligand, something which was not possible to infer from NBO analysis due to the absence of LThIIIX NBO data. Indeed, the two main QTAIM metrics for indicating covalency and the magnitude of it – δ(A,B) and H – increased to a lesser extent as the X ligand changed from boron to oxygen-based for the Th(III) complexes and their associated An-X bond lengths, where instead of following a linear trend, the Th(III) trend line appeared to be tending towards a plateau as the OPh ligand was reached (see figures 4.22 and 4.23 in chapter 4).

The QTAIM metrics were next compared with the homolytic bond energies, as shown first of all with the delocalisation index in figure 5.8 below.

Fig.5.8. An-X bond enthalpies from equation 5.7 (solid points) and Gibbs free energies from equation 5.8 (hollow points) against An-X delocalisation indices. For the different actinides, circles = [LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue =

BH4, orange = BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

The actinide complexes do not show a correlation with the QTAIM metrics and bond energies, where in fact in the case of the U(III) complexes, the lowest δ(An,X) value corresponds to the most stable U-X, and the highest δ(An,X) value corresponds to the least stable U-X bond.

174

The strength of the An-X interactions

Fig.5.9. An-X bond enthalpies from equation 5.7 (solid points) and Gibbs free energies from equation 5.8 (hollow points) against An-X electron density. For the different actinides, circles =

[LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue = BH4, orange

= BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

Figure 5.9 also shows little correlation between the electron densities and bond energies.

Fig.5.10. An-X bond enthalpies from equation 5.7 (solid points) and Gibbs free energies (hollow points) from equation 5.8 against An-X energy density. For the different actinides, circles =

[LThIVX]+, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue = BH4, orange

= BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh.

175

The strength of the An-X interactions

Finally, as with the other QTAIM metrics, the energy density metric continues to show a lack of any trend with the bond energies. As mentioned previously, an increasing magnitude of a negative H value, according to the QTAIM, is indicative of an increasing magnitude of covalency. This does not fit with the increasing bond energies, except for the Th(IV) complexes where the X =

N(SiH3)2 and X = OPh have the largest H values along with the largest bond energies, but this may be coincidental rather than a sign of any correlation of data.

A recent study7 found a correlation between the interaction energy of an An-X bond and the change in the QTAIM charge of the actinide when going from its fragment in the coordination geometry to the fully coordinated complex, which is a good indicator of how much charge is transferred to or from the actinide centre upon the formation of the full complex. The interaction energy is calculated in the same way as equation 5.1, except the fragments are not optimised, but are instead kept in the same geometry they adopt in the full complex. For this reason no thermal corrections are taken into account since the fragments are not at their true energy minima. The U(III) complexes were unable to be calculated due to the failure of the SCF cycle to converge and so the following data only concern the thorium-based complexes.

Table 5.14. Change in QTAIM charge of ThIV and ThIII centres from fragment to full complexes, and the corresponding Th-X interaction energies.

|ΔQQTAIMAn| ThIV-X interaction |ΔQQTAIMAn| ThIII-X interaction energy (eV) energy (eV)

[LThBH4]n+ 0.050 -9.64 0.155 -5.89

[LThBO2C2H4]n+ 0.223 -11.33 0.065 -7.08

[LThMe]n+ 0.106 -11.95 0.161 -7.84

[LThN(SiH3)2]n+ 0.056 -10.90 0.195 -6.47

[LThOPh] n+ 0.003 -11.26 0.397 -3.99

176

The strength of the An-X interactions

Fig.5.11. Change in QTAIM charge of An centre from fragment to full complex against An-X interaction energy. For the different actinides, circles = LThIVX and squares = LThIIIX. For the different X ligands, blue = BH4, orange = BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh. R2 value relates to the Th(III) data only.

Figure 5.11 shows that only the Th(III) complexes showed a trend for interaction energy and changes in the QTAIM actinide charge, with a reasonable R2 value of 0.709, showing some agreement with previous studies of organoactinide complexes, which gave an R2 value of 0.882 for a range of actinide complexes from Th - Pu7.

5.6. Functional dependence of QTAIM vs bond energies

As shown in the earlier parts of this chapter, there was little correlation between the bond energies and QTAIM metrics for any of the actinide complexes. However, since the EDA results in this chapter were acquired from the PBE functional, it was first checked whether there may be a functional dependence of the results. As such, before moving onto EDA analysis, the same bond energy and QTAIM metrics for the [LAnX]n+ complexes were re-calculated at the PBE functional level. To probe the functional dependence of the above conclusions, single point calculations were carried out on the PBE0-optimised fragments and full complexes using the PBE functional. These SCF energies were then put into equation 5.1 to obtain ΔE values, and QTAIM data from the PBE single-point calculations are presented in tables 5.15 and 5.16 and plotted against each other in figure 5.12 below. 177

The strength of the An-X interactions

Table 5.15. PBE ΔE (eV) for [LAnX]n+ (n = 1 (Th(IV)), 0 (Th(III) and U(III)) at PBE0 geometries.

X ligand [LThIVX]+ LThIIIX LUIIIX

BH4 -9.16 -5.37 -5.54

BO2C2H4 -10.73 -6.83 -6.83

Me -11.36 -7.23 -7.33

N(SiH3)2 -9.70 -5.62 -5.54

OPh -10.30 -6.03 -6.05

Table 5.16. QTAIM An-X BCP metrics and delocalisation indices at PBE0-optimised geometries using the PBE functional.

X ligand ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

ThIV-X UIII-X ThIII-X ThIV-X UIII-X ThIII-X ThIV-X UIII-X ThIII-X

BH4 0.050 0.042 0.043 -0.021 -0.013 -0.015 0.366 0.365 0.465

BO2C2H4 0.069 0.065 0.069 -0.021 -0.019 -0.022 0.569 0.574 0.504

Me 0.089 0.077 0.080 -0.032 -0.024 -0.026 0.678 0.634 0.621

N(SiH3)2 0.106 0.084 0.089 -0.041 -0.023 -0.029 0.804 0.661 0.688

OPh 0.127 0.100 0.103 -0.049 -0.025 -0.031 0.825 0.737 0.720

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The strength of the An-X interactions

Fig.5.12. An-X ΔE vs An-X electron densities (top), energy densities (middle) and delocalisation indices (bottom) from single point PBE calculations on the PBE0-optimised [LAnX]n+ (n = 1 (Th(IV)), 0 (Th(III) and U(III)). For the different actinides, circles = LThIVX, triangles = LThIIIX and squares = LUIIIX. For the different X ligands, blue = BH4, orange = BO2C2H4, green = Me, purple = N(SiH3)2 and red = OPh. R2 for ΔE vs ρ = 0.060 (Th(IV)), 0.042 (Th(III)), 0.017 (U(III)); vs H = 0.004 (Th(IV)), 0.047 (Th(III)), 0.120 (U(III)); vs δ(An,X) = 0.121 (Th(IV)), 0.000 (Th(III)), 0.070 (U(III)).

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The strength of the An-X interactions

As can be seen, although the values are slightly different from the PBE0 data, the overall patterns found in figures 5.3 to 5.5 are still present in figure 5.12, and hence we conclude that the QTAIM metrics are essentially uncorrelated with bond energy data for the An-X interactions at either the PBE0 or PBE level.

5.7. QTAIM metrics vs EDA data for [LAnX]n+ complexes

The PBE QTAIM metrics (table 5.16) were next compared with EDA data for the same set of fifteen [LAnX]n+ complexes. These EDA data, also calculated using the PBE functional at the PBE0 geometries, are presented in tables 5.17 to 5.19. The energy terms are those described in equation 1.43 of chapter 1.7.

Table 5.17. Th-X EDA energies (eV) for the [LThIVX]+ complexes from the LTh2+ and X- fragments.

X EB EE EP EO

BH4 -9.36 -10.76 4.61 -3.21

BO2C2H4 -10.82 -16.13 9.65 -4.34

Me -11.33 -16.97 10.04 -4.41

N(SiH3)2 -10.40 -13.04 8.17 -5.53

OPh -10.69 -12.08 7.49 -6.10

Table 5.18. Th-X EDA energies (eV) for the LThIIIX complexes from the LTh+ and X- fragments.

X EB EE EP EO

BH4 -5.75 -7.48 4.74 -3.01

BO2C2H4 -6.95 -15.03 15.18 -7.09

Me -7.40 -13.04 9.82 -4.18

N(SiH3)2 -6.41 -9.44 7.55 -4.52

OPh -6.48 -9.65 9.62 -6.45

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The strength of the An-X interactions

Table 5.19. U-X EDA energies (eV) for the LUIIIX complexes from the LU+ and X- fragments.

X EB EE EP EO

BH4 -5.80 -3.80 5.65 -7.65

BO2C2H4 -6.97 -12.91 9.55 -3.60

Me -7.42 -1.12 6.71 -13.02

N(SiH3)2 -6.10 -8.65 6.36 -3.81

OPh -6.51 -9.46 9.01 -6.06

EB follows a similar trend to the ΔE and ΔH298 values in tables 5.8 to 5.10; the values increase in absolute terms from the boron to carbon-based ligand but then decrease at nitrogen, yet increase again for the oxygen-based ligand. The break-down of EB shows, however, that this trend is unique to the total energy since the EE, EP and EO terms all show different trends as a function of X-ligand, and unlike with EB, the trends in these differ depending on which actinide and oxidation state is present.

For EE, the largest energy is seen for the ThIV-Me bond (table 5.17), whereas for the Th(III) and U(III) complexes the An-BO2C2H4 gives the largest EE value. This is also true for the EP term, whereas the EO term is different altogether; there is a steady increase in energy as a function of X ligand for the Th(IV) complexes, but for Th(III) and U(III) there is no apparent trend at all, with the An-BO2C2H4 bond giving the largest EO value for Th(III), and An-Me giving the largest EO value for U(III).

These EDA terms are plotted against the PBE-based QTAIM metrics (table 5.16) in figures 5.13 to 5.16.

181

The strength of the An-X interactions

Fig.5.13. PBE ρ (top), H (middle) and An-X Fig.5.14. PBE ρ (top), H (middle) and An-X

δ(An,X) (bottom) against EB for [LAnX]n+ (n = δ(An,X) (bottom) against EO for [LAnX]n+ (n = 1 (Th(IV)), 0 (Th(III) and U(III)). Th(IV) 1 (Th(IV)), 0 (Th(III) and U(III)). Th(IV) circles; Th(III) squares; U(III) triangles. BH4 circles; Th(III) squares; U(III) triangles. BH4 blue; BO2C2H4 orange; Me green; N(SiH3)2 blue; BO2C2H4 orange; Me green; N(SiH3)2 purple; OPh red. purple; OPh red.

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The strength of the An-X interactions

Fig.5.15. PBE ρ (top), H (middle) and An-X Fig.5.16. PBE ρ (top), H (middle) and An-X n+ δ(An,X) (bottom) against EP for [LAnX]n+ (n = 1 δ(An,X) (bottom) against EE for [LAnX] (n = 1 (Th(IV)), 0 (Th(III) and U(III)).. Th(IV) circles; (Th(IV)), 0 (Th(III) and U(III)).. Th(IV) circles;

Th(III) squares; U(III) triangles. BH4 blue; Th(III) squares; U(III) triangles. BH4 blue;

BO2C2H4 orange; Me green; N(SiH3)2 purple; BO2C2H4 orange; Me green; N(SiH3)2 purple; OPh red. OPh red.

183

The strength of the An-X interactions

As can be seen from figure 5.13, the graphs for EB are very similar to the graphs in figure 5.12. Close inspection of figure 5.14 reveals strong correlation of the [LThIVX]+ complexes’ QTAIM metrics with the orbital mixing energy term (the best correlation being with the Th-X electron density with an R2 value of 0.938) but this is the exception; in general the QTAIM metrics for the rest of the complexes do not correlate well with the EDA data.

It was thought that the general lack of correlation across the EDA energies arises from the X ligand as a whole, rather than the atom ligating directly to the actinide centre. So far the chemical environments of the X ligands have been significantly different, bar the actual ligating atom, i.e. the X ligands contain pinacolato, hydrogen, silane and phenyl groups. In the correlations found between EDA data and QTAIM metrics reported previously,3 the ligands in question were all of similar chemical nature as they were either tautomers of imidazole bonded to (CO)5M- units, or followed an isoelectronic series in the case of M2X6 where X = CH3, NH2, OH, F and Cl. To test this hypothesis, a new set of complexes were modelled with simplified X ligands, labelled X’ (see section 5.2 of this chapter).

5.7.1. QTAIM metrics vs EDA data for [LAnX’]n+ complexes

The Th(IV) complexes were first examined, so that the new set of complexes were [LThMe]+, [LThNH2]+, [LThOH]+ and, to extend the series, [LThF]+. Boron- based ligands were omitted since, for the BH4 complex, there is no direct Th-B bond, and there is no other suitable boron-based candidate that would both satisfy the isoelectronicity of this series of X’ ligands and have a direct bond with the actinide centre.

As above, single point calculations on the PBE0-optimised geometries of [LThX’]+ were carried out with the PBE functional to obtain EDA and QTAIM data, which are presented in tables 5.20 and 5.21.

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The strength of the An-X interactions

Table 5.20. An-X’ EDA energies (eV) for the [LAnX’]n+ (n = 1 (Th(IV)), 0 (Th(III) and U(III)) complexes from the LAnn+ (n = 2 (Th(IV), 1 (Th(III) and U(III)) and X’ fragments.

X’ EB EE EP EO

ThIV-X’ ThIII-X’ UIII-X’ ThIV-X’ ThIII-X’ UIII-X’ ThIV-X’ ThIII-X’ UIII-X’ ThIV-X’ ThIII-X’ UIII- X’

CH3 -11.33 -7.40 -7.42 -16.97 -13.04 -1.12 10.04 9.82 6.71 -4.41 -4.18 -13.02

NH2 -12.29 -8.32 -8.30 -16.12 -12.43 -12.27 9.16 9.32 9.93 -5.32 -5.21 -5.96

OH -12.51 -8.82 -8.52 -15.08 -11.33 -11.41 8.48 7.96 7.59 -5.91 -5.45 -4.71

F -12.04 -8.23 -8.10 -14.98 -11.24 -9.20 7.83 8.21 6.36 -5.10 -5.20 -5.26

Table 5.21. PBE An-X’ QTAIM metrics from PBE0-optimised geometries for the [LAnX’]n+ (n = 1 (Th(IV)), 0 (Th(III) and U(III)) complexes from the LAnn+ (n = 2 (Th(IV), 1 (Th(III) and U(III)) and X’ fragments.

X’ ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

ThIV-X’ ThIII-X’ UIII-X’ ThIV-X’ ThIII-X’ UIII-X’ ThIV-X’ ThIII-X’ UIII-X’

CH3 0.089 0.081 0.076 -0.032 -0.028 -0.024 0.678 0.605 0.593

NH2 0.111 0.101 0.100 -0.045 -0.036 -0.033 0.818 0.793 0.744

OH 0.125 0.117 0.118 -0.050 -0.043 -0.041 0.918 0.882 0.887

F 0.127 0.116 0.109 -0.049 -0.039 -0.029 0.825 0.768 0.755

Table 5.20 shows that EB and EO both increase from C to O then decrease at F. This pattern is seen for the δ(Th,X) values and, to a lesser extent, H in table 5.21.

On the other hand, EE and EP both show a clear decrease, in absolute terms, of energy across this ligand series; a trend mirrored in ρ in table 5.21.

Analysis of the [LAnX’]n+ complexes was extended to the Th(III) and U(III) variants, with the results also given in tables 5.20 and 5.21. The R2 values for correlations between the data in these two tables are collected in table 5.22.

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The strength of the An-X interactions

Table 5.22. R2 values for the EDA energies vs QTAIM metrics for [LAnX’]n+ (X’=CH3, NH2, OH and F, n = 1 (Th(IV)), 0 (Th(III), U(III)) complexes.

ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

ThIV-X’ ThIII-X’ UIII-X’ ThIV-X’ ThIII-X’ UIII-X’ ThIV-X’ ThIII-X’ UIII-X’

EB 0.677 0.786 0.863 0.825 0.927 0.856 0.930 0.999 0.903

EE 0.971 0.952 0.728 0.900 0.856 0.642 0.749 0.653 0.703

EP 0.934 0.920 0.012 0.826 0.895 0.143 0.562 0.604 0.043

EO 0.621 0.859 0.916 0.752 0.900 0.608 0.961 0.945 0.803

In general, the thorium complexes show the better correlations of EDA energies with the QTAIM metrics than do the uranium complexes, with the Th(III) complexes showing overall the best R2 values; the lowest R2 for ρ vs EDA energy is 0.786 (for EB), 0.856 for H vs EE and 0.604 for δ(Th-X) vs EP. For the Th(IV) complexes, the delocalisation indices correlate very well for both EB and EO, whereas the electron and energy densities correlate less well. Note that these correlations are found for EB and EO despite the EE and EP terms not cancelling to near zero, which was a prerequisite for the good correlations of EB and EO with QTAIM metrics seen in previous work.3 The electron density gives the best correlation with both EE and EP, with δ(Th,X) giving the poorest correlations with R2 values of 0.562 and 0.749 for EP and EE respectively. This is the opposite of what was found with the EB and EO data.

For the U(III) complexes, all three QTAIM metrics show appreciable correlations with the EB and EO data but EE has the poorest linear correlation for the U(III) QTAIM metrics, whereas for the U(III) EP data, there is no discernible trend at all with the QTAIM metrics.

When compared with the previous EDA results for the [LAnX]n+ complexes (figures 5.13 to 5.16), and focusing only on the C-, N- and O-based ligands in both the X and X’ series, one sees generally improved correlations for the X’ ligands (tables 5.23 to 5.25), although it should be noted that there only are three points in each data set.

186

The strength of the An-X interactions

Table 5.23. R2 values for EDA energies vs QTAIM metrics for C-, N- and O-based ligands in [LThIVX]+ (non-italics) and [LThIVX’]+ (italics).

ρ (e bohr-3) H (Hartrees bohr-3) δ(Th,X)

EB 0.393 0.962 0.486 0.991 0.817 0.940

EE 0.849 0.961 0.910 0.914 0.997 0.978

EP 0.897 0.995 0.947 0.972 0.943 1.000

EO 0.940 1.000 0.977 0.987 0.959 0.999

Table 5.24. R2 values for EDA energies vs QTAIM metrics for C-, N- and O-based ligands in LThIIIX (non-italics) and LThIIIX’ (italics).

ρ (e bohr-3) H (Hartrees bohr-3) δ(Th,X)

EB 0.612 0.989 0.770 0.976 0.861 0.999

EE 0.621 0.949 0.778 0.969 0.867 0.872

EP 0.000 0.898 0.027 0.927 0.077 0.800

EO 0.916 0.925 0.797 0.896 0.696 0.981

Table 5.25. R2 values for EDA energies vs QTAIM metrics for C-, N- and O-based ligands in LUIIIX (non-italics) and LUIIIX’ (italics).

ρ (e bohr-3) H (Hartrees bohr-3) δ(U,X)

EB 0.232 0.936 0.024 0.918 0.201 0.904

EE 0.615 0.755 0.058 0.726 0.585 0.703

EP 0.841 0.113 0.939 0.093 0.863 0.079

EO 0.297 0.908 0.006 0.888 0.269 0.871

Except for the R2 values for EB vs ρ and H (table 5.23), both the [LThIVX]+ and [LThIVX’]+ EDA data correlate very well with the QTAIM metrics, with the [LThIVX’]+ data correlating better overall. The LThIIIX’ data also correlate much better than the LThIIIX (table 5.24) with the biggest contrasts found with the EP vs QTAIM metrics. On the other hand, in table 5.25, it is the LUIIIX data that

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The strength of the An-X interactions

correlate much better than LUIIIX’ for EP vs QTAIM metrics, although the rest of the EDA vs QTAIM metrics R2 values are much better for the LUIIIX’ complexes.

5.7.2. QTAIM metrics vs EDA data for [LAnX*]n+ complexes

Spurred on by the improved correlations for the simplified ligands, [LAnX*]+ complexes were explored, where the X* ligands are the second row p-block- based ligands SiH3, PH2, SH and Cl. As with the [LAnX]n+ and [LAnX’]n+ complexes, the [LAnX*]n+ complexes were optimised at the PBE0 level and their QTAIM and EDA data obtained from PBE calculations at the PBE0 geometries. These data are presented in tables 5.26 and 5.27 below.

Table 5.26. PBE An-X* EDA energies (eV) from PBE0-optimised geometries for the [LAnX*]n+ complexes from ionic fragments.

X* EB EE EP EO

ThIV-X* ThIII-X* UIII-X* ThIV-X* ThIII-X* UIII-X* ThIV-X* ThIII-X* UIII-X* ThIV-X* ThIII-X* UIII-X*

SiH3 -9.51 -5.90 -5.84 -12.96 -10.01 -9.46 7.01 7.28 6.27 -3.56 -3.18 -2.65

PH2 -9.71 -5.99 -6.09 -12.56 -9.44 -8.56 6.62 6.98 4.95 -3.77 -3.53 -2.49

SH -9.92 -6.21 -2.72 -12.26 -8.72 -22.26 6.19 5.80 28.39 -3.85 -3.30 -8.80

Cl -9.92 -6.21 -5.66 -11.79 -8.40 -8.71 5.64 5.66 6.60 -3.77 -3.46 -3.55

Table 5.27. PBE An-X* QTAIM metrics from PBE0-optimised geometries of [LAnX*]n+.

X* ρ (e bohr-3) H (Hartrees bohr-3) δ(Th,X)

ThIV-X* ThIII-X* UIII-X* ThIV-X* ThIII-X* UIII-X* ThIV-X* ThIII-X* UIII-X*

SiH3 0.052 0.049 0.107 -0.015 -0.013 -0.060 0.549 0.518 0.747

PH2 0.060 0.054 0.142 -0.017 -0.014 -0.081 0.686 0.618 1.196

SH 0.068 0.060 0.202 -0.019 -0.015 -0.147 0.782 0.686 1.437

Cl 0.074 0.064 0.204 -0.021 -0.015 -0.137 0.775 0.667 1.463

As can be seen from table 5.26, all EE and EP energies decrease as a function of

X* ligand for the Th(IV) complexes, whereas for EB the energies generally

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The strength of the An-X interactions

increase from Th-SiH3 to Th-Cl, and the EO energies follow no clear trend. The ρ and H metrics (table 5.27) increase as a function of X* ligand whereas the

δ(Th,X) metric, as with the EO energies, follows no clear trend. Table 5.28 summarises the correlations found for the X* series.

Table 5.28. R2 values for the An-X* EDA energies vs QTAIM metrics for [LAnX*]n+ ( n = 1 (Th(IV)), 0 (Th(III), U(III)) complexes.

ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

ThIV-X* UIII-X* ThIII-X* ThIV-X* UIII-X* ThIII-X* ThIV-X* UIII-X* ThIII-X*

EB 0.929 0.345 0.930 0.938 0.476 0.995 0.985 0.229 0.871

EE 0.981 0.255 0.997 0.973 0.376 0.949 0.799 0.167 0.867

EP 0.980 0.309 0.938 0.975 0.436 0.968 0.782 0.208 0.800

EO 0.608 0.419 0.224 0.613 0.551 0.099 0.888 0.296 0.268

These are poor for LUX*, but rather better for the Th(IV) and Th(III) complexes, with the exception of EO vs all three QTAIM metrics for LThIIIX*. The EDA vs QTAIM correlations for the Th(IV) complexes show strong linear correlations for the EB vs all three QTAIM metrics, with all R2 values above 0.900. The EO data do not correlate so well with the QTAIM metrics generally, although R2 for

EO vs δ(Th,X) is high. EE and EP also give good linear correlations with the QTAIM metrics for the Th(IV) and Th(III) complexes. The worst correlations are those found with the delocalisation indices, with R2 values of 0.782 and 0.799 for EE and EP respectively, but these are still better than the [LThIVX’]+ analogues where R2 values for EE and EP vs δ(An,X) are 0.749 and 0.562 respectively (see table 5.22).

When correlating all the EDA and QTAIM data for the [LAnX’]n+ and [LAnX*]+ together there are no strong trends found, as shown in table 5.29.

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The strength of the An-X interactions

Table 5.29. R2 values for EDA energies vs QTAIM metrics for all [LAnX’]n+ and [LAnX*]+ complexes. An = Th(IV), Th(III), U(III); n = 1 (Th(IV)), 0 (Th(III) and U(III)).

ρ (e bohr-3) H (Hartrees bohr-3) δ(An,X)

EB 0.048 0.160 0.097

EE 0.117 0.115 0.094

EP 0.271 0.350 0.225

EO 0.047 0.026 0.006

Closer analysis reveals that the U(III) data in general correlate the least well, and so the data were re-analysed for just the thorium complexes. The results for

EO are presented in figure 5.18; the rest of the EDA vs QTAIM data – with the exception of EB vs ρ – give poor correlations, as presented in table 5.30.

190

The strength of the An-X interactions

Fig.5.17. Th-X ρ (top), H (middle) and δ(Th,X) (bottom) against EO for [LThX’/X*]n+ complexes. Diamonds = Th(IV) complexes, circles = Th(III) complexes. Solid points are X’ ligands: green =

CH3, purple = NH2, red = OH, black = F. Hollow points are X* ligands; pink = SiH3, yellow = PH2, brown = SH, blue = Cl.

191

The strength of the An-X interactions

Table 5.30. R2 values for EDA EB, EE and EP terms vs QTAIM metrics for all [LThX’]n+ and [LThX*]+ complexes (n = 1 (Th(IV)), 0 (Th(III)).

ρ (e bohr-3) H (Hartrees bohr-3) δ(An,X)

EB 0.812 0.469 0.390

EE 0.316 0.426 0.142

EP 0.325 0.411 0.029

As with the full data set (table 5.30), the worst correlation in figure 5.17 is found with the delocalisation indices, although it is much improved over the full data set with an R2 value of 0.671. The electron and energy densities now correlate extremely well with EO, suggesting that, for the Th(III) and Th(IV) X’ and X* complexes, the covalency of the Th–X bond is described consistently by both the EDA and QTAIM approaches.

Summarising, it would appear that by employing consistently simple and isoelectronic X ligands, and focussing only on the change of the ligating atom to the actinide centre, then correlations can be found between EDA and QTAIM data that were absent in the primary set of BH4, BO2C2H4, CH3, N(SiH3)2 and OPh ligands. The fact that EO appears to correlate best with the QTAIM metrics, particularly for the Th(III) and Th(IV) systems as shown in figure 5.17, makes sense, in that the chosen QTAIM metrics are indicators of covalency.

5.7.3. QTAIM metrics vs EDA data for [LAnX’’]n+ complexes

To test these improved correlations further another set of [LAnX’’]n+ complexes with an isoelectronic series of phenyl-based X’’ ligands was modelled. Phenyl groups were chosen since one of the experimentally characterised complexes has an arene ring on the X ligand (LUIIIDTBP). As with the other [LAnX’]n+ and [LThX*]+ complexes, the [LAnX’’]n+ complexes were optimised with PBE0 and these optimised geometries treated with PBE for the single point QTAIM and

EDA calculations. The new set of X’’ ligands was thus; CH2Ph, NHPh and OPh and the EDA energies and QTAIM metrics are presented in tables 5.31 and 5.32 below.

192

The strength of the An-X interactions

Table 5.31. PBE An-X’’ EDA energies (eV) from PBE0-optimised geometries for the [LAnX’’]n+ complexes from ionic fragments.

X’’ EB EE EP EO

ThIV-X’’ ThIII-X’’ UIII-X’’ ThIV-X’’ ThIII-X’’ UIII-X’’ ThIV-X’’ ThIII-X’’ UIII-X’’ ThIV-X’’ ThIII-X’’ UIII-X’’

CH2Ph -10.42 -6.08 -6.45 -13.45 -8.78 -11.28 7.90 6.58 7.32 -4.87 -3.88 -2.49

NHPh -10.51 -4.21 -6.66 -13.73 -10.02 -9.34 8.77 7.41 6.80 -5.55 -4.21 -4.13

OPh -10.69 -6.48 -6.51 -12.08 -9.65 -12.08 7.49 9.62 9.01 -6.10 -6.45 -6.10

Table 5.32. PBE An-X’’ QTAIM metrics from PBE0-optimised geometries of [LAnX’’]n+ complexes from ionic fragments.

X’’ ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

ThIV-X’’ ThIII-X’’ UIII-X’’ ThIV-X’’ ThIII-X’’ UIII-X’’ ThIV-X’’ ThIII-X’’ UIII-X’’

CH2Ph 0.086 0.067 0.081 -0.030 -0.020 -0.026 0.626 0.523 0.600

NHPh 0.109 0.101 0.098 -0.043 -0.036 -0.033 0.774 0.732 0.744

OPh 0.116 0.103 0.118 -0.045 -0.031 -0.041 0.857 0.720 0.887

The EB and EO energy terms steadily increase in magnitude as a function of X’’ ligand and this increase is mirrored in the QTAIM metrics in table 5.32.

Although, as with the [LAnX’]n+ complexes, EO gives the best R2 values against the QTAIM metrics, the trend is weak, with the highest R2 being for EO vs ρ at 0.548. As previously, the U(III) data were excluded and the data reanalysed; the results for both analyses are presented in table 5.33.

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The strength of the An-X interactions

Table 5.33. R2 values for EDA energies vs QTAIM metrics for all LAnX’’ complexes: non-italics = Th(IV), Th(III) and U(III); italics = Th(IV) and Th(III)

ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

EB 0.065 0.127 0.205 0.261 0.052 0.140

EE 0.147 0.194 0.331 0.392 0.123 0.179

EP 0.326 0.275 0.178 0.095 0.232 0.158

EO 0.548 0.551 0.411 0.317 0.491 0.486

The previous conclusions found for the X’ and X* ligand sets does not hold as well for the X’’ ligand set, in that R2 shows only modest improvements on the exclusion of the U(III) data, and actually decreases in several cases.

5.7.4. QTAIM metrics vs EDA data for [LAnX**]n+ complexes

These phenyl-based ligands were then extended to the 2nd row p-block, giving the X** ligands SiH2Ph, PHPh and SPh. These EDA and QTAIM results are presented in tables 5.34 and 5.35.

Table 5.34. PBE An-X** EDA energies (eV) from PBE0-optimised geometries for the [LAnX**]n+ complexes from ionic fragments.

X** EB EE EP EO

ThIV-X** ThIII-X** UIII- ThIV-X** ThIII-X** UIII- ThIV-X** ThIII-X** UIII- ThIV-X** ThIII-X** UIII- X** X** X** X**

SiH2Ph -9.34 -5.50 -3.75 -11.14 -8.30 -16.88 5.68 5.96 18.07 -3.87 -3.16 -4.94

PHPh -9.45 -5.56 -5.60 -10.46 -7.64 11.44 5.25 5.56 -1.21 -4.24 -3.48 -15.83

SPh -9.46 -5.61 -5.66 -10.16 -7.44 -10.04 4.98 5.44 7.65 -4.29 -3.62 -3.27

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The strength of the An-X interactions

Table 5.35. PBE An-X** QTAIM metrics from PBE0-optimised geometries of [LAnX**]n+ complexes from ionic fragments.

X** ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

ThIV-X** ThIII-X** UIII-X** ThIV-X** ThIII-X** UIII-X** ThIV-X** ThIII-X** UIII-X**

SiH2Ph 0.050 0.044 0.105 -0.014 -0.011 -0.058 0.532 0.477 0.819

PHPh 0.058 0.051 0.049 -0.016 -0.012 -0.012 0.690 0.590 0.617

SPh 0.066 0.055 0.054 -0.018 -0.013 -0.012 0.763 0.632 0.669

As with the [LAnX’’]n+ complexes, the [LAnX**]n+ complexes were analysed for correlations of EDA energies vs QTAIM metrics for the full data set of the Th(IV), Th(III) and U(III) systems, and also for just the [LThX**]n+ complexes, and these R2 values are presented in table 5.36.

Table 5.36. R2 values for EDA energies vs QTAIM metrics for all LAnX** complexes: non-italics = Th(IV), Th(III) and U(III); italics = Th(IV) and Th(III)

ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

EB 0.095 0.336 0.148 0.741 0.002 0.275

EE 0.253 0.102 0.234 0.470 0.103 0.064

EP 0.711 0.992 0.758 0.804 0.279 0.989

EO 0.746 0.745 0.666 0.929 0.634 0.701

Unlike the [LAnX’’]n+ complexes, the [LAnX**]n+ show some strong correlations, notably for EP vs QTAIM metrics for the thorium-only data set and the EO vs QTAIM metrics for both the thorium-only data set and the full data set.

5.7.5. QTAIM metrics vs EDA data for [LAnX†]n+ complexes

Finally, a set of phenyl-based ligands were analysed where the X atom’s substituents were all replaced with Ph groups. Thus the new set of X ligands – which are labelled X† – are CPh3, NPh2, OPh, SiPh3, PPh2 and SiPh3. Due to the poor correlations of the EDA energies against the QTAIM metrics with the U(III)

195

The strength of the An-X interactions

complexes, as observed previously with the X – X** data sets, only the Th(IV) and Th(III) complexes of LAnX† are considered here, and the results for the EDA and QTAIM metrics are presented in tables 5.37 and 5.38 below.

Table 5.37. PBE An-X† EDA energies (eV) from PBE0-optimised geometries for the [LAnX†]n+ complexes from ionic fragments.

X† EB EE EP EO

ThIV-X† ThIII-X† ThIV-X† ThIII-X† ThIV-X† ThIII-X† ThIV-X† ThIII-X†

CPh3 -9.71 -5.83 -3.83 -1.56 6.17 5.06 -5.87 -4.27

NPh2 -10.00 -6.11 -12.23 -8.77 8.05 7.18 -5.83 -4.52

OPh -10.69 -6.48 -12.08 -9.65 7.49 9.62 -6.10 -6.45

SiPh3 -9.26 -5.26 -10.04 -7.20 5.05 5.06 -4.27 -3.12

PPh2 -9.35 -5.22 -10.03 -7.28 5.32 5.56 -4.64 -3.51

SPh -9.46 -5.61 -10.16 -7.44 4.98 5.44 -4.29 -3.62

Table 5.38. PBE An-X† QTAIM metrics from PBE0-optimised geometries of [LAnX†]n+ complexes from ionic fragments.

X† ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

ThIV-X† ThIII-X† ThIV-X† ThIII-X† ThIV-X† ThIII-X†

CPh3 0.063 0.054 -0.018 -0.013 0.477 0.377

NPh2 0.105 0.088 -0.040 -0.028 0.715 0.607

OPh 0.116 0.103 -0.045 -0.031 0.857 0.720

SiPh3 0.047 0.040 -0.012 -0.009 0.504 0.442

PPh2 0.058 0.049 -0.016 -0.011 0.692 0.521

SPh 0.066 0.055 -0.018 -0.013 0.763 0.632

The R2 values for correlations between these data are presented in table 5.39.

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The strength of the An-X interactions

Table 5.39. R2 values for EDA energies vs QTAIM metrics for all [LThX†]n+ complexes.

ρ (e bohr-3) H (Hartrees bohr-3) δ(An-X)

EB 0.180 0.259 0.287

EE 0.500 0.590 0.525

EP 0.766 0.658 0.269

EO 0.682 0.638 0.276

The correlations in table 5.39 range from poor to good, EP vs ρ having the largest R2 value of 0.766. This is a similar observation to that found in table 5.36, where systems with low ρ value correlate with the Pauli repulsion term of the EDA analysis; for the QTAIM data corresponding to the R2 values in table

5.37, all ρ values for Th-X†, with the exception of ThIV-NPh2 and ThIV-OPh, are below 0.1 e bohr-3.

Finally, all the Th(IV) and Th(III) data bar those for the original X ligands were collated. The strongest correlations were found between the QTAIM data and the EO energies, and these are shown in figure 5.18. δ(Th,X) has a low R2 value of only 0.408, but the BCP metrics show appreciable R2 values; it is promising that such a large data set (twenty four compounds) shows good correlations between the QTAIM BCP covalency metrics and the EO term of the EDA.

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The strength of the An-X interactions

Fig.5.18. Th-X ρ (top), H (middle) and δ(Th,X) (bottom) against EO for all [LThX]n+ complexes where X = X’, X’’, X*, X** and X† and n = 1 (for Th(IV) complexes) and 0 (for Th(III) complexes).

Data point for ThIV-CPh3 omitted as it was a significant outlier.

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The strength of the An-X interactions

The lack of correlations with the U(III) complexes is probably due to these having a high spin multiplicity, which adversely affects the terms in the EDA. Open shell-closed shell intermolecular interactions are less well understood compared with those between two closed shell fragments8 and as mentioned in chapter 2, the constrained space orbital variation (CSOV) method9 has proved useful for describing the bonding energies of open-shell f-element systems, where a polarised energy term (Epol) is used, made up of energy from unpaired electrons10. These contributions are clearly not negligible, and it may be that for the ADF-implemented EDA approach, the f-elements with more than one unpaired electron become more difficult to describe compared to their lower spin-state, closed shell counterparts.

5.8. Conclusions and future work

Reaction energies for [LAnX]n+ complexes all showed that the An-X bonds were stable and favourable, with the Th(IV) complexes being the most stable of them all. With regards to the X ligand present however, there was no clear indication that the An-X bond became more stable as a more electronegative X ligand was adopted, which was what was expected given the progressive shortening of this bond distance and the increasing magnitude of the QTAIM metrics at the An-X BCPs.

Given the reaction energies as a function of QTAIM metrics showed no apparent correlation, and coupled with the actinide orbital contributions from the NBO in chapter 4.6, it is apparent that covalency and ionicity still prove to be difficult to establish unambiguously when studying such actinide systems, where different interpretations of the nature of these An-X bonds can arise from different computational methods for analysing them.

On the other hand, there was a correlation found between the difference of the Th(III) QTAIM charge going from the fragment to the full molecule against the ThIII-X interaction energy. However, these energies bear no relation to the reaction or interaction energies of the Th-X bonds discussed previously, but they nevertheless give some insight into the energies of stabilising these thorium-based complexes depending on the X ligand present.

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The strength of the An-X interactions

Comparing these same QTAIM metrics at the PBE level with the energies from the EDA scheme also showed a similar lack of correlation for the EB and EO values for the An-X bonds. However, changing the X ligand so as to have consistent chemical environments in the form of;

 X’ ligands; CH3, NH2, OH and F.

 X’’ ligands; CH2Ph, NHPh and OPh.

 X* ligands; SiH3, PH2, SH and Cl.

 X** ligands; SiH2Ph, PHPh and SPh.

 X† ligands; CPh3, SiPh3, NPh2, PPh2, OPh and SPh.

Resulting in the complexes [LAnX’]n+, [LAnX’’]n+, [LAnX*]n+, [LAnX**]n+ and [LAnX†]n+, did show a correlation with these QTAIM metrics and EDA energies, particularly for the BCP properties in the QTAIM.

This latter correlation supported evidence that in order to use the QTAIM as a measure of relative bond energy, one has to take into account the chemical environments around the bond in question, as it appears to be the case that it is not as simple as focussing solely on the atoms about the bond of interest.

Having said that, poor results for the U(III) systems were perhaps down to the choice of the EDA method used, as there are more sophisticated methods for calculating high-spin fragments in the EDA8-10, as was discussed at the end of the last section. Using these methods in future work may be of use for obtaining better correlations with open-shell systems.

This is all the analysis for the [LAnX]n+-type complexes. The next chapter focuses on another set of complexes incorporating the L2-/4- ligand but with predominantly bi-metallic centres and a different set of X ligands featuring alkynyl groups.

200

References

1. R. J. Boyd and S. C. Choi, Chem. Phys. Lett., 1985, 120, 80. 2. R. J. Boyd and S. C. Choi, Chem. Phys. Lett., 1986, 129, 62. 3. A. R. E. Mountain and N. Kaltsoyannis, Dalton Trans., 2013, 42, 13477. 4. T. Ziegler and A. Rauk, Theor. Chim. Acta., 1977, 46, 1. 5. T. Ziegler and A. Rauk, Inorg. Chem., 1979, 18, 1558. 6. K. T. P. O'Brien and N. Kaltsoyannis, Dalton Trans., 2017, 46, 760. 7. Q-R. Huang, J. R. Kingham and N. Kaltsoyannis, Dalton Trans., 2015, 44, 2554. 8. P. R. Horn, E. J. Sundstrom T. A. Baker and M. Head-Gordon, J. Chem. Phys., 2013, 138, 134119. 9. P. S. Bagus, K. Hermann and C. W. Bauschlicher J. Chem. Phys., 1984, 80, 4378. 10. A. Marjolin, C. Gourlaouen, C. Clavaguéra, J.-P. Dognon and J.-P. Piquemal, Chem. Phys. Lett., 2013, 563, 25.

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Bimetallic L alkyl and alkynyl complexes

Chapter 6. Bimetallic L2-/4- alkyl and alkynyl complexes

6.1. Introduction

Another series of actinide complexes, but still including the L ligand, some of which have been synthesised by Suvova et al1, are studied in this chapter. These complexes fall into three main groups; complexes 1 and 2 (M[LThR]) (M = Li,

Na, K, Cs and Rb; R = Me(1), CH2Ph(2)); complexes 3, 4 and 5 (LTh(CCR’)2) (R’ =

SiH3(3), SiMe3(4) and SiiPr3(5)); and complexes 6 and 7

([LM(CCSiMe3)2][M’PR’’3]) (M = Hf, Th, Pa, U, Np, Pu, Am; M’ = Ni, Pt; R’’ = Cy(6), Ph(7)). The L ligand in all these groups differs in conformation from that studied so far, in that it binds to the actinide centre in the η5:η5 bonding mode, with complexes 6 and 7 also being able to exhibit the η6:κ1:η6:κ1 bonding mode. For the purposes of discussion, all subsequent mention of the η6:κ1:η6:κ1 bonding mode will be referred to as the “a” form, and all subsequent mention of the η5:η5 bonding mode will be referred to as the “b” form. In all cases, the actinide centre and Hf is in the 4+ oxidation state, and so 1 and 2 require a stabilising M+ cation which occupies the bis-arene cavity of L4-.

Fig.6.1. Schematic of the M[LThR] complexes 1 and 2 with the M+ cation occupying the bis- arene cavity. (M = Li, Na, K, Cs and Rb; R = Me(1), CH2Ph(2)). Image taken from reference 1.

202

Bimetallic L alkyl and alkynyl complexes

Upon reaction with 2HCCSiR’ (R’ = SiH3, SiMe3 and SiiPr3), Li1 and K2 lose the M+ cation as an MR salt, and the new LTh(CCR’)2 (R’ = SiH3 (3), SiMe3 (4) and SiiPr3 (5)) complex is formed. This reaction also reprotonates L4- to L2-.

Fig.6.2. Schematic of the LTh(CCR’)2 complexes 3, 4 and 5. (R’ = SiH3(3), SiMe3(4) and SiiPr3(5)). Image taken from reference 1.

As described by Suvova and co-workers1, reacting 4 with [Ni(COD)2] and P(R)3

(R = Cy, Ph) in hexane, yields the product [LTh(CCSiMe3)2][NiPR3] (Th6 and Th7). This product can take either one of the a or b forms of the L2- ligand. A schematic of this structure of [LTh(CCSiMe3)2][NiPR3] is shown below.

Fig.6.3. Schematic of the [LTh(CCSiMe3)2][NiPR3] complexes Th6 and Th7 (R = Cy(6), Ph(7)) in the a form (left) and b form (right). Image taken from reference 1.

The structures shown in figure 6.3, determined experimentally1, show that one of the Th-C alkynyl bonds present in 4 has been activated by the introduction of the Ni0 centre, and the coordination of each alkynyl group is η1 to one metal centre and η2 to the other metal centre.

203

Bimetallic L alkyl and alkynyl complexes

In this chapter, the main focuses are on reaction energies of 1 and 2 forming the products 3, 4 and 5, to determine whether a choice of the M+ cation and the R and R’ groups affects the overall stability of the LTh(CCR’)2 product, and therefore potentially giving insight into synthetic targets for future work, and secondly, on the family of complexes 6 and 7 in terms of their energies and electronic structures. Energies for complexes 6 and 7 were calculated to investigate the reasons for the L2- ligand being able to coordinate both the a and the b forms to the Th(IV) cation centre and which of these conformations is preferred. A series of hypothetical complexes were also modelled where Th6 and Th7 instead had a platinum centre in place of the nickel centre –

[LTh(CCSiMe3)2]PtPR3 (R = Cy, Ph) – to see how the changing of the transition metal centre affects the stability and coordination preferences of L2- and alkynyl bonding modes. These Pt-based analogues are here referred to as Th6’ and Th7’. Further to this, a series of 6 and 7 was modelled in which Th(IV) was replaced with Hf(IV) and other actinides in the 4+ oxidation state. The results in section 6.5.2 have been published in Organometallics1.

6.2. Computational details

All complexes in this chapter were studied with the PBE0 hybrid functional2, and since studies were also carried out for some of the complexes in a solvent environment, the polarisable continuum model (PCM) devised by Tomasi, Pascual-Ahuir and coworkers3-8 was employed to model these solvation effects on the selected complexes. In Gaussian09, the PCM implementation uses a continuous surface charge and an external iteration procedure which makes the solvent reaction field self-consistent with the solute electrostatic potential to compute the overall energy in solution9, 10. All total SCF energies are quoted in Hartrees; reaction energies and thermal energy differences are quoted in kJ mol-1; and molecular orbital energies are quoted in eV.

6.3. Results - Complexes 1 and 2.

Geometry optimisations were carried out for Li1 and K2 starting from structures of the experimentally characterised complexes1. The geometry-optimised structure of Li1 appeared to contradict the experimentally-determined structure

204

Bimetallic L alkyl and alkynyl complexes

which showed the Li+ cation residing in the bis-arene cavity of the L4- ligand. This is shown in figure 6.4 below.

Fig.6.4. Left: solid state structure of Li1 (thermal ellipsoids set at 50% probability level)1. Right: PBE0 geometry-optimised structure of Li1 (right). Hydrogens omitted for clarity.

The Li+ cation in the solid state structure of Li1 from figure 6.4 (left) sits 3.71 and 3.53 Å away from N1 and N2 respectively, whereas in the geometry- optimised structure in figure 6.4 (right) these Li-N distances are 1.90 and 4.12 Å for Li-N1 and Li-N2 respectively. This appears to show that at the PBE0 level, the Li+ cation prefers to migrate towards one of the pyrrole nitrogens, and given the short distance of 1.90 Å, forms a bond. It was thought that the lack of treatment of long-range dispersion phenomena may be responsible for causing this disparity between experiment and theory. With this in mind, Li1 was re- optimised from its original starting structure with all the standard basis sets and PPs so far used with the PBE0 functional, but with the addition of Grimme’s dispersion using the D3 damping function11. This did very little to change the effect of the Li+ moving towards N1, however, with Li-N1 and Li-N2 now having bond separations of 1.90 and 4.15 Å respectively.

On the other hand, K2 at the PBE0 level matched the experimentally-determined solid state structure well, as shown below.

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Bimetallic L alkyl and alkynyl complexes

Fig.6.5. Left: solid state structure of K2 (thermal ellipsoids set at 50% probability level)1. Right: PBE0 geometry-optimised structure of K2 (right). Hydrogens omitted for clarity.

The coordinated THF molecule in the crystal structure in figure 6.5 (left) was omitted for the geometry optimisation as it was not thought to contribute much to the K+ ion residing in the bis-arene cavity. Indeed, as seen in figure 6.5, the optimised structure (right) does show the K+ ion residing in the bis-arene cavity without having to be coordinated to a THF molecule, and unlike the Li+ ion in Li1, the K+ ion does not migrate to one of the pyrrole nitrogen atoms. In the experimentally-determined crystal structure, the distances for K-N1 and K-N2 are 3.62 and 3.08 Å respectively, and for the geometry-optimised structure, these K-N1 and K-N2 separations are 3.15 and 3.12 Å respectively. Whilst these are an improvement on the Li-N distances seen in figure 6.4 – with respect to the M+ ion remaining in the bis-arene pocket – there is nevertheless a 0.47 Å difference in the K-N1 distances seen between experiment and calculation, which might, of course, be an effect of the THF omission.

A series of complexes 1 was then modelled with the other alkali metals. This was to see if the size of the M+ ion had any effect on the stability of M+ residing in the bis-arene cavity or being coordinated closer to one of the pyrrole nitrogens. These results are collected in table 6.1 below.

206

Bimetallic L alkyl and alkynyl complexes

Table 6.1. M-N separation distances for a variety of alkali metals in complex 1.

Complex M-N1 separation (Å) M-N2 separation (Å)

Li1 1.90 4.12

Na1 2.36 4.33

K1 3.15 3.15

Rb1 3.28 3.28

Cs1 3.43 3.43

As can be seen, Li+ and Na+ are the only alkali metal ions which prefer to coordinate to one of the pyrrole nitrogens, and that it is only with the introduction of K+ through to Cs+ that the M-N1 and M-N2 distances become more equal, as these M+ ions instead reside in the bis-arene cavity. It was also found however that for K1, Rb1 and Cs1, these consistently converged to C2 symmetry – despite having no initial symmetry constraints – and so it is not known whether this symmetry during convergence forced the M+ ions into the bis-arene pocket, or whether the M+ ions, preferring to reside in the bis-arene pocket anyway, forced the complexes to then converge to C2 symmetry.

Before continuing it was first considered important to rule out any functional dependence for the cause of this discrepancy between the experimentally- determined and calculated geometries of the Li+ cation position. Since the PBE functional has been used for studies in previous chapters, this was employed for the geometry optimisation of Li1, as well as the meta-GGA and meta-hybrid functionals TPSS and TPSSh12 respectively. The Li-N separations from these different density functional methods are collected in table 6.2.

207

Bimetallic L alkyl and alkynyl complexes

Table 6.2. Li-N separation distances for a variety of density functional methods for complex Li1.

Functional Li-N1 separation (Å) Li-N2 separation (Å)

PBE 1.91 4.12

TPSS 1.91 4.10

TPSSh 1.91 4.10

As is seen from table 6.2, and comparing with the results in table 6.1, the choice of functional has a negligible effect on the Li-N separations, and so the tendency for the Li+ cation to relax at a closer proximity to one of the pyrrole nitrogens is not a function of the DFT method used.

This series of complexes will be revisited later in section 6.4 of this chapter, where reaction energies for the reaction of 1 → 3/4/5 were investigated.

6.4. Complexes 3, 4 and 5

Geometry optimisations for 3, 4 and 5 were also obtained from starting structures found from experiment1, with the aim to calculate the reaction energies for complexes 1 and 2 going to complexes 3, 4 and 5. The reaction scheme chosen and modelled was that outlined in the work by Suvova and co- workers1 and is shown here below.

Fig.6.6. Reaction scheme for 1 going to 3, 4 and 5 where M = Li, Na, K, Rb, Cs; An = Th; R’ = SiH3

(3), SiMe3 (4), SiiPr3 (5).

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Bimetallic L alkyl and alkynyl complexes

Optimisations for complexes 1 to 5, as well as molecules MMe and HCCR’, underwent vibrational frequencies calculations to obtain thermal corrections to the SCF energies. The reaction energies are collected in table 6.3.

Table 6.3. Energies for the reactions outlined in figure 6.6 where 1 and 2 react with 2HCCR’ to give the products 3, 4 and 5. Red numbers indicate experimentally-characterised reactions1. All data in kJ mol-1.

Products

3 4 5

ΔH298 ΔG298 ΔH298 ΔG298 ΔH298 ΔG298

Li1 121.0 150.8 132.2 176.9 149.7 206.5

Na1 8.1 39.6 19.3 65.8 36.8 95.4

K1 86.5 117.9 97.6 144.1 115.1 173.7

Rb1 93.3 123.3 104.5 149.4 122.0 179.0 Reactants Cs1 105.3 133.8 116.5 159.9 134.0 189.5

K2 20.0 45.4 31.2 71.5 48.6 101.1

As seen in table 6.3, all reactions have more positive ΔG values than ΔH values, which would be expected as the reactions (figure 6.6) have three molecules on the left-hand side, and two molecules on the right-hand side, which is not entropically favourable. However, all reactions are seen to be endothermic, including Li1 → 4/5 and K2 → 4/5 (indicated by the red numbers), which are known to work experimentally.

To see if the position of the Li+ cation in Li1 plays a role in these energies, the computational methods were altered when optimising the starting structures, to first of all try and stop the Li+ cation from migrating towards a pyrrole nitrogen during optimisation, and secondly to try and obtain negative reaction energies for Li1 → 3/4/5 as a result of changing the starting parameters of Li1. These changes were to replace all light atom cc-pVTZ basis sets with the cc- pVDZ basis set; modelling the THF molecules found in the experimental crystal structure of Li1, as shown in figure 6.7 below (these THF molecules were

209

Bimetallic L alkyl and alkynyl complexes

originally omitted for the same reason THF was omitted in the K2 optimisation); modelling Li1 in a PCM of THF; investigating the functional dependence of the reaction energies by adopting the three different functionals used for the results in table 6.2; freezing the Li+ ion in its starting geometry and allowing the rest of the complex to relax; and finally, as just a single point calculation, replacing the

K+ ion in K2 with Li+, and replacing the CH2Ph group with CH3. This last complex was labelled as Li1’, and, for reasons similar to freezing the Li+ and allowing the rest of the complex to relax, was used to calculate the SCF energy based on the Li+ ion staying in the bis-arene pocket. Note that for the frozen lithium complexes and Li1’, no thermal corrections for the energies were calculated as these were not true minima.

Fig.6.7. a) Solid state structure of Li1 with THF molecules from the experimental crystal structure1. b) PBE0 geometry-optimised structure of Li1 with THF molecules. Hydrogens omitted for clarity.

As seen in figure 6.7, incorporating the THF molecules into the structure still did not stop the Li+ ion from migrating towards one of the nitrogen atoms. The results for the reaction energies from different Li1 parameters mentioned above are collected in table 6.4.

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Bimetallic L alkyl and alkynyl complexes

Table 6.4. Energies for the reactions outlined in figure 6.6 where Li1 reacts with 2HCCR’ to give the products 3, 4 and 5. Values in red are ΔE, not ΔH298. All data in kJ mol-1.

Products

3 4 5

ΔH298 ΔG298 ΔH298 ΔG298 ΔH298 ΔG298

cc-pVDZ 7.1 44.5 19.3 69.4 34.5 101.1 eactants

Li1 with THF 507.6 383.1 680.7 683.1 154.9 59.6

Li1 THF PCM 118.5 150.8 129.7 176.9 147.2 206.5

Parameters for r for Parameters Li1PBE 14.9 67.3 25.7 70.5 50.1 109.7

Li1TPSS 15.9 47.8 -4.7 28.9 13.0 66.1

Li1TPSSh 382.6 419.7 393.9 439.0 412.7 485.0

Li+ frozen -371.7 - -193.4 - -724.7 -

Li1’ -87.3 - -76.2 - -58.9 -

As seen in table 6.4, neither changing the basis set nor incorporating THF into the structure – either explicitly or with a PCM – gives favourable reaction energies. It is also clear that there is a functional dependence on the magnitude of these reaction energies, however they nearly all still show an unfavourable reaction energy; TPSS is also the only functional which yields a negative ΔH298 when there are no solvation effects and all molecules in the reaction were allowed to relax to a minimum stationary point. This is for the reaction of Li1 →

4. However, this reaction also shows a positive ΔG298 value. The use of TPSS also yields unique results in that it is the only functional which does not show a steady increase in reaction energy when the products change from 3 to 5, which is seen with PBE, PBE0 (table 6.3) and TPSSh. In fact, the ΔG298 values are generally quite significantly larger than the ΔH298 values. It was not clear what exactly was causing this discrepancy, and for the interests of time constraints, the other complexes (6 and 7) were yet to be modelled and analysed (see section 6.5). This problem will be addressed at the end of this chapter and chapter 7.

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Bimetallic L alkyl and alkynyl complexes

The only other negative energies in table 6.4 are with the Li+ ion frozen and with Li1’, which were single point calculations, and neither of these had thermal correction energies accounted for. Whilst this fits with experiment based purely on the Li+ residing in the bis-arene pocket, they are nevertheless not true optimised structures. It may be that in the gas phase, a realistic representation of Li1 is indeed that the Li+ cation prefers to bond to pyrrole nitrogen rather than sit in the bis-arene pocket, and that the crystal structure found by experiment is different due to crystal packing effects. Whatever the true structure of Li1 when reacted with HCCR’, the endothermic reaction energies found remain dubious, since it has been shown in experiment that these reactions are thermodynamically favourable.

6.5. Complexes 6 and 7

Complexes Th6 and Th7 were successfully optimised and agreed well with available experimental data, the structures of which are shown below in figure 6.8.

Fig.6.8. Experimental structures1 of Th6a(a) and Th6b(b) (thermal ellipsoids set at 50% probability level), and the PBE0 geometry-optimised structures of Th6a(c) and Th6b(d). Hydrogens omitted for clarity. 212

Bimetallic L alkyl and alkynyl complexes

A more detailed comparison of the computational data with the available experimental data for the Th6a and Th6b geometries is highlighted in table 6.5, where a selection of bond lengths are compared between experiment and theory.

Table 6.5. Selected bond lengths in Th6 from PBE0 geometry-optimised structures and experimental data1 and their differences, with MAD analysis. Atom labels refer to those labelled in figures 6.8a and 6.8b. All values in Å.

Th6a Th6b

Bond PBE0 Experiment |Difference| PBE0 Experiment |Difference|

Th1-C1 2.684 2.653 0.031 2.646 2.645 0.001

Th1-C2 3.052 3.029 0.023 2.970 2.937 0.033

Th1-C3 2.399 2.436 0.037 2.385 2.411 0.026

C1-C2 1.248 1.250 0.002 1.256 1.267 0.011

C3-C4 1.283 1.272 0.011 1.281 1.268 0.013

Th1-N1 2.625 2.604 0.021 - - -

Th1-N2 2.596 2.587 0.009 - - -

Ni1-C1 1.817 1.830 0.013 1.808 1.814 0.006

Ni1-C3 1.923 1.933 0.010 1.917 1.938 0.021

Ni1-C4 1.993 2.005 0.012 2.001 2.025 0.024

Ni1-P1 2.222 2.200 0.022 2.221 2.205 0.016

Σ|Difference| 0.191 Σ|Difference| 0.151

Mean absolute deviation 0.017 Mean absolute deviation 0.017

The MAD analysis in table 6.5 shows values of 0.017 for both Th6a and Th6b, and since these are lower than any of the MAD values for PBE0 seen previously (tables 4.3 to 4.6 in chapter 4) it is found that the PBE0 data in table 6.5 differs very little from experiment. Confident that these geometry optimisations were suitable for carrying out further calculations on the final PBE0 structure, based on the results in table 6.5, the SCF and thermal energies of Th6 and Th7 were next examined.

The SCF, enthalpy and Gibbs thermal correction energies for Th6 and Th7 are shown in table 6.6.

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Bimetallic L alkyl and alkynyl complexes

Table 6.6. SCF, enthalpy and Gibbs free energies (in Hartrees) of the Th-based 6 and 7 complexes.

Complex SCF Enthalpy Gibbs

6a -3944.716388 -3943.313232 -3943.496847

6b -3944.725817 -3943.322333 -3943.505905

7a -3933.892211 -3932.713156 -3932.880947

7b -3933.905041 -3932.700605 -3932.891299

These energies for Th6a and Th6b showed that Th6b was energetically more stable, with an absolute ΔH298 between Th6a and Th6b of 23.9 kJ mol-1 and an absolute ΔG298 of 23.8 kJ mol-1. Similarly, Th7b was shown to be more thermodynamically stable than Th7a, with an absolute ΔH298 between Th7a and

Th7b of 33.0 kJ mol-1 and an absolute ΔG298 of 27.2 kJ mol-1 (table 6.8).

Analogous complexes of Th6 and Th7 where the Ni was replaced by Pt (Th6’ and Th7’) were next modelled. The Pt(0) metal centre retained the η1/η2 coordination to the alkynyl groups, as was found with the Ni coordination in Th6 and Th7, and SCF, enthalpy and Gibbs energies are given in table 6.7.

Table 6.7. SCF and Gibbs free energies (in Hartrees) of the Th-based 6’ and 7’ complexes.

Complex SCF Enthalpy Gibbs

6a’ -3893.327046 -3891.924005 -3892.110618

6b’ -3893.336782 -3891.933552 -3892.119812

7a’ -3882.501152 -3881.321147 -3881.492286

7b’ -3882.512781 -3881.309434 -3881.502673

As with Th6b and Th6a, Th6b’ is more stable than Th6a’, with an absolute ΔH298 and ΔG298 of 25.1 and 24.1 kJ mol-1 respectively. Similarly Th7b’ is 30.8 kJ mol-1 more stable than Th7a’, with the Gibbs energy being 27.3 kJ mol-1 larger as well. These energy differences are summarised in table 6.8.

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Bimetallic L alkyl and alkynyl complexes

Table 6.8. ΔE, ΔH and ΔG values (in kJ mol-1) between the η6:κ1:η6:κ1 and η5:η5 bonding modes of L to the ThIV centre for Th6, Th7, Th6’ and Th7’.

Complexes ΔE ΔH298 ΔG298

Th6a – Th6b -24.8 -23.9 -23.8

Th7a – Th7b -33.7 -33.0 -27.2

Th6a’ – Th6b’ -25.6 -25.1 -24.1

Th7a’ – Th7b’ -30.5 -30.8 -27.3

As shown in table 6.8 changing the transition metal to Pt does little to affect the overall energy preferences. I.e. whether or not M’ is Ni or Pt, the difference in energy for | Th6a – Th6b| and | Th6a’ – Th6b’| is respectively 23.9 and 25.1 kJ mol-

1 for ΔH298, and 23.8 and 24.1 kJ mol-1 for ΔG298, in favour of b in each case, and likewise for Th7a – Th7b and Th7a’ – Th7b’. This indicates that it is not the transition metal which dictates the preference for L2- to adopt the η5:η5 bonding mode over η6:κ1:η6:κ1, given that for all four groups of complexes (Th6, Th7, Th6’ and Th7’), the b form is consistently more stable than the a form. Note that this preference appears to be slightly stronger for the complexes where R = Ph, regardless of the transition metal centre being Ni(0) or Pt(0). The reasons behind this will be studied further in section 6.5.2.

6.5.1. Dipoles of Th6 and Th7

Since two different solvents – THF and hexane – are used in the synthesis of Th6 and Th71, the polarisable continuum model (PCM) was employed to model the solvation effects on the dipole moment in Th6 and Th7 and to see if the stabilities of the compounds are affected by the solvent environments.

The dipole moments for Th6 and Th7 were calculated in a solvent-free environment, as well as in environments of THF and hexane.

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Bimetallic L alkyl and alkynyl complexes

Table 6.9. Dipole moments (Debye) in solvent-free and solvated environments for Th6 and Th7.

Complex Solvent-free THF Hexane

Th6a 3.509 5.170 4.345

Th6b 2.311 3.615 2.900

Th7a 3.684 4.979 4.245

Th7b 2.459 3.333 2.942

As seen in table 6.9, both Th6 and Th7 in both solvent-free and solvated environments show the a forms to have the larger dipole moment compared to the b forms, and whilst Th7 shows the largest dipoles out of Th6 and Th7 in the solvent-free model, in THF, Th6 shows the largest dipoles between both Th6 and Th7 instead. In hexane, the dipoles are larger than in the solvent-free model, but not as large as the dipoles in the THF-solvated complexes, which would be expected as THF is a more polar solvent than hexane.

The energy differences between the different conformations of Th6 and Th7 were next investigated using these solvation models. Since the geometries of Th6 and Th7 changed very little between the gas phase and PCM models, the optimised geometries of the PCM-modelled complexes had their thermodynamic corrections calculated by adding the enthalpy and Gibbs energy corrections from the solvent-free geometry optimisations onto the total SCF energy of the PCM-based optimisations. This is presented in table 6.10.

Table 6.10. SCF energies (Hartrees) of complexes Th6 and Th7 in the THF and hexane PCM models.

Complex THF Hexane

Th6a -3944.728910 -3944.720734

Th6b -3944.739188 -3944.730356

Th6a -3933.908275 -3933.897579

Th7b -3933.921597 -3933.911039

The enthalpy and Gibbs energy differences between the a and b forms in both the THF and hexane PCM models are shown in table 6.11.

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Bimetallic L alkyl and alkynyl complexes

Table 6.11. Energy differences between a and b forms of Th6 and Th7 in THF and hexane. Negative numbers indicate a more stable b form. All data in kJ mol-1.

In THF In hexane

Complexes ΔH298 ΔG298 ΔH298 ΔG298

Th6a – Th6b -26.1 -26.0 -24.4 -24.3

Th6a – Th6b -34.2 -28.5 -34.6 -28.8

Table 6.11 shows that for both solvation models, the b forms of Th6 and Th7 are more stable than the a forms, as was found with the unsolvated energies (see table 6.8). Since it was found that the a forms of Th6 and Th7 have a higher dipole moment in the unsolvated and PCM models, and higher still in the THF PCM models, it is perhaps surprising that the less polar b forms are still energetically more favourable than the a forms even in the THF PCM model.

When comparing the ΔG298 values in table 6.11 to table 6.8, Th6b shows values of 26.0 and 24.3kJ mol-1 in the THF and hexane PCM models respectively, which are only slightly larger than the 23.8kJ mol-1 value found in the gas-phase model.

Similarly for Th7b, the ΔG298 values in table 6.8 are similar to those in table 6.11, and table 6.11 also shows slightly larger ΔG298 values than those found in table 6.8. From this it is seen that the energy differences between the a and b forms are not dependent on solvent models.

Further investigations into the reasons behind this energetic preference for b are discussed in the following section.

6.5.2. Molecular orbitals of Th6 and Th7

To establish what causes this energetic preference for the b form, the SCF energies from single-point calculations of the [LThIV]2+ fragments in Th6 in both the a and b bonding modes were examined in isolation. Interestingly, the a binding mode of the ancillary ligand was found to be more energetically stable than the b binding mode, by 19.0 kJ mol-1. Analysis of the rest of Th6 minus the

[LThIV]2+ fragment – i.e. [(CCSiMe3)2NiPCy3]2- – taken as a single point calculation in their geometries from the full Th6a and Th6b complexes, showed a

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Bimetallic L alkyl and alkynyl complexes

very small energy difference of 1.0 kJ mol-1, which is unsurprising given that the

[(CCSiMe3)2NiPCy3]2- substituent changes very little in geometry between complexes Th6a and Th6b. As such, the energy differences found from tables 6.6 to 6.11 must be due to the difference in binding energy between the LTh-M in the different L2- orientations.

In order to probe this further, the energies of the valence Kohn-Sham molecular orbitals (KS-MOs) of Th6 and Th7 were examined to identify those with thorium- alkyne and nickel-alkyne overlap which displayed significant changes between the two L2- ligand conformations. The energies and metal orbital contributions for the Th6 and Th7 MOs are given in tables 6.12 and 6.13 respectively, and are also presented for complex Th6 in figure 6.9 below.

Table 6.12. MO energies for Th6 and Th7. All data in eV. Negative energy differences indicate MOs in the b forms being more stable than those in a.

MO for Th6a Th6b Difference Th6a/ Th6b

266/267 -7.260 -7.050 0.210

266/255 -7.260 -8.052 -0.791

265/265 -7.500 -7.129 0.371

MO for Th7a Th7b Difference Th7a/ Th7b

256/257 -7.278 -7.054 0.224

256/243 -7.278 -8.037 -0.760

251/254 -7.591 -7.266 0.324

251/245 -7.591 -7.820 -0.229

250/249 -7.654 -7.552 0.102

250/245 -7.654 -7.820 -0.166

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Bimetallic L alkyl and alkynyl complexes

Table 6.13. Metal contributions to selected MOs (%, Mulliken analysis) for Th6 and Th7.

MO for Th6a Th Th6a Ni MO for Th6b Th Th6b Ni Th6a contribution contribution Th6b contribution contribution

266 - 10d 267 - 3p, 10d

265 - 14d 265 3d 5d

- - - 255 7d 4d

MO for Th7a Th Th7a Ni MO for Th7b Th Th7b Ni Th7a contribution contribution Th7b contribution contribution

256 - 11d 257 - 6d

251 - 10d 254 - -

250 - 7d 249 - -

- - - 245 3d 13d

- - 243 6d 3d

Fig.6.9. Energies (eV) of MOs of complex Th6 relative to MO 255 for Th6a (left) and Th6b (right). Hydrogens omitted for clarity. Isovalue = 0.025.

The MOs labelled in red indicate the Ni-alkynyl interactions where a Ni d-orbital and the π-orbitals of both alkynyl ligands are all in phase. For Th6a, there is only one such orbital (MO 266), whereas for Th6b, there are two (MOs 267 and 255).

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Bimetallic L alkyl and alkynyl complexes

This split of MO 266 in Th6a, when changing to Th6b, arises from the fact that in Th6a this Ni-alkynyl interaction is localised in one MO (266), with no L-Th contribution (see table 6.13). Moving to Th6b brings a Th-pyrrole bonding MO of π-orbitals in the pyrrole rings and a Th d-orbital into approximate degeneracy with the Ni-alkynyl interaction, and results in in-phase (MO 255) and out-of- phase (MO 267) combinations, the former of which is much more stable than MO 266 in Th6a, with a mixture of Ni and Th MO contributions, and the latter (MO 267) exhibiting no Th contribution, similar to MO 266 in Th6a. Since the L2- ligand is in a different orientation in Th6a, there is no such contribution from the pyrrole rings, whose π-orbitals do not contribute to MO 266, and thus there is only one MO for this particular Ni(CCSiMe3)2 interaction. More detailed pictures of this stabilised MO 255 are shown in figure 6.10.

Fig.6.10. Two representations of MO 255 in Th6b visualising the two significant bonding interactions contributing to the η5:η5 conformation stability, the front view on the left, side view on the right hand side. Atom labels correspond to those labelled in figure 6.8. Isovalue = 0.025.

Z-clip used to omit the visibility of the SiMe3 π-orbital interactions.

The MOs labelled in green (figure 6.9) are interactions in which a Ni d-orbital is in phase with π-orbitals of the two alkynyl ligands which are out of phase with each other. This interaction is more stable in Th6a than it is in Th6b, and does not split from one conformation to the other. MO 265 in Th6a does not have any Th contribution, but does in Th6b. However, since MO 265 in Th6b is less stable than in Th6a, this Th contribution is clearly not a stabilising factor as was found for MO 255. Rather, there are π-orbital contributions in MO 265 from the arene rings and pyrrole rings in Th6a and Th6b respectively, and it may be this particular arene interaction is more stable than a Th-pyrrole interaction in this

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Bimetallic L alkyl and alkynyl complexes

case, hence why MO 265 in Th6a is 0.371 eV more stable than its counterpart in Th6b. Indeed, when looking at the isolated L2- fragment from both the η6:κ1:η6:κ1 and η5:η5 geometries, these same π-orbitals were found to have relative energies consistent with those found in figure 6.9, albeit with a larger energy difference, in that the pyrrole π-orbital in the η5:η5 geometry was found to be less stable than the arene π-orbital in the η6:κ1:η6:κ1 geometry by 2.312 eV.

Overall, the sum of the energy differences between Th6a and Th6b for the orbitals identified in figure 6.9 gives a preference for Th6b of 0.210 eV. As the differences in the energies of these MOs are the largest located, it is likely that they are the driver for the stability of the η5:η5 mode, especially the MO 266 (Th6a) to MO 255 (Th6b) transition.

For Th7, the MO picture is rather different, as shown below in figure 6.11.

Fig.6.11. Energies (eV) of MOs of complex Th7 relative to MO 243 in the η6:κ1:η6:κ1 (left) and η5:η5 (right) bonding modes of L. Hydrogens omitted for clarity. Isovalue = 0.025.

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Bimetallic L alkyl and alkynyl complexes

The orbitals labelled in red in Th7a and Th7b follow the same trends as those shown in figure 6.9, and this is due to similar splitting of MO 256 in Th7a into in- phase and out-of-phase MOs in Th7b for the Th-pyrrole and Ni-alkynyl interactions (see figure 6.12).

Fig.6.12. MO 256 in Th7a splitting to the out-of-phase MO 257 in Th7b and the in-phase MO 243 also in Th7b. Hydrogens omitted for clarity. Isovalue = 0.025. The orbitals labelled in green, however, show different behaviour from those shown in figure 6.9. For Th7a there are two such interactions in which a Ni d- orbital is in phase with π-orbitals of the two alkynyl ligands which are out of phase with each other (MOs 251 and 250), and for Th7b, the character of these orbitals is found in three MOs (254, 249 and 245). MO 251 splits into MOs 254 and 245, and MO 250 into MOs 249 and 245 when going from Th7a to Th7b. Inspection of these orbitals shows that the Ni-alkynyl character of MO 265 in Th6a is found in two MOs in Th7a because of mixing with Ph π-orbitals, which cannot happen for Cy ligands.

In complex Th7b however, there is only one Ni-alkynyl interaction (MO 245), which is much more stabilised than in Th7a and which has no contribution from the Ph rings. The latter character is now found in MOs 249 and 254. Essentially, two Ni-alkynyl interactions in Th7a converge to just one in Th7b, and the π- bonding orbitals in the Ph rings of the PPh3 group play no role in this MO, hence

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Bimetallic L alkyl and alkynyl complexes

the absence of any metal contribution for MOs 254 and 249 in table 6.12. This makes this Ni-alkynyl interaction therefore more stable in Th7b, the opposite of which was found for Th6b (see figure 6.9). As such, the overall energy differences between the red and green ligands in Th7 favour Th7b by 0.504 eV.

For both Th6 and Th7, these MO energy differences qualitatively match the observations of the ΔE, ΔH298 and ΔG298 values from table 6.8, insofar as in both the thermal energy differences and MO energy differences, the η5:η5 bonding mode of L2- is preferred for both Th6 and Th7, and that this energy preference is larger in magnitude for the PPh3-based complexes than for the PCy3-based complexes.

Overall, SCF, enthalpy and Gibbs energies show that the η5:η5 bonding mode is preferred, independent of the R group present – although when R = Ph this preference is larger – and the orbital analysis for the Ni systems shows that this preference is due to the L2- ligand being able to stabilise a Ni d-orbital contribution to the two alkynyl ligands in the red MOs (figures 6.9 and 6.11) by over 0.7 eV in both Th6 and Th7. The green MOs (figures 6.9 and 6.11) are destabilised going from Th6a to Th6b, seemingly due to a slight Th-pyrrole π interaction in Th6b rather than an arene π interaction in Th6a. By contrast, these green MOs are instead stabilised going from Th7a to Th7b, due to two Ni-alkynyl interactions becoming just one Ni-alkynyl interaction as a result of the π- bonding orbitals in PPh3 being the same energy in Th7a but not in Th7b. This result of one set of MOs being stabilised and one set being destabilised in Th6a/ Th6b, and both sets of the analogous MOs being stabilised in Th7a/ Th7b, appears to also explain why when R = Ph3, this correlates qualitatively with η5:η5 bonding being energetically favourable by a larger magnitude than that found when R = Cy3.

The Pt-based Th6’ and Th7’ complexes were next studied to see if the above arguments for the preference of η5:η5 bonding still holds. The analogous orbitals to those shown in tables 6.11 and 6.12 are presented in tables 6.14 below and 6.15 below.

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Bimetallic L alkyl and alkynyl complexes

Table 6.14. MO energies for Th6’ and Th7’. All data in eV. Negative energy differences indicate MOs in the b forms being more stable than those in a.

MO for Th6a’/ Th6b’ Th6a’ Th6b’ Difference (eV)

266/267 -7.473 -7.205 0.269 266/255 -7.473 -8.156 -0.682 263/257 -7.888 -8.108 0.220 261/257 -7.986 -8.108 0.122

MO for Th7a’/ Th7b’ Th7a’ Th7b’ Difference (eV)

254/257 -7.523 -7.238 0.285 253/257 -7.568 -7.238 0.330 254/243 -7.523 -8.162 -0.639 253/243 -7.568 -8.162 -0.594 248/244 -7.981 -8.028 -0.047

Table 6.15. Metal contributions to selected MOs (%, Mulliken analysis) for Th6’ and Th7’.

MO for Th6a’ Th Th6a’ Pt MO for Th6b’ Th Th6b’ Pt Th6a’ contribution contribution Th6b’ contribution contribution

266 - 19d 267 - 11d

263 - 9d 257 3d 10d

261 - 13d 255 5d 14d

MO for Th7a’ Th Th7a’ Pt MO for Th7b’ Th Th7b’ Pt Th7a’ contribution contribution Th7b’ contribution contribution

254 - 7d 257 - 12d

253 - 11d 244 - 7d

248 - 15d 243 5d 11d

Th6’ has a slightly different MO makeup than that found in Th6. Unlike Th6a, Th6a’ has three MOs with significant metal contributions to the alkynyl ligands. These contributions are shown in figure 6.13.

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Bimetallic L alkyl and alkynyl complexes

Fig.6.13. MO energy levels for complex Th6’ by energies (eV) relative to MO 255 in Th6b’ for the a form (left) and b form (right). MO representations from top to bottom correspond to MO levels 266, 263 and 261 respectively (left), and from top to bottom correspond to MO levels 267, 257 and 255 respectively. Isovalue = 0.025.

As can be seen clearly in figure 6.13, for the red-labelled MOs, the MO diagrams for complex Th6’ follow the trend found in Th6 (figure 6.9), in that, for Th6a’, one orbital (MO 266) where the Pt-alkynyl orbitals are all in phase with each other but is out of phase with the π-orbitals in the L2- ligand, splits into two orbitals in Th6b’, where one Pt-alkynyl interaction is out of phase with the L2- ligand and is destabilised (MO 267) and one where this Pt-alkynyl interaction is also in phase with the Th-L ligand interaction and is stabilised (MO 255).

The green-labelled MOs show a different trend to that seen in figure 6.9 for the Th6 complexes. Whereas in Th6, there is only one green-labelled MO in both the a and b forms, from figure 6.13 it is seen that in Th6a’ there two such MOs (MOs 263 and 261), and just one in Th6b’ (MO 257). Furthermore, MO 257 is more stable than both MOs 263 and 261, whereas in Th6b, this analogous MO (MO 265 in figure 6.9) is less stable than MO 265 in Th6a. Inspection of the orbitals in figure 6.13 shows that this difference arises from the fact that the Pt-alkynyl interaction in Th6a’ is in approximate degeneracy with two different π-orbitals in the arene rings of the L2- ligand, but in Th6b’, these π-orbitals are not same energy as this Pt-alkynyl interaction, and thus the Pt-alkynyl interaction is not

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Bimetallic L alkyl and alkynyl complexes

competing with arene π-orbitals of the same energy. Overall, the total energy difference of these particular MOs is -0.755 eV, which equates to -72.8kJ mol-1. Again, as with Th6, this fits with the result of Th6b’ being more stable than Th6a’ (table 6.8).

The MOs for Th7’ also show differences to Th7.

Fig.6.14. MO energy levels for complex Th7’ by energies (eV) relative to MO 243 in Th7b’ for the a form (left) and b form (right). MO representations from top to bottom correspond to MO levels 254, 253 and 248 respectively (left), and from top to bottom correspond to MO levels 257, 244 and 243 respectively. Isovalue = 0.025.

Unlike Th7, with Th7’ there is only one green-labelled MO in both the a and b forms, since the π-orbitals of the Ph rings are no longer in approximate degeneracy with this particular Pt-alkynyl interaction. Furthermore, as with Th6’, this MO is more stable in the b form, although by only a relatively small amount. The total of MO energy differences between Th7a’ and Th7b’ is 0.665 eV in favour of the b form.

In summary, the total MO energy differences from the results for the Pt-based MOs, together with the energies in table 6.8, lend further evidence to the suggestion that for complexes Th6 and Th7, the choice of transition metal in the

M’PR3 group does not significantly affect the overall energetic stability of the b forms over the a forms, and in fact this preference appears to come from the

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Bimetallic L alkyl and alkynyl complexes

energy differences in orbital contributions from Th-alkynyl-M’ interactions between the different forms, independent of whether M’ = Ni or Pt.

6.5.3. Comparisons with M(IV) and other An(IV) centres for 6

Further complexes of 6 and 7 were studied to see if the orbital rationalisation of the relative stabilities of the a and b forms still holds for different tetra-valent transition metal, lanthanide and actinide centres, first of all with closed-shell systems (Hf6/7 and Ce6/7) and secondly with open shell systems across the actinide series (Pa6/7, U6/7, Np6/7, Pu6/7 and Am6/7). Hf(IV) was included in the comparison because, although not an actinide, it is above thorium in the periodic table, and since Th(IV) has no f-electrons, Hf(IV) is a suitable 5d- element analogue of Th(IV). Comparisons of Hf and Th complexes in both experiment and theory are therefore common throughout the literature13-16. Similarly, Ce(IV) also has no f-electrons, and also being above thorium in the periodic table, was thought to be a good comparison as a closed-shell analogue of Th6/7.

Modelling these complexes at the PBE0 level proved difficult, with many of the more open shell systems either failing to converge the SCF energy or running out of computer time. It was decided therefore to instead model them at the PBE level. Due to this change of functional, Th6 and Th7 were also re-modelled at the PBE level in order to compare the results of the other analogues of 6 and 7 consistently. Unfortunately, even at the PBE level, both Ce6 and Ce7 failed to converge the SCF energy, and so for the interests of time, were not analysed further. Hf6 showed a large energy difference between a and b, and upon investigation this was down to the stark differences in their respective geometries. Whilst Hf6b still retained the η5:η5 binding to both pyrrole rings, Hf6a showed only η6 binding to just one arene ring. Due to these geometry differences with Hf6, they were also not compared with the rest of the actinide series.

Th6 and Th7 at the PBE level still retained the energetic preference of b over a, with absolute ΔH298 and ΔG298 values of 20.7 and 19.8 kJ mol-1 respectively for Th6a - Th6b. These were slightly lower than the analogous energies at the PBE0

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Bimetallic L alkyl and alkynyl complexes

level in table 6.8, but still in qualitative agreement with the PBE0 results, and hence Th6 and Th7 at the PBE level were compared to the Pa through to Am analogues at the same level of theory.

The PBE energy differences between a and b for the full set of An6 are given in table 6.16.

Table 6.16. PBE energies of the a and b forms and their differences of An6, An = Th – Am. Negative numbers indicate a more stable b form.

a b a b Difference (kJ mol-1)

An Enthalpy (Hartrees) Gibbs (Hartrees) ΔH298 ΔG298

Th -3943.021575 -3943.029472 -3943.210805 -3943.218341 -20.7 -19.8

Pa -3976.720286 -3976.720437 -3976.906702 -3976.909840 -0.4 -8.2

U -4012.267727 -4012.269031 -4012.457940 -4012.458279 -3.4 -0.9

Np -4049.765341 -4049.767221 -4049.957428 -4049.957802 -4.9 -1.0

Pu -4089.242506 -4089.245436 -4089.437144 -4089.437620 -7.7 -1.2

Am -4130.783097 -4130.783361 -4130.980119 -4130.978230 -0.7 5.0

From table 6.16, all the b forms were found to be more stable than the a forms, with the exception of Am6, where Am6a showed a ΔG298 value 5.0 kJ mol-1 more stable than Am6b; however, the ΔH298 value showed in fact that Am6b was the more stable form. These energies are plotted as a function of An centre in figure 6.15.

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Bimetallic L alkyl and alkynyl complexes

Fig.6.15. Energy differences between a and b forms of An6 as a function of An centre. Blue =

ΔH298; red = ΔG298.

Figure 6.15 shows a significant decrease in magnitude of ΔH298 and ΔG298 differences with Pa6 onwards in comparison with the Th-based analogues

As with Th6 at the PBE0 level, this set of PBE-optimised 6 was investigated with regards to their KS-MOs and whether MOs analogous to the ones indicated in red and green in figure 6.9 are present in all Th-Am6 complexes. The MOs of interest, their energies, and their difference in energies between the a and b forms are presented in table 6.17. The MOs labelled in red and green are ones in which very similar Ni-alkyne interactions to those shown in figure 6.9 are present.

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Bimetallic L alkyl and alkynyl complexes

Table 6.17. MO energies (eV) for An6 where An = Th-Am. Negative energy differences indicate MOs in the b forms being more stable than those in a.

MO for Th6a Th6b Difference Th6a/ Th6b

266/268 -6.110 -5.883 0.227

266/255 -6.110 -6.783 -0.673

265/264 -6.242 -6.047 0.195

MO for Pa6a Pa6b Difference Pa6a/ Pa6b

266/268 -6.061 -5.829 0.232

266/255 -6.061 -6.878 -0.817

265/258 -6.243 -6.573 -0.330

MO for U6a U6b Difference U6a/ U6b

266/268 -6.047 -5.841 0.205

266/255 -6.047 -6.858 -0.812

265/259 -6.217 -6.551 -0.334

MO for Np6a Np6b Difference Np6a/ Np6b

267/268 -5.979 -5.800 0.178

267/255 -5.979 -6.813 -0.834

265/260 -6.191 -6.499 -0.307

265/259 -6.191 -6.542 -0.351

MO for Pu6a Pu6b Difference Pu6a/ Pu6b

267/269 -6.055 -5.744 0.312

267/255 -6.055 -6.764 -0.709

265/264 -6.249 -6.044 0.205

265/259 -6.249 -6.430 -0.180

MO for Am6a Am6b Difference Am6a/ Am6b

267/268 -6.038 -5.779 0.259

267/257 -6.038 -6.611 -0.573

265/260 -6.211 -6.396 -0.184

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Bimetallic L alkyl and alkynyl complexes

The lowest energy out of all of these MOs was MO 258 in Pa6b, with an energy of -7.763 eV. As such, this energy was the reference point for all other MO energies when plotted in figure 6.16. As with figure 6.9, “uphill” lines and “downhill” lines when reading from left to right indicate respectively a destabilisation and stabilisation of the MO when going from the a to the b form of An6.

Fig.6.16. MO energy levels (eV) for complex An6 by energies relative to MO 255 in Pa6b for the a form (left) and b form (right) for each An centre of 6. Top x-axis is the total energy difference (eV) of each red- and green-labelled MO energy change from the a and b forms of each M6 complex. All negative total energy differences indicate a more stable b form.

The MO pattern for Th6a and Th6b in figure 6.16 is similar to that shown in figure 6.9, and with an overall energy preference for Th6b of 0.252 eV, is similar to the PBE0 model in figure 6.9, which showed an overall preference of 0.210 eV. Overall, both functionals showed qualitative agreement between the thermal energy differences and the overall MO energy differences. As seen in figure 6.16, Th6b was the only complex where the MO labelled in green was destabilised when compared to the same MO in the a form. The rest of the series showed that all the green-labelled MOs were more stable in the b form, except for Pu6b, where one MO was stabilised but the other was destabilised. Pu6 was also one of two complexes where the MOs labelled in green split from one

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orbital to two orbitals depending on whether it was in the a or b conformation, the other complex being Np6.

As with the thermal energies (table 6.16), the total MO energy differences (figure 6.16) showed little trend as a function of actinide centre in the L2- ligand.

As such, the absolute ΔH298 values and the absolute total MO energy differences between the a and b forms did not correlate with each other as shown in figure 6.17, which shows an R2 of only 0.313.

Fig.6.17. Absolute total MO energy differences from figure 6.15 against absolute total enthalpy differences from table 6.14. Labels for each metal centre in the L2- ligand.

What is apparent, however, from the data so far, is that all open-shell actinide complexes (Pa-Am6) have small thermal energy differences between the a and b form compared with Th6. Therefore the argument put forward for the MO energies in Th6 qualitatively matching the relative thermal energy differences does not apply with the later actinides. These complexes are open shell, with unpaired f-electrons. Examination of these singly-occupied molecular orbitals (SOMOs) showed that for one of the f-electrons, there is significant overlap with the π*-orbitals of the arene and pyrrole rings in the a and b forms respectively, resulting in δ-type interactions from the actinide to the L2- ligand. Moving across the actinide series, these f-orbitals become increasingly contracted, and therefore no longer extend far enough to overlap with the π*-orbitals of the arene and pyrrole rings, as shown in figure 6.18.

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Fig.6.18. Interaction of key An f-orbitals, as discussed in the main text with the π*-orbitals of the arene and pyrrole rings respectively for a forms (left) and b forms (right) for a) Pa6, b) U6, c) Np6, d) Pu6, e) Am6. Isovalue = 0.025.

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As is shown in figure 6.18, as the Z of the actinide increases, the SOMOs in the a form become increasingly dominated by contributions from one or both of the pyrrole rings, and the f-orbital on the actinide loses degeneracy with the π*- orbitals of the arene rings. In the b forms, the contributions from the pyrrole rings continue to show some mixing with the f-orbital on the actinide centre beyond U6, with some slight mixing of these two contributions seen in Np6b and Am6b – with the a forms, this degeneracy stops with U6a. In figure 6.18, all these SOMOs shown were the lowest SOMOs (MO 277 for all open-shell 6 complexes). However, for Am6, this particular f-orbital interaction was found in the higher- energy SOMO energy levels. Therefore, Am6a shows the second-highest SOMO (MO 280) and Am6b shows the second-lowest SOMO (MO 278). The energies, orbital make-up and energy differences for all these SOMOS are shown in table 6.18.

Table 6.18. SOMO energies and their difference between the a and b forms of open-shell An6 complexes, as well as percentage of f-orbital contribution from each actinide.

An SOMO for An6a f-orbital An6b f-orbital Energy centre An6a/ An6b (eV) contribution (eV) contribution difference (eV) (%) (%) (An6b – An6a) Pa 277/277 -3.410 74 -2.976 85 0.434

U 277/277 -3.791 80 -3.600 90 0.191

Np 277/277 -4.072 10 -3.957 70 0.114

Pu 277/277 -4.123 72 -4.124 61 -0.001

Am 280/278 -3.995 11 -4.163 59 -0.168

From table 6.18, it is seen that the MOs for the δ-type interactions between the actinide centre and L2- are more negative in energy for the a form, until Pu6, where the b form shows more negative SOMO energies. This follows the observations shown in figure 6.18 where δ-type interactions in both a and b for Pa6 and U6 show f-orbital overlap with arene and pyrrole π*-orbitals. For Np6, the f-orbitals no longer overlap with the arene or pyrrole rings, however Np6a also shows more contribution from the L2- ligand, making this SOMO still higher in energy – in an absolute sense – than its counterpart in Np6b. For Pu6 and Am6, the f-orbitals are a lot more contracted in the a forms compared to the b forms,

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and the a forms now also exhibit significant contribution from both the pyrrole rings in the L2- ligand. These factors appear to explain why SOMOs in the b form are more stable than those in the a form for Pu6 and Am6. It was also found from the contributions of the f-orbitals to each SOMO, that for all the complexes in table 6.18, the SOMOs in the An6b series were dominated by the actinide contributions, whereas in the An6a series, the actinide contributions dominate in some of the complexes, but not in others, e.g. Np6a and Am6a have f-orbital contributions of only 10 and 11% respectively. This is seen clearly in figure 6.18, where for these two complexes, the majority of the SOMO is made up of contributions from the pyrrole rings and other π*-orbitals of the L2- ligand.

Since it was found with the open-shell systems that the MOs in table 6.15 and the SOMOs in table 6.18 both appeared to play important roles in the stability of b over a, various comparisons of these energies against the ΔH298 values from table 6.16 were examined for Pa-Am6 as follows; just the total energy of the MOs labelled in red and green; these MO energies plus the SOMO energies; and finally, just the SOMO energies. These are collected in table 6.19 and correlated against the ΔH298 values from table 6.19 in figure 6.20 below.

Table 6.19. Total energy differences (eV) between An6a and An6b for various combinations of MOs and SOMOs.

An Total difference in “red” Total difference in “red” and SOMO energies and “green” MO “green” MO energies plus (table 6.18) energies (table 6.17) SOMO energies.

Pa -0.916 -0.481 0.434

U -0.940 -0.748 0.191

Np -1.314 -1.199 0.114

Pu -0.373 -0.374 -0.001

Am -0.499 -0.667 -0.168

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Fig.6.19. Total MO energy differences (top); MO + SOMO energy differences (middle); and

SOMO energy differences (bottom) against absolute ΔH298 differences between An6a and An6b. For the bottom graph, R2 was obtained by omitting Am6 data which is in outlier.

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For the SOMO values, Am6 is seen to be quite a strong outlier, and so R2 was obtained for this graph by omitting the Am data point. Indeed, when including Am6 R2 becomes 0.064. Nevertheless, even without the inclusion of the Am6 data, the only good correlation is found with the ΔH298 values vs the SOMO energy differences, with an R2 value of 0.966. Considering the total energy differences of the MOs from table 6.17 on their own, and combining these with the SOMO energy differences, gives worse correlations against the ΔH298 values, with R2 values of 0.218 and 0.000 respectively. It is not clear therefore whether the correlation with just the SOMO energies were significant or coincidental, considering that by just taking these SOMO energies into account, one would assume that for Pa6, U6 and Np6, the a forms were more stable than the b forms (assuming also that energy differences of the SOMOs qualitatively match the thermal energy differences) given that these SOMOs were more stable in a than in b. From table 6.16, this is not the case.

6.5.4. Comparisons with other An(IV) centres for 7

The set of An7 was optimised at the PBE level and the energy differences between the a and b forms are presented in table 6.20. As with Hf6, Hf7 showed large thermal energy differences due to the different geometries of the a and b forms. Hf7 was the only complex where the a form was more stable than the b form, albeit by only a very small amount compared with the rest of series from Th – Am. The geometries of Hf7 were different than the rest of the actinide series in that neither of the arene rings are bound to the Hf centre, yet Hf7b still retains the η5:η5 binding. For these reasons, as with Hf6, Hf7 was not included in the rest of this analysis.

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Table 6.20. Energies of the a and b forms and their differences, of An7 where An = Th-Am.

a b a b Difference (kJ mol-1)

An Enthalpy (Hartrees) Gibbs (Hartrees) ΔH298 ΔG298

Th -3932.475390 -3932.486116 -3932.661163 -3932.669316 -28.2 -21.4

Pa -3966.171553 -3966.177475 -3966.356913 -3966.361584 -15.5 -12.3

U -4001.720028 -4001.725192 -4001.905607 -4001.909946 -13.6 -11.4

Np -4039.217693 -4039.223947 -4039.404908 -4039.409460 -16.4 -12.0

Pu -4078.695040 -4078.702292 -4078.884541 -4078.888810 -19.0 -11.2

Am -4120.235253 -4120.238609 -4120.427124 -4120.427434 -8.8 -0.8

The largest energy difference, i.e. where the b form is more stable, is found with Th7, the smallest energy difference being with Am7. The energy differences for the rest of the actinide complexes showed a similar trend as a function of actinide centre to An6, with the exception of Pa7, where this energy difference was lower than U7, whereas in the An6 series, the Pa6 energy difference was higher than U6 (figure 6.15).

Fig.6.20. Energy differences between a and b forms of M6 as a function of An centre. Blue =

ΔH298; red = ΔG298.

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Although figures 6.15 and 6.20 showed similar trends, the fact that the Pa-based data points for 6 and 7 are quite different requires caution when concluding that having an actinide centre becoming progressively more open-shell has any bearing on the magnitude of energetic stability of b over a.

As was found in table 6.8 for Th6 and Th7 (at the PBE0 level) the b forms were more stable by a larger degree in 7 compared to 6 – i.e. when R on PR3 = Ph.

The KS-MOs were next investigated, with the red-labelled and green-labelled MOs indicating orbitals exhibiting the same type of Ni-alkynyl interactions found throughout this family of complexes so far studied.

Table 6.21. MO energies (eV) for An7 where An = Th-Am. Negative energy differences indicate MOs in the b forms being more stable than those in a.

MO for Th7a Th7b Difference Th7a/ Th7b

257/259 -6.061 -5.829 0.232

257/243 -6.061 -7.763 -1.701

256/251 -6.218 -6.394 -0.176

255/249 -6.288 -6.277 0.011

256/246 -6.288 -6.556 -0.268

MO for Pa7a Pa7b Difference Pa7a/ Pa7b

257/260 -6.057 -5.823 0.234

257/243 -6.057 -6.841 -0.784

256/255 -6.244 -6.091 0.153

255/246 -6.334 -6.566 -0.232

MO for U7a U7b Difference U7a/ U7b

257/259 -6.039 -5.850 0.189

257/243 -6.039 -6.831 -0.792

256/255 -6.225 -6.067 0.158

256/246 -6.225 -6.581 -0.356

MO for Np7a Np7b Difference Np7a/ Np7b

258/259 -5.983 -5.815 0.168

258/260 -5.983 -5.783 0.201

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258/243 -5.983 -6.790 -0.807

256/248 -6.198 -6.453 -0.255

255/246 -6.270 -6.574 -0.303

MO for Pu7a Pu7b Difference Pu7a/ Pu7b

258/260 -6.060 -5.739 0.321

258/243 -6.060 -6.753 -0.693

255/255 -6.263 -6.077 0.185

255/248 -6.263 -6.401 -0.138

255/245 -6.263 -6.520 -0.257

MO for Am7a Am7b Difference Am7a/ Am7b

258/259 -5.999 -5.788 0.211

258/244 -5.999 -6.645 -0.646

255/250 -6.237 -6.359 -0.122

255/248 -6.237 -6.439 -0.202

The lowest energy in table 6.21 was found with Pa7b (MO 243) with an energy of -6.841 eV. This was the same for Pa6b, where the lowest MO energy across this actinide series was the stabilised red-labelled MO 258 (table 6.17). As such, this was used as the energy to which all the other MOs were made relative to, in figure 6.21.

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Fig.6.21. MO energy levels for complex An7 by energies relative to MO 243 in Pa7b (eV) for the a form (left) and b form (right) for each M centre of 7. Top x-axis is the total energy difference (eV) of each MO energy change from the a and b forms of each M7 complex.

All complexes of 7 showed either splits of or multiple green-labelled MOs when changing from the a to b forms. Similar to the MO diagram in figure 6.11, Th7 shows green-labelled MOs which split into just one green and two black- labelled MOs in Th7b, indicating the π-orbitals in the phenyl rings being in approximate degeneracy with the Ni-alkynyl interactions in Th7a, and these same contributions being in separate MOs in Th7b (labelled in black). In figure 6.11 however, these black-labelled MOs were less stable than the green-labelled MOs in Th7a, whereas in figure 6.21, both the black and the green-labelled MOs were all more stable than the green-labelled MOs in Th7a. This difference was most likely down to the different functionals used (PBE0 in figure 6.11, and PBE in figure 6.21), nevertheless, the total energy difference of the MOs between

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Bimetallic L alkyl and alkynyl complexes

Th7a and Th7b in figure 6.21 showed a value of 0.896 eV in favour of b, much larger than the 0.504 eV found from figure 6.11, although still in qualitative agreement with the total MO differences showing a more favourable b form. As with 6, these MO differences were compared with the ΔH298 values in figure 6.22.

Fig.6.22. Absolute total MO energy differences from figure 6.23 against absolute total enthalpy differences from table 6.18. Labels for each metal centre in the L2- ligand.

As with figure 6.17, there is little correlation between the MO and enthalpy energy differences between the a and b forms of 7. As such, the f-orbital contributions in the SOMOs of Pa7 – Am7 were analysed.

Table 6.22. SOMO energies and their difference between the a and b forms of open-shell An7 complexes, as well as percentage of f-orbital contribution from each actinide.

An SOMO for An7a f-orbital An7b f-orbital Energy centre An7a/ An7b (eV) contribution (eV) contribution difference (eV) (%) (%) (An7b – An7a) Pa 268/268 -3.455 75 -3.036 85 0.419

U 269/268 -3.656 93 -3.657 91 -0.002

Np 270/268 -3.952 18 -4.019 75 -0.067

Pu 269/268 -4.116 40 -4.226 36 -0.110

Am 269/269 -4.200 58 -4.240 71 -0.040

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Bimetallic L alkyl and alkynyl complexes

In contrast to 6, all open-shell 7 complexes showed SOMO energy preferences for the b form, with the exception of Pa7 only. Also, whilst Np7a and Am7a showed a lot less f-orbital contribution from the actinide centres, as was found with Np6a and Am6a (table 6.18), Pu7a and Pu7b also showed significantly less contribution from a Pu f-orbital. As with An6, the SOMO energy differences from table 6.22 examined in isolation were combined with the MO energy differences in table 6.21 and are tabulated table 6.23.

Table 6.23. Total energy differences (eV) between An7a and An7b for various combinations of MOs and SOMOs.

An Total difference in “red” Total difference in “red” and SOMO energies and “green” MO “green” MO energies plus (table 6.22) energies (table 6.21) SOMO energies.

Pa -0.630 -0.211 0.419

U -0.801 -0.803 -0.002

Np -0.996 -1.063 -0.067

Pu -0.582 -0.692 -0.110

Am -0.758 -0.798 -0.040

These energy differences were then correlated against the ΔH298 values from table 6.20, and are shown in figure 6.23 below.

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Fig.6.23. Total MO energy differences (top), MO + SOMO energy differences (middle) and SOMO energy differences (bottom) against enthalpy differences between An7a and An7b.

As is quite clear from this figure, none of the orbital energy differences correlated at all with the ΔH298 values from table 6.20, with even the highest R2 value (for MO energy differences vs ΔH298) only being 0.041. From this, it is

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perhaps now more apparent that the high R2 value from figure 6.19 – for the

SOMO energy differences vs ΔH298 – was merely coincidental, and whilst the orbital energies and their make-up can explain to some extent the energetic preferences for the b form over the a form, the numbers alone of these energies cannot give much insight into the extent by which one form is more stable than the other.

A summary of these findings for complexes 6 and 7 are discussed at the end of the next section.

6.6. Conclusions and future work

Overall, whilst the original motives for modelling the reaction energies of 1 → 3/4/5 (trying to find possible synthetic targets based on changes to the M+ cation centre) were problematic, as focus became more concerned with the differences in the geometries of 1 compared to experiment, and the reaction of 1 → 3/4/5 appearing to be unfavourable according to computational models, this nevertheless leaves scope for further studies of these families of complexes to try and obtain more comparable results with experiment. As was mentioned at the end of section 6.4, the differences in geometries with respect to the Li+ ion in 1 could have been down to the fact that these were modelled in the gas phase or in a PCM model, instead of taking into account potential crystal packing effects on this complex resulting in the geometries observed with experimental data. This is the only complex in this thesis where this has been a consideration, and modelling 1 as a crystal rather than as in a gas phase or PCM model is worth investigating for future studies to see if this geometry difference between experiment and computation is resolved. The thermal correction values for the reaction of Li1 → 3/4/5 (see table 6.4) were also found to be problematic with the large difference in enthalpy and Gibbs energy differences. It could be that the model reactions were missing something pertinent to the experimentally- characterised reactions, again, potentially arising from the fact the complexes were modelled in the gas phase or in a PCM model. Unfortunately, due to more time constraints, these possibilities could not be investigated further for this thesis, but they of course leave open possible avenues of research for the future.

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Bimetallic L alkyl and alkynyl complexes

For complexes 6 and 7, analysis of Th6 and Th7 complexes showed promising results explaining why the b forms are more readily synthesised than a, based on analysis of their respective MOs and comparing them to thermal energy differences. Whilst this explanation did not fit quite as well as was hoped for a range of actinide centres in 6 and 7, the general MO picture found with Th6 and Th7 appeared to largely hold. However, with the open-shell actinide complexes showing smaller thermal energy differences between the a and b forms, it is reasonable to suggest that attempting to synthesise these complexes – if possible at all – may result in a mixture of both the a and b forms rather than a clear preference of one product over the other.

Based on the fact that the qualitative agreements of MO energies and thermal energies showing preferences for the b form for both Th6 and Th7 does not translate into a quantitative agreement for the rest of the actinide series, when attempting to correlate these two different types of energies, it is worth considering that the effect of having open-shell actinide centres may be the underlying cause behind this lack of correlation. It has already been demonstrated that the addition of unpaired f-electrons further complicates the MO energy differences in An6 and An7 (tables 6.19 and 6.22) and that in some cases the SOMO energies are more stabilised in a rather than b, despite overall the b forms being more thermodynamically stable. Initially, having progressively more open-shell complexes was due to wanting to find trends for 6 and 7 when having actinide centres other than thorium that were, like in Th6 and Th7, all in the 4+ oxidation state. Considering this did not create any trends, it is logical to consider next that if all the An6 and An7 complexes remained closed-shell across the actinide series – therefore keeping the complexes’ multiplicities the same as Th6 and Th7 whilst instead changing the oxidation state for each actinide centre – then this might show some better correlations. The problem arising from this approach however would be that except for Th6 and Th7, the rest of An6/7 would be charged cationic complexes. What effect this would have on the energetic preferences of b and on their MO energies has not been investigated here, and for now remains a matter of speculation. Trying to model Hf6/7 and Ce6/7 went some way into keeping the systems closed-shell, whilst also not having charged species, however it was seen that these 246

Bimetallic L alkyl and alkynyl complexes

unfortunately did not work either by having radically different geometries or failing to converge the SCF for both PBE and PBE0.

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References

1. M. Suvova, K. T. P. O'Brien, J. H. Farnaby, N. Kaltsoyannis and P. L. Arnold, Organometallics, 2017, 36, 4669. 2. C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158. 3. S. Miertuš, E. Scrocco and J. Tomasi, Chem. Phys., 1981, 55, 117. 4. S. Miertuš and J. Tomasi, Chem. Phys., 1982, 65, 239. 5. M. Cossi, V. Barone, R. Cammi, and J. Tomasi, Chem. Phys. Lett., 1996, 255, 327. 6. E. Cancès, B. Mennucci and J. Tomasi, J. Chem. Phys., 1997, 107, 3032. 7. J. L. Pascual-Ahuir, E. Silla and I. Tuñón, J. Comp. Chem., 1994, 15, 1127. 8. J. Tomasi, B. Mennucci and R. Cammi, Chem. Rev., 2005, 105, 2999. 9. R. Improta, V. Barone, G. Scalmani, and M. J. Frisch, J. Chem. Phys., 2006, 125, 1. 10. R. Improta, G. Scalmani, M. J. Frisch and V. Barone, J. Chem. Phys., 2007, 127, 1. 11. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 154104. 12. J. M. Tao, J. P. Perdew, V. N. Staroverov and G. E. Scuseria, Phys. Rev. Lett., 2003, 91, 146401. 13. Y. Tang, S. Zhao, B. Long, J. C. Liu and J. Li, J. Phys. Chem. C., 2016, 120, 17514. 14. M. A. Denecke, D. Bublitz, J. I. Kim, H. Moll and I. Farkes, J. Synchrotron Rad., 1999, 6, 394. 15. M. G. Barker and I. C. Alexander, Dalton Trans., 1974, 0, 2166. 16. M. Pajek, A. P. Kobzev, R. Sandrik, A. V. Skrypnik, R. A. Ilkhamov, S. H. Khusmurodov and G. Lapicki, Phys. Rev. A., 1990, 42, 261.

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Chapter 7. Overall conclusions and future work

Throughout this thesis it has been demonstrated that computational chemistry techniques have helped to better understand a large family of actinide and metal complexes adopting the novel trans-calix[2]benzene[2]pyrrolide ligand. With KS-DFT being the main method used, a variety of computational techniques were able to give insights into the chemistry of these systems with regards to bond strengths, orbital composition, relative covalency, aromaticity and reaction energies. The main findings from each results chapter and suggestions for future work are presented in this concluding chapter.

7.1. Geometry optimisations and electronic structures

Having adopted the PBE0 functional for the set of [LAnX]n+ complexes, a variety of partitioning techniques to probe the charge differences across the An-X bonds were adopted. These were the Mulliken population analysis (MPA); Hirshfeld population analysis (HPA); natural population analysis (NPA), and the derived natural bond orbital (NBO) analysis from this; and the quantum theory of atoms in molecules (QTAIM).

Particular attention focussed on the MPA and NBO methods. The former to investigate the actinide contributions to the KS-MOs, the latter to investigate the actinide contributions to the NBOs and see if this could describe relative covalency across the An-X bond. The QTAIM analysis was also used extensively to probe the covalency of these An-X bonds. It was found that across the X ligand series, actinide orbital contributions to the An-X decreased according to NBO data, and therefore suggested increasing ionicity, whereas according to the QTAIM metrics, this bond increased in relative covalency across the X ligand series.

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Overall conclusions and future work

Fixing the An-X bond length, and using these analyses to compare with analogous transition metal complexes of [LMX]n+, showed that the QTAIM metrics were far more sensitive to changes in bond length, whereas no major differences were found with the NBO data. Based on these findings, it is more likely that the QTAIM is a more reliable method for probing the character of such An-X bonds, based on the fact the QTAIM results changed so dramatically when altering the bond lengths, and that one might expect increased levels of electron density from both actinide centre and X ligand atom if this bond length descreases, which they indeed did across the series.

This increase in electron density across the An-X bond was further supported by the NICS values representing the spatial aromaticity between the Th(IV) centres and the arene ring in L2- as a function of X ligand. Being able to accurately derive the isotropy for the open-shell LUIIIX and LThIIIX complexes, so as to obtain NICS values for these complexes as well, would be the next logical step in future work in order to continue this particular means of investigating the change in aromaticity of the L2- ligand in this set of [LAnX]n+ complexes.

It would also be of interest, for future considerations, to simplify the complexes so that NBO and QTAIM comparisons between the actinide complexes and transition metal complexes are more direct for the M-X bond. This is because, as mentioned in chapter 4.6.1, the transition metal complexes of [LMX]n+ did not adopt the bis-arene motif with L2-, and instead had to be fixed in the analogous actinide-based geometries. This simplification could take the form of a system more akin to the (benzene)chromium tricarbonyl1 structure, where one of the CO groups is replaced with an X ligand. Of course, this will no longer be an analysis of the target complexes which have the L2- ligand. Nevertheless, it could still be an insightful set of results to probe the behaviour of this series of X ligands when bonded to either a transition metal or an actinide, and when comparing the results of the two computational methods of NBO and QTAIM analysis.

7.2. The strength of the An-X interactions

Chapter 5 revealed that the linear relationships expected and found with the An- X bond separations and their associated QTAIM metrics discussed in chapter 4,

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Overall conclusions and future work

did not necessarily translate into progressively stronger An-X bonds from BH4 across to OPh. As later discussed and published in Dalton Transactions2, trends with the QTAIM metrics and bond strength only started to be found using the EDA technique and drastically simplifying the X ligand series so that the ligating X-atoms were all in similar chemical environments, as has been done elsewhere in the literature3. The uranium-based complexes proved problematic for this particular analysis, however, and so more sophisticated methods of the EDA which are better suited for more open-shell systems – such as the ALMO-EDA scheme4 and CSOV5 method (see chapter 2.2.3) – are worth investigating.

Furthermore, for the original set of X ligands (BH4, BO2C2H4, CH3, N(SiH3)2 and OPh), a simple but effective measure of bond strength would be to investigate the wavenumbers of the vibrational modes for the An-X bonds. This was not considered at the time as focus was more on the bond energies and QTAIM metrics, however, seeing as such wavenumbers are computationally cheaper than the more “aggressive” method of physically breaking the bond and calculating this energy, it will not be so much of an ordeal for future studies. Indeed, such wavenumbers could be compared with the already-available QTAIM metrics as well, as well as seeing if they correlate with the heterolytic and homolytic bond-cleavage energies.

7.3. Bimetallic L2-/4- alkyl and alkynyl complexes

The results in chapter 6 proved to be the most problematic and yet at the same time, perhaps some of the more interesting of this thesis. Problematic because, as has been discussed, the computed geometry of the first complex studied – Li[LThMe] (1) – did not match that of experiment with regards the Li+ ion residing more-or-less centrally in the bis-arene pocket of L4-. These problems were further compounded when modelling a whole series of M[LThMe] (M = Li, Na, K, Cs and Rb) and the reaction energies of these complexes forming

LTh(CCR’)2 (R’ = SiH3 (3), SiMe3 (4), and SiiPr3 (5)), where enthalpy and Gibbs values were quite varied, as well as all computed reaction being apparently energetically unfavourable. Similar problems with the reaction energies persisted when modelling different functionals, basis sets, and incorporating PCM models. As was already suggested, future work could focus on remodelling

251

Overall conclusions and future work these complexes in the solid state to first of all address the problem of the geometry inconsistency between model and experiment; and second of all to redress the reaction energies in table 6.3 and 6.4 of chapter 6.4.

Nevertheless, what was interesting about the results in chapter 6 was the indication that the relative stability of particular MOs in the complex

[LTh(CCSiMe3)2][MPR”2] (R” = Cy3 (6/6’), Ph (7/7’); M = Ni (6/7); Pt (6’/7’)) dictated whether or not the Th(IV) centre bonded to L2- in the η6:κ1: η6:κ1 fashion (labelled the ‘a’ form) or the η5:η5 fashion (‘b’ form). The relative stability of these Ni- and Pt-based MOs in the b forms compared to the a forms qualitatively matched the thermal stabilities found with b over a. The results from these sections (chapters 6.5.1 and 6.5.2) were published in Organometallics6 as a joint experimental-computational study, since it was not known why the b form of 6 and 7 was more readily obtained synthetically.

The sections afterwards (chapters 6.5.3 and 6.5.4) attempted to find similar results and patterns of the MO energies and thermal energies, with the rest of the actinide series in place of Th(IV), up to Am(IV). This, however, did not prove as successful, as the open-shell actinide centres naturally had a more complex electronic structure, and therefore SOMOs of unpaired electrons appeared to contribute to the stability of the b form over the a forms quite significantly as well as the analogous Ni-based MOs fond in Th6 and Th7.

It was suggested that to keep the series of complexes closed-shell, modelling 6 and 7 with different actinide centres would necessitate a series with various oxidation states of the actinides. It would be very interesting to see how changing this parameter affects the MOs in 6 and 7, and whether or not qualitative correlations can be found between MO energies and thermal stabilities of the a and b forms across the series.

7.4. Concluding remarks

There were two main objectives set out at the start of this thesis (chapter 1.1), the first of which concerning increasing the electronegativity of the X ligand in [LAnX]n+ complexes, and how covalency and ionicity can be described in such complexes by various computational methods. From this, the notion of being able

252

Overall conclusions and future work to model and predict relative An-X bond strengths for a series of different X ligands using the QTAIM method, rather than the computationally more expensive EDA approach, was investigated and produced promising results.

The second objective outlined in chapter 1.1 was more acutely concerned with complimenting experimental data to help find potential synthetic targets for an array of bimetallic organoactinide complexes, still incorporating the L2/4- ligand, but with additional alkali- or transition-metal centres. The use of computational modelling of such systems was also hoped to explain why particular conformations of two complexes were more readily synthesised than another conformation.

This second objective was only partly met, since the ability to understand the reaction energies and therefore propose new synthetic targets was fraught with problems, as has been discussed both in this chapter and at the end of chapter 6. Some of the objective was met however, with regards to explaining the conformational preference of a couple of particular complexes, and from these results there is much more scope for future research.

In summary, this thesis has demonstrated the need and appreciation for using different computational techniques to investigate bonding properties of chemical systems, particularly when actinides are involved. In addition to this, it has demonstrated quite clearly that the debate over covalency in the actinides is far from over. Furthermore, being able to complement experimental data and help with the understanding of these real-life complexes is a testament to the fact that computational studies do not necessarily have to be in the domain of pure theoretical chemistry, and can indeed be a useful tool for experimentalists.

Finally, having had work in this thesis published as a stand-alone computational study2 and as a study in conjunction with experiment6, this work can hopefully be of some contribution to the fascinating and ever-growing field of computational actinide chemistry.

253

References

1. P. Corradini and G. Allegra, J. Am. Chem. Soc., 1959, 81, 2271-2272. 2. K. T. P. O’Brien and N. Kaltsoyannis, Dalton Trans., 2017, 46, 760. 3. A. R. E. Mountain and N. Kaltsoyannis, Dalton Trans., 2013, 42, 13477. 4. R. Z. Khaliullin, E. A. Cobar, R. C. Lochan, A. T. Bell and M. Head-Gordon, J. Chem. Phys. A., 2007, 111, 873. 5. P. S. Bagus, K. Hermann and C. W. Bauschlicher, J. Chem. Phys., 1984, 80, 4370. 6. M. Suvova, K. T. P. O’Brien, J. H. Farnaby, N. Kaltsoyannis and P. L. Arnold, Organometallics, 2017, 36, 4669.

254

Appendix

255

1. PBE0 Cartesian coordinates (Å) and SCF energies (Hartrees) of all complexes studied in chapter 4.

[LThIVX]+ complexes. C -3.139659 0.518549 -0.763243 C -2.845535 0.341294 -1.873985 C -4.128662 -0.021097 -1.534393 C -1.365863 3.401754 -0.539491

[LThIV(µ-H)3BH]+. SCF energy = - H -5.087981 0.430037 -1.745269 C 0.000000 2.891734 -0.211387 C -3.663998 -1.279281 -1.986599 C 0.837463 2.428540 -1.244969 1469.95841 H -4.191911 -1.975938 -2.622324 H 0.506445 2.534066 -2.274221 C -2.406781 -1.446351 -1.481903 C 2.047810 1.798759 -0.972301 C -3.165537 0.296438 -0.683179 C -3.168676 1.813185 -0.011995 C 2.439001 1.642606 0.368696 C -4.107254 -0.280408 -1.485041 C -1.778009 2.289660 0.254161 H 3.367336 1.125902 0.589597 H -5.099953 0.103012 -1.674509 C -0.873998 2.400740 -0.817486 C 1.638736 2.117627 1.396297 C -3.537351 -1.463917 -2.011813 H -1.236080 2.226993 -1.826662 H 1.953446 2.010215 2.427574 H -4.002217 -2.162939 -2.692494 C 0.475442 2.662917 -0.607273 C 0.413600 2.730004 1.105870 C -2.267481 -1.548496 -1.519877 C 0.927642 2.853246 0.709623 H -0.232501 3.040742 1.919636 C -3.285235 1.568114 0.092058 H 1.983472 3.033119 0.884754 C 2.845326 1.146687 -2.053731 C -1.944198 2.209863 0.257946 C 0.042024 2.792747 1.771814 C 2.845535 -0.341294 -1.873985 C -1.067880 2.286418 -0.843520 H 0.395607 2.934617 2.785385 C 3.710859 -1.247190 -2.424628 H -1.424444 1.974585 -1.820282 C -1.305331 2.488065 1.547522 H 4.562125 -1.015445 -3.049109 C 0.247522 2.697039 -0.689159 H -1.978038 2.385445 2.391840 C 3.271557 -2.530731 -2.031070 C 0.694103 3.081583 0.588659 C 1.466005 2.585045 -1.721525 H 3.723059 -3.478624 -2.287744 H 1.731412 3.373073 0.719325 C 2.407221 1.446580 -1.481385 C 2.166144 -2.351574 -1.245219 C -0.181351 3.103477 1.655235 C 3.663941 1.278751 -1.987050 C 1.365863 -3.401754 -0.539491 H 0.159976 3.423704 2.633608 H 4.191713 1.975003 -2.623334 C 0.000000 -2.891734 -0.211387 C -1.493247 2.646134 1.495164 C 4.128347 0.020450 -1.534891 C -0.837463 -2.428540 -1.244969 H -2.155064 2.599576 2.353750 H 5.087289 -0.431199 -1.746384 H -0.506445 -2.534066 -2.274221 C 1.228618 2.604997 -1.808470 C 3.139756 -0.518459 -0.762708 C -2.047810 -1.798759 -0.972301 C 2.274502 1.591326 -1.477254 C 3.168824 -1.812679 -0.010803 C -2.439001 -1.642606 0.368696 C 3.554274 1.532368 -1.947418 C 1.778137 -2.289619 0.254547 H -3.367336 -1.125902 0.589597 H 4.024751 2.254442 -2.599608 C 0.874562 -2.400353 -0.817496 C -1.638736 -2.117627 1.396297 C 4.124418 0.338291 -1.446247 H 1.237046 -2.226252 -1.826472 H -1.953446 -2.010215 2.427574 H 5.123336 -0.031949 -1.629095 C -0.474963 -2.662591 -0.607907 C -0.413600 -2.730004 1.105870 C 3.172360 -0.270237 -0.680693 C -0.927699 -2.853301 0.708752 H 0.232501 -3.040742 1.919636 C 3.291249 -1.564719 0.057647 H -1.983618 -3.033133 0.883397 C -2.845326 -1.146687 -2.053731 C 1.946888 -2.199141 0.215198 C -0.042498 -2.793197 1.771316 N -1.871624 0.996103 -1.126288 C 1.075451 -2.265984 -0.888122 H -0.396503 -2.935365 2.784700 N 1.871624 -0.996103 -1.126288 H 1.437090 -1.953403 -1.862698 C 1.304955 -2.488497 1.547656 Th 0.000000 0.000000 0.007995 C -0.245159 -2.667788 -0.738540 H 1.977327 -2.386080 2.392269 H -3.877532 -1.515162 -2.025669 C -0.698344 -3.046480 0.536507 C -1.465118 -2.584304 -1.722534 H -2.435143 -1.434451 -3.029246 H -1.739176 -3.326037 0.664573 N -2.043129 -0.342613 -0.706551 H -1.857130 3.731506 0.383875 C 0.169915 -3.065090 1.611672 N 2.043658 0.343243 -0.705398 H -1.284196 4.285530 -1.183447 H -0.179851 -3.376221 2.589406 Th -0.000056 -0.000023 0.492679 H 2.435143 1.434451 -3.029246 C 1.485604 -2.623630 1.455168 H -2.035801 -3.518108 -1.781334 H 3.877532 1.515162 -2.025669 H 2.146977 -2.588495 2.313774 H -0.933367 -2.478505 -2.675895 H 1.284196 -4.285530 -1.183447 C -1.224652 -2.564221 -1.858379 H -3.707461 1.719499 0.938532 H 1.857130 -3.731506 0.383875 N -1.998895 -0.470195 -0.671494 H -3.709059 2.560692 -0.605153 C -0.552257 0.527855 4.860336 N 1.999139 0.486492 -0.666135 H 0.934626 2.480106 -2.675183 C 0.552257 -0.527855 4.860336 Th 0.000923 -0.015382 0.567971 H 2.036976 3.518735 -1.779406 H -1.511991 0.134754 5.211656 H -1.706877 -3.533429 -2.027496 H 3.710070 -2.560194 -0.603149 H -0.300918 1.413110 5.449173 H -0.695609 -2.308419 -2.784592 H 3.706763 -1.718273 0.940143 H 0.300918 -1.413110 5.449173 H -3.734160 1.411786 1.081038 B -0.000974 -0.000534 3.330130 H 1.511991 -0.134754 5.211656 H -3.957698 2.246181 -0.447341 H 0.998096 0.188699 2.575855 B 0.000000 0.000000 2.705707 H 0.701046 2.354490 -2.737103 H -0.194378 0.995139 3.976551 O -0.689896 0.904325 3.477675 H 1.708227 3.576726 -1.969907 H -0.999522 -0.189641 2.575243 O 0.689896 -0.904325 3.477675 H 3.955101 -2.231980 -0.505355 H 0.192150 -0.996265 3.976563 H 3.747909 -1.438125 1.047230 B -0.047297 -0.164325 3.168151 [LThIVMe]+. SCF energy = - H -0.045878 -0.267857 4.357572 [LThIVBO2C2H4]+. SCF energy = - H 1.058000 -0.443721 2.667182 1482.60413 H -0.879495 -0.907964 2.620141 1696.53211 H -0.304997 0.969257 2.782921 C 3.186029 -0.438175 -0.711087 C -2.166144 2.351574 -1.245219 C 4.163727 0.122762 -1.485309 C -3.271557 2.530731 -2.031070 H 5.129824 -0.310342 -1.702977 IV + [LTh (µ-H)2BH2] . SCF energy = - H -3.723059 3.478624 -2.287744 C 3.669104 1.366948 -1.937910 C -3.710859 1.247190 -2.424628 H 4.177588 2.074722 -2.577260 1469.96141 H -4.562125 1.015445 -3.049109 C 2.405509 1.502290 -1.432637 256

Appendix

C 3.227723 -1.751043 0.006128 C -1.362318 -2.045791 -2.654147 C -2.792469 -1.544544 1.458749 C 1.843148 -2.264963 0.238888 C -2.306250 -0.974982 -2.208517 C -2.374604 -2.795072 0.747305 C 0.944092 -2.360006 -0.839478 C -3.542994 -0.694487 -2.719406 C -0.907748 -2.781054 0.463117 H 1.304400 -2.143174 -1.840872 H -4.044909 -1.241420 -3.504982 C 0.000000 -2.573182 1.517716 C -0.398828 -2.661551 -0.641599 C -4.016546 0.452726 -2.044299 H -0.382064 -2.517363 2.532876 C -0.849473 -2.904574 0.667410 H -4.959464 0.957296 -2.201524 C 1.353310 -2.369808 1.280100 H -1.901911 -3.112249 0.832120 C -3.054642 0.810597 -1.140885 C 1.819349 -2.414042 -0.046670 C 0.034266 -2.869017 1.731057 C -3.101751 1.949991 -0.171870 H 2.871411 -2.230979 -0.240891 H -0.317710 -3.066202 2.737019 C -1.720194 2.366010 0.215834 C 0.948460 -2.678438 -1.088679 C 1.373390 -2.530870 1.519738 C -0.762617 2.601517 -0.788626 H 1.312642 -2.710138 -2.109727 H 2.050924 -2.456349 2.363760 H -1.077174 2.571486 -1.827313 C -0.416651 -2.839436 -0.836795 C -1.391083 -2.577486 -1.754727 C 0.575410 2.800991 -0.480630 H -1.102321 -2.985124 -1.665211 C -2.371257 -1.477167 -1.489315 C 0.964667 2.803060 0.871528 C 2.281357 -1.954412 2.373660 C -3.629081 -1.336404 -2.007171 H 2.014105 2.929865 1.117292 N 2.057460 0.364434 1.382864 H -4.130361 -2.037542 -2.659377 C 0.021012 2.652527 1.871060 N -2.057460 -0.364434 1.382864 C -4.129867 -0.097706 -1.545814 H 0.322375 2.680354 2.912394 Th 0.000000 0.000000 0.158171 H -5.094312 0.336487 -1.768534 C -1.315593 2.412377 1.543891 H 3.137059 -2.638031 2.416098 C -3.161811 0.455031 -0.753911 H -2.041223 2.239655 2.332016 H 1.764265 -2.037789 3.337415 C -3.213467 1.756063 -0.015924 C 1.617169 2.859002 -1.547271 H 2.922222 2.930134 -0.193510 C -1.832276 2.266523 0.244224 N 2.113201 0.467392 -0.892726 H 2.619349 3.660449 1.375101 C -0.919972 2.379357 -0.822109 N -1.970646 -0.060601 -1.211814 H -1.764265 2.037789 3.337415 H -1.268152 2.178846 -1.831137 Th 0.000318 -0.033922 0.189003 H -3.137059 2.638031 2.416098 C 0.420273 2.675337 -0.602823 H 2.204448 3.778883 -1.447559 H -2.619349 -3.660449 1.375101 C 0.854598 2.900428 0.715348 H 1.128606 2.901595 -2.528496 H -2.922222 -2.930134 -0.193510 H 1.904537 3.107636 0.895615 H 3.636989 -1.919188 0.424219 O 0.000000 0.000000 -1.947826 C -0.042105 2.849653 1.766408 H 3.754470 -2.425405 -1.254270 C 0.000000 0.000000 -3.302078 H 0.298473 3.037997 2.778026 H -0.774417 -1.731968 -3.525417 C -1.198518 -0.135393 -3.994776 C -1.378169 2.509496 1.535061 H -1.938245 -2.925651 -2.962676 C 1.198518 0.135393 -3.994776 H -2.063041 2.413885 2.371091 H -3.624014 2.792953 -0.640703 C -1.191230 -0.134582 -5.380883 C 1.428305 2.604407 -1.701857 H -3.669633 1.697226 0.732222 H -2.126903 -0.241260 -3.442283 N 2.074391 0.397499 -0.651277 Si -1.792891 -0.860504 3.057402 C 1.191230 0.134582 -5.380883 N -2.050334 -0.380785 -0.692250 H -1.847915 -2.229590 3.648523 H 2.126903 0.241260 -3.442283 Th -0.002436 -0.000144 0.510370 H -2.244940 0.139922 4.068514 C 0.000000 0.000000 -6.078514 H 1.967898 3.555841 -1.773643 H -2.725925 -0.806630 1.878894 H -2.127173 -0.240593 -5.919291 H 0.912471 2.462247 -2.659388 Si 1.285780 -0.377880 3.208702 H 2.127173 0.240593 -5.919291 H 3.751117 -1.678824 0.967503 H 1.366661 0.699082 4.236490 H 0.000000 0.000000 -7.162530 H 3.791574 -2.470256 -0.600121 H 1.761106 -1.668037 3.785763 H -0.860709 -2.426229 -2.702888 H 2.207263 -0.005900 2.060678 H -1.930600 -3.527366 -1.844548 N -0.234208 -0.481068 2.403996 LThIIIX complexes. H -3.769228 2.485557 -0.617373 H -3.749688 1.667258 0.936930 LThIII(µ-H)2BH2. SCF energy = - C -0.150701 -0.083954 2.979075 [LThIVOPh]+. SCF energy = - H -1.092265 -0.611121 3.213006 1470.13391 1749.43247 H 0.646363 -0.662351 3.463692 H -0.198773 0.865223 3.520729 C -3.127942 0.557746 -0.831643 C 2.792469 1.544544 1.458749 C -4.140865 0.043448 -1.599903 C 3.914805 1.360497 2.218233 H -5.081586 0.528237 -1.821987 H 4.662122 2.109142 2.440691 [LThIVN(SiH3)2]+. SCF energy = - C -3.721257 -1.239680 -2.020974 C 3.910474 0.012428 2.641869 H -4.268980 -1.936270 -2.641194 2079.88776 H 4.647239 -0.475954 3.263956 C -2.467483 -1.434734 -1.501052 C 2.778158 -0.562076 2.133951 C -3.072741 1.858222 -0.094918 C 3.201504 -0.387352 -1.038006 C 2.374604 2.795072 0.747305 C -1.654772 2.234846 0.191268 C 4.244919 0.262172 -1.638050 C 0.907748 2.781054 0.463117 C -0.729807 2.381920 -0.892186 H 5.208824 -0.166237 -1.874245 C 0.000000 2.573182 1.517716 H -1.094910 2.268513 -1.908605 C 3.820357 1.587117 -1.882138 H 0.382064 2.517363 2.532876 C 0.617868 2.553728 -0.667020 H 4.389019 2.377276 -2.351690 C -1.353310 2.369808 1.280100 C 1.094187 2.617558 0.678432 C 2.531380 1.680888 -1.434800 C -1.819349 2.414042 -0.046670 H 2.156070 2.717133 0.863442 C 3.170617 -1.805902 -0.562492 H -2.871411 2.230979 -0.240891 C 0.158166 2.713493 1.736620 C 1.764699 -2.307124 -0.501406 C -0.948460 2.678438 -1.088679 H 0.505372 2.861236 2.751291 C 0.920793 -2.134030 -1.613698 H -1.312642 2.710138 -2.109727 C -1.185274 2.516951 1.499839 H 1.339417 -1.727617 -2.529195 C 0.416651 2.839436 -0.836795 H -1.880307 2.502793 2.332973 C -0.437830 -2.406696 -1.540028 H 1.102321 2.985124 -1.665211 C 1.612002 2.461488 -1.779143 C -0.965097 -2.899966 -0.332379 C -2.281357 1.954412 2.373660 C 2.497755 1.275110 -1.559639 H -2.031905 -3.086089 -0.260230 C -2.778158 0.562076 2.133951 C 3.755663 1.041313 -2.054796 C -0.133102 -3.148182 0.743722 C -3.910474 -0.012428 2.641869 H 4.320640 1.701665 -2.698196 H -0.539992 -3.549465 1.665350 H -4.647239 0.475954 3.263956 C 4.151834 -0.226731 -1.572704 C 1.225525 -2.832819 0.666472 C -3.914805 -1.360497 2.218233 H 5.088424 -0.734150 -1.759724 H 1.864272 -2.982018 1.530866 H -4.662122 -2.109142 2.440691 C 3.121042 -0.693535 -0.795917 257

Appendix

C 3.083956 -1.953820 0.011003 H -0.893764 -3.123408 -1.453783 H 3.614189 -1.898723 0.823270 C 1.673669 -2.364186 0.288438 C 3.341075 -1.149592 1.204629 H 3.542117 -2.666272 -0.750533 C 0.766443 -2.448794 -0.778795 N 1.998142 0.959381 1.075195 H -1.154609 -2.412433 -2.708260 H 1.130735 -2.278535 -1.787171 N -1.998142 -0.959381 1.075195 H -2.293056 -3.364805 -1.759001 C -0.584234 -2.685863 -0.569744 Th 0.000000 0.000000 -0.042413 H -3.556905 2.800631 -0.617206 C -1.040640 -2.862230 0.744487 H 4.209274 -1.071594 0.536959 H -3.611856 1.948682 0.918590 H -2.100897 -3.012710 0.919439 H 3.633628 -1.799311 2.036904 C -0.117393 0.055272 3.046010 C -0.156011 -2.810255 1.805274 H 1.787390 3.959074 0.553479 H -0.270317 -0.891872 3.574256 H -0.512874 -2.925075 2.820780 H 0.856935 3.951407 2.051646 H 0.880769 0.412900 3.361360 C 1.197846 -2.544130 1.580404 H -3.633628 1.799311 2.036904 H -0.838919 0.763250 3.473732 H 1.870913 -2.448622 2.424943 H -4.209274 1.071594 0.536959 C -1.562475 -2.609238 -1.695656 H -0.856935 -3.951407 2.051646

N -2.073970 -0.335974 -0.756037 H -1.787390 -3.959074 0.553479 LThIIIN(SiH3)2. SCF energy = - N 2.078744 0.214205 -0.776826 C 0.737849 0.196798 -4.846155 2080.04932 Th -0.023208 0.135143 0.536171 C -0.737849 -0.196798 -4.846155 H -2.161929 -3.526469 -1.735453 H 1.384264 -0.629957 -5.169499 H -1.013028 -2.548756 -2.644002 H 0.949622 1.066929 -5.474631 C 3.329751 -0.810907 -0.419037 H -3.623711 1.799045 0.853219 H -0.949622 -1.066929 -5.474631 C 4.484931 -0.476122 -1.080504 H -3.572695 2.635057 -0.690230 H -1.384264 0.629957 -5.169499 H 5.448762 -0.951767 -0.960415 H 1.078568 2.399534 -2.736076 B 0.000000 0.000000 -2.694062 C 4.165682 0.605711 -1.930119 H 2.225641 3.370263 -1.812686 O 1.024044 0.508305 -3.482609 H 4.828655 1.122138 -2.611298 H 3.599567 -2.750745 -0.539798 O -1.024044 -0.508305 -3.482609 C 2.828968 0.864356 -1.754356 H 3.616066 -1.840412 0.964398 C 3.137640 -1.861302 0.630099 B 0.004441 -0.042113 3.418626 C 1.690004 -2.185543 0.814935 C 0.923835 -2.718030 -0.253146 H 0.994576 0.174625 2.664060 LThIIIMe. SCF energy = -1482.76330 H -0.200978 0.940996 4.088861 H 1.420324 -2.926387 -1.197295 H -0.996458 -0.251498 2.681788 C -0.447549 -2.829516 -0.173076 C 3.152867 -0.574595 -0.806735 C -1.101839 -2.494942 1.069611 H 0.233268 -1.041504 4.061424 C 4.186328 -0.062277 -1.552087 H -2.177892 -2.588894 1.144053 H 5.115769 -0.564406 -1.783621 C -0.315243 -2.230557 2.202866 C 3.797035 1.237746 -1.945518 H -0.795298 -2.088494 3.165551 LThIIIBO2C2H4. SCF energy = - H 4.359177 1.933807 -2.553596 C 1.045530 -2.037380 2.086835 1696.69507 C 2.541304 1.444204 -1.430251 H 1.636155 -1.769399 2.956241 C 3.059138 -1.902872 -0.124909 C -1.286843 -3.141005 -1.368042 C 1.996192 2.177619 1.730327 C 1.634583 -2.263613 0.158429 C -2.157236 -1.968890 -1.700475 C 2.888997 2.168911 2.773861 C 0.697716 -2.411998 -0.894413 C -3.300713 -1.938032 -2.457691 H 3.095889 2.992571 3.443495 H 1.039987 -2.279194 -1.917796 H -3.773391 -2.785691 -2.934378 C 3.502744 0.896759 2.770582 C -0.651503 -2.561715 -0.650860 C -3.717624 -0.588795 -2.504141 H 4.277399 0.543196 3.437314 C -1.104699 -2.682242 0.712793 H -4.583657 -0.189331 -3.014522 C 2.951699 0.196945 1.725267 H -2.159888 -2.817668 0.912695 C -2.819116 0.132834 -1.757640 C 1.184822 3.323519 1.215772 C -0.150028 -2.795380 1.733564 C -2.887247 1.592289 -1.436225 C 0.000000 2.817288 0.460040 H -0.478600 -2.996505 2.747040 C -1.542950 2.194869 -1.161261 C -1.085356 2.251315 1.167367 C 1.185789 -2.553911 1.489184 C -0.448077 1.855445 -1.969776 H -1.106161 2.288686 2.251134 H 1.901024 -2.565337 2.304575 H -0.610737 1.204786 -2.824135 C -2.202410 1.759574 0.454516 C -1.668186 -2.462252 -1.739391 C 0.833682 2.312709 -1.692609 C -2.155612 1.692989 -0.926851 C -2.538552 -1.263808 -1.521815 C 1.024192 3.148736 -0.585906 H -2.992223 1.256518 -1.463161 C -3.780885 -1.003742 -2.045115 H 2.026888 3.486196 -0.343172 C -1.014312 2.119060 -1.648807 H -4.348402 -1.656440 -2.694170 C -0.054749 3.541226 0.183770 H -1.046616 2.196257 -2.726719 C -4.151787 0.280157 -1.588506 H 0.095721 4.200784 1.031763 C 0.028117 2.742251 -0.921359 H -5.066793 0.813940 -1.807248 C -1.330272 3.056220 -0.093420 H 0.893764 3.123408 -1.453783 C -3.124551 0.729403 -0.795448 H -2.162997 3.332332 0.545499 C -3.341075 1.149592 1.204629 C -3.064368 2.014262 -0.031068 C 1.993385 1.845021 -2.510519 C -2.951699 -0.196945 1.725267 C -1.651457 2.411172 0.256762 N 2.285633 0.005401 -0.816255 C -3.502744 -0.896759 2.770582 C -0.713584 2.457626 -0.788153 N -1.836901 -0.699204 -1.253497 H -4.277399 -0.543196 3.437314 H -1.051387 2.268145 -1.802565 Th 0.034263 -0.139526 0.241139 C -2.888997 -2.168911 2.773861 C 0.630969 2.697240 -0.546463 H 2.618474 2.698045 -2.797192 H -3.095889 -2.992571 3.443495 C 1.053635 2.894647 0.776942 H 1.611742 1.407007 -3.442908 C -1.996192 -2.177619 1.730327 H 2.110497 3.040736 0.975253 H 3.548852 -1.530762 1.593562 C -1.184822 -3.323519 1.215772 C 0.138463 2.885704 1.810549 H 3.707172 -2.759174 0.352201 C 0.000000 -2.817288 0.460040 H 0.469397 3.033254 2.832126 H -0.631576 -3.406086 -2.207647 C 1.085356 -2.251315 1.167367 C -1.210923 2.638039 1.551114 H -1.918911 -4.016587 -1.170559 H 1.106161 -2.288686 2.251134 H -1.918311 2.591080 2.371569 H -3.352545 2.112815 -2.283457 C 2.202410 -1.759574 0.454516 C 1.642079 2.619804 -1.642401 H -3.536592 1.781033 -0.570672 C 2.155612 -1.692989 -0.926851 N 2.122065 0.340226 -0.712663 Si -2.356531 0.966188 2.770361 H 2.992223 -1.256518 -1.463161 N -2.110357 -0.207401 -0.739573 H -2.584629 0.106208 3.977131 C 1.014312 -2.119060 -1.648807 Th 0.016913 -0.149817 0.532692 H -2.770061 2.360335 3.140934 H 1.046616 -2.196257 -2.726719 H 2.239862 3.539002 -1.663772 H -3.272886 0.489717 1.686812 C -0.028117 -2.742251 -0.921359 H 1.120223 2.560773 -2.606597 Si 0.668236 1.341859 3.056008 258

Appendix

H 0.792357 2.803847 3.349525 H 0.000000 0.000000 -7.208882 C -4.156498 0.046565 -1.600186 H 0.936139 0.590250 4.321741 H -5.099714 0.523371 -1.829937 H 1.781641 0.991471 2.077940 C -3.711888 -1.221226 -2.038693 N -0.737037 0.888073 2.198605 LUIIIX complexes. H -4.236779 -1.909643 -2.686958 C -2.464264 -1.408126 -1.495982 C -3.146949 1.850436 -0.051632 LUIII(µ-H3)-BH. SCF energy = - LThIIIOPh. SCF energy = - C -1.739844 2.274864 0.230181 1539.38749 C -0.821095 2.370527 -0.828896 1749.57967 H -1.172397 2.198609 -1.841792 C -3.229309 -0.127702 -0.680737 C 0.527497 2.620260 -0.602223 C 2.843756 1.548779 1.492390 C -4.151412 -1.005099 -1.193139 C 0.966275 2.801714 0.717863 C 3.983812 1.366358 2.234603 H -5.217193 -0.838945 -1.271980 H 2.022655 2.961819 0.905527 H 4.728539 2.119026 2.455503 C -3.431616 -2.147257 -1.603237 C 0.068761 2.745195 1.769680 C 3.991954 0.012456 2.641965 H -3.829649 -3.036238 -2.073605 H 0.412601 2.864689 2.788801 H 4.736316 -0.481607 3.251408 C -2.106806 -1.907927 -1.328710 C -1.278282 2.463732 1.528633 C 2.849926 -0.556256 2.136580 C -3.503141 1.252068 -0.151529 H -1.959675 2.360757 2.365627 C 2.384322 2.794155 0.800056 C -2.239022 1.967398 0.197150 C 1.529698 2.558337 -1.709657 C 0.921066 2.727108 0.492334 C -1.327985 2.325693 -0.811114 C 2.464520 1.408231 -1.495819 C 0.000000 2.539220 1.522851 H -1.592487 2.139770 -1.847387 C 3.712117 1.221172 -2.038536 H 0.361279 2.508784 2.546993 C -0.072944 2.847874 -0.505635 H 4.237103 1.909521 -2.686796 C -1.354610 2.295724 1.264164 C 0.260346 3.057038 0.842866 C 4.156659 -0.046594 -1.599839 C -1.800664 2.355088 -0.083821 H 1.245069 3.440279 1.088097 H 5.099878 -0.523452 -1.829474 H -2.852843 2.192907 -0.294416 C -0.637205 2.739569 1.849416 C 3.161000 -0.556893 -0.803457 C -0.910962 2.586065 -1.106358 H -0.366629 2.891118 2.888014 C 3.146928 -1.850159 -0.051038 H -1.256813 2.606241 -2.133939 C -1.878824 2.177840 1.527945 C 1.739798 -2.274801 0.230390 C 0.465918 2.716267 -0.836255 H -2.563565 1.893032 2.319498 C 0.821340 -2.370453 -0.828935 H 1.169611 2.835188 -1.651689 C 0.970379 3.045376 -1.557570 H 1.172889 -2.198340 -1.841710 C -2.320420 1.938762 2.345464 C 2.082284 2.053468 -1.377609 C -0.527289 -2.620296 -0.602602 C -2.849926 0.556256 2.136580 C 3.317294 2.051111 -1.975751 C -0.966314 -2.802126 0.717329 C -3.991954 -0.012456 2.641965 H 3.702853 2.801132 -2.652606 H -2.022717 -2.962365 0.904753 H -4.736316 0.481607 3.251408 C 3.969615 0.874995 -1.540701 C -0.069035 -2.745821 1.769371 C -3.983812 -1.366358 2.234603 H 4.967804 0.549362 -1.800927 H -0.413214 -2.866107 2.788275 H -4.728539 -2.119026 2.455503 C 3.105425 0.225019 -0.692803 C 1.277976 -2.463984 1.528716 C -2.843756 -1.548779 1.492390 C 3.376260 -1.018369 0.085663 H 1.959220 -2.361117 2.365857 C -2.384322 -2.794155 0.800056 C 2.259111 -2.028418 0.121782 C -1.529320 -2.558067 -1.710142 C -0.921066 -2.727108 0.492334 C 1.217497 -1.996827 -0.808257 N -2.100856 -0.322428 -0.722648 C 0.000000 -2.539220 1.522851 H 1.272188 -1.284362 -1.630357 N 2.100913 0.322518 -0.722645 H -0.361279 -2.508784 2.546993 C 0.148969 -2.895054 -0.753881 U 0.000037 0.000042 0.516033 C 1.354610 -2.295724 1.264164 C 0.156676 -3.877039 0.229764 H -2.102588 -3.492380 -1.747942 C 1.800664 -2.355088 -0.083821 H -0.665622 -4.583165 0.289601 H -0.999981 -2.475270 -2.668136 H 2.852843 -2.192907 -0.294416 C 1.214831 -3.959015 1.122656 H -3.692123 1.775206 0.898055 C 0.910962 -2.586065 -1.106358 H 1.220615 -4.737059 1.879208 H -3.656753 2.620944 -0.643664 H 1.256813 -2.606241 -2.133939 C 2.245835 -3.036171 1.082670 H 1.000458 2.475914 -2.667734 C -0.465918 -2.716267 -0.836255 H 3.047510 -3.087077 1.813258 H 2.103043 3.492621 -1.747075 H -1.169611 -2.835188 -1.651689 C -0.961818 -2.774689 -1.753874 H 3.657153 -2.620750 -0.642603 C 2.320420 -1.938762 2.345464 N -1.953661 -0.667474 -0.736977 H 3.691690 -1.774517 0.898855 N 2.122304 0.371265 1.413319 N 1.926764 0.934172 -0.579668 B -0.001103 -0.000120 3.371146 N -2.122304 -0.371265 1.413319 U -0.088277 0.209211 0.548119 H 0.980378 0.253250 2.624826 Th 0.000000 0.000000 0.170553 H -1.364574 -3.767148 -1.977082 H -0.258872 0.979001 4.034825 H 3.155871 -2.651403 2.361455 H -0.535459 -2.393555 -2.693348 H -0.981762 -0.253646 2.623919 H 1.817940 -2.029314 3.317735 H -4.148532 1.213435 0.734093 H 0.256247 -0.978665 4.035807 H 2.935255 2.961099 -0.134576 H -4.048698 1.830570 -0.908731 H 2.590773 3.662013 1.438753 H 0.504943 2.948090 -2.546364 H -1.817940 2.029314 3.317735 H 1.371593 4.065007 -1.498274 LUIIIBO2C2H4. SCF energy = - H -3.155871 2.651403 2.361455 H 4.269565 -1.492900 -0.339393 H -2.590773 -3.662013 1.438753 H 3.637838 -0.778178 1.126852 1765.94545 H -2.935255 -2.961099 -0.134576 B 0.306424 -0.673279 2.906440 O 0.000000 0.000000 -1.997394 H 0.452462 -1.078734 4.025300 C 2.174914 2.388586 1.280264 C 0.000000 0.000000 -3.328021 H 1.337410 -0.161995 2.431965 C 3.277541 2.587287 2.077237 C -1.198290 -0.115615 -4.037024 H -0.056804 -1.556260 2.110359 H 3.709353 3.541620 2.346896 C 1.198290 0.115615 -4.037024 H -0.569667 0.212618 2.839000 C 3.736098 1.306222 2.454178 C -1.191259 -0.115044 -5.422238 H 4.585931 1.074757 3.082021 H -2.127372 -0.206429 -3.482886 C 2.879706 0.398045 1.877002 C 1.191259 0.115044 -5.422238 C 1.337479 3.410943 0.580565 LUIII(µ-H2)-BH2. SCF energy = - H 2.127372 0.206429 -3.482886 C 0.000000 2.839381 0.230866 C 0.000000 0.000000 -6.124486 1539.39098 C -0.841533 2.350399 1.251702 H -2.130544 -0.206242 -5.959193 H -0.530871 2.460604 2.286043 H 2.130544 0.206242 -5.959193 C -3.160966 0.556951 -0.803702 C -2.044013 1.719173 0.954012 259

Appendix

C -2.406576 1.551810 -0.392355 C -2.454890 -1.418224 -1.502534 C 0.983525 -0.450549 -2.831684 H -3.321821 1.019772 -0.628387 C -3.696833 -1.235691 -2.064249 H 2.044810 -0.331345 -3.023056 C -1.592094 2.032802 -1.407830 H -4.206764 -1.922544 -2.726164 C 0.100125 0.578557 -3.105837 H -1.889355 1.924463 -2.443649 C -4.153953 0.027062 -1.627516 H 0.461807 1.509262 -3.527690 C -0.391140 2.677936 -1.090598 H -5.092743 0.503931 -1.874990 C -1.252481 0.442442 -2.789505 H 0.264417 3.004396 -1.890617 C -3.171593 0.537524 -0.812069 H -1.932801 1.269074 -2.965700 C -2.878960 1.092425 2.023900 C -3.158289 1.840207 -0.077039 C 1.500768 -2.719584 -1.905791 C -2.879706 -0.398045 1.877002 C -1.752662 2.263940 0.218474 N 2.067572 -1.183899 -0.000648 C -3.736098 -1.306222 2.454178 C -0.814148 2.357526 -0.826708 N -2.142360 -0.920325 0.545885 H -4.585931 -1.074757 3.082021 H -1.145924 2.182935 -1.845475 U -0.006206 0.156115 -0.081969 C -3.277541 -2.587287 2.077237 C 0.526869 2.624820 -0.574790 H 2.086449 -3.017835 -2.784033 H -3.709353 -3.541620 2.346896 C 0.940455 2.812939 0.752655 H 0.950808 -3.611177 -1.577799 C -2.174914 -2.388586 1.280264 H 1.992122 2.984147 0.956472 H 3.666209 0.879751 1.647065 C -1.337479 -3.410943 0.580565 C 0.026012 2.750292 1.787859 H 3.625565 -0.403110 2.848345 C 0.000000 -2.839381 0.230866 H 0.353862 2.892341 2.810058 H -1.121331 -2.289255 3.114677 C 0.841533 -2.350399 1.251702 C -1.315392 2.463423 1.522041 H -2.205831 -1.134342 3.879212 H 0.530871 -2.460604 2.286043 H -2.017198 2.365291 2.343375 H -3.671968 -1.619503 -2.326213 C 2.044013 -1.719173 0.954012 C 1.553440 2.579346 -1.660082 H -3.667890 0.099997 -1.956562 C 2.406576 -1.551810 -0.392355 N 2.146232 0.355455 -0.662389 N 0.131165 2.449014 -0.617945 H 3.321821 -1.019772 -0.628387 N -2.112677 -0.338692 -0.716507 Si -1.376992 3.243557 -0.639515 C 1.592094 -2.032802 -1.407830 U -0.008306 0.012020 0.525272 H -1.515173 4.347965 0.366951 H 1.889355 -1.924463 -2.443649 H 2.112294 3.523245 -1.683607 H -1.764032 3.818156 -1.972216 C 0.391140 -2.677936 -1.090598 H 1.045406 2.491730 -2.629187 H -2.411447 2.200613 -0.293630 H -0.264417 -3.004396 -1.890617 H 3.714595 -1.787264 0.915761 Si 1.660285 3.116009 -0.977689 C 2.878960 -1.092425 2.023900 H 3.697517 -2.590279 -0.647723 H 1.784619 3.635753 -2.381283 N 1.908554 1.043332 1.142124 H -0.970014 -2.439676 -2.684817 H 2.073742 4.234336 -0.064638 N -1.908554 -1.043332 1.142124 H -2.054094 -3.493113 -1.784746 H 2.680300 2.020103 -0.822787 U 0.000000 0.000000 -0.022283 H -3.656447 2.605008 -0.686331 H 3.907019 -1.470945 1.961294 H -3.716317 1.784685 0.867036 H 2.491492 -1.398496 3.004066 C -0.159384 -0.085488 3.038191 LUIIIOPh. SCF energy = -1818.83801 H 1.820106 3.770884 -0.337350 H -1.113478 -0.612912 3.226779 H 1.208526 4.286518 1.229396 H 0.614893 -0.690121 3.532383 C 2.831556 1.536622 1.499048 H -2.491492 1.398496 3.004066 H -0.222219 0.845911 3.611830 C 3.960861 1.356253 2.262922 H -3.907019 1.470945 1.961294 H 4.700861 2.109202 2.498643 H -1.208526 -4.286518 1.229396 C 3.962977 0.002608 2.662208 H -1.820106 -3.770884 -0.337350 III LU N(SiH3)2. SCF energy = - H 4.693981 -0.494719 3.285375 C 0.623182 0.440433 -4.867674 2149.29793 C 2.827906 -0.563231 2.130633 C -0.623182 -0.440433 -4.867674 C 2.389359 2.790902 0.809733 H 1.513553 -0.098463 -5.215458 C 0.924588 2.751523 0.508252 H 0.509098 1.344840 -5.472804 C 3.105900 -1.066357 0.899493 C 4.083115 -1.997131 0.639283 C 0.000000 2.537992 1.542860 H -0.509098 -1.344840 -5.472804 H 0.364655 2.466292 2.563022 H -1.513553 0.098463 -5.215458 H 5.007671 -2.121957 1.186657 C 3.649057 -2.735320 -0.483012 C -1.350698 2.341010 1.281718 B 0.000000 0.000000 -2.699181 C -1.796466 2.402587 -0.049432 O 0.804208 0.803110 -3.496372 H 4.161436 -3.557042 -0.964604 C 2.424143 -2.222603 -0.837043 H -2.846155 2.227582 -0.260956 O -0.804208 -0.803110 -3.496372 C -0.905133 2.650086 -1.075151 C 3.109517 -0.012964 1.961704 C 1.715853 0.395168 2.325887 H -1.248996 2.672987 -2.103186 C 0.752216 -0.587529 2.606574 C 0.456989 2.800493 -0.799850 LUIIIMe. SCF energy = -1552.01607 H 1.059220 -1.628882 2.625120 H 1.158371 2.934751 -1.616506 C -0.583322 -0.261294 2.804870 C -2.308370 1.949150 2.360271 C 3.199347 -0.526770 -0.763347 C -0.964451 1.087719 2.740557 C -2.827906 0.563231 2.130633 C 4.189296 -0.015201 -1.569279 H -2.011750 1.346663 2.857100 C -3.962977 -0.002608 2.662208 H 5.126554 -0.495801 -1.815536 C -0.016252 2.070913 2.528861 H -4.693981 0.494719 3.285375 C 3.743073 1.254671 -1.995452 H -0.314174 3.112499 2.483904 C -3.960861 -1.356253 2.262922 H 4.259854 1.944235 -2.649176 C 1.316468 1.724923 2.308094 H -4.700861 -2.109202 2.498643 C 2.500354 1.440199 -1.435940 H 2.044599 2.499010 2.088407 C -2.831556 -1.536622 1.499048 C 3.178942 -1.836544 -0.041664 C -1.622411 -1.322991 2.970030 C -2.389359 -2.790902 0.809733 C 1.770924 -2.275280 0.217381 C -2.542861 -1.358522 1.790928 C -0.924588 -2.751523 0.508252 C 0.850130 -2.340288 -0.843112 C -3.813234 -1.882274 1.737976 C 0.000000 -2.537992 1.542860 H 1.198367 -2.131740 -1.850200 H -4.366117 -2.301502 2.567662 H -0.364655 -2.466292 2.563022 C -0.494957 -2.615620 -0.622995 C -4.230545 -1.788776 0.393258 C 1.350698 -2.341010 1.281718 C -0.930864 -2.838954 0.691748 H -5.177391 -2.106586 -0.021954 C 1.796466 -2.402587 -0.049432 H -1.985625 -3.015453 0.874306 C -3.197778 -1.199077 -0.296319 H 2.846155 -2.227582 -0.260956 C -0.030186 -2.814482 1.741148 C -3.149681 -0.845595 -1.749309 C 0.905133 -2.650086 -1.075151 H -0.372498 -2.981120 2.755293 C -1.734286 -0.731438 -2.220472 H 1.248996 -2.672987 -2.103186 C 1.313669 -2.522605 1.505182 C -0.832802 -1.786091 -1.994604 C -0.456989 -2.800493 -0.799850 H 2.004690 -2.456118 2.338769 H -1.201156 -2.700993 -1.541328 H -1.158371 -2.934751 -1.616506 C -1.498962 -2.548553 -1.729049 C 0.520089 -1.658238 -2.285716 C 2.308370 -1.949150 2.360271 260

Appendix

N 2.115134 0.363343 1.398191 H -0.192825 -3.361484 2.729064 H 2.460963 -2.869560 -1.749207 N -2.115134 -0.363343 1.398191 C 1.479641 -2.635433 1.561346 H 3.428479 2.411487 1.450886 U 0.000000 0.000000 0.143507 H 2.153515 -2.591185 2.419265 H 3.720152 1.184849 2.694928 H 3.149027 -2.653556 2.386684 C -1.270351 -2.627144 -1.756332 H -0.075274 -2.003697 3.456000 H 1.801928 -2.029108 3.331020 N -2.019032 -0.482483 -0.605073 H -1.530873 -1.152955 3.999733 H 2.937442 2.954749 -0.127409 N 2.015466 0.452046 -0.624161 H -2.541162 -3.002765 -2.084343 H 2.611829 3.651708 1.453001 Hf 0.000073 -0.020300 0.618202 H -3.348936 -1.445620 -1.839078 H -1.801928 2.029108 3.331020 H -1.770116 -3.601236 -1.895181 H -3.149027 2.653556 2.386684 H -0.740327 -2.406615 -2.700411 [LHfIVMe]+. SCF energy = - H -2.611829 -3.651708 1.453001 H -3.740979 1.465459 1.127305 1122.8922257 H -2.937442 -2.954749 -0.127409 H -3.961828 2.276079 -0.425606 O 0.000000 0.000000 -2.015173 H 0.733256 2.330020 -2.726802 C -0.106177 -0.070373 2.665433 C 0.000000 0.000000 -3.342606 H 1.761771 3.555783 -1.968040 H -1.027759 -0.624106 2.907754 C -1.197164 -0.120167 -4.055955 H 3.946266 -2.306305 -0.455113 H 0.720664 -0.624200 3.120577 C 1.197164 0.120167 -4.055955 H 3.776303 -1.500407 1.107909 H -0.169211 0.881665 3.189884 C -1.190415 -0.119389 -5.441020 C 3.205817 -0.459058 -0.671226 H -2.126239 -0.214854 -3.502005 [LHfIVBO2C2H4]+. SCF energy = - C 4.193176 0.107553 -1.450013 C 1.190415 0.119389 -5.441020 1336.8080136 H 5.163728 -0.331257 -1.671561 H 2.126239 0.214854 -3.502005 C 3.702232 1.360757 -1.902763 C 0.000000 0.000000 -6.144353 C -1.914187 3.644277 -1.395140 H 4.220597 2.072247 -2.542034 H -2.129679 -0.213883 -5.977823 C -3.099614 2.945882 -0.725024 C 2.426787 1.504970 -1.397346 H 2.129679 0.213883 -5.977823 H -2.016784 3.693107 -2.484678 C 3.237398 -1.782753 0.041176 H 0.000000 0.000000 -7.228780 H -1.739919 4.654915 -1.018450 C 1.843593 -2.288387 0.284143 H -3.962381 2.833058 -1.385534 C 0.930363 -2.378346 -0.795615 H -3.427062 3.454278 0.188454 H 1.287517 -2.166951 -1.807226 [LHfIVX]+ complexes. B -1.238210 1.642223 -0.536225 C -0.422220 -2.680402 -0.587720 O -0.780638 2.819401 -1.076615 C -0.867240 -2.924125 0.732928 O -2.600979 1.645012 -0.371662 H -1.925577 -3.133227 0.905783 [LHfIV(µ-H)2BH2]+. SCF energy - C 3.553332 0.373613 0.718847 C 0.030358 -2.893238 1.798256 1110.167512 C 4.807894 -0.131626 0.423131 H -0.317165 -3.096443 2.812419 H 5.737270 0.114826 0.933677 C 1.377480 -2.556847 1.577204 B -0.007191 0.055728 2.729821 C 4.643739 -1.014767 -0.677104 H 2.066735 -2.488420 2.421821 H 0.815957 0.370285 2.071383 H 5.420934 -1.587268 -1.180530 C -1.425583 -2.596427 -1.700902 H -0.306333 1.024304 3.364485 C 3.294913 -1.015549 -0.990597 C -2.403423 -1.484535 -1.436286 H -0.872368 -0.162041 2.085525 C 3.165672 1.382623 1.759315 C -3.676118 -1.336825 -1.947565 H 0.307658 -0.924591 3.340131 C 1.687996 1.311115 2.016023 H -4.190802 -2.043997 -2.594545 C -3.186193 0.305359 -0.628257 C 1.119792 0.107459 2.515721 C -4.170856 -0.087673 -1.487420 C -4.142231 -0.283185 -1.425242 H 1.780118 -0.722607 2.778741 H -5.141080 0.351308 -1.709996 H -5.137041 0.110196 -1.623667 C -0.265699 -0.020125 2.687002 C -3.188799 0.473565 -0.698180 C -3.586172 -1.489986 -1.932305 C -1.105784 1.051134 2.300574 C -3.226084 1.788077 0.030917 H -4.067250 -2.200499 -2.600979 H -2.187747 0.933180 2.387664 C -1.834047 2.289825 0.292784 C -2.304856 -1.585588 -1.439298 C -0.562453 2.240601 1.793934 C -0.913172 2.395085 -0.779950 C -3.287660 1.597992 0.127948 H -1.209577 3.086407 1.562426 H -1.263584 2.198833 -1.796918 C -1.936368 2.240930 0.282632 C 0.839003 2.364304 1.666001 C 0.437926 2.691260 -0.558153 C -1.046957 2.283723 -0.822350 H 1.257314 3.275148 1.232688 C 0.874020 2.917513 0.769103 H -1.400851 1.947389 -1.800299 C -0.877810 -1.319819 3.123580 H 1.930998 3.125066 0.951596 C 0.277056 2.707609 -0.672472 C -1.679296 -1.907900 1.997830 C -0.030906 2.873230 1.826891 C 0.716394 3.138111 0.602382 C -2.631911 -2.911880 2.044268 H 0.310641 3.068050 2.844802 H 1.758395 3.440802 0.731167 H -2.979435 -3.427300 2.938021 C -1.376622 2.536734 1.593056 C -0.173283 3.195680 1.669433 C -3.056490 -3.135632 0.707454 H -2.069072 2.449281 2.433302 H 0.161796 3.557137 2.643747 H -3.799090 -3.854997 0.366583 C 1.450886 2.618410 -1.662575 C -1.490206 2.725703 1.516132 C -2.351983 -2.248141 -0.087951 N 2.086724 0.389063 -0.611200 H -2.163526 2.709846 2.376276 C -2.449319 -2.029150 -1.569006 N -2.069550 -0.374422 -0.639664 C 1.265898 2.585874 -1.792877 C -1.229874 -1.303807 -2.060298 Hf -0.002911 0.001284 0.556175 C 2.306802 1.562155 -1.446042 C 0.050644 -1.903718 -1.912907 H 2.001823 3.572888 -1.728768 C 3.602092 1.488313 -1.906865 H 0.119047 -2.918781 -1.513923 H 0.931212 2.487456 -2.628765 H 4.088042 2.208595 -2.561488 C 1.215924 -1.218562 -2.284235 H 3.775627 -1.725472 1.004435 C 4.162463 0.286690 -1.394309 C 1.108110 0.110244 -2.758912 H 3.792296 -2.508428 -0.580025 H 5.166622 -0.092738 -1.571564 H 2.019074 0.661164 -3.001342 H -0.896509 -2.457853 -2.660943 C 3.194050 -0.320687 -0.626887 C -0.146382 0.721425 -2.898314 H -1.976666 -3.549702 -1.780632 C 3.297620 -1.620648 0.119209 H -0.227507 1.719532 -3.328374 H -3.775142 2.522480 -0.585211 C 1.939726 -2.237174 0.300363 C -1.311800 0.000080 -2.555958 H -3.772592 1.717896 0.988629 C 1.052963 -2.318571 -0.802637 H -2.284146 0.492041 -2.625948 H 1.413115 -2.032324 -1.793987 C 2.574811 -1.809693 -2.042415 [LHfIVN(SiH3)2]+. SCF energy = - C -0.279204 -2.713157 -0.634873 N 2.593460 -0.161398 -0.141154 1720.1625278 C -0.728064 -3.065154 0.659572 N -1.485962 -1.475501 0.686793 H -1.775915 -3.339971 0.801438 Hf -0.063296 -0.026198 0.012150 Si 1.540036 0.022478 3.212649 C 0.153893 -3.068160 1.736806 H 3.159970 -1.804626 -2.980256 H 1.447316 1.181267 4.144552 261

Appendix

H 1.823640 -1.223700 3.979202 H 1.863246 -1.055930 -5.913448 C 0.821724 -2.370320 -0.765609 H 2.612293 0.260577 2.200199 H 0.000000 0.000000 -7.153179 H 1.172982 -2.198312 -1.778505 Si -1.455291 -0.446275 3.207241 C 3.181686 -0.447931 1.476260 C -0.526804 -2.620400 -0.538936 H -1.349735 -1.715569 3.980034 C 3.971915 -1.280428 2.241725 C -0.965533 -2.801980 0.781149 H -1.728534 0.690632 4.131173 H 5.025329 -1.130959 2.469288 H -2.021874 -2.962342 0.968814 H -2.541464 -0.553534 2.186570 C 3.155139 -2.362309 2.663230 C -0.068011 -2.745264 1.832970 N 0.034809 -0.153736 2.316690 H 3.454783 -3.202536 3.286060 H -0.411855 -2.864643 2.852100 C -3.172636 0.644093 -1.034855 C 1.892834 -2.141879 2.152176 C 1.278931 -2.463388 1.591921 C -4.190793 0.156129 -1.827998 C 3.599666 0.812384 0.767462 H 1.960302 -2.360257 2.428914 H -5.155050 0.631826 -1.994446 C 2.413025 1.685159 0.476511 C -1.529020 -2.558734 -1.646370 C -3.740286 -1.072246 -2.377935 C 1.553224 2.069400 1.534795 C -2.464121 -1.408850 -1.432565 H -4.286384 -1.724667 -3.055932 H 1.824812 1.799855 2.559098 C -3.711783 -1.222129 -1.975249 C -2.457888 -1.278487 -1.913255 C 0.343248 2.729177 1.290454 H -4.236592 -1.910614 -2.623509 C -3.173620 1.907733 -0.220199 C 0.000000 3.044315 -0.046890 C -4.156650 0.045522 -1.536552 C -1.769999 2.377041 0.031799 H -0.953955 3.538339 -0.246333 H -5.099992 0.522138 -1.766187 C -0.868416 2.490406 -1.054782 C 0.863761 2.726280 -1.093272 C -3.161143 0.556056 -0.740129 H -1.242892 2.332715 -2.069384 H 0.595536 2.975129 -2.121894 C -3.147383 1.849346 0.012249 C 0.492022 2.741417 -0.849582 C 2.057006 2.027916 -0.834746 C -1.740363 2.274350 0.293677 C 0.960601 2.915159 0.475441 H 2.701142 1.730283 -1.665575 C -0.821929 2.370238 -0.765648 H 2.027173 3.082628 0.643059 C -0.654266 2.963269 2.386500 H -1.173434 2.198034 -1.778423 C 0.071777 2.882185 1.547315 C -1.892834 2.141879 2.152176 C 0.526636 2.620428 -0.539315 H 0.433556 3.043506 2.564617 C -3.155139 2.362309 2.663230 C 0.965612 2.802385 0.780616 C -1.286297 2.592953 1.327973 H -3.454783 3.202536 3.286060 H 2.021975 2.962881 0.968040 H -1.970858 2.520511 2.176324 C -3.971915 1.280428 2.241725 C 0.068324 2.745882 1.832661 C 1.475015 2.676805 -1.980144 H -5.025329 1.130959 2.469288 H 0.412508 2.866055 2.851574 C 2.415396 1.522461 -1.779812 C -3.181686 0.447931 1.476260 C -1.278585 2.463632 1.592004 C 3.689279 1.377816 -2.287875 C -3.599666 -0.812384 0.767462 H -1.959806 2.360610 2.429144 H 4.225557 2.111772 -2.885563 C -2.413025 -1.685159 0.476511 C 1.528683 2.558456 -1.646855 C 4.147974 0.090341 -1.904254 C -1.553224 -2.069400 1.534795 N 2.100793 0.322932 -0.659369 H 5.109711 -0.358526 -2.143704 H -1.824812 -1.799855 2.559098 N -2.100810 -0.323027 -0.659366 C 3.143684 -0.495433 -1.162171 C -0.343248 -2.729177 1.290454 W -0.000017 -0.000049 0.579296 C 3.157985 -1.852744 -0.515603 C 0.000000 -3.044315 -0.046890 H 2.101711 3.492916 -1.684655 C 1.759387 -2.356175 -0.302491 H 0.953955 -3.538339 -0.246333 H 0.999365 2.475523 -2.604849 C 0.837271 -2.326876 -1.378714 C -0.863761 -2.726280 -1.093272 H 3.692599 -1.774261 0.961342 H 1.193012 -2.033540 -2.369716 H -0.595536 -2.975129 -2.121894 H 3.657446 -2.620008 -0.580377 C -0.518773 -2.607776 -1.185376 C -2.057006 -2.027916 -0.834746 H -0.999802 -2.476175 -2.604447 C -0.961153 -2.961626 0.112390 H -2.701142 -1.730283 -1.665575 H -2.102125 -3.493166 -1.683788 H -2.023795 -3.155735 0.275704 C 0.654266 -2.963269 2.386500 H -3.657806 2.619806 -0.579316 C -0.051492 -3.073038 1.161493 N 1.873285 -0.954802 1.396677 H -3.692126 1.773565 0.962142 H -0.393425 -3.377129 2.152683 N -1.873285 0.954802 1.396677 C 1.301367 -2.748868 0.960422 Hf 0.000000 0.000000 0.162961 LWIIIBO2C2H4. SCF energy = - H 1.999572 -2.785486 1.799924 H 0.932878 -4.031051 2.418688 1355.8877125 C -1.522654 -2.395974 -2.278890 H 0.186874 -2.730782 3.360314 N -2.071704 -0.226994 -1.061112 H 4.132170 0.597281 -0.176491 C -0.159696 0.751327 4.317573 N 2.043096 0.372461 -1.058760 H 4.314020 1.360684 1.407488 C 0.159696 -0.751327 4.317573 Hf 0.004204 -0.012974 0.208606 H -0.186874 2.730782 3.360314 H -1.219870 0.895684 4.325922 H -2.109961 -3.317368 -2.435184 H -0.932878 4.031051 2.418688 H 0.261226 1.259640 5.159808 H -0.992255 -2.195584 -3.227384 H -4.314020 -1.360684 1.407488 H -0.261226 -1.259640 5.159808 H -3.693505 1.780107 0.746745 H -4.132170 -0.597281 -0.176491 H 1.219870 -0.895684 4.325922 H -3.732556 2.685508 -0.771181 B 0.000000 0.000000 2.215437 H 0.927092 2.600955 -2.936694 LWIIX complexes. O 0.395682 1.211804 3.083065 H 2.059976 3.611798 -2.024999 O -0.395682 -1.211804 3.083065 III H 3.708621 -2.551729 -1.170668 LW (µ-H)2BH2. SCF energy = - C 1.495711 2.747503 -1.296226 H 3.693889 -1.847860 0.450883 1129.3006807 C 1.356130 3.881902 -2.019901 H 2.145991 4.516815 -2.363272 [LHfIVOPh]+. SCF energy = - B 0.000431 0.000119 2.620296 C 0.000000 4.073767 -2.225091 1389.6945388 H -0.910742 -0.119294 1.931701 H -0.458813 4.899225 -2.728094 H 0.148225 -0.988634 3.276380 C -0.629479 3.015607 -1.678177 O 0.000000 0.000000 -1.950039 H 0.911243 0.119386 1.931289 C 2.849172 2.187858 -0.802003 C 0.000000 0.000000 -3.305536 H -0.147095 0.989036 3.276220 C 2.692918 0.731858 -0.306979 C -1.052415 0.596300 -3.988108 C 3.161150 -0.556121 -0.740374 C 2.573961 -0.336037 -1.191121 C 1.052415 -0.596300 -3.988108 C 4.156530 -0.045501 -1.536899 H 2.579147 -0.160304 -2.246571 C -1.044551 0.591952 -5.374009 H 5.099868 -0.522065 -1.766650 C 2.434941 -1.644030 -0.696769 H -1.863042 1.055850 -3.432255 C 3.711594 1.222176 -1.975406 C 2.531928 -1.903543 0.672046 C 1.044551 -0.591952 -5.374009 H 4.236308 1.910727 -2.623671 H 2.517076 -2.909996 1.035005 H 1.863042 -1.055850 -3.432255 C 2.463905 1.408737 -1.432728 C 2.630933 -0.829587 1.564868 C 0.000000 0.000000 -6.069131 C 3.147445 -1.849631 0.011655 H 2.671052 -1.011423 2.618546 H -1.863246 1.055930 -5.913448 C 1.740448 -2.274421 0.293468 C 2.674668 0.486777 1.076747 262

Appendix

H 2.705855 1.307446 1.762605 C -0.939178 -2.814933 0.793082 N 2.185441 0.397447 -0.878038 C 2.147660 -2.756750 -1.704147 H -1.992236 -2.986947 0.988883 W 0.018037 -0.051152 0.225228 C 0.629479 -3.015607 -1.678177 C -0.032342 -2.754158 1.835022 H -2.037163 -3.157162 -2.582471 C 0.000000 -4.073767 -2.225091 H -0.367619 -2.897119 2.854528 H -0.873431 -2.058110 -3.313597 H 0.458813 -4.899225 -2.728094 C 1.310789 -2.465699 1.579616 H -3.647511 1.797307 0.608369 C -1.356130 -3.881902 -2.019901 H 2.006559 -2.368981 2.406233 H -3.563085 2.803688 -0.830563 H -2.145991 -4.516815 -2.363272 C -1.534630 -2.576936 -1.623615 H 1.227719 2.755069 -2.621467 C -1.495711 -2.747503 -1.296226 N -2.135659 -0.354849 -0.626222 H 2.295725 3.665807 -1.561091 C -2.849172 -2.187858 -0.802003 N 2.123142 0.341278 -0.647618 H 3.693918 -2.558983 -1.126043 C -2.692918 -0.731858 -0.306979 W 0.009999 -0.014420 0.578133 H 3.656118 -1.948740 0.523051 C -2.573961 0.336037 -1.191121 H -2.092868 -3.521035 -1.653031 H -2.579147 0.160304 -2.246571 H -1.019568 -2.487238 -2.588812 LWIIIOPh. SCF energy = - C -2.434941 1.644030 -0.696769 H -3.716540 1.783772 0.944718 1408.7568955 C -2.531928 1.903543 0.672046 H -3.688403 2.589791 -0.617059 H -2.517076 2.909996 1.035005 H 0.993958 2.445155 -2.620271 O 0.000000 0.000000 -1.909762 C -2.630933 0.829587 1.564868 H 2.070952 3.497343 -1.710286 C 0.000000 0.000000 -3.240578 H -2.671052 1.011423 2.618546 H 3.668013 -2.602164 -0.611865 C -1.075963 0.552828 -3.936445 C -2.674668 -0.486777 1.076747 H 3.716156 -1.784796 0.943465 C 1.075963 -0.552828 -3.936445 H -2.705855 -1.307446 1.762605 C -1.065801 0.547016 -5.320687 C -2.147660 2.756750 -1.704147 LWIIIN(SiH3)2. SCF energy = - H -1.903094 0.980252 -3.379894 N 0.279726 2.198591 -1.088042 1739.2571328 C 1.065801 -0.547016 -5.320687 N -0.279726 -2.198591 -1.088042 H 1.903094 -0.980252 -3.379894 W 0.000000 0.000000 0.035446 N -0.267817 -0.306523 2.229911 C 0.000000 0.000000 -6.022041 H -2.665592 3.660090 -1.457875 Si 1.205046 -0.256581 3.105538 H -1.904899 0.978129 -5.857548 H -2.460880 2.424421 -2.671819 H 1.260383 0.838812 4.127030 H 1.904899 -0.978129 -5.857548 H 3.214604 2.769340 0.018528 H 1.492699 -1.542118 3.823413 H 0.000000 0.000000 -7.106111 H 3.541832 2.237929 -1.616012 H 2.321128 -0.025635 2.129127 C 3.187900 -0.464983 1.486779 H 2.460880 -2.424421 -2.671819 Si -1.857849 -0.592535 2.821343 C 3.984322 -1.285699 2.250653 H 2.665592 -3.660090 -1.457875 H -1.979082 -1.934181 3.483895 H 5.027859 -1.125816 2.486374 H -3.541832 -2.237929 -1.616012 H -2.294423 0.425863 3.833628 C 3.175411 -2.371067 2.649939 H -3.214604 -2.769340 0.018528 H -2.835581 -0.560107 1.691677 H 3.463039 -3.207112 3.273106 C -3.053371 0.775612 -1.198086 C 1.927519 -2.144517 2.118364 LWIIIMe. SCF energy = - C -4.012769 0.394908 -2.105622 C 3.584858 0.804340 0.797464 1141.9901227 H -4.927327 0.927584 -2.328873 C 2.388178 1.649954 0.495983 C -3.576533 -0.824884 -2.666586 C 1.519830 2.032614 1.530591 C 0.002097 0.074611 2.617175 H -4.076475 -1.413551 -3.423699 H 1.768936 1.756825 2.550753 H 0.978881 0.512605 2.883864 C -2.367935 -1.113872 -2.079724 C 0.320130 2.683697 1.269449 H -0.762116 0.720521 3.057028 C -3.067103 1.976707 -0.306390 C 0.000000 2.999952 -0.061701 H -0.062190 -0.883772 3.133125 C -1.678414 2.382183 0.079139 H -0.945468 3.488382 -0.273225 C -3.188559 0.526635 -0.732788 C -0.689614 2.511400 -0.910129 C 0.862057 2.664410 -1.087420 C -4.172261 0.016268 -1.547112 H -0.973035 2.384654 -1.950619 H 0.600379 2.888667 -2.115455 H -5.107914 0.496925 -1.799292 C 0.640704 2.741583 -0.583505 C 2.043015 1.969186 -0.812119 C -3.722357 -1.252587 -1.972443 C 0.990779 2.866053 0.769709 H 2.685132 1.656700 -1.628775 H -4.234033 -1.941125 -2.631245 H 2.033424 3.008441 1.034450 C -0.681503 2.943350 2.348002 C -2.483634 -1.438590 -1.404307 C 0.018272 2.805051 1.750053 C -1.927519 2.144517 2.118364 C -3.173927 1.835124 -0.008670 H 0.292275 2.905773 2.794302 C -3.175411 2.371067 2.649939 C -1.768040 2.273984 0.261497 C -1.309071 2.549792 1.407133 H -3.463039 3.207112 3.273106 C -0.839550 2.341432 -0.792111 H -2.057016 2.449118 2.186936 C -3.984322 1.285699 2.250653 H -1.180323 2.134662 -1.802115 C 1.705237 2.744522 -1.632763 H -5.027859 1.125816 2.486374 C 0.503767 2.616935 -0.561644 C 2.611301 1.563808 -1.478699 C -3.187900 0.464983 1.486779 C 0.929953 2.837941 0.756676 C 3.892282 1.425138 -1.959146 C -3.584858 -0.804340 0.797464 H 1.983271 3.014555 0.947275 H 4.464810 2.181650 -2.478484 C -2.388178 -1.649954 0.495983 C 0.021642 2.811059 1.799417 C 4.290402 0.103519 -1.665923 C -1.519830 -2.032614 1.530591 H 0.356458 2.975903 2.816353 H 5.238793 -0.361443 -1.898918 H -1.768936 -1.756825 2.550753 C -1.320320 2.519041 1.553077 C 3.236110 -0.485618 -1.009224 C -0.320130 -2.683697 1.269449 H -2.017384 2.450651 2.381463 C 3.161805 -1.873128 -0.454484 C 0.000000 -2.999952 -0.061701 C 1.515858 2.552433 -1.660456 C 1.738383 -2.310079 -0.308501 H 0.945468 -3.488382 -0.273225 C 2.470669 1.422150 -1.429025 C 0.863589 -2.227966 -1.405760 C -0.862057 -2.664410 -1.087420 C 3.716717 1.241186 -1.982097 H 1.257966 -1.912738 -2.366638 H -0.600379 -2.888667 -2.115455 H 4.231159 1.929533 -2.638951 C -0.495384 -2.485337 -1.270268 C -2.043015 -1.969186 -0.812119 C 4.171209 -0.022200 -1.544452 C -0.992517 -2.849824 -0.008771 H -2.685132 -1.656700 -1.628775 H 5.112000 -0.498179 -1.785971 H -2.058529 -3.012418 0.110982 C 0.681503 -2.943350 2.348002 C 3.183079 -0.534729 -0.737327 C -0.135842 -2.983192 1.069624 N 1.911539 -0.975617 1.385922 C 3.165068 -1.838754 -0.004767 H -0.523505 -3.265134 2.041843 N -1.911539 0.975617 1.385922 C 1.757512 -2.263673 0.279653 C 1.223349 -2.702029 0.922371 W 0.000000 0.000000 0.131238 C 0.826704 -2.355669 -0.772537 H 1.882769 -2.765314 1.781651 H 0.932944 -4.010903 2.374415 H 1.165836 -2.178978 -1.788516 C -1.447253 -2.250950 -2.397893 H 0.228025 -2.704113 3.318751 C -0.515997 -2.624038 -0.530939 N -2.024118 -0.141734 -1.161930 H 4.121921 0.607352 -0.139678 263

Appendix

H 4.278506 1.360516 1.440732 H -0.932944 4.010903 2.374415 H -4.121921 -0.607352 -0.139678 H -0.228025 2.704113 3.318751 H -4.278506 -1.360516 1.440732

2. PBE0 Cartesian coordinates (Å) and SCF energies (Hartrees) of all complexes studied in chapter 5

LThIVOH. SCF energy = -1518.58942 H 4.212507 2.026389 -2.554675 [LThIVX’]+ complexes. C 2.422036 1.472255 -1.431639 C -3.160738 0.446275 -0.752180 C 3.179133 -1.827591 -0.049277 C -4.142015 -0.122428 -1.516199 [LThIVNH2]+ SCF energy = - C 1.794890 -2.305163 0.246009 H -5.109843 0.307944 -1.731921 C 0.867237 -2.427292 -0.804263 1498.69114 C -3.650440 -1.371960 -1.956539 H 1.205776 -2.259514 -1.822676 H -4.161050 -2.086275 -2.586889 C -0.475868 -2.688195 -0.560774 C 3.163681 -0.464352 -0.753454 C -2.385601 -1.502635 -1.453610 C -0.897141 -2.868331 0.769521 C 4.143942 0.089513 -1.530857 C -3.217736 1.758667 -0.032895 H -1.948925 -3.046876 0.969705 H 5.106400 -0.350121 -1.751828 C -1.841857 2.279236 0.229489 C 0.015014 -2.809035 1.809177 C 3.659206 1.340283 -1.975999 C -0.928042 2.389673 -0.834629 H -0.316551 -2.942610 2.832688 H 4.171025 2.045479 -2.615572 H -1.272607 2.180442 -1.843030 C 1.354295 -2.505974 1.550477 C 2.399535 1.485029 -1.461962 C 0.409656 2.688698 -0.612848 H 2.050800 -2.398851 2.375601 C 3.206958 -1.769018 -0.019428 C 0.839499 2.922988 0.706051 C -1.489280 -2.622151 -1.655696 C 1.824752 -2.277364 0.239525 H 1.888864 3.131652 0.888497 C -2.422074 -1.472308 -1.431556 C 0.912154 -2.381284 -0.824646 C -0.061847 2.883919 1.754205 C -3.681349 -1.314404 -1.938897 H 1.260359 -2.171934 -1.831952 H 0.275433 3.074087 2.766773 H -4.212386 -2.026266 -2.554931 C -0.430397 -2.676404 -0.609619 C -1.395429 2.540165 1.519986 C -4.140135 -0.044825 -1.520184 C -0.865064 -2.911680 0.705165 H -2.085164 2.451424 2.352706 H -5.097313 0.405376 -1.742585 H -1.915096 -3.118013 0.885462 C 1.416676 2.614084 -1.712444 C -3.146634 0.510992 -0.763670 C 0.033908 -2.872968 1.756694 C 2.385606 1.502655 -1.453604 C -3.179138 1.827553 -0.049237 H -0.310251 -3.077319 2.764892 C 3.650298 1.371762 -1.956889 C -1.794895 2.305208 0.245933 C 1.370430 -2.532958 1.530011 H 4.160793 2.085897 -2.587537 C -0.867314 2.427329 -0.804405 H 2.060531 -2.454291 2.363534 C 4.141869 0.122257 -1.516499 H -1.205921 2.259526 -1.822793 C -1.432453 -2.600615 -1.714725 H 5.109567 -0.308265 -1.732490 C 0.475816 2.688185 -0.561001 C -2.399411 -1.485183 -1.462021 C 3.160714 -0.446237 -0.752128 C 0.897184 2.868294 0.769265 C -3.659207 -1.340647 -1.975802 C 3.217750 -1.758486 -0.032611 H 1.948995 3.046761 0.969381 H -4.171052 -2.045938 -2.615248 C 1.841885 -2.279254 0.229512 C -0.014903 2.809030 1.808980 C -4.143953 -0.089847 -1.530756 C 0.928153 -2.389561 -0.834700 H 0.316738 2.942571 2.832471 H -5.106460 0.349706 -1.751677 H 1.272793 -2.180157 -1.843041 C -1.354213 2.506027 1.550367 C -3.163592 0.464238 -0.753625 C -0.409539 -2.688619 -0.613064 H -2.050656 2.398886 2.375541 C -3.206923 1.769107 -0.019932 C -0.839508 -2.923105 0.705783 C 1.489176 2.622003 -1.655964 C -1.824775 2.277532 0.239155 H -1.888901 -3.131784 0.888057 N 2.054673 0.351837 -0.686296 C -0.911982 2.381309 -0.824856 C 0.061744 -2.884222 1.754007 N -2.054744 -0.351939 -0.686131 H -1.260003 2.171880 -1.832207 H -0.275538 -3.074567 2.766539 Th -0.000003 0.000008 0.515840 C 0.430538 2.676418 -0.609609 C 1.395367 -2.540424 1.519919 H 2.067687 3.552491 -1.684675 C 0.864984 2.911809 0.705222 H 2.085004 -2.451767 2.352727 H 0.973780 2.542366 -2.620907 H 1.914986 3.118148 0.885685 C -1.416536 -2.613900 -1.712695 H 3.747055 -1.766219 0.886956 C -0.034202 2.873331 1.756585 N -2.047893 -0.387892 -0.688403 H 3.695464 -2.562714 -0.678437 H 0.309751 3.077856 2.764823 N 2.048063 0.388084 -0.688100 H -0.973930 -2.542706 -2.620678 C -1.370698 2.533373 1.529680 Th -0.000027 0.000040 0.550357 H -2.067830 -3.552622 -1.684217 H -2.060987 2.454873 2.363067 H -1.965553 -3.560063 -1.780868 H -3.695609 2.562672 -0.678288 C 1.432727 2.600604 -1.714600 H -0.897277 -2.481794 -2.669860 H -3.746941 1.766077 0.887063 N 2.061064 0.379377 -0.687805 H -3.760590 1.680864 0.917223 F -0.000053 0.000035 2.606026 N -2.061024 -0.379547 -0.687801 H -3.772399 2.477335 -0.648401 Th 0.000007 -0.000009 0.533448 H 0.897413 2.482311 -2.669661 H 1.983044 3.546130 -1.781998 H 1.965778 3.560218 -1.780384 LThIIIX’ complexes. H 0.908569 2.473277 -2.669766 H 3.772700 -2.477185 -0.647823 H 3.742706 -1.683919 0.934099 H 3.760324 -1.680476 0.917654 LThIIINH2. SCF energy = - H 3.760471 -2.499508 -0.621950 O 0.000262 -0.000194 2.640223 H -0.908229 -2.473163 -2.669842 H -0.000144 -0.000516 3.600815 1498.84839 H -1.982645 -3.546203 -1.782228 H -3.760349 2.499447 -0.622717 C 3.148857 -0.542490 -0.818645 IV H -3.742818 1.684239 0.933530 LTh F. SCF energy = -1542.62451 C 4.170890 -0.015884 -1.570520 N -0.000186 -0.000128 2.774110 H 5.111945 -0.498916 -1.795932 C 3.146656 -0.510984 -0.763642 H 0.135972 -0.797261 3.386346 C 3.753980 1.272104 -1.974991 C 4.140246 0.044927 -1.519973 H -0.136489 0.798148 3.384878 H 4.302381 1.976207 -2.586440 H 5.097498 -0.405191 -1.742218 C 2.493392 1.455974 -1.461493 C 3.681423 1.314472 -1.938744 C 3.083874 -1.863000 -0.117007 264

Appendix

C 1.667789 -2.244799 0.175158 H 4.414546 1.738984 -2.551526 C 1.658239 2.596503 -1.644318 C 0.725363 -2.398816 -0.895152 C 4.108999 -0.230184 -1.530286 N 2.110585 0.303638 -0.716394 H 1.071496 -2.272657 -1.916899 H 4.992999 -0.802741 -1.777393 N -2.088851 -0.222704 -0.744773 C -0.616338 -2.579251 -0.648337 C 3.068033 -0.655755 -0.739884 Th 0.017618 -0.150767 0.549461 C -1.071637 -2.665945 0.706154 C 2.992006 -1.939788 0.021454 H 2.271341 3.504705 -1.680623 H -2.128773 -2.781778 0.907147 C 1.620588 -2.544687 0.151690 H 1.135252 2.531232 -2.607688 C -0.111343 -2.787502 1.743197 C 0.636092 -2.311994 -0.813465 H 3.630067 -1.928733 0.839327 H -0.444295 -2.991062 2.755300 H 0.900802 -1.742189 -1.702200 H 3.521930 -2.702355 -0.729961 C 1.223245 -2.572976 1.488408 C -0.657095 -2.822695 -0.688265 H -1.159715 -2.504038 -2.648401 H 1.944532 -2.597405 2.299842 C -0.955658 -3.612634 0.418716 H -2.311175 -3.406989 -1.665350 C -1.633350 -2.488351 -1.740048 H -1.959069 -4.009774 0.536718 H -3.547388 2.785908 -0.643739 C -2.519463 -1.300034 -1.520288 C 0.025363 -3.897935 1.355063 H -3.599404 1.938044 0.893587 C -3.768520 -1.060429 -2.039931 H -0.210123 -4.532442 2.203823 F -0.221830 0.164479 2.635831 H -4.327052 -1.720817 -2.689146 C 1.296589 -3.359067 1.232395 C -4.160214 0.215760 -1.578350 H 2.048170 -3.562166 1.989564 H -5.087197 0.731980 -1.788893 C -1.685731 -2.490512 -1.726775 LUIIIX’ complexes. C -3.136101 0.679490 -0.788008 N -2.076285 -0.182219 -0.765580 C -3.095662 1.954619 -0.005286 N 2.115427 0.337549 -0.637352 LUIIINH2. SCF energy = -1568.09841 C -1.689028 2.388989 0.263546 Th -0.036003 0.247290 0.540251 C -0.764413 2.434176 -0.790111 H -2.328138 -3.359146 -1.902050 C 3.187865 -0.530106 -0.797174 H -1.108274 2.208047 -1.794823 H -1.165310 -2.289738 -2.674366 C 4.175105 -0.015073 -1.605100 C 0.578825 2.709740 -0.571642 H -3.658556 2.217627 0.697552 H 5.113821 -0.491674 -1.853910 C 1.009160 2.960986 0.737632 H -3.369486 2.809611 -0.925683 C 3.724218 1.254693 -2.028147 H 2.063496 3.138973 0.922113 H 1.343238 2.755266 -2.495064 H 4.237558 1.946251 -2.682584 C 0.104083 2.958771 1.781498 H 2.478918 3.534708 -1.396109 C 2.482027 1.435299 -1.464470 H 0.447707 3.156294 2.790974 H 3.652494 -2.663773 -0.473408 C 3.172762 -1.834558 -0.064078 C -1.239433 2.659975 1.549177 H 3.400328 -1.818291 1.035757 C 1.767251 -2.266103 0.221953 H -1.939277 2.617500 2.377421 O 0.061252 -0.612397 2.465579 C 0.832943 -2.347528 -0.824059 C 1.574963 2.616089 -1.681242 H 0.087267 -0.992249 3.345597 H 1.168108 -2.154611 -1.838611 N 2.098404 0.349378 -0.735420 C -0.511438 -2.620195 -0.582987 N -2.106943 -0.237374 -0.740539 III C -0.929181 -2.827086 0.738441 Th 0.025252 -0.151566 0.567111 LTh F. SCF energy = -1542.78658 H -1.981093 -3.000578 0.938496 H 2.163429 3.539885 -1.733292 C 3.149838 -0.606583 -0.785944 C -0.015070 -2.785247 1.776928 H 1.037300 2.530910 -2.634889 C 4.197484 -0.088164 -1.505656 H -0.351470 -2.947531 2.794226 H 3.643542 -1.834429 0.828176 H 5.135615 -0.584426 -1.713519 C 1.326331 -2.492498 1.521987 H 3.578115 -2.625394 -0.736474 C 3.812566 1.211588 -1.904227 H 2.032024 -2.417993 2.342701 H -1.117856 -2.430902 -2.707201 H 4.388243 1.913358 -2.492768 C -1.529303 -2.572019 -1.678005 H -2.246908 -3.398113 -1.759127 C 2.544336 1.413082 -1.419652 C -2.481948 -1.435302 -1.464601 H -3.619954 2.736602 -0.569602 C 3.056663 -1.933005 -0.097691 C -3.724462 -1.255007 -2.027661 H -3.623919 1.860308 0.953118 C 1.636056 -2.282189 0.210175 H -4.237857 -1.946627 -2.681986 N -0.028172 0.086330 2.832937 C 0.690105 -2.455448 -0.842592 C -4.175376 0.014737 -1.604562 H -0.272443 0.875607 3.421033 H 1.032234 -2.368527 -1.870353 H -5.114206 0.491240 -1.853130 H 0.162795 -0.691440 3.456434 C -0.655652 -2.591796 -0.587492 C -3.187935 0.529904 -0.796945

C -1.106372 -2.638813 0.777913 C -3.172762 1.834711 -0.064380 H -2.163740 -2.741995 0.985686 C -1.767211 2.266010 0.221874 LThIIIOH. SCF energy = -1518.74566 C -0.146562 -2.728758 1.810806 C -0.832836 2.347526 -0.824075 H -0.475155 -2.860235 2.835945 H -1.167896 2.154793 -1.838690 C -3.146313 0.697783 -0.730279 C 1.189044 -2.530446 1.546069 C 0.511543 2.620194 -0.582931 C -4.266089 0.111845 -1.266327 H 1.908087 -2.517988 2.359143 C 0.929241 2.826984 0.738502 H -5.240193 0.571031 -1.366166 C -1.673305 -2.513817 -1.678559 H 1.981131 3.000473 0.938675 C -3.891967 -1.190884 -1.662230 C -2.527471 -1.296548 -1.498284 C 0.015065 2.785005 1.776925 H -4.516501 -1.934747 -2.138773 C -3.770244 -1.040828 -2.021654 H 0.351429 2.947211 2.794257 C -2.560355 -1.334352 -1.358287 H -4.345590 -1.705033 -2.651854 C -1.326304 2.492246 1.521937 C -3.009548 2.088345 -0.178111 C -4.132226 0.255028 -1.591312 H -2.032001 2.417608 2.342636 C -1.601838 2.412241 0.208730 H -5.047843 0.786203 -1.813742 C 1.529276 2.571882 -1.678072 C -0.600467 2.630394 -0.787222 C -3.099680 0.717116 -0.812720 N 2.133798 0.347991 -0.694289 H -0.892666 2.606428 -1.833668 C -3.047950 2.006858 -0.053481 N -2.133658 -0.347899 -0.694561 C 0.733092 2.729788 -0.460754 C -1.641917 2.425746 0.241237 U -0.000043 0.000107 0.538159 C 1.114708 2.705040 0.926298 C -0.697178 2.456787 -0.797006 H 2.085766 3.516903 -1.709184 H 2.161405 2.782450 1.191146 H -1.025848 2.238396 -1.808795 H 1.010744 2.483198 -2.641686 C 0.106050 2.743373 1.917403 C 0.644737 2.708180 -0.552038 H 3.723216 -1.776636 0.884457 H 0.384118 2.832605 2.962428 C 1.053168 2.952121 0.767884 H 3.678631 -2.597142 -0.670009 C -1.218416 2.576539 1.576821 H 2.107034 3.112612 0.972081 H -1.010977 -2.483814 -2.641765 H -1.978795 2.537322 2.350791 C 0.127663 2.971835 1.793308 H -2.085873 -3.517022 -1.708569 C 1.804602 2.674900 -1.502762 H 0.449657 3.148167 2.813391 H -3.678186 2.597135 -0.670877 C 2.596360 1.405868 -1.371637 C -1.214911 2.697024 1.533339 H -3.723563 1.777378 0.883973 C 3.812804 1.093865 -1.926231 H -1.923438 2.650998 2.353200 N 0.000560 0.000011 2.807663 265

Appendix

H -0.259468 0.765125 3.420706 C 2.556312 0.887139 -0.527278 H -5.003906 0.526252 -2.031433 H 0.260421 -0.765099 3.420741 C 2.904309 0.639079 0.809615 C -3.102237 0.564548 -0.956539 H 3.579680 -0.179656 1.035074 C -3.140348 1.843619 -0.180601 C 2.376804 1.414507 1.827713 C -1.753332 2.292295 0.149504 LUIIIOH. SCF energy = -1587.99144 H 2.628275 1.201752 2.859757 C -0.808488 2.435188 -0.886070 C 1.455427 2.420184 1.535691 H -1.135294 2.304869 -1.913640 C 3.189021 -0.539061 -0.778200 H 0.999245 2.982127 2.343732 C 0.533086 2.678550 -0.615598 C 4.202452 0.002338 -1.534008 C 3.053497 -0.022617 -1.605624 C 0.937119 2.815146 0.724854 H 5.156628 -0.458546 -1.751424 C 2.519198 -1.410995 -1.423954 H 1.987082 2.981095 0.943491 C 3.750563 1.270906 -1.956690 C 2.994215 -2.573994 -1.983302 C 0.014101 2.721033 1.751282 H 4.279448 1.979323 -2.580090 H 3.869587 -2.670947 -2.611194 H 0.327330 2.838070 2.781592 C 2.481608 1.425924 -1.447538 C 2.104775 -3.599435 -1.594994 C -1.327125 2.436667 1.465189 C 3.168089 -1.862630 -0.077821 H 2.166365 -4.648921 -1.849686 H -2.035673 2.317140 2.278797 C 1.764402 -2.276650 0.234207 C 1.143953 -3.007828 -0.809190 C 1.569072 2.631686 -1.689504 C 0.820527 -2.409478 -0.800518 C 0.000000 -3.666335 -0.101843 N 2.112040 0.364992 -0.709477 H 1.145420 -2.268658 -1.826554 C -1.076299 -2.677494 0.222186 N -2.020319 -0.311058 -0.875612 C -0.521953 -2.657004 -0.531250 C -1.652382 -1.908208 -0.803043 Th 0.000276 -0.003687 0.358821 C -0.927354 -2.799662 0.805704 H -1.348598 -2.093665 -1.829079 H 2.142949 3.565666 -1.693824 H -1.978538 -2.957826 1.021916 C -2.556312 -0.887139 -0.527278 H 1.077997 2.558651 -2.667374 C -0.005238 -2.704169 1.834649 C -2.904309 -0.639079 0.809615 H 3.704672 -1.792915 0.894103 H -0.329748 -2.808494 2.863445 H -3.579680 0.179656 1.035074 H 3.724908 -2.562792 -0.685510 C 1.334440 -2.426971 1.550747 C -2.376804 -1.414507 1.827713 H -0.855982 -2.412979 -2.864466 H 2.046817 -2.308401 2.360338 H -2.628275 -1.201752 2.859757 H -1.987403 -3.457588 -2.013272 C -1.556348 -2.633905 -1.610362 C -1.455427 -2.420184 1.535691 H -3.644657 2.612013 -0.778746 C -2.490231 -1.476617 -1.419376 H -0.999245 -2.982127 2.343732 H -3.717550 1.741112 0.746292 C -3.726438 -1.289311 -1.991628 C -3.053497 0.022617 -1.605624 Si -0.349207 -0.178307 3.397729 H -4.246779 -1.985716 -2.635267 N -1.377874 1.654980 -0.688899 H -1.728325 -0.771632 3.562529 C -4.158599 -0.004329 -1.596239 N 1.377874 -1.654980 -0.688899 H 0.559725 -1.118854 4.137141 H -5.089755 0.480990 -1.856570 U 0.000000 0.000000 0.516464 H -0.376459 1.075949 4.221820 C -3.168115 0.514827 -0.795099 H -4.150095 0.049460 -1.591904 C -3.166966 1.832338 -0.084661 H -2.763967 -0.391779 -2.580119 C -1.777182 2.332436 0.172365 IV + H -0.324789 4.150453 0.828592 [LTh PH2] . SCF energy = - C -0.830826 2.339837 -0.864035 H 0.408659 4.461784 -0.737995 H -1.144098 2.038398 -1.859501 1785.18430 H 2.763967 0.391779 -2.580119 C 0.500280 2.667746 -0.633346 H 4.150095 -0.049460 -1.591904 C 0.887729 3.027490 0.664763 H -0.408659 -4.461784 -0.737995 C 3.098842 -0.515489 -0.951756 H 1.931282 3.252474 0.860360 H 0.324789 -4.150453 0.828592 C 4.046893 0.004676 -1.787466 C -0.045588 3.084245 1.681934 F 0.000000 0.000000 2.649317 H 4.996537 -0.449257 -2.033104 H 0.262748 3.352204 2.685914 C 3.552894 1.245358 -2.253317 C -1.368243 2.721417 1.441337 H 4.045793 1.926927 -2.932034 H -2.079647 2.702007 2.259972 C 2.318326 1.419937 -1.693625 [LThIVX*]+ complexes. C 1.526217 2.546993 -1.716178 C 3.158753 -1.790337 -0.170698 N 2.116946 0.323506 -0.705632 C 1.778003 -2.274563 0.136538 IV + N -2.126430 -0.377058 -0.670511 [LTh SiH3] . SCF energy = - C 0.842427 -2.400138 -0.907045 U 0.013531 -0.063221 0.547471 1733.90618 H 1.173946 -2.234320 -1.927910 H 2.087435 3.485090 -1.802399 C -0.499173 -2.669200 -0.653621 H 1.010387 2.403504 -2.675134 C 3.200034 -0.505033 -0.765277 C -0.910509 -2.848526 0.677133 H 3.745120 -1.839147 0.856167 C 4.212343 0.046659 -1.498987 H -1.959826 -3.031526 0.884650 H 3.643349 -2.618681 -0.715931 H 5.170700 -0.409054 -1.704050 C 0.007173 -2.779649 1.712009 H -1.052643 -2.584135 -2.584350 C 3.768284 1.318922 -1.927030 H -0.315105 -2.946446 2.732210 H -2.126252 -3.571673 -1.600058 H 4.317185 2.029282 -2.528958 C 1.346715 -2.471262 1.444871 H -3.715487 2.562176 -0.694113 C 2.498400 1.482351 -1.448723 H 2.052787 -2.371335 2.262740 H -3.697860 1.774424 0.875184 C 3.186328 -1.831000 -0.071597 C -1.525906 -2.606994 -1.736700 O -0.045351 0.195748 2.652412 C 1.780273 -2.289915 0.141689 C -2.474112 -1.478991 -1.471543 H 0.043001 -0.124380 3.551973 C 0.904089 -2.374860 -0.957931 C -3.749444 -1.325910 -1.938006 H 1.296399 -2.193447 -1.954398 H -4.290825 -2.030693 -2.553150 LUIIIF. SCF energy = -1611.98194 C -0.452684 -2.628888 -0.788068 C -4.210862 -0.070402 -1.477567 C -0.943354 -2.827284 0.514727 H -5.178770 0.373195 -1.663659 C -1.143953 3.007828 -0.809190 H -2.005639 -2.995901 0.658914 C -3.201934 0.480598 -0.738714 C -2.104775 3.599435 -1.594994 C -0.087628 -2.785694 1.602933 C -3.204676 1.785824 -0.005741 H -2.166365 4.648921 -1.849686 H -0.469359 -2.956347 2.603476 C -1.805100 2.272534 0.192896 C -2.994215 2.573994 -1.983302 C 1.270347 -2.500195 1.417630 C -0.945240 2.368622 -0.916104 H -3.869587 2.670947 -2.611194 H 1.923375 -2.423125 2.280484 H -1.347480 2.173746 -1.906059 C -2.519198 1.410995 -1.423954 C -1.413461 -2.527675 -1.927026 C 0.411098 2.639365 -0.766865 C 0.000000 3.666335 -0.101843 C -2.354816 -1.385779 -1.698388 C 0.914974 2.856211 0.527334 C 1.076299 2.677494 0.222186 C -3.588264 -1.191196 -2.253664 H 1.976391 3.039713 0.658444 C 1.652382 1.908208 -0.803043 H -4.095573 -1.866290 -2.928252 C 0.071392 2.819032 1.624425 H 1.348598 2.093665 -1.829079 C -4.060819 0.057757 -1.788007 H 0.469462 3.004353 2.615544 266

Appendix

C -1.282816 2.503926 1.462204 H 3.776925 -2.509540 -0.589498 H 5.205355 -0.746253 -1.731156 H -1.928585 2.431484 2.330427 H 3.723131 -1.627182 0.929802 C 3.887310 1.046286 -1.988617 C 1.357206 2.545515 -1.918518 S -0.026996 0.267185 3.137012 H 4.454296 1.708092 -2.628878 N 2.003917 0.340991 -0.869131 H 0.231428 -0.957624 3.626025 C 2.633297 1.286063 -1.484255 N -2.099996 -0.371547 -0.712171 C 3.159399 -1.989142 0.003358 Th -0.003714 0.001967 0.391163 C 1.731967 -2.347941 0.270754 H 1.915962 3.483143 -2.018839 [LThIVCl]+. SCF energy = - C 0.828993 -2.481525 -0.799686 H 0.788435 2.416473 -2.847366 H 1.202925 -2.382185 -1.814618 1902.89946 H 3.715167 -1.668576 0.766553 C -0.526641 -2.694363 -0.583565 H 3.694283 -2.546642 -0.757104 C -0.991988 -2.785421 0.737617 H -1.025737 -2.498790 -2.706751 C 3.152542 -0.450872 -0.827912 H -2.054702 -2.913119 0.914591 H -2.085693 -3.548592 -1.773966 C 4.128258 0.107979 -1.602759 C -0.113971 -2.677736 1.799682 H -3.773627 2.522402 -0.585708 H 5.098255 -0.321433 -1.810049 H -0.478784 -2.749487 2.817870 H -3.701584 1.706326 0.968824 C 3.630797 1.347645 -2.067884 C 1.244482 -2.444801 1.565918 P 0.499156 0.135449 3.214356 H 4.140065 2.052666 -2.709540 H 1.917031 -2.315185 2.407005 H 0.110168 -1.033099 3.915495 C 2.367512 1.484778 -1.568251 C -1.511319 -2.692336 -1.708974 H -0.381780 1.025870 3.879126 C 3.210722 -1.747145 -0.082665 C -2.446504 -1.530803 -1.576480 C 1.831640 -2.266275 0.162599 C -3.689885 -1.371300 -2.135655 C 0.934387 -2.374774 -0.916892 H -4.219933 -2.100706 -2.732854 H 1.296441 -2.171856 -1.920429 [LThIVSH]+. SCF energy = - C -4.118871 -0.066274 -1.803247 C -0.407429 -2.670075 -0.715795 H -5.054785 0.401506 -2.076518 1841.46361 C -0.860543 -2.897381 0.596886 C -3.120078 0.501250 -1.051008 H -1.913547 -3.100827 0.763381 C -3.102560 1.857763 -0.410160 C -3.153467 0.427456 -0.849104 C 0.021779 -2.852400 1.660638 C -1.707517 2.271115 -0.041167 C -4.129127 -0.144221 -1.615998 H -0.331617 -3.027318 2.669871 C -0.730268 2.348921 -1.027701 H -5.097003 0.283555 -1.836200 C 1.362582 -2.514908 1.446453 H -1.016306 2.200898 -2.065084 C -3.633973 -1.395192 -2.052786 H 2.032681 -2.416936 2.293672 C 0.645485 2.523785 -0.699365 H -4.143112 -2.111743 -2.681682 C -1.396846 -2.592405 -1.830316 C 0.968256 2.803176 0.656426 C -2.372456 -1.524676 -1.544764 C -2.367502 -1.484858 -1.568219 H 2.000052 3.021420 0.914853 C -3.204197 1.738568 -0.129055 C -3.630785 -1.347726 -2.067858 C 0.015677 2.725810 1.641943 C -1.822043 2.258657 0.102180 H -4.140057 -2.052758 -2.709498 H 0.278006 2.923138 2.673008 C -0.924513 2.336568 -0.977397 C -4.128241 -0.108049 -1.602760 C -1.334904 2.373087 1.314422 H -1.286501 2.106870 -1.975285 H -5.098237 0.321363 -1.810060 H -2.083994 2.313205 2.093519 C 0.420668 2.635881 -0.785929 C -3.152536 0.450799 -0.827898 C 1.725614 2.452068 -1.732223 C 0.873452 2.898889 0.517521 C -3.210722 1.747073 -0.082656 N 2.216653 0.220814 -0.707527 H 1.926483 3.104690 0.680154 C -1.831641 2.266227 0.162573 N -2.074163 -0.389087 -0.893617 C -0.009425 2.883156 1.583744 C -0.934382 2.374615 -0.916923 Th -0.008338 0.145382 0.334144 H 0.345091 3.095030 2.585635 H -1.296427 2.171580 -1.920441 H 2.314611 3.378985 -1.740304 C -1.351345 2.540415 1.380957 C 0.407421 2.669995 -0.715856 H 1.262867 2.378882 -2.725526 H -2.023335 2.475204 2.229622 C 0.860517 2.897486 0.596800 H 3.696435 -1.938991 0.959408 C 1.408813 2.528058 -1.900219 H 1.913508 3.101023 0.763275 H 3.636774 -2.785650 -0.580984 C 2.378124 1.424269 -1.613910 C -0.021813 2.852608 1.660553 H -0.966602 -2.666972 -2.661786 C 3.637808 1.264575 -2.118063 H 0.331564 3.027693 2.669764 H -2.085577 -3.626713 -1.700136 H 4.147185 1.946283 -2.784359 C -1.362600 2.515027 1.446402 H -3.538085 2.590366 -1.100205 C 4.131657 0.037280 -1.617266 H -2.032708 2.417161 2.293626 H -3.724079 1.872279 0.493829 H 5.098299 -0.403327 -1.816650 C 1.396834 2.592295 -1.830383 Si -0.375551 0.044399 3.381389 C 3.157070 -0.490237 -0.818261 N 2.033239 0.381223 -0.779929 H -1.650414 -0.711926 3.699737 C 3.205869 -1.760132 -0.028236 N -2.033221 -0.381280 -0.779928 H 0.649731 -0.736229 4.178250 C 1.822252 -2.265726 0.224572 Th 0.000005 0.000001 0.427689 H -0.534749 1.310983 4.181506 C 0.929411 -2.399497 -0.854471 H 1.943861 3.538438 -1.912074 H 1.297157 -2.222216 -1.860845 H 0.865900 2.451590 -2.779727

C -0.415809 -2.687609 -0.654685 H 3.735120 -1.645599 0.875202 LThIIIPH2. SCF energy = - C -0.875783 -2.882437 0.659039 H 3.780661 -2.473681 -0.674268 1785.35234 H -1.929198 -3.082716 0.825800 H -0.865919 -2.451763 -2.779672 C 0.001906 -2.810910 1.725927 H -1.943894 -3.538541 -1.911950 C 3.109071 -0.594954 -0.969465 H -0.361261 -2.987524 2.731838 H -3.780678 2.473590 -0.674266 C 4.117631 -0.101458 -1.758701 C 1.344741 -2.478859 1.513033 H -3.735107 1.645542 0.875221 H 5.044149 -0.604849 -1.998584 H 2.018828 -2.373936 2.356520 Cl -0.000009 0.000140 3.046333 C 3.713351 1.187200 -2.176812 C -1.399521 -2.637623 -1.776452 H 4.260243 1.870184 -2.812771 N -2.039251 -0.406473 -0.780287 C 2.473027 1.406276 -1.632423 N 2.044720 0.348708 -0.790832 LThIIIX* complexes. C 3.040253 -1.890382 -0.225422 Th 0.000245 0.006329 0.416393 C 1.620122 -2.246443 0.083504 H -1.944298 -3.586694 -1.837605 C 0.679031 -2.410543 -0.973561 LThIIISiH3. SCF energy = - H -0.863315 -2.519682 -2.725969 H 1.025357 -2.310642 -1.998593 H -3.724518 1.656985 0.832924 1734.07782 C -0.667195 -2.561180 -0.723939 H -3.773961 2.456067 -0.731778 C -1.117524 -2.626137 0.636347 H 0.875934 2.366102 -2.845100 C 3.244916 -0.701113 -0.751690 H -2.175572 -2.725709 0.842216 H 1.956974 3.471239 -2.005362 C 4.275878 -0.232293 -1.526315 C -0.166681 -2.712403 1.670603 267

Appendix

H -0.498499 -2.887121 2.686496 C -0.575050 -2.722809 -0.559332 H -0.963044 -2.420802 -2.840645 C 1.174639 -2.501987 1.414764 C -0.949081 -2.934419 0.776311 H -2.129431 -3.397395 -1.948587 H 1.891369 -2.503071 2.229082 H -1.993611 -3.116432 1.007627 H -3.589548 2.715009 -0.752194 C -1.684804 -2.475442 -1.813986 C -0.001523 -2.898811 1.778599 H -3.609728 1.831042 0.766719 C -2.554059 -1.275895 -1.597396 H -0.296259 -3.078225 2.806895 Cl -0.394212 0.083626 3.103883 C -3.811848 -1.029167 -2.087576 C 1.328920 -2.592448 1.481316 H -4.391103 -1.689791 -2.717930 H 2.055560 -2.504949 2.280538 C -4.184978 0.251544 -1.621652 C -1.628138 -2.677578 -1.617834 LUIIIX* complexes. H -5.113507 0.772295 -1.812475 N -2.165524 -0.401722 -0.711337 C -3.141916 0.713084 -0.857954 N 2.073346 0.232424 -0.881635 LUIIISiH3. SCF energy = -1803.33184 C -3.074927 1.989165 -0.078508 Th -0.002539 0.166096 0.398285 C -1.655546 2.376158 0.186578 H -2.181413 -3.624017 -1.635426 C 3.214820 -0.555448 -0.818152 C -0.751615 2.445662 -0.886029 H -1.145890 -2.576642 -2.599216 C 4.237437 -0.033629 -1.572891 H -1.124475 2.283489 -1.892760 H -3.743121 1.851089 0.810364 H 5.176711 -0.519022 -1.800648 C 0.603558 2.664730 -0.684583 H -3.718154 2.529861 -0.810407 C 3.823190 1.255186 -1.975409 C 1.070646 2.824305 0.628988 H 0.915938 2.310898 -2.862246 H 4.374365 1.958131 -2.585139 H 2.134167 2.953766 0.799827 H 2.034131 3.358287 -2.006078 C 2.565401 1.443359 -1.454928 C 0.189910 2.790389 1.694386 H 3.626525 -2.721486 -0.728379 C 3.152454 -1.880911 -0.128850 H 0.560239 2.916209 2.705120 H 3.678305 -1.809329 0.774526 C 1.728746 -2.277038 0.105028 C -1.171872 2.553850 1.475619 S 0.599836 0.247130 3.121500 C 0.834038 -2.334428 -0.981656 H -1.849915 2.488768 2.318769 H 0.212200 -0.969676 3.545678 H 1.214745 -2.156805 -1.982720 C 1.576884 2.589715 -1.814939 C -0.521292 -2.573351 -0.791405 N 2.076512 0.318413 -0.876753 C -0.998295 -2.759501 0.516711 III N -2.114908 -0.211674 -0.831150 LTh Cl. SCF energy = -1903.06655 H -2.061507 -2.904362 0.675223 Th 0.019298 -0.126831 0.420345 C -0.127388 -2.730402 1.593238 C 3.184761 -0.546239 -0.789621 H 2.181088 3.504294 -1.849123 H -0.497263 -2.886673 2.600156 C 4.229609 -0.025796 -1.509489 H 1.023503 2.541051 -2.761721 C 1.233070 -2.482434 1.385448 H 5.182646 -0.505129 -1.686460 H 3.603122 -1.832945 0.715931 H 1.898217 -2.414824 2.239754 C 3.818441 1.250363 -1.956909 H 3.522515 -2.678755 -0.819850 C -1.494981 -2.490175 -1.922479 H 4.385994 1.948062 -2.557835 H -1.172294 -2.433746 -2.783499 C -2.421584 -1.332107 -1.717945 C 2.538938 1.435150 -1.499237 H -2.309143 -3.377947 -1.822220 C -3.643643 -1.108692 -2.304468 C 3.105537 -1.851379 -0.065048 H -3.576348 2.784374 -0.644711 H -4.154399 -1.771044 -2.990083 C 1.679432 -2.235818 0.163014 H -3.605854 1.907389 0.878850 C -4.085716 0.153046 -1.847928 C 0.796339 -2.398791 -0.942991 P 0.238020 0.099748 3.301746 H -5.010225 0.652821 -2.103207 H 1.190184 -2.276959 -1.948147 H -0.577364 1.040522 3.991545 C -3.115399 0.624053 -0.997323 C -0.557387 -2.570110 -0.760906 H -0.200965 -1.042912 4.017389 C -3.103590 1.897948 -0.214126 C -1.074537 -2.660172 0.576237 C -1.699747 2.278123 0.138208 H -2.139756 -2.779413 0.727341 C -0.737568 2.404750 -0.883277 III C -0.170976 -2.764958 1.652728 LTh SH. SCF energy = -1841.62692 H -1.052468 2.290227 -1.915866 H -0.549341 -2.931337 2.654233 C 0.601546 2.629049 -0.591230 C -3.253336 0.451954 -0.752952 C 1.173387 -2.532965 1.464033 C 0.990972 2.741907 0.754167 C -4.313425 -0.148953 -1.385226 H 1.846405 -2.523143 2.314942 H 2.041040 2.882736 0.987173 H -5.286787 0.290993 -1.554222 C -1.521250 -2.485368 -1.898004 C 0.054831 2.646379 1.767859 C -3.881885 -1.439014 -1.766669 C -2.418018 -1.303292 -1.705907 H 0.355937 2.734473 2.804049 H -4.447840 -2.185370 -2.307495 C -3.653473 -1.067877 -2.252465 C -1.287829 2.400574 1.459354 C -2.578312 -1.554429 -1.353606 H -4.191710 -1.727931 -2.918611 H -2.008105 2.283227 2.262719 C -3.206738 1.822704 -0.146253 C -4.066239 0.201669 -1.789055 C 1.649828 2.611120 -1.655792 C -1.792111 2.261764 0.079937 H -4.991061 0.713174 -2.018840 N 2.168300 0.339167 -0.728129 C -0.914109 2.342215 -0.988439 C -3.069812 0.668448 -0.969284 N -2.074200 -0.276245 -0.899521 H -1.291635 2.166887 -1.992072 C -3.064642 1.939440 -0.180029 U -0.002974 -0.004922 0.380593 C 0.486276 2.497478 -0.791990 C -1.668709 2.387270 0.116811 H 2.229148 3.542213 -1.624238 C 0.928879 2.834817 0.526487 C -0.723270 2.427869 -0.921437 H 1.162970 2.576895 -2.638814 H 1.975343 3.075717 0.684983 H -1.047707 2.203274 -1.932873 H 3.680720 -1.867725 0.833321 C 0.060211 2.796154 1.587335 C 0.613232 2.697565 -0.675061 H 3.652136 -2.636943 -0.747516 H 0.413988 3.019169 2.586547 C 1.019473 2.945260 0.645627 H -0.941701 -2.402662 -2.866278 C -1.297269 2.400218 1.399322 H 2.071433 3.116684 0.850165 H -2.075421 -3.419033 -1.983301 H -1.963891 2.322956 2.247746 C 0.094580 2.950708 1.670261 H -3.566939 2.695606 -0.808349 C 1.467163 2.421377 -1.918665 H 0.412043 3.126942 2.691248 H -3.692281 1.814984 0.708622 C 2.414095 1.279744 -1.719355 C -1.247122 2.661911 1.408263 Si -0.333943 -0.193915 3.425363 C 3.629903 1.042811 -2.308048 H -1.953176 2.605853 2.228603 H -1.717442 -0.772022 3.663900 H 4.136636 1.691085 -3.009568 C 1.631247 2.592561 -1.761704 H 0.540291 -1.148489 4.209756 C 4.072809 -0.215201 -1.834851 N 2.119997 0.338252 -0.765168 H -0.354240 1.031201 4.312450 H 4.994102 -0.721231 -2.090447 N -2.030996 -0.242922 -0.904286

C 3.112287 -0.674595 -0.970231 Th 0.018491 -0.151861 0.460553 C 3.117595 -1.931826 -0.161193 H 2.224254 3.513281 -1.812714 C 1.723500 -2.366318 0.170732 H 1.116120 2.494364 -2.726236 LUIIIPH2. SCF energy = -1853.89517 C 0.756550 -2.454313 -0.844816 H 3.618262 -1.798076 0.904953 H 1.058964 -2.270388 -1.871696 H 3.634352 -2.621683 -0.643625 C 3.181152 -0.368317 -0.785828 268

Appendix

C 4.157579 0.222805 -1.539361 H 0.298950 2.989402 2.736153 C 0.409548 2.688615 -0.687147 H 5.142900 -0.178354 -1.730804 C -1.364946 2.523508 1.454777 C 0.839517 2.923101 0.631700 C 3.631648 1.446668 -2.009325 H -2.062711 2.424009 2.279922 H 1.888910 3.131780 0.813974 H 4.128260 2.169118 -2.641504 C 1.486952 2.621888 -1.743119 C -0.061735 2.884218 1.679924 C 2.352369 1.538660 -1.534617 C 2.428485 1.482410 -1.502334 H 0.275547 3.074563 2.692456 C 3.266287 -1.669933 -0.052411 C 3.691129 1.330634 -2.005195 C -1.395358 2.540420 1.445836 C 1.902558 -2.241731 0.159365 H 4.219404 2.042966 -2.623128 H -2.084995 2.451763 2.278644 C 1.017373 -2.338409 -0.929870 C 4.153908 0.064037 -1.582887 C 1.416545 2.613896 -1.786778 H 1.379587 -2.086284 -1.921730 H 5.112978 -0.383679 -1.802377 N 2.047902 0.387888 -0.762486 C -0.315371 -2.680805 -0.750463 C 3.158699 -0.494351 -0.829170 N -2.048054 -0.388088 -0.762183 C -0.771398 -2.969783 0.548873 C 3.190120 -1.814266 -0.121058 U 0.000036 -0.000044 0.476274 H -1.819506 -3.208517 0.698548 C 1.805514 -2.302950 0.155855 H 1.965562 3.560059 -1.854951 C 0.106323 -2.954342 1.617136 C 0.885939 -2.414914 -0.903031 H 0.897286 2.481790 -2.743943 H -0.244390 -3.199508 2.613570 H 1.230335 -2.229258 -1.916225 H 3.760599 -1.680868 0.843140 C 1.435885 -2.570795 1.426226 C -0.456442 -2.686723 -0.671937 H 3.772408 -2.477339 -0.722484 H 2.107823 -2.511170 2.276154 C -0.885066 -2.890999 0.652457 H -0.897404 -2.482315 -2.743744 C -1.294523 -2.599128 -1.873308 H -1.937200 -3.078870 0.841633 H -1.965769 -3.560222 -1.854467 C -2.300474 -1.527619 -1.597342 C 0.019233 -2.844717 1.698515 H -3.772691 2.477181 -0.721906 C -3.568148 -1.430891 -2.100200 H -0.316622 -3.001612 2.717709 H -3.760315 1.680472 0.843571 H -4.051127 -2.148571 -2.748159 C 1.358290 -2.529013 1.453253 Cl -0.000253 0.000190 2.566140 C -4.104200 -0.210140 -1.632723 H 2.048886 -2.433877 2.284919 H -5.085176 0.192441 -1.842528 C -1.465823 -2.610481 -1.769678 C -3.145635 0.374869 -0.852720 N -2.051876 -0.357273 -0.775471 [LThIVX’’]+ complexes. C -3.247690 1.671677 -0.112920 N 2.064430 0.363460 -0.755760 C -1.889456 2.243468 0.132726 U 0.000977 -0.000132 0.459062 [LThIVCH2Ph]+. SCF energy = - C -0.980063 2.346697 -0.936716 H -2.036304 -3.545184 -1.817047 H -1.320739 2.099743 -1.937552 H -0.947193 -2.509653 -2.730936 1713.44894 C 0.348182 2.688378 -0.726984 H -3.747944 1.754485 0.799146 C 0.774177 2.972260 0.583663 H -3.706007 2.548459 -0.767212 C -1.088091 -2.852564 1.043666 H 1.818204 3.211998 0.757827 H 0.976662 2.526137 -2.709347 C -1.505288 -3.482961 2.184255 C -0.127617 2.952258 1.631793 H 2.057799 3.556815 -1.780625 H -1.913988 -4.481756 2.246449 H 0.200138 3.196688 2.636184 H 3.718493 -2.542312 -0.748493 C -1.290118 -2.584765 3.254080 C -1.452043 2.567187 1.410796 H 3.746855 -1.756601 0.822330 H -1.497120 -2.758041 4.300656 H -2.140816 2.499697 2.246589 S -0.008136 -0.005679 2.565032 C -0.736478 -1.453650 2.719416 C 1.352583 2.611463 -1.827716 H -0.860152 -0.315722 2.880533 C -1.087939 -3.388613 -0.353718 N 2.038430 0.425108 -0.758257 C -0.037514 -2.708788 -1.173842 N -2.003924 -0.420866 -0.804061 C 1.266839 -2.589023 -0.660537 U -0.001398 0.000238 0.484449 LUIIICl. SCF energy = -1972.12644 H 1.504383 -3.075056 0.280674 H 1.874403 3.570119 -1.926221 C 2.230925 -1.820854 -1.300179 C 1.895144 -1.180042 -2.504572 H 0.834794 2.435119 -2.778561 C 3.160747 -0.446279 -0.826263 H 2.635619 -0.556288 -2.994890 H 3.767218 -1.563263 0.917963 C 4.142024 0.122424 -1.590282 C 0.640119 -1.348142 -3.057281 H 3.873691 -2.369615 -0.639549 H 5.109852 -0.307948 -1.806004 H 0.397580 -0.874644 -4.002136 H -0.755605 -2.418211 -2.811423 C 3.650449 1.371956 -2.030622 C -0.333050 -2.090056 -2.382941 H -1.813796 -3.557410 -1.987708 H 4.161059 2.086271 -2.660972 H -1.331179 -2.173634 -2.800465 H -3.842512 2.374339 -0.709243 C 2.385610 1.502631 -1.527693 C 3.554814 -1.546447 -0.667679 H -3.770140 1.558112 0.845157 C 3.217745 -1.758671 -0.106978 C 3.676113 -0.088115 -0.362481 P -0.140545 -0.033393 2.751747 C 1.841866 -2.279240 0.155406 C 4.820175 0.648612 -0.233443 H -0.932864 -0.217400 3.159756 C 0.928051 -2.389677 -0.908712 H 5.828383 0.288242 -0.381205 H 0.667862 0.153286 3.125552 H 1.272616 -2.180446 -1.917113 C 4.429995 1.951774 0.152402 C -0.409647 -2.688702 -0.686931 H 5.079273 2.792351 0.352846 C -0.839490 -2.922992 0.631968 III C 3.065124 1.955012 0.225545 LU SH. SCF energy = -1910.51130 H -1.888855 -3.131656 0.814414 C 2.170063 3.094768 0.595584 C 0.061856 -2.883923 1.680122 C 0.878947 2.582355 1.149880 C -3.145489 0.500939 -0.853828 H -0.275424 -3.074091 2.692690 C 0.898198 1.589864 2.145244 C -4.134125 -0.053449 -1.619060 C 1.395438 -2.540169 1.445903 H 1.853904 1.283797 2.559734 H -5.091269 0.395439 -1.844481 H 2.085173 -2.451428 2.278623 C -0.266414 0.943905 2.549546 C -3.667679 -1.317814 -2.044014 C -1.416667 -2.614088 -1.786527 C -1.486986 1.341733 1.982661 H -4.190571 -2.026869 -2.670239 C -2.385597 -1.502659 -1.527687 H -2.397788 0.826605 2.269137 C -2.409431 -1.472266 -1.531051 C -3.650289 -1.371766 -2.030972 C -1.530788 2.374600 1.062521 C -3.183066 1.817106 -0.139071 H -4.160784 -2.085901 -2.661620 H -2.481707 2.684851 0.648688 C -1.800920 2.304293 0.152384 C -4.141860 -0.122261 -1.590582 C -0.348459 2.969923 0.619546 C -0.872218 2.421812 -0.897900 H -5.109558 0.308261 -1.806573 H -0.383436 3.737626 -0.145897 H -1.207829 2.241504 -1.915000 C -3.160705 0.446233 -0.826211 C -0.233703 -0.247784 3.449485 C 0.468106 2.692369 -0.653768 C -3.217741 1.758482 -0.106694 N -0.608212 -1.582322 1.339634 C 0.885248 2.889657 0.675343 C -1.841876 2.279250 0.155429 N 2.557625 0.698606 -0.095997 H 1.935701 3.076504 0.874605 C -0.928144 2.389557 -0.908783 Th 0.231847 0.085251 -0.199120 C -0.028069 2.837886 1.713277 H -1.272784 2.180153 -1.917124 H -0.864686 -0.069138 4.327516 269

Appendix

H 0.787765 -0.396377 3.820901 H -2.531951 -2.572623 -1.550111 H 3.266044 -2.908163 -2.110179 H -2.061976 -3.276342 -0.847305 H -1.360704 -3.805287 -1.995022 H 3.854790 1.973513 -0.653503 H -0.887413 -4.466544 -0.320249 H 3.357441 -1.885411 -1.870368 H 3.259344 3.055545 -1.912507 H 3.661482 -2.160756 0.234893 H 3.594269 -0.735702 -3.180207 H -0.871011 3.260582 2.968738 H 4.362465 -1.841325 -1.347127 H 3.463639 2.457964 2.367155 H -1.820281 3.109391 1.497189 H 2.675699 3.715529 1.345133 H 2.434774 3.374927 1.279224 C -3.436679 -0.450635 -1.034399 H 1.960278 3.751591 -0.257920 N -1.271720 1.757462 -0.555240 C -4.225539 0.697400 -0.874034 C -2.521852 1.127916 -1.597673 H -0.983966 2.666536 -0.911857 C -4.064811 -1.681799 -0.796471 C -3.382433 2.229530 -1.679537 C -2.656384 1.674319 -0.459736 C -5.552492 0.621301 -0.482727 C -3.041397 -0.046673 -1.042594 C -3.494344 2.731040 -0.829394 H -3.786689 1.670975 -1.081739 C -4.686371 2.157781 -1.222243 C -3.252337 0.498957 0.018242 C -5.391498 -1.759583 -0.405384 H -3.018360 3.151184 -2.125060 C -4.868995 2.612549 -0.725485 H -3.496596 -2.598359 -0.938592 C -4.347179 -0.121336 -0.572355 H -3.056265 3.653604 -1.201156 C -6.148014 -0.608041 -0.238403 H -2.433303 -0.950873 -0.998040 C -4.630545 0.388243 0.119017 H -6.131390 1.534318 -0.377392 C -5.174894 0.984257 -0.657089 H -2.646415 -0.356173 0.327391 H -5.842625 -2.733356 -0.237861 H -5.334959 3.023319 -1.313417 C -5.448872 1.443213 -0.252213 H -7.187943 -0.668476 0.063497 H -4.715307 -1.049225 -0.147000 H -5.496782 3.447619 -1.018883 C -2.024510 -0.370276 -1.436662 H -6.197507 0.932349 -0.300434 H -5.064952 -0.532861 0.493715 H -1.760591 -1.258859 -2.029884 C -1.095810 1.199114 -2.003839 H -6.526175 1.356732 -0.172819 H -1.889872 0.496039 -2.104428 H -0.931977 0.620580 -2.919405 H -0.798411 2.227433 -2.241657 LThIIIX’’ complexes. LThIIINHPh. SCF energy = - 1729.69633 IV + [LTh NHPh] . SCF energy = - LThIIICH2Ph. SCF energy = 1729.53641 C 3.398388 -1.128822 -0.886559 C 2.382830 -2.749332 -0.182415 C 4.062480 -2.329880 -0.826826 C -1.071288 -3.053290 -0.031065 C 3.084463 -3.655218 0.572486 H 4.817865 -2.674788 -1.519561 C -1.284777 -4.159160 0.744238 H 3.712517 -4.449801 0.193513 C 3.603748 -2.990342 0.335007 H -1.771543 -5.071405 0.429159 C 2.818983 -3.347082 1.926026 H 3.936706 -3.945793 0.717702 C -0.751508 -3.877710 2.021839 H 3.207084 -3.850682 2.801099 C 2.674385 -2.165645 0.922488 H -0.739600 -4.533597 2.880897 C 1.981807 -2.260208 1.924336 C 3.638525 0.015262 -1.828498 C -0.222701 -2.618084 1.965851 C 2.297873 -2.630882 -1.669081 C 2.407865 0.851109 -1.979080 C -1.476126 -2.855627 -1.458692 C 1.907314 -1.240675 -2.053866 C 2.235643 1.999958 -1.230388 C -0.631581 -1.806241 -2.104368 C 2.691246 -0.127439 -1.615115 H 3.055872 2.343190 -0.603724 C 0.770825 -1.912747 -2.051712 H 3.589162 -0.316620 -1.034307 C 0.979315 2.648048 -1.128951 H 1.213105 -2.807590 -1.624112 C 2.267084 1.166703 -1.812068 C -0.046496 2.241008 -2.050941 C 1.589024 -0.871071 -2.468798 C 1.040654 1.399178 -2.512449 H -0.975986 2.799503 -2.089822 C 0.992064 0.290891 -2.990698 H 0.695644 2.415316 -2.655804 C 0.136732 1.143508 -2.861990 H 1.627847 1.115866 -3.296219 C 0.435568 0.317064 -3.196483 H -0.658787 0.833796 -3.530900 C -0.383297 0.381616 -3.106598 H -0.404379 0.501556 -3.856658 C 1.309781 0.356209 -2.760749 H -0.839549 1.274177 -3.518684 C 0.844132 -0.972884 -2.960969 H 1.438069 -0.528503 -3.371676 C -1.195806 -0.657378 -2.645724 H 0.324260 -1.802510 -3.430404 C 0.738433 3.751098 -0.146389 H -2.275112 -0.552227 -2.676950 C 2.945008 2.324710 -1.156864 C 0.037466 3.267441 1.092325 C 3.063374 -0.893361 -2.234334 C 2.003195 2.979262 -0.196442 C -0.238797 3.958095 2.245706 C 3.451267 0.183068 -1.268804 C 2.038455 4.259647 0.296298 H 0.048087 4.977648 2.463807 C 4.684029 0.753804 -1.114358 H 2.762529 5.020836 0.040155 C -0.979560 3.084783 3.074853 H 5.560441 0.543901 -1.711122 C 0.966177 4.372582 1.209130 H -1.378177 3.300535 4.057252 C 4.594601 1.641014 -0.018048 H 0.691809 5.240594 1.793038 C -1.126732 1.904307 2.388607 H 5.386704 2.254226 0.388060 C 0.322913 3.159967 1.213446 C -1.958319 0.729599 2.783528 C 3.307433 1.584119 0.439293 C -0.897235 2.772096 1.986421 C -1.392589 -0.621874 2.444636 C 2.711442 2.355504 1.575661 C -0.954925 1.288498 2.160108 C -0.016380 -0.871880 2.519939 C 1.505174 1.656618 2.114737 C 0.170073 0.609527 2.659741 H 0.639936 -0.080394 2.884683 C 1.598361 0.304358 2.497297 H 1.033134 1.187544 2.974864 C 0.521591 -2.122239 2.205274 H 2.570753 -0.179005 2.478235 C 0.216571 -0.774009 2.710974 C -0.349061 -3.144879 1.832784 C 0.470131 -0.431592 2.829844 C -0.891725 -1.505318 2.254042 H 0.054924 -4.120957 1.581839 C -0.783838 0.207750 2.811400 H -0.843206 -2.589423 2.257242 C -1.714506 -2.922377 1.793775 H -1.673441 -0.369645 3.041243 C -2.014494 -0.852316 1.787499 H -2.385589 -3.727067 1.511292 C -0.883524 1.550290 2.498448 H -2.870187 -1.410602 1.426344 C -2.232318 -1.669300 2.082297 H -1.853802 2.033671 2.484058 C -2.041194 0.544407 1.729786 H -3.301323 -1.495561 2.013729 C 0.258204 2.268605 2.132518 H -2.912632 1.038285 1.314448 C 2.005596 -2.346115 2.248153 H 0.166753 3.307837 1.835107 C 1.463293 -1.495664 3.098995 N 2.511866 -1.016029 0.174156 C 0.535928 -1.907142 3.042658 N 1.687825 -1.872226 0.629269 N -0.490134 1.987926 1.163312 N -0.412683 -2.066149 0.699177 N 0.945732 2.276673 0.351661 Th 0.409466 0.185559 -0.196153 N 2.561140 0.686603 -0.321356 Th 0.272895 -0.029343 -0.272391 H 2.212064 -3.361958 2.597554 Th 0.229369 0.141797 -0.060322 H 1.255207 -2.187866 3.923815 H 2.444665 -1.661097 2.986750 H 0.102624 -2.164772 4.015886 H 2.198812 -0.770951 3.471322 H 3.957356 -0.376954 -2.800670 H 1.585914 -2.223204 3.072202 H 1.564460 -3.334959 -2.086082 H 4.455911 0.646010 -1.454786 270

Appendix

H 1.693774 4.218003 0.121887 H -3.762442 1.826866 -0.537971 H -3.378446 -1.147872 -3.267855 H 0.139408 4.540078 -0.622986 H -4.157350 1.386085 -2.193259 H -3.488789 -1.272391 3.101468 H -2.121176 0.780326 3.867998 H -2.757972 -3.598598 1.493415 H -2.367306 -2.572596 2.725986 H -2.957384 0.794803 2.330003 H -1.826585 -3.976639 0.051581 N 1.402757 -1.606479 -0.002507 N -1.183807 -1.181462 -1.098653 C 2.714054 -1.071147 -1.529742 H 1.067454 -2.554676 -0.169618 H -0.832027 -2.077063 -1.434995 C 3.418869 -2.284354 -1.503960 C 2.763413 -1.609938 0.198096 C -2.533791 -1.069329 -1.370175 C 3.453247 0.090164 -1.256206 C 3.518740 -2.791618 0.266984 C -3.237256 0.090423 -1.008770 C 4.770534 -2.333958 -1.206638 C 3.458225 -0.396006 0.342474 C -3.255879 -2.093114 -1.998428 H 2.888683 -3.204291 -1.738180 C 4.885877 -2.758265 0.475553 C -4.590700 0.213134 -1.267306 C 4.805510 0.041545 -0.960720 H 3.011243 -3.746940 0.156237 H -2.714638 0.908872 -0.516052 H 2.952482 1.055611 -1.286454 C 4.824787 -0.372897 0.558207 C -4.610390 -1.962362 -2.251898 C 5.477505 -1.172001 -0.927685 H 2.915252 0.545348 0.269546 H -2.735497 -3.001865 -2.290783 H 5.281853 -3.292347 -1.203782 C 5.555001 -1.551443 0.627718 C -5.292900 -0.809894 -1.890432 H 5.341110 0.963712 -0.755235 H 5.437627 -3.692694 0.522017 H -5.104386 1.124353 -0.975700 H 6.536818 -1.211049 -0.698442 H 5.327819 0.583797 0.664214 H -5.139134 -2.774838 -2.741515 C 1.267869 -1.014995 -1.763353 H 6.626478 -1.529369 0.791562 H -6.353592 -0.709239 -2.091188 H 1.008727 -0.201114 -2.458688 H 0.869835 -1.949336 -2.177240 [LThIVX**]+ complexes. LUIIIX’’ complexes. III LU NHPh. SCF energy = - [LThIVSiH2Ph]+. SCF energy = - III LU CH2Ph. SCF energy = - 1798.94096 1964.75961 1782.85842 C 0.783930 2.909078 -1.284136 C 2.048447 -3.033021 -0.081525 C 0.665108 2.988082 1.204185 C 0.765008 4.276966 -1.148923 C 2.572644 -3.998872 0.731003 C 0.743967 3.763955 2.336593 H 1.129150 4.992887 -1.873563 H 3.080170 -4.896282 0.406533 H 0.974868 4.820323 2.369180 C 0.200658 4.557738 0.116584 C 2.319182 -3.600943 2.063746 C 0.485199 2.914116 3.436040 H 0.030911 5.531888 0.554458 H 2.597798 -4.130484 2.963853 H 0.463291 3.187222 4.482114 C -0.109493 3.345269 0.681823 C 1.664926 -2.402231 2.006272 C 0.247908 1.665970 2.914227 C 1.357370 2.117169 -2.415565 C 2.040421 -2.997470 -1.577134 C 0.921291 3.413985 -0.204518 C 0.644956 0.821506 -2.690426 C 1.894876 -1.590709 -2.058990 C 0.043178 2.746823 -1.228403 C -0.747734 0.728760 -2.558111 C 2.793302 -0.605559 -1.605870 C -1.263617 2.359249 -0.905937 H -1.311720 1.625368 -2.311761 H 3.631711 -0.907873 -0.985159 H -1.652447 2.605228 0.079459 C -1.421934 -0.478820 -2.734622 C 2.596664 0.741592 -1.888148 C -2.078082 1.684491 -1.814771 C -0.686581 -1.605274 -3.108579 C 1.484378 1.112660 -2.663863 C -1.586016 1.438046 -3.096347 H -1.199521 -2.552859 -3.242978 H 1.305749 2.164537 -2.862046 H -2.204349 0.905335 -3.812105 C 0.679431 -1.513085 -3.309294 C 0.614045 0.151582 -3.149999 C -0.321821 1.876087 -3.452972 H 1.243704 -2.390513 -3.607518 H -0.234060 0.442322 -3.759723 H 0.048451 1.696121 -4.457043 C 1.344400 -0.316424 -3.077600 C 0.810021 -1.197446 -2.833698 C 0.494645 2.506421 -2.522565 H 2.424160 -0.269648 -3.178602 H 0.096150 -1.936644 -3.180601 H 1.499317 2.808962 -2.802932 C -2.897163 -0.559197 -2.479664 C 3.433081 1.802285 -1.251911 C -3.435604 1.212041 -1.388629 C -3.238868 -1.174925 -1.157744 C 2.587444 2.636559 -0.340898 C -3.481879 -0.240852 -1.030439 C -4.379413 -1.879957 -0.855024 C 2.833799 3.905776 0.102154 C -4.548749 -1.087797 -1.210539 H -5.155321 -2.162504 -1.553708 H 3.675332 4.524139 -0.176528 H -5.473446 -0.843806 -1.715938 C -4.354233 -2.123051 0.535545 C 1.792003 4.242069 0.997164 C -4.217090 -2.307063 -0.580435 H -5.096703 -2.648046 1.121103 H 1.674383 5.171143 1.536752 H -4.826731 -3.198139 -0.518280 C -3.192329 -1.564150 1.008483 C 0.947018 3.169314 1.049458 C -2.958281 -2.145970 -0.057331 C -2.681014 -1.566816 2.419094 C -0.322496 3.035781 1.829901 C -2.143297 -3.151389 0.701375 C -1.523669 -0.631572 2.578012 C -0.641573 1.593068 2.054193 C -0.930049 -2.515904 1.303370 C -1.701671 0.752516 2.391039 C 0.325736 0.754579 2.642450 C -1.072652 -1.506283 2.274018 H -2.701807 1.130626 2.201899 H 1.249831 1.195204 3.005048 H -2.068239 -1.256583 2.627736 C -0.620230 1.630581 2.372754 C 0.145082 -0.621721 2.712665 C 0.023009 -0.777613 2.737116 C 0.672197 1.111866 2.579467 C -1.046182 -1.173067 2.207171 C 1.298117 -1.089237 2.233240 H 1.522278 1.784520 2.542572 H -1.179961 -2.249704 2.235464 H 2.152770 -0.507205 2.560439 C 0.862799 -0.244706 2.799552 C -2.024793 -0.359059 1.664157 C 1.461911 -2.106531 1.301050 H 1.863871 -0.637510 2.934736 H -2.947769 -0.780045 1.280875 H 2.446608 -2.328561 0.907338 C -0.233497 -1.114682 2.785381 C -1.812199 1.021545 1.568926 C 0.348619 -2.808691 0.829356 H -0.075088 -2.180531 2.908730 H -2.569763 1.641881 1.100912 H 0.476348 -3.571896 0.069434 C -0.783627 3.069708 1.993814 C 1.242983 -1.533351 3.150135 C -0.143062 0.409141 3.634366 N 0.242162 2.312858 -0.164870 N 1.469577 -2.019327 0.680063 N 0.354946 1.687458 1.538601 N -2.479206 -0.978824 -0.020360 N 1.411069 2.146394 0.224125 N -2.474832 -0.879439 -0.330036 U -0.246573 -0.037437 0.173356 Th 0.422381 -0.007323 -0.108700 U -0.197545 -0.165595 0.064315 H -0.351960 3.711108 2.772732 H 0.895745 -2.165271 3.975841 H 0.478288 0.286467 4.530611 H -1.853858 3.308357 1.950701 H 2.078989 -0.938607 3.537576 H -1.183791 0.454776 3.979273 H 2.418925 1.889319 -2.244303 H 1.233312 -3.609149 -1.998148 H 1.969462 3.243031 -0.490766 H 1.329852 2.741421 -3.318287 H 2.979966 -3.421622 -1.951092 H 0.775752 4.500517 -0.263677 H -3.315491 0.454814 -2.549688 H 4.268331 1.335217 -0.716165 271

Appendix

H 3.873054 2.443189 -2.024728 H -0.131204 3.630422 2.717497 S -1.982965 -0.296159 -1.529083 H -0.206351 3.543814 2.794743 H -1.123917 3.556254 1.267481 C -3.645713 -0.292484 -0.909851 H -1.166957 3.518213 1.323009 P -2.102439 0.111286 -1.528001 C -4.348878 0.904438 -0.799101 Si -2.212503 0.034068 -1.737096 H -2.138464 -0.769662 -2.637196 C -4.284472 -1.497324 -0.624486 C -3.947485 -0.094816 -1.010769 C -3.809385 -0.083427 -0.914009 C -5.671986 0.893579 -0.382599 C -4.678463 1.044463 -0.664827 C -4.542049 1.049377 -0.558964 H -3.866021 1.839532 -1.063759 C -4.535351 -1.343663 -0.785511 C -4.419813 -1.336386 -0.814923 C -5.607513 -1.496909 -0.208997 C -5.945210 0.941693 -0.106841 C -5.844398 0.932104 -0.093603 H -3.748650 -2.432924 -0.745604 H -4.268040 2.032419 -0.860906 H -4.102222 2.035090 -0.681841 C -6.303518 -0.303785 -0.081761 C -5.801970 -1.450027 -0.231351 C -5.726188 -1.448234 -0.367586 H -6.214890 1.829899 -0.304941 H -4.006027 -2.251966 -1.065008 H -3.870102 -2.229356 -1.096384 H -6.099245 -2.439795 0.006816 C -6.507912 -0.306139 0.114222 C -6.439061 -0.315754 0.003081 H -7.339623 -0.308415 0.238040 H -6.501098 1.839929 0.142428 H -6.402624 1.823512 0.173112 H -6.245143 -2.428744 -0.077516 H -6.190978 -2.426937 -0.306543 H -7.500758 -0.387836 0.543705 H -7.460811 -0.406960 0.355358 LThIIIX** complexes. H -2.178676 -0.927665 -2.895237 H -2.134230 1.403362 -2.374511 LThIIISiH2Ph. SCF energy = - [LThIVSPh]+. SCF energy = - 1964.92645 2072.30397 [LThIVPHPh]+. SCF energy = - C 2.690318 -2.653233 -0.272166 2016.03070 C 2.161468 -2.910108 -0.115355 C 3.397669 -3.588244 0.441651 C 2.779337 -3.837746 0.675202 H 4.081756 -4.318954 0.032364 C 2.003029 -3.032927 -0.040447 H 3.313707 -4.711725 0.330274 C 3.048987 -3.411854 1.799580 C 2.546416 -3.984732 0.776068 C 2.578127 -3.439150 2.017406 H 3.417793 -3.972054 2.648227 H 3.024929 -4.899614 0.456133 H 2.935349 -3.941285 2.905343 C 2.157393 -2.369818 1.844158 C 2.350955 -3.548621 2.107513 C 1.858480 -2.278504 1.984463 C 2.656925 -2.430411 -1.749979 H 2.658570 -4.057958 3.009829 C 2.064393 -2.900980 -1.608507 C 2.142850 -1.063609 -2.070652 C 1.709243 -2.343916 2.042248 C 1.861308 -1.506850 -2.107596 C 2.846072 0.092706 -1.625877 C 1.914562 -3.047444 -1.534462 C 2.715356 -0.483787 -1.660040 H 3.775733 -0.039534 -1.079117 C 1.780419 -1.654609 -2.059743 H 3.563027 -0.746762 -1.034210 C 2.319894 1.358227 -1.772932 C 2.701297 -0.675507 -1.653950 C 2.458887 0.852857 -1.943867 C 1.060657 1.515202 -2.438560 H 3.543167 -0.974894 -1.036508 C 1.339930 1.173200 -2.730087 H 0.629208 2.502361 -2.543607 C 2.520712 0.669964 -1.963685 H 1.117869 2.215742 -2.933599 C 0.482093 0.400372 -3.079503 C 1.408278 1.038059 -2.736411 C 0.523241 0.173093 -3.227640 H -0.402183 0.533454 -3.692172 H 1.241367 2.086596 -2.960037 H -0.337304 0.424922 -3.835106 C 0.994318 -0.866158 -2.887144 C 0.521489 0.077421 -3.194195 C 0.768504 -1.164411 -2.896877 H 0.495468 -1.721897 -3.330323 H -0.322691 0.374803 -3.804401 H 0.088009 -1.935109 -3.241065 C 2.937069 2.540110 -1.100009 C 0.689927 -1.264853 -2.834804 C 3.248255 1.948912 -1.308018 C 2.008588 3.071157 -0.053333 H -0.028486 -2.008270 -3.161605 C 2.369482 2.742917 -0.393797 C 1.992620 4.317824 0.519276 C 3.386934 1.730364 -1.368103 C 2.549399 4.030322 0.026771 H 2.660400 5.135039 0.283737 C 2.575784 2.598104 -0.456991 H 3.348284 4.692057 -0.276694 C 0.951184 4.313908 1.473335 C 2.852979 3.873758 -0.051239 C 1.509113 4.316451 0.941356 H 0.649159 5.129759 2.115809 H 3.697166 4.471477 -0.364752 H 1.346919 5.244452 1.471272 C 0.373790 3.070011 1.423196 C 1.840492 4.246238 0.862846 C 0.732887 3.195461 1.027128 C -0.822628 2.590481 2.183695 H 1.750158 5.189450 1.382911 C -0.507216 2.997148 1.840238 C -0.865793 1.097927 2.215384 C 0.982442 3.186757 0.962004 C -0.715868 1.542031 2.108104 C 0.242898 0.387654 2.711339 C -0.270554 3.089221 1.773958 C 0.337701 0.785037 2.653465 H 1.077814 0.944398 3.126069 C -0.588687 1.656170 2.055252 H 1.246819 1.296263 2.955901 C 0.305901 -0.994516 2.644823 C 0.396328 0.830226 2.626312 C 0.262916 -0.599235 2.750030 C -0.765681 -1.692293 2.059598 H 1.336093 1.276029 2.938595 C -0.909650 -1.243620 2.318032 H -0.703781 -2.772229 1.973521 C 0.213498 -0.544115 2.744714 H -0.962528 -2.326586 2.364039 C -1.871574 -1.010729 1.588529 C -0.992489 -1.106153 2.295214 C -1.972155 -0.509415 1.823096 H -2.704961 -1.542379 1.143056 H -1.126269 -2.181469 2.353630 H -2.877397 -1.005097 1.492628 C -1.917309 0.386221 1.659660 C -1.988942 -0.303437 1.763783 C -1.867280 0.880796 1.697458 H -2.779892 0.906553 1.258115 H -2.924339 -0.734899 1.426890 H -2.687558 1.436195 1.255918 C 1.536284 -1.736351 3.047574 C -1.779344 1.075235 1.632632 C 1.446129 -1.420918 3.139080 N 1.912780 -1.883769 0.572784 H -2.550079 1.689341 1.180176 N 1.572971 -1.918966 0.667351 N 1.014158 2.276205 0.487968 C 1.326672 -1.442042 3.173757 N 1.237641 2.189662 0.205155 Th 0.480471 -0.018118 -0.229032 N 1.471016 -1.990962 0.715339 Th 0.324373 -0.011053 -0.110938 H 1.281363 -2.510882 3.781244 N 1.409205 2.138676 0.151414 H 1.193005 -2.060134 3.992768 H 2.226732 -1.043727 3.545814 Th 0.371737 -0.013710 -0.112509 H 2.257970 -0.760922 3.467897 H 2.018362 -3.173334 -2.246600 H 1.007439 -2.049007 4.028843 H 1.247027 -3.536459 -1.970648 H 3.664660 -2.574797 -2.163200 H 2.173658 -0.835102 3.515842 H 2.989283 -3.314401 -2.028463 H 3.902860 2.245914 -0.669775 H 1.068645 -3.649813 -1.887771 H 4.104957 1.518751 -0.775002 H 3.142953 3.328518 -1.834900 H 2.819702 -3.512096 -1.943674 H 3.657319 2.611376 -2.079278 H -0.781466 2.982299 3.207936 H 4.226578 1.260866 -0.841196 H -0.405353 3.538641 2.788395 H -1.756172 2.964284 1.744171 H 3.820189 2.347743 -2.163393 H -1.395399 3.404108 1.341811 Si -2.261968 -0.176123 -1.750491 272

Appendix

C -4.000188 -0.369771 -0.998728 C -3.856313 0.103807 -0.931545 C -5.623217 0.588620 -0.347129 C -4.746690 0.741996 -0.596186 C -4.463124 1.272492 -0.465720 H -3.801338 1.448536 -1.094053 C -4.569978 -1.630312 -0.793874 C -4.600982 -1.079309 -0.895992 C -5.635730 -1.792582 -0.100607 C -5.998250 0.604540 -0.013110 C -5.753594 1.256046 0.042968 H -3.823446 -2.805931 -0.655189 H -4.350252 1.741970 -0.760913 H -3.923792 2.213075 -0.529316 C -6.290591 -0.574758 0.008615 C -5.820951 -1.776183 -0.211272 C -5.897505 -1.091057 -0.408466 H -6.128312 1.547466 -0.280003 H -4.032321 -2.520036 -1.115137 H -4.153640 -2.002425 -1.251785 H -6.150323 -2.712038 0.161542 C -6.539410 -0.657459 0.184628 C -6.478210 0.074661 0.072819 H -7.316365 -0.533169 0.358977 H -6.558722 1.487462 0.279894 H -6.201652 2.178275 0.400149 H -6.241667 -2.768005 -0.073949 H -6.457105 -2.021539 -0.396434 H -7.519705 -0.768090 0.636977 H -7.491306 0.062251 0.460927 LUIIIX** complexes. H -2.205453 -1.305794 -2.756143 H -2.413424 1.054629 -2.615168 LUIIISiH2Ph. SCF energy = - LThIIISPh. SCF energy = - 2033.89215 2072.46921 LThIIIPHPh. SCF energy = - C -1.583204 -3.191850 -0.114272 2016.19604 C 2.817451 -2.450609 -0.265726 C -2.234953 -4.086943 -0.918798 C 3.635190 -3.286881 0.451204 H -2.530892 -5.091453 -0.649100 C 1.697842 -3.194814 -0.045605 H 4.346902 -3.989379 0.039704 C -2.439888 -3.444054 -2.156864 C 2.142631 -4.217921 0.753933 C 3.352696 -3.057659 1.817388 H -2.945603 -3.849982 -3.022096 H 2.509505 -5.177080 0.414436 H 3.810402 -3.539719 2.670681 C -1.920178 -2.179021 -2.046391 C 2.011626 -3.776373 2.089570 C 2.388531 -2.083066 1.861016 C -1.101921 -3.400885 1.284467 H 2.266525 -4.322788 2.987185 C 2.676763 -2.313557 -1.747058 C -0.946321 -2.088260 1.975992 C 1.509235 -2.500818 2.034584 C 2.100830 -0.977372 -2.090477 C -2.020672 -1.190677 1.978163 C 1.564322 -3.196774 -1.535737 C 2.756043 0.212464 -1.653946 H -2.966992 -1.509403 1.551564 C 1.565232 -1.801731 -2.071680 H 3.691036 0.123491 -1.108520 C -1.885575 0.105212 2.451003 C 2.587722 -0.919970 -1.693305 C 2.165890 1.447830 -1.797063 C -0.645775 0.510282 2.970874 H 3.395299 -1.293940 -1.071424 C 0.898524 1.540296 -2.457423 H -0.525163 1.531010 3.318503 C 2.562774 0.421454 -2.052063 H 0.416816 2.505291 -2.550449 C 0.410832 -0.382226 3.027240 C 1.487090 0.893140 -2.816549 C 0.376231 0.404081 -3.105884 H 1.359515 -0.067605 3.447678 H 1.438127 1.947766 -3.066475 H -0.527994 0.490078 -3.695013 C 0.270024 -1.673612 2.509521 C 0.487255 0.029851 -3.228280 C 0.946608 -0.837716 -2.910766 H 1.113783 -2.355103 2.510845 H -0.339087 0.403309 -3.820891 H 0.488570 -1.718155 -3.348816 C -2.984952 1.093668 2.274072 C 0.518876 -1.314988 -2.844843 C 2.711646 2.664282 -1.124943 C -2.559136 2.181133 1.344149 H -0.282188 -1.981502 -3.142714 C 1.724234 3.162489 -0.117015 C -3.097995 3.434124 1.263720 C 3.577732 1.381760 -1.524427 C 1.609610 4.420982 0.417470 H -3.884396 3.833175 1.889472 C 2.922986 2.351627 -0.593138 H 2.226009 5.275233 0.173414 C -2.457373 4.079012 0.194377 C 3.364781 3.594235 -0.214700 C 0.551230 4.369731 1.351981 H -2.653026 5.078028 -0.170251 H 4.259151 4.088292 -0.569721 H 0.181476 5.178584 1.967421 C -1.550590 3.194444 -0.329558 C 2.438295 4.082023 0.735505 C 0.064502 3.086623 1.327071 C -0.691640 3.480092 -1.516535 H 2.469161 5.033289 1.248898 C -1.092929 2.533119 2.096802 C -0.340948 2.202337 -2.199232 C 1.472808 3.117087 0.876340 C -0.971121 1.049271 2.228524 C -1.350338 1.263883 -2.497515 C 0.233551 3.136590 1.713104 C 0.231715 0.499518 2.700603 H -2.386283 1.526571 -2.304694 C -0.255563 1.744581 1.962877 H 1.020128 1.170056 3.027954 C -1.034057 -0.017297 -2.943992 C 0.580611 0.800828 2.620862 C 0.450143 -0.869059 2.706686 C 0.300671 -0.344479 -3.153075 H 1.558912 1.123461 2.966744 C -0.561784 -1.717171 2.230437 H 0.557837 -1.344855 -3.486576 C 0.235814 -0.529987 2.708379 H -0.378794 -2.786064 2.194034 C 1.274076 0.597760 -2.951023 C -1.034179 -0.954475 2.190157 C -1.760992 -1.193363 1.788340 H 2.297511 0.345264 -3.155115 H -1.305324 -2.001304 2.240184 H -2.543286 -1.843798 1.416302 C 0.962701 1.853888 -2.442319 C -1.956109 0.009870 1.752904 C -1.962908 0.190664 1.780008 H 1.748218 2.564691 -2.231259 H -2.955298 -0.291023 1.461280 H -2.892925 0.590109 1.391324 C -2.056331 -1.083518 -3.071658 C -1.576048 1.332843 1.612722 C 1.782797 -1.437445 3.065074 N -1.351641 -1.997370 -0.777727 H -2.279794 2.059038 1.222270 N 2.034090 -1.690126 0.582525 N -1.560073 1.990664 0.392718 C 1.208841 -1.566249 3.163994 N 0.776013 2.314875 0.427170 U -0.213733 -0.053914 0.172587 N 1.304438 -2.114463 0.722145 Th 0.379502 -0.036960 -0.258696 H -1.996150 -1.502205 -4.083245 N 1.749414 2.032953 0.065136 H 1.671597 -2.182348 3.862171 H -3.050662 -0.630346 -2.972414 Th 0.296367 0.030879 -0.011042 H 2.419322 -0.637675 3.465107 H -0.145706 -3.938450 1.313003 H 0.791986 -2.135725 4.004482 H 2.026299 -3.097134 -2.158650 H -1.823807 -4.024811 1.826007 H 2.116808 -1.072334 3.532777 H 3.658188 -2.453284 -2.221280 H -3.877425 0.569312 1.910205 H 0.644279 -3.700575 -1.859815 H 3.675424 2.419610 -0.660716 H -3.253198 1.538246 3.239801 H 2.397995 -3.762382 -1.970922 H 2.903596 3.452085 -1.864237 H -1.275458 4.099969 -2.208289 H 4.379392 0.819189 -1.028532 H -1.116322 2.994507 3.092166 H 0.214598 4.051486 -1.279273 H 4.042230 1.928324 -2.353890 H -2.053269 2.770639 1.621041 Si 2.104180 -0.218430 0.995936 H 0.439355 3.656203 2.658986 S -1.999250 -0.764205 -1.548664 C 3.698001 -0.053944 0.513365 H -0.564817 3.708315 1.220827 C -3.642414 -0.682279 -0.898004 C 4.395959 1.160245 0.637778 P -2.153523 0.160276 -1.581674 C -4.313550 0.538195 -0.798703 C 4.409545 -1.155678 -0.004669 H -2.292213 -0.821398 -2.601307 C -4.325615 -1.849082 -0.551729 C 5.729121 1.271046 0.253396 273

Appendix

H 3.880732 2.034248 1.046676 H -4.032809 2.082632 -0.597211 C -6.308229 -0.313980 0.004676 C 5.742440 -1.045873 -0.384969 C -5.808288 -1.323161 -0.339422 H -6.106039 1.800128 -0.313618 H 3.902069 -2.119569 -0.104863 H -4.028544 -2.161344 -1.181883 H -6.205204 -2.451084 0.190838 C 6.404848 0.169492 -0.259485 C -6.450010 -0.178186 0.113994 H -7.334028 -0.248717 0.351427 H 6.250251 2.226868 0.358219 H -6.289474 1.947586 0.367401 H 6.271196 -1.916294 -0.783337 H -6.314010 -2.283103 -0.292799 H 7.452190 0.258103 -0.558289 H -7.456368 -0.235388 0.515200 [LThIVX†]+ complexes. H 2.402380 -1.406353 1.384810 H 2.273211 0.614724 1.959413 [LThIVCPh3]+. SCF energy = - LUIIISPh at PBE. SCF energy = - 2175.11529 2141.72523 LUIIIPHPh. SCF energy = - C -1.116729 -3.297949 1.241939 2085.45256 C 2.403039 -2.797541 -0.157392 C -1.699145 -4.498776 0.937185 C 3.122431 -3.681005 0.610349 H -1.557694 -5.426937 1.473275 C 1.918937 -3.115940 0.000691 H 3.731636 -4.496500 0.244686 C -2.523989 -4.279274 -0.186224 C 2.454048 -4.077541 0.823034 C 2.894614 -3.322573 1.957532 H -3.153967 -5.001000 -0.686669 H 2.920152 -5.001243 0.507782 H 3.305258 -3.795681 2.839121 C -2.415469 -2.952343 -0.502782 C 2.258947 -3.627963 2.147804 C 2.059106 -2.232327 1.935613 C -0.167836 -3.024722 2.366003 H 2.558220 -4.127568 3.059117 C 2.274009 -2.761119 -1.646874 C -0.129326 -1.563907 2.657719 C 1.626329 -2.411776 2.058555 C 1.926324 -1.380352 -2.107318 C -1.339573 -0.875207 2.847415 C 1.831462 -3.120753 -1.491903 C 2.696106 -0.289949 -1.670728 H -2.268949 -1.434448 2.857728 C 1.716650 -1.721982 -2.009371 H 3.573522 -0.481207 -1.060587 C -1.365736 0.501684 2.988066 C 2.657178 -0.757629 -1.614969 C 2.326788 1.020307 -1.952884 C -0.155593 1.213766 2.947307 H 3.491078 -1.065990 -0.991837 C 1.168395 1.246534 -2.709463 H -0.182130 2.295269 3.037866 C 2.512640 0.582742 -1.956931 H 0.855388 2.266965 -2.903453 C 1.044189 0.545448 2.807983 C 1.404909 0.965799 -2.726238 C 0.421925 0.182177 -3.183139 H 1.982888 1.086199 2.790242 H 1.262080 2.014431 -2.963953 H -0.477256 0.359712 -3.758910 C 1.054946 -0.842151 2.643830 C 0.492268 0.019817 -3.162753 C 0.790301 -1.128965 -2.867975 H 2.003430 -1.346222 2.497668 H -0.356923 0.325767 -3.761685 H 0.165650 -1.952962 -3.194021 C -2.647270 1.250989 3.041161 C 0.638389 -1.319016 -2.790255 C 3.056677 2.181568 -1.359042 C -2.753213 2.115848 1.832270 H -0.099606 -2.049971 -3.101183 C 2.168156 2.918932 -0.406673 C -3.466361 3.276586 1.719346 C 3.430734 1.629963 -1.415135 C 2.295982 4.212950 0.036602 H -4.006924 3.768968 2.515347 C 2.683071 2.547836 -0.499185 H 3.047720 4.924394 -0.277191 C -3.399460 3.662257 0.364181 C 3.039073 3.811373 -0.093933 C 1.273238 4.415294 0.989927 H -3.873053 4.518197 -0.096130 H 3.910820 4.364174 -0.416693 H 1.069591 5.318713 1.548646 C -2.636285 2.726485 -0.279615 C 2.058523 4.228372 0.833589 C 0.570273 3.237630 1.065203 C -2.337084 2.694255 -1.742946 H 2.016381 5.172107 1.360211 C -0.627115 2.924285 1.905087 C -1.956095 1.318980 -2.164913 C 1.151386 3.201624 0.931941 C -0.737421 1.447132 2.116410 C -2.765504 0.236686 -1.796166 C -0.095254 3.137275 1.754976 C 0.363397 0.735596 2.624992 H -3.696469 0.429220 -1.273165 C -0.471197 1.711293 2.008702 H 1.251486 1.285983 2.919681 C -2.384338 -1.072607 -2.059133 C 0.473284 0.834706 2.573804 C 0.355145 -0.651620 2.706976 C -1.175177 -1.304392 -2.726637 H 1.436923 1.229184 2.880539 C -0.787827 -1.346653 2.283652 H -0.858945 -2.323766 -2.917643 C 0.209549 -0.523556 2.707975 H -0.784732 -2.431116 2.310569 C -0.398439 -0.239611 -3.151626 C -1.026159 -1.020357 2.267449 C -1.890374 -0.660279 1.807989 H 0.517415 -0.426830 -3.695761 H -1.217987 -2.086071 2.332727 H -2.772081 -1.196151 1.478995 C -0.775073 1.067014 -2.851560 C -1.975246 -0.169953 1.726124 C -1.859445 0.734221 1.711433 H -0.145276 1.896674 -3.149330 H -2.932063 -0.551770 1.392066 H -2.713634 1.255590 1.293472 C -3.186337 -2.218100 -1.545733 C -1.691612 1.194120 1.592704 C 1.576251 -1.419277 3.096038 N -1.532464 -2.307193 0.357334 H -2.429019 1.848370 1.141546 N 1.734918 -1.889962 0.637679 N -2.196124 1.746879 0.607572 C 1.260143 -1.479587 3.170784 N 1.101684 2.294812 0.209465 Th -0.553586 -0.055943 0.131071 N 1.399504 -2.073168 0.739458 U 0.308003 -0.016963 -0.114411 H -3.427466 -2.905975 -2.363235 N 1.513559 2.149368 0.116704 H 1.347468 -2.082762 3.939101 H -4.140563 -1.845465 -1.152666 U 0.346792 -0.003664 -0.115211 H 2.345037 -0.718668 3.446464 H 0.848606 -3.383608 2.158152 H 0.889214 -2.056369 4.026980 H 1.507948 -3.458995 -2.008978 H -0.504219 -3.568460 3.257506 H 2.130492 -0.913110 3.526023 H 3.222381 -3.077263 -2.099476 H -3.484058 0.545153 3.111843 H 0.972939 -3.703872 -1.850052 H 3.965341 1.817552 -0.862267 H -2.681859 1.877694 3.939377 H 2.727417 -3.599589 -1.906767 H 3.384939 2.862623 -2.153591 H -3.234855 3.008608 -2.290076 H 4.268297 1.141312 -0.900824 H -0.535583 3.433636 2.872677 H -1.539601 3.390833 -2.021893 H 3.863894 2.208605 -2.240169 H -1.556547 3.288333 1.448295 C 2.053089 0.276148 -0.379942 H 0.070333 3.654663 2.708352 S -2.017316 -0.606999 -1.534464 C 2.086396 -0.965337 -1.228828 H -0.936030 3.645787 1.265624 C -3.657545 -0.482341 -0.893361 C 2.693610 -1.131575 -2.482044 P -2.154190 0.113595 -1.605473 C -4.308410 0.750497 -0.812665 C 1.489935 -2.107520 -0.683709 H -2.201031 -1.007623 -2.479537 C -4.364300 -1.631189 -0.530046 C 2.653288 -2.345489 -3.145519 C -3.841216 -0.032688 -0.929427 C -5.618400 0.831252 -0.365436 H 3.247070 -0.323615 -2.937887 C -4.512391 1.113144 -0.491332 H -3.780466 1.646981 -1.122246 C 1.429704 -3.330246 -1.344438 C -4.520658 -1.253656 -0.845308 C -5.674235 -1.544820 -0.084523 H 1.144109 -2.083537 0.349669 C -5.793455 1.040381 0.035595 H -3.876349 -2.597225 -0.612154 C 2.005068 -3.447032 -2.594326 274

Appendix

H 3.152420 -2.441401 -4.104714 N -2.598081 1.701520 0.417583 C 2.205590 2.405837 1.725885 H 0.939253 -4.173898 -0.869721 Th -1.021614 -0.107570 0.087792 C 3.478226 2.905867 1.732797 H 1.978911 -4.390965 -3.127586 H -2.987167 -2.660359 -3.276794 H 3.907845 3.538293 2.496847 C 3.231287 0.328190 0.565626 H -4.036566 -1.746761 -2.199666 C 4.100567 2.463846 0.544050 C 3.726504 1.541022 1.065549 H 0.227957 -3.570350 1.904460 H 5.108132 2.680183 0.217689 C 3.928738 -0.828216 0.941572 H -1.268797 -3.873844 2.774605 C 3.185009 1.701324 -0.127413 C 4.816471 1.588398 1.921315 H -4.281432 0.242604 2.581364 C 3.382867 0.989399 -1.429282 H 3.270402 2.478664 0.770936 H -3.617387 1.511518 3.604793 C 2.068777 0.732129 -2.090019 C 5.017875 -0.779658 1.798067 H -2.978979 3.235899 -2.524628 C 1.163368 1.792797 -2.266305 H 3.638869 -1.792634 0.540559 H -1.416311 3.569940 -1.787048 H 1.477903 2.799072 -2.006638 C 5.467982 0.428036 2.306074 Si 2.126747 0.255693 -0.054292 C -0.135412 1.569619 -2.704345 H 5.166125 2.552354 2.277363 C 2.898233 -1.131052 -1.100569 C -0.532895 0.253619 -2.993503 H 5.528753 -1.702192 2.055428 C 4.203741 -1.028427 -1.593962 H -1.554683 0.071543 -3.311013 H 6.324253 0.466167 2.969887 C 2.222150 -2.333885 -1.319922 C 0.364847 -0.793895 -2.876284 C 1.808735 1.615544 -1.016663 C 4.789803 -2.066651 -2.301604 H 0.053696 -1.806865 -3.105894 C 2.350395 2.092530 -2.218730 H 4.784894 -0.129987 -1.405758 C 1.662866 -0.556021 -2.419656 C 1.018159 2.520246 -0.295087 C 2.805597 -3.383454 -2.017184 H 2.347965 -1.385487 -2.284413 C 2.100308 3.379386 -2.662141 H 1.216283 -2.475790 -0.924084 C -1.148272 2.665423 -2.721530 H 3.018994 1.477596 -2.802342 C 4.090343 -3.245778 -2.518220 N -2.003677 1.620827 -0.581186 C 0.757903 3.814878 -0.733465 H 5.802865 -1.960595 -2.676206 N 1.988542 1.638539 0.582149 H 0.676855 2.258812 0.709315 H 2.259487 -4.310156 -2.162970 Th -0.001852 0.378155 -0.000018 C 1.296453 4.247326 -1.929969 H 4.551946 -4.060210 -3.066677 H -1.593730 2.747782 -3.719505 H 2.558254 3.720751 -3.585137 C 3.237615 0.314636 1.492716 H -0.649842 3.621547 -2.519573 H 0.145156 4.474717 -0.128446 C 3.591374 1.507346 2.130824 H -3.909639 0.000219 1.297739 H 1.115147 5.256566 -2.282980 C 3.740710 -0.876364 2.028210 H -4.025579 1.571780 2.081692 C 4.396993 1.509513 3.261022 H 0.616523 3.625803 2.522167 H 3.258477 2.459069 1.727372 H 1.568523 2.759504 3.721097 IV + [LTh SiPh3] . SCF energy = - C 4.544883 -0.879506 3.158507 H 4.011200 1.608946 -2.080761 H 3.529851 -1.822204 1.533825 H 3.908713 0.036236 -1.297243 2426.46177 C 4.870996 0.315374 3.782735 N 0.009677 -1.911682 -0.000906 H 4.666406 2.451245 3.728793 C -1.204820 -2.604573 0.034656 C -1.574027 -3.426795 0.720551 H 4.930723 -1.817638 3.544874 C -1.379246 -3.774373 0.784422 C -2.144698 -4.569795 0.236146 H 5.504741 0.316799 4.663282 C -2.321176 -2.053120 -0.601601 H -2.138400 -5.536879 0.718808 C 2.293721 1.959074 -0.884685 C -2.630467 -4.351595 0.898003 C -2.734856 -4.243377 -1.007073 C 2.946574 2.188687 -2.098116 H -0.524664 -4.223651 1.279444 H -3.275885 -4.909085 -1.664629 C 1.643566 3.048908 -0.290735 C -3.579547 -2.624709 -0.461445 C -2.510298 -2.912417 -1.219698 C 2.947706 3.444770 -2.690871 H -2.215745 -1.179171 -1.242892 C -0.816048 -3.247147 1.996904 H 3.463323 1.375577 -2.598959 C -3.740897 -3.777198 0.287401 C -0.851245 -1.813595 2.416234 C 1.647506 4.308969 -0.871653 H -2.744770 -5.260888 1.479332 C -2.091669 -1.152814 2.523919 H 1.116337 2.918695 0.654367 H -4.429333 -2.174242 -0.963739 H -3.005023 -1.724079 2.387939 C 2.298534 4.508521 -2.080904 H -4.717962 -4.236396 0.384852 C -2.162367 0.215738 2.743892 H 3.464867 3.595194 -3.633305 C 1.229977 -2.594331 -0.036070 C -0.964681 0.942075 2.884965 H 1.142970 5.135564 -0.381140 C 1.413948 -3.763515 -0.784481 H -1.018559 2.016177 3.030660 H 2.304350 5.489977 -2.543069 C 2.341785 -2.032946 0.599456 C 0.258035 0.300012 2.827165 C 2.669837 -4.330710 -0.897292 H 1.184565 0.849759 2.950333 H 0.563096 -4.220257 -1.279103 C 0.314484 -1.075345 2.571744 [LThIVNPh2]+. SCF energy = - C 3.604714 -2.594523 0.460143 H 1.283408 -1.555230 2.490207 H 2.229271 -1.158744 1.239235 1960.38059 C -3.453976 0.956577 2.673601 C 3.775474 -3.746648 -0.287228 C -3.417214 1.913852 1.525246 H 2.791567 -5.239712 -1.477571 C -4.180538 3.034176 1.348946 C -3.200849 1.671837 0.128055 H 4.450811 -2.136538 0.961876 H -4.902993 3.427478 2.050138 C -4.123625 2.425557 -0.543485 H 4.756245 -4.198025 -0.384008 C -3.861831 3.553108 0.073846 H -5.133314 2.632055 -0.217323 H -4.288423 4.426866 -0.398244 C -3.505289 2.873881 -1.731956

C -2.907259 2.734783 -0.463536 H -3.940801 3.502341 -2.495942 [LThIVPPh2]+. SCF energy = - C -2.248694 2.856121 -1.799983 C -2.227831 2.386279 -1.724796 2246.87572 C -1.739451 1.523855 -2.242845 C -3.392083 0.957892 1.429848 C -2.601455 0.412640 -2.255345 C -2.075612 0.712005 2.090143 H -3.653212 0.560731 -2.028904 C -1.179913 1.780740 2.267236 C -1.849216 -3.094559 -0.976586 C -2.124084 -0.869663 -2.505716 H -1.503666 2.784323 2.008486 C -2.508702 -3.775374 -1.961222 C -0.753402 -1.043925 -2.751525 C 0.120894 1.569073 2.704987 H -2.702084 -4.838740 -1.978202 H -0.366029 -2.044645 -2.910236 C 0.530425 0.256507 2.992965 C -2.877231 -2.828215 -2.944024 C 0.102292 0.045759 -2.774837 H 1.553850 0.083466 3.310246 H -3.419560 -3.017719 -3.859578 H 1.157497 -0.097215 -2.975834 C -0.357704 -0.799079 2.874899 C -2.437104 -1.610512 -2.507633 C -0.391661 1.327562 -2.518428 H -0.037271 -1.809351 3.103620 C -1.234986 -3.660768 0.264516 H 0.287564 2.171887 -2.509268 C -1.657902 -0.572675 2.418601 C -1.091944 -2.598063 1.303406 C -2.999636 -2.069342 -2.353912 H -2.335460 -1.408222 2.282794 C -2.207027 -1.823561 1.659170 N -1.777224 -2.369329 -0.165393 C 1.123692 2.674072 2.723095 H -3.176518 -2.072434 1.238143 275

Appendix

C -2.081557 -0.716603 2.495011 C 0.625729 -1.075952 3.163441 H 5.801938 0.361899 1.247914 C -0.814426 -0.388702 2.997579 C 0.502840 -1.886690 4.265862 H 6.253267 2.709440 0.557894 H -0.705174 0.493695 3.619441 H 1.135948 -1.861342 5.142474 C 0.858979 0.857514 -1.988950 C 0.287646 -1.173356 2.694848 C -0.592173 -2.749563 4.028625 C 0.295525 0.356398 -3.179045 H 1.259286 -0.928699 3.104228 H -0.978022 -3.513292 4.689570 C 0.306646 2.077425 -1.524836 C 0.150287 -2.271066 1.838468 C -1.094796 -2.414760 2.797314 C -0.651963 1.074242 -3.897436 H 1.020293 -2.862196 1.577855 C 1.650156 -0.015756 2.937562 H 0.631486 -0.593911 -3.571997 C -3.230899 0.202605 2.741897 C 1.128898 1.319189 2.471255 C -0.644446 2.785092 -2.241270 C -2.955266 1.545780 2.143837 C -0.238455 1.564215 2.363578 H 0.659844 2.485986 -0.580906 C -3.544161 2.735228 2.470869 H -0.937530 0.808763 2.715301 C -1.120667 2.298170 -3.448204 H -4.270195 2.889717 3.256543 C -0.742789 2.796539 1.949499 H -1.028123 0.660229 -4.828780 C -3.040974 3.705462 1.574707 C 0.148621 3.819860 1.667830 H -1.041811 3.705981 -1.828809 H -3.296485 4.755231 1.542179 H -0.222999 4.791723 1.357148 H -1.870668 2.845770 -4.006810 C -2.156841 3.067129 0.750806 C 1.515237 3.598943 1.793291 C -1.342993 3.661858 -0.353849 H 2.212777 4.402257 1.578652

C -0.951928 2.599626 -1.327706 C 2.005349 2.361565 2.173302 LThIIISiPh3. SCF energy = - C -1.945520 1.781938 -1.898211 H 3.076534 2.203407 2.242768 2426.623483 H -2.989126 2.001036 -1.693972 C -2.224662 2.945367 1.835697 C -1.610166 0.682320 -2.680467 C -2.815482 2.436998 0.557770 C -0.253733 0.387969 -2.893996 C -3.827719 3.075162 -0.117964 C -1.653958 -3.448712 0.823590 H 0.007388 -0.493773 -3.470040 H -4.235726 4.045159 0.133197 C -2.184742 -4.633710 0.379799 C 0.736825 1.200553 -2.364004 C -4.261309 2.201746 -1.135305 H -2.174398 -5.574230 0.913587 H 1.783256 0.994552 -2.550839 H -5.060393 2.362774 -1.846101 C -2.727468 -4.382273 -0.900054 C 0.381185 2.306102 -1.579554 C -3.482420 1.076690 -1.038343 H -3.227439 -5.088131 -1.548934 H 1.160486 2.920908 -1.143603 C -3.580202 -0.154584 -1.883828 C -2.513898 -3.053312 -1.164847 C -2.649640 -0.278263 -3.152481 C -2.779566 -1.273198 -1.306249 C -0.911789 -3.201652 2.098295 N -1.781751 -1.736539 -1.283273 C -3.056515 -1.751561 0.015475 C -0.955636 -1.752376 2.457581 N -2.072944 1.715371 1.077627 H -3.896089 -1.332490 0.560110 C -2.197454 -1.093906 2.512029 Th -0.725076 0.017400 0.009568 C -2.204163 -2.638073 0.632647 H -3.103657 -1.672237 2.360706 H -2.588105 -0.388110 -4.241383 C -1.066468 -3.112082 -0.083073 C -2.282460 0.273620 2.709022 H -3.645235 0.125255 -2.931421 H -0.372181 -3.775128 0.415499 C -1.094388 1.010795 2.857865 H -0.252063 -4.106320 0.068686 C -0.938658 -2.845816 -1.464409 H -1.157785 2.087234 2.980338 H -1.873697 -4.467591 0.643876 H -0.144818 -3.315085 -2.034701 C 0.130568 0.374427 2.836213 H -4.145677 -0.241433 2.330566 C -1.782569 -1.936519 -2.063830 H 1.051125 0.933243 2.962186 H -3.392953 0.313480 3.820235 H -1.658943 -1.684086 -3.110262 C 0.199956 -1.006815 2.623373 H -1.935770 4.432047 -0.861852 C -2.300315 -2.956037 2.089825 H 1.171520 -1.484554 2.577207 H -0.439518 4.157770 0.021214 N -0.353118 -1.389165 2.238534 C -3.586745 0.991657 2.626223 P 2.075480 0.165223 0.420619 N -2.562554 1.195604 -0.006611 C -3.579320 1.900804 1.440415 C 3.084413 -1.350178 0.514132 Th -0.627984 -0.385324 0.026012 C -4.369568 2.999012 1.212252 C 4.099829 -1.453576 1.469037 H -2.357862 -4.041462 2.238794 H -5.106660 3.405477 1.891643 C 2.856742 -2.432254 -0.339377 H -3.225794 -2.527220 2.494104 C -4.045736 3.468405 -0.080598 C 4.858766 -2.607904 1.568364 H 2.423363 -0.333380 2.222393 H -4.476923 4.315707 -0.595970 H 4.298016 -0.619016 2.134591 H 2.188864 0.132356 3.880624 C -3.064756 2.640324 -0.566196 C 3.609792 -3.593258 -0.229690 H -2.685974 2.427795 2.689970 C -2.349484 2.700340 -1.876050 H 2.095157 -2.357983 -1.110694 H -2.502640 3.999495 1.923884 C -1.763977 1.366451 -2.210534 C 4.611011 -3.682956 0.724739 H -4.637823 -0.443209 -1.971399 C -2.604157 0.217920 -2.320507 H 5.646478 -2.671266 2.311895 H -3.229878 0.040577 -2.905347 H -3.676518 0.338651 -2.197132 H 3.424263 -4.422853 -0.904296 C 1.783109 0.130430 -1.103967 C -2.073366 -1.043334 -2.479734 H 5.205603 -4.586539 0.806660 C 2.103945 -1.303171 -1.412260 C -0.655180 -1.196256 -2.563261 C 3.240323 1.465756 -0.086773 C 2.564310 -1.736829 -2.664098 H -0.234623 -2.187292 -2.672061 C 4.250645 1.227417 -1.022370 C 2.053538 -2.259595 -0.392834 C 0.156355 -0.045175 -2.683899 C 3.134906 2.739919 0.477354 C 2.903884 -3.058141 -2.891008 H 1.216730 -0.153174 -2.880063 C 5.121218 2.240865 -1.388896 H 2.694887 -1.012012 -3.460240 C -0.385897 1.210180 -2.508941 H 4.364061 0.238163 -1.455167 C 2.408320 -3.586321 -0.610290 H 0.254464 2.084230 -2.546508 C 3.999274 3.755401 0.096208 H 1.761329 -1.968221 0.616476 C -2.923890 -2.265713 -2.368649 H 2.387288 2.926782 1.243076 C 2.820682 -3.994337 -1.865207 N -1.847007 -2.449438 -0.113851 C 4.993961 3.508918 -0.838073 H 3.261744 -3.359883 -3.870643 N -2.754284 1.659434 0.356594 H 5.905364 2.039099 -2.111412 H 2.363967 -4.295054 0.210592 Th -1.051444 -0.111956 -0.072344 H 3.909365 4.737431 0.549192 H 3.097971 -5.028013 -2.043416 H -2.811686 -2.887620 -3.265505 H 5.678298 4.299245 -1.127027 C 2.988765 0.868685 -0.616473 H -3.978840 -1.968144 -2.315852 C 3.296936 2.174242 -1.027746 H 0.136510 -3.519235 2.027631 C 3.946546 0.243804 0.197582 H -1.364296 -3.798537 2.900298 H -4.400057 0.256521 2.572254 LThIIIX† complexes. C 4.444281 2.825888 -0.607515 H 2.637390 2.693058 -1.712292 H -3.750119 1.578363 3.538424 C 5.095386 0.893305 0.617192 H -3.048586 3.029813 -2.657248 LThIIICPh3. SCF energy = - H 3.808086 -0.789109 0.493957 H -1.541388 3.443600 -1.854970 2175.28305 C 5.352645 2.200058 0.232440 Si 2.150392 0.212200 -0.022710 H 4.636185 3.835082 -0.960396 C 3.185784 -0.988566 -1.092706 276

Appendix

C 4.524008 -0.714117 -1.396222 C 2.207741 -0.117434 -2.040425 C -1.181336 -0.501547 -2.868106 C 2.673295 -2.215114 -1.518577 C 1.953959 1.274795 -2.224427 H -1.045412 -1.495259 -3.275863 C 5.301915 -1.608981 -2.114498 H 2.734610 1.986526 -1.970076 C -0.186812 0.474799 -3.000396 H 4.974355 0.212242 -1.049512 C 0.705758 1.737204 -2.577025 H 0.739782 0.229611 -3.503568 C 3.447545 -3.122684 -2.230281 C -0.340058 0.789668 -2.845581 C -0.325605 1.712418 -2.397015 H 1.644919 -2.476220 -1.279194 H -1.322726 1.148241 -3.124407 H 0.480011 2.436012 -2.446292 C 4.763676 -2.817029 -2.536531 C -0.016778 -0.584832 -2.916981 C -3.512297 -1.180770 -2.188865 H 6.336836 -1.367902 -2.338259 H -0.774046 -1.299368 -3.221587 C -3.018470 -2.298390 -1.326056 H 3.021024 -4.071187 -2.542502 C 1.220138 -1.035953 -2.513022 C -3.475901 -3.590176 -1.259134 H 5.372911 -3.520899 -3.094889 H 1.431200 -2.100197 -2.495483 H -4.271603 -4.015230 -1.855354 C 3.217633 0.269293 1.572908 C 0.359345 3.188636 -2.503331 C -2.722249 -4.236184 -0.254339 C 3.570656 1.449811 2.233056 N -0.847756 2.486529 -0.416956 H -2.815427 -5.261554 0.076798 C 3.668540 -0.930734 2.135619 N 2.589372 0.343202 0.694710 C -1.831634 -3.310424 0.228390 C 4.320560 1.433779 3.402021 Th 0.294227 0.317090 -0.228795 C -0.782158 -3.512246 1.274811 H 3.274623 2.408755 1.817407 H -0.049566 3.530008 -3.462951 C -0.388301 -2.203357 1.877630 C 4.417289 -0.955304 3.302497 H 1.273951 3.767562 -2.323021 C -1.381519 -1.359828 2.410382 H 3.450565 -1.872006 1.634643 H -3.282251 1.695131 1.268505 H -2.407966 -1.711907 2.441602 C 4.742610 0.230488 3.945592 H -2.765207 3.017641 2.296242 C -1.078586 -0.085289 2.858192 H 4.584780 2.370072 3.884959 H 2.345807 2.357776 2.928706 C 0.247565 0.372292 2.757700 H 4.757225 -1.904204 3.706855 H 2.708058 1.010056 4.000693 H 0.478218 1.386183 3.067895 H 5.330827 0.216306 4.857590 H 4.349833 -0.195498 -2.040507 C 1.236611 -0.451630 2.253543 C 2.289424 1.974872 -0.750492 H 3.551233 -1.679238 -1.548899 H 2.261348 -0.106913 2.180803 C 2.949685 2.294953 -1.939396 N -1.159583 -1.529383 -0.013377 C 0.915561 -1.742434 1.818136 C 1.579108 3.007043 -0.123565 C -2.548524 -1.610428 -0.040731 H 1.693004 -2.369825 1.397352 C 2.904496 3.576612 -2.472798 C -3.248269 -2.679726 0.534248 C -2.149113 0.854218 3.304409 H 3.505566 1.527340 -2.469691 C -3.295823 -0.558147 -0.583024 N -1.795817 1.874243 1.045911 C 1.533820 4.292052 -0.644056 C -4.631867 -2.686973 0.563320 N -1.993923 -2.097894 -0.417955 H 1.035852 2.805422 0.799651 H -2.691992 -3.504054 0.968278 Th -0.707047 -0.001489 -0.164563 C 2.197768 4.580809 -1.827893 C -4.680422 -0.565692 -0.536334 H -1.925507 1.225617 4.311813 H 3.426238 3.792162 -3.400596 H -2.783171 0.277421 -1.056520 H -3.100336 0.310632 3.370692 H 0.973404 5.066735 -0.129450 C -5.361415 -1.630812 0.033695 H -0.753172 3.899005 -1.052675 H 2.162027 5.581702 -2.245760 H -5.148147 -3.528235 1.016100 H -2.459835 3.963270 -1.455650 H -5.230028 0.267076 -0.964163 H -4.422127 -0.726113 -1.776233 H -6.445406 -1.641125 0.060820 H -3.775605 -1.575516 -3.178525 III LTh NPh2. SCF = -1960.53762 C -0.377741 -2.669713 -0.151580 H -1.174318 -4.178397 2.053731 C -0.690879 -3.721101 -1.031863 H 0.113064 -3.999576 0.868032 C -1.822886 3.020416 0.405241 C 0.858709 -2.722316 0.508477 P 2.144536 -0.154670 -0.990474 C -2.217818 4.249439 -0.063597 C 0.209563 -4.741667 -1.256111 C 2.875506 1.491973 -0.665865 H -2.966740 4.887889 0.385394 H -1.645837 -3.711769 -1.546357 C 4.117115 1.834879 -1.215383 C -1.478528 4.498673 -1.241771 C 1.774295 -3.736969 0.248544 C 2.189569 2.484965 0.039052 H -1.532673 5.373053 -1.875632 H 1.097061 -1.994778 1.283088 C 4.644182 3.105138 -1.061132 C -0.655212 3.416864 -1.424161 C 1.457268 -4.752162 -0.633488 H 4.668103 1.088406 -1.779597 C -2.402431 2.280303 1.568013 H -0.055379 -5.540463 -1.942525 C 2.701541 3.769287 0.172218 C -1.438093 1.355194 2.249411 H 2.728491 -3.732261 0.765481 H 1.236271 2.266544 0.519214 C -0.093961 1.721867 2.395781 H 2.159985 -5.555090 -0.826389 C 3.934482 4.083289 -0.374574 H 0.222199 2.702916 2.051057 H 5.610908 3.341061 -1.495541 C 0.838877 0.868663 2.977358 H 2.137259 4.517989 0.719688 III H 4.343501 5.082366 -0.265892 C 0.405994 -0.372257 3.450460 LTh PPh2. SCF energy = - C 3.351088 -1.326805 -0.294175 H 1.126144 -1.052414 3.895272 2247.03916 C -0.927134 -0.729773 3.352234 C 4.377679 -0.994137 0.595921 C 3.232820 -2.670550 -0.676490 H -1.257146 -1.694364 3.723583 C -2.066105 3.090992 0.446165 C -1.842374 0.120183 2.743034 C 5.240434 -1.963929 1.085200 C -2.648401 3.951005 1.342814 H 4.510564 0.039066 0.901894 H -2.876265 -0.188765 2.629226 H -2.962259 4.965858 1.140243 C 2.280875 1.264987 3.025173 C 4.085518 -3.638853 -0.174598 C -2.745932 3.255162 2.569798 H 2.462919 -2.951417 -1.391248 C 3.085416 0.587734 1.963381 H -3.159953 3.621947 3.499338 C 4.407654 0.224835 2.039396 C 5.098032 -3.291804 0.710643 C -2.229520 2.003317 2.353112 H 6.031680 -1.676213 1.771341 H 5.042065 0.320208 2.910478 C -1.693315 3.335899 -0.980624 C 4.774544 -0.252026 0.761889 H 3.969147 -4.671369 -0.490222 C -1.535383 2.042280 -1.714426 H 5.774211 -4.047436 1.096175 H 5.745611 -0.614223 0.452744 C -2.619107 1.135657 -1.803420 C 3.653333 -0.170099 -0.026450 H -3.568805 1.410671 -1.352307 C 3.502687 -0.586417 -1.459134 C -2.454852 -0.135535 -2.314449

277

3. PBE0 (unless stated otherwise) Cartesian coordinates (Å) and SCF energies (Hartrees) of all complexes studied in chapter 6.

Complex 1 C 0.905509 -2.253390 -2.751739 H 2.230308 4.617179 1.953932 H 0.079090 -2.896844 -3.064331 H 0.658610 4.911164 1.200835 Li1 SCF energy = -1803.3091325 H 1.712297 -2.318174 -3.488791 C -3.139459 1.514458 -0.810811 H 0.503583 -1.232798 -2.743748 C 4.786334 1.470612 1.356064 Th -0.051619 -0.017001 0.721506 C 3.899915 -2.096683 -1.278368 H 5.767176 1.798637 1.686858 C 1.672902 2.144701 0.504924 H 4.131739 -3.070268 -1.696382 C -2.381231 -1.679082 1.103805 C -1.682071 -2.144339 0.455430 C 4.667372 0.028929 -0.475503 C 1.248808 2.825933 1.169645 N -0.917610 -2.103086 -0.678647 H 5.495784 0.696325 -0.258522 C 0.687090 2.501407 2.560440 N 0.932187 2.116329 -0.653567 C 4.936817 -1.215137 -1.009938 H -0.244289 3.047983 2.758433 C 0.391714 -2.802922 1.032977 H 5.962481 -1.505453 -1.216682 H 1.416916 2.782962 3.324340 H 1.254873 -3.136447 1.593326 C 3.875986 2.898351 -0.275130 H 0.541773 1.417675 2.665328 C -0.908237 -2.586039 1.535253 H 3.530571 2.980351 -1.310820 C -3.526419 0.978441 -2.192430 H -1.229020 -2.721760 2.556616 H 4.955938 2.730514 -0.289608 H -3.434438 1.756588 -2.956691 C 0.328945 -2.518431 -0.339125 H 3.690323 3.860066 0.213103 H -4.565737 0.635885 -2.181455 C -0.409833 2.818047 1.014978 Li 1.616998 0.891984 -1.939425 H -2.896567 0.131611 -2.479687 H -1.289558 3.145208 1.550539 C -0.990753 -3.402418 2.360703 C -0.330222 2.532849 -0.347921 H -0.343397 -4.274105 2.228345 C -2.295185 0.512128 -0.342207 Na 1 SCF energy = -1957.9965659 H -1.826212 -3.702007 2.999673 C -3.148503 -1.789976 0.417590 H -0.402594 -2.636031 2.870768 C 0.874364 2.587780 1.554714 Th 0.125327 -0.077224 -0.844849 C -3.415179 -1.684865 2.053111 H 1.165474 2.709649 2.586397 C -1.706278 1.983662 -0.800639 H -3.496234 -2.491170 2.775464 C -3.363287 -0.386181 -0.164837 C 1.820930 -2.102264 -0.307050 C -4.306474 0.333945 1.109141 C -3.736250 -1.849935 1.830195 N 0.866524 -2.105310 0.675671 H -5.082755 1.091620 1.100280 H -3.637111 -2.853980 2.256746 N -1.017716 2.066722 0.385316 C -4.365988 -0.680302 2.062050 H -4.799692 -1.597964 1.805403 C -0.066143 -2.915384 -1.223093 H -5.172369 -0.697764 2.789298 H -3.242448 -1.138078 2.500356 H -0.780845 -3.328799 -1.920261 C -4.039604 2.712591 -0.491032 C -4.666717 -0.017974 -0.503922 C 1.278557 -2.592785 -1.498200 H -3.828177 3.121807 0.502108 H -5.492689 -0.703198 -0.337448 H 1.781346 -2.710560 -2.445429 H -5.100765 2.447958 -0.540985 C 2.274791 -0.467345 -0.453171 C -0.266269 -2.630403 0.132761 H -3.861239 3.506000 -1.222309 C -0.000295 0.071023 3.233907 C 0.346061 2.760353 -1.275093 Na -1.809020 0.899756 2.274720 H 1.022780 0.230327 3.610463 H 1.224753 3.111288 -1.797502 H -0.370941 -0.835099 3.728941 C 0.222305 2.552852 0.100074 H -0.601815 0.909117 3.618388 C 2.241512 0.619978 0.440251 K1 SCF energy = -1824.1324934 C -2.590319 1.741965 -0.969731 C 3.246562 -1.702065 -0.022667 C 1.836739 -4.133955 -1.428225 C -0.896075 2.413644 -1.848039 Th 0.005293 -0.000023 -1.065616 H 2.309467 -4.454151 -0.495328 H -1.150282 2.451615 -2.896291 C 1.094556 -2.456757 -0.437162 H 2.530092 -4.330033 -2.252011 C 3.347713 -0.251630 0.459475 C -1.099809 2.457995 -0.451357 H 0.948752 -4.752122 -1.588034 C 4.087351 -1.871918 -1.291856 N -0.007824 2.249258 0.345988 C -3.835870 -2.851307 -0.456158 H 4.062187 -2.908521 -1.644385 N -0.007757 -2.248533 0.345897 H -3.454866 -2.803857 -1.478946 H 5.129174 -1.608694 -1.093326 C 0.713096 2.712398 -1.753212 H -4.920372 -2.715781 -0.479070 H 3.729374 -1.221194 -2.096586 H 1.360453 2.887009 -2.599985 H -3.630092 -3.850203 -0.056745 C 4.599718 0.180759 0.902932 C -0.700807 2.714455 -1.761479 C -3.888239 2.093033 -1.317664 H 5.448586 -0.496681 0.893537 H -1.338008 2.892906 -2.615097 H -4.103181 3.045575 -1.791106 C -2.230303 -0.610665 0.199340 C 1.094504 2.456811 -0.437241 C 3.351143 0.411819 -0.196362 C 0.386949 -0.038251 -3.345119 C -0.700775 -2.715233 -1.761220 C 1.428189 -2.657820 -1.369779 H -0.595807 0.019986 -3.840727 H -1.337991 -2.894391 -2.614679 C -1.785641 4.110402 -1.548874 H 0.891884 -0.916494 -3.765971 C -1.099750 -2.458001 -0.451232 H -2.237811 4.506038 -0.635398 H 0.952074 0.843931 -3.681988 C -2.219822 0.000038 0.345408 H -2.488913 4.260428 -2.372878 C 2.458810 1.916354 0.961466 C -2.469367 2.488112 0.163912 H -0.887518 4.697500 -1.766493 C -2.317147 -4.014051 0.341412 C 0.713133 -2.713132 -1.752987 C 3.134677 1.780745 0.477604 H -2.711574 -3.692695 -0.626772 H 1.360475 -2.888413 -2.599633 C -4.931983 1.218261 -1.059424 H -3.169426 -4.271279 0.977529 C -2.682562 1.196081 0.936360 H -5.951093 1.495694 -1.311330 H -1.712223 -4.913577 0.190868 C -3.546623 2.562173 -0.922287 C 2.586887 -1.729405 -1.011551 C 3.768401 -2.665835 1.055331 H -3.444137 3.478398 -1.513887 C -1.418239 2.631398 -1.386377 H 3.192466 -2.550380 1.976278 H -4.539483 2.562513 -0.462754 C -0.907948 2.108887 -2.735728 H 4.823995 -2.486877 1.276225 H -3.485275 1.698645 -1.590905 H -0.033499 2.673144 -3.083237 H 3.664767 -3.700828 0.711854 C -3.390470 1.197491 2.138076 H -1.694735 2.201187 -3.489223 C 3.707093 2.337539 1.402474 H -3.707293 2.130063 2.593277 H -0.674539 1.036412 -2.671731 H 3.853847 3.341234 1.788275 C 2.197419 0.000090 0.382935 C 3.678556 1.712545 1.907564 C -3.252519 0.374307 0.200158 C 0.164696 -0.000355 -3.563238 H 3.564629 2.676669 2.413399 C -1.478790 -2.906475 0.995444 H 1.242513 -0.001217 -3.805528 H 4.742220 1.461346 1.897209 C 1.579065 4.322794 1.126315 H -0.261281 0.883633 -4.055568 H 3.158446 0.949930 2.494834 H 2.076041 4.588068 0.189523 H -0.262617 -0.883832 -4.055343 278

Appendix

C -2.682535 -1.195963 0.936457 H 3.426448 -3.501727 -1.661294 C -1.100738 -2.461481 -0.712721 C 3.547623 2.559759 -0.873985 H 4.535935 -2.584875 -0.625509 C 0.688314 2.701255 -2.049449 H 3.495504 1.695712 -1.542725 H 3.478705 -1.723066 -1.752164 H 1.321029 2.865027 -2.909157 H 4.534001 2.560687 -0.400712 C 3.443021 -1.197136 1.961633 C 1.093757 2.462029 -0.737800 H 3.453166 3.475287 -1.467960 H 3.771695 -2.129471 2.409061 C 2.239358 -0.000006 0.041152 C -2.561503 3.752479 1.025152 C -2.210299 -0.000202 0.242277 C 2.472786 -2.496697 -0.139128 H -1.846638 3.719219 1.851935 C -0.171504 0.000214 -3.684938 C -0.724493 2.699125 -2.035181 H -3.568522 3.889078 1.431167 H -1.249987 0.001319 -3.924564 H -1.374618 2.858928 -2.882603 H -2.329939 4.630435 0.414390 H 0.252736 -0.883949 -4.178366 C 2.727872 -1.196757 0.609604 C -3.390420 -1.197282 2.138187 H 0.254583 0.883359 -4.178599 C 3.530130 -2.605175 -1.242409 H -3.707190 -2.129825 2.593484 C 2.703784 1.196701 0.778851 H 3.404205 -3.529112 -1.817278 C 2.658622 -1.196117 0.974314 C -3.547130 -2.578634 -1.017631 H 4.530413 -2.612012 -0.799369 C 2.455284 2.487235 0.197284 H -3.497730 -1.718839 -1.692071 H 3.470329 -1.751974 -1.924364 C -3.546613 -2.562503 -0.921884 H -4.535536 -2.582470 -0.548643 C 3.505927 -1.196646 1.767090 H -3.485434 -1.699108 -1.590690 H -3.444031 -3.497441 -1.605079 H 3.849046 -2.128673 2.204409 H -4.539423 -2.562857 -0.462247 C 2.562268 -3.751243 0.886256 C -2.222101 -0.000176 0.099004 H -3.444084 -3.478841 -1.513303 H 1.856274 -3.706120 1.720118 C -0.187993 -0.001110 -3.810813 C 2.455303 -2.487086 0.197462 H 3.572125 -3.894517 1.282679 H -1.268812 0.000250 -4.040472 C -3.710793 0.000127 2.759427 H 2.316221 -4.631267 0.284162 H 0.231163 -0.885341 -4.308229 H -4.249528 0.000160 3.702701 C 3.442742 1.197534 1.961780 H 0.233429 0.881829 -4.308636 C 2.658576 1.196346 0.974264 H 3.771186 2.129886 2.409336 C 2.727773 1.197104 0.608888 C -2.469252 -2.488092 0.164187 C -2.679912 1.196475 0.826035 C -3.548053 -2.600922 -1.162852 C -2.561180 -3.752285 1.025698 C -2.460156 -2.491380 0.058249 H -3.503476 -1.746452 -1.844406 H -2.329610 -4.630346 0.415089 C 3.539119 2.582554 -1.077049 H -4.537895 -2.608425 -0.696962 H -3.568142 -3.888886 1.431858 H 3.478475 1.723829 -1.751920 H -3.435566 -3.523610 -1.742451 H -1.846222 -3.718795 1.852391 H 4.535453 2.585776 -0.625139 C 2.561584 -3.749305 0.740223 C 3.547714 -2.559841 -0.873718 H 3.425826 3.502472 -1.660910 H 1.866398 -3.689339 1.582221 H 3.453252 -3.475462 -1.467550 C -2.460677 2.490904 0.058090 H 3.574552 -3.900737 1.125393 H 4.534058 -2.560738 -0.400376 C 3.780917 0.000200 2.573422 H 2.298124 -4.631704 0.149038 H 3.495685 -1.695900 -1.542602 H 4.346591 0.000208 3.500918 C 3.505906 1.197732 1.766345 C 2.535616 3.752611 1.058304 C -2.679653 -1.196952 0.826109 H 3.849031 2.130043 2.203052 H 2.311707 4.629816 0.443617 C 2.470968 2.492524 0.017186 C -2.702944 1.197112 0.672225 H 3.537172 3.890176 1.477253 C 2.561487 3.751578 0.886636 C -2.465476 -2.495634 -0.083917 H 1.810026 3.719753 1.875703 H 2.315355 4.631618 0.284599 C 3.529919 2.604760 -1.243780 C 3.360655 1.197546 2.179328 H 3.571277 3.894987 1.283173 H 3.470297 1.751212 -1.925321 H 3.676231 2.130102 2.635404 H 1.855439 3.706256 1.720439 H 4.530174 2.611971 -0.800679 C 3.360678 -1.197233 2.179390 C -3.547589 2.577781 -1.017882 H 3.403871 3.528396 -1.819108 H 3.676258 -2.129759 2.635525 H -3.444692 3.496565 -1.605399 C -2.465765 2.495095 -0.085639 C 3.677098 0.000177 2.802566 H -4.536032 2.581392 -0.548969 C 3.865793 0.000740 2.365655 H 4.210628 0.000206 3.748776 H -3.497902 1.717940 -1.692240 H 4.463973 0.001018 3.272663 C 2.535541 -3.752319 1.058697 C -2.536547 -3.751816 0.927099 C -2.702760 -1.197147 0.673060 H 1.809882 -3.719314 1.876028 H -2.300793 -4.630989 0.319665 C 2.472523 2.496629 -0.140524 H 3.537060 -3.889832 1.477752 H -3.539621 -3.895564 1.340188 C 2.561006 3.749667 0.738249 H 2.311666 -4.629619 0.444133 H -1.816621 -3.707848 1.749032 H 2.297280 4.631738 0.146695 K -0.027009 0.000101 2.547624 C -3.406699 -1.197656 2.016323 H 3.573952 3.901595 1.123292 H -3.731749 -2.130005 2.466345 H 1.865878 3.689879 1.580301 C -3.406953 1.197098 2.016261 C -3.548256 2.599486 -1.164756 Rb1 SCF energy = -1819.9135665 H -3.732179 2.129406 2.466236 H -3.435876 3.521811 -1.744949 C -3.737637 -0.000295 2.631857 H -4.538139 2.607123 -0.698958 Th -0.008365 0.000024 -1.186007 H -4.293287 -0.000334 3.565375 H -3.503472 1.744576 -1.845739 C -1.097415 2.459134 -0.572577 C -2.537472 3.751390 0.926818 C -2.535024 -3.749758 0.795001 C 1.097542 -2.460350 -0.590072 H -1.817487 3.707786 1.748711 H -2.285929 -4.631332 0.196393 N 0.006678 -2.259025 0.211051 H -3.540579 3.894808 1.339952 H -3.539007 -3.901174 1.203013 N 0.006187 2.259018 0.211117 H -2.302132 4.630601 0.319279 H -1.820618 -3.691575 1.620891 C -0.717238 -2.706565 -1.890758 Rb 0.029703 0.000026 2.589004 C -3.461172 -1.196923 1.843454 H -1.365510 -2.874000 -2.738212 H -3.797934 -2.128934 2.285700 C 0.696127 -2.708433 -1.901214 C -3.461403 1.197600 1.842588 H 1.331652 -2.879610 -2.757483 Cs 1 SCF energy = -1815.9745545 H -3.798375 2.129871 2.284131 C -1.096953 -2.459334 -0.572540 C -3.809818 0.000525 2.448534 C 0.695742 2.708543 -1.901087 Th -0.013411 -0.000535 -1.310703 H -4.391891 0.000799 3.365941 H 1.331308 2.879837 -2.757302 C -1.100966 2.460697 -0.714307 C -2.535610 3.749852 0.792369 C 1.097083 2.460537 -0.589904 C 1.093976 -2.462614 -0.736320 H -1.821364 3.692377 1.618434 C 2.230276 0.000170 0.197443 N 0.005221 -2.268470 0.069807 H -3.539687 3.901428 1.200088 C 2.471462 -2.492113 0.016931 N 0.004977 2.268280 0.068393 H -2.286494 4.631002 0.193155 C -0.717622 2.706452 -1.890757 C -0.724312 -2.700662 -2.033473 Cs 0.036829 0.001498 2.646592 H -1.365837 2.873803 -2.738266 H -1.374495 -2.861000 -2.880749

C 2.704042 -1.196329 0.778719 C 0.688487 -2.702657 -2.047814

C 3.539577 -2.581831 -1.077365 H 1.321187 -2.866834 -2.907458 Li1PBE SCF energy = -1803.1536816 279

Appendix

Th -0.050652 -0.016587 0.715556 H 6.011493 -1.520085 -1.171154 H 3.210713 1.004225 2.513193 C 1.676249 2.160473 0.511946 C 3.891695 2.923504 -0.277965 C 0.911867 -2.225841 -2.772627 C -1.683879 -2.158744 0.465872 H 3.537791 3.002027 -1.318620 H 0.070472 -2.852650 -3.088755 N -0.922591 -2.108796 -0.686968 H 4.978344 2.751637 -0.298069 H 1.715372 -2.288584 -3.517986 N 0.933102 2.129568 -0.661570 H 3.709181 3.893595 0.211033 H 0.527607 -1.194336 -2.738044 C 0.410265 -2.823661 1.027425 Li 1.611874 0.884381 -1.945174 C 3.939451 -2.113960 -1.254064 H 1.283159 -3.158453 1.586132 H 4.176559 -3.094508 -1.660904 C -0.893393 -2.611036 1.543692 C 4.702193 0.027624 -0.444300 H -1.205780 -2.755660 2.574193 Li1TPSS SCF energy = -1805.1110729 H 5.530387 0.696271 -0.213892 C 0.339898 -2.527639 -0.352592 C 4.979914 -1.228947 -0.967399 Th -0.048030 -0.016556 0.715270 C -0.425335 2.833636 1.019385 H 6.011520 -1.525314 -1.150060 C 1.675178 2.156831 0.511592 H -1.312469 3.159350 1.558043 C 3.880900 2.925200 -0.316761 C -1.683497 -2.155433 0.466672 C -0.344561 2.543491 -0.353830 H 3.507312 2.993200 -1.346988 N -0.915855 -2.103735 -0.683737 C -2.313399 0.510535 -0.334999 H 4.962040 2.746730 -0.354475 N 0.923057 2.125805 -0.658052 C -3.160356 -1.808167 0.439987 H 3.709413 3.894736 0.168019 C 0.408204 -2.819442 1.035178 C 0.865034 2.607860 1.565654 Li 1.582214 0.885850 -1.953591 H 1.273155 -3.156800 1.595804 H 1.153230 2.734756 2.604933 C -0.897403 -2.605639 1.545523 C -3.385562 -0.396782 -0.147486 H -1.212860 -2.751343 2.570209 Li C -3.742196 -1.867539 1.866557 1TPSSh SCF energy = - C 0.345155 -2.526421 -0.343691 H -3.636167 -2.876597 2.297982 1804.9789194 C -0.423432 2.827269 1.031644 H -4.813640 -1.617922 1.848044 H -1.301286 3.154307 1.575394 Th -0.048723 -0.016883 0.718070 H -3.243186 -1.147773 2.535986 C -0.352971 2.542785 -0.341059 C 1.673547 2.151432 0.507879 C -4.700302 -0.029404 -0.482704 C -2.317110 0.509689 -0.334814 C -1.682205 -2.150729 0.461772 H -5.529999 -0.720487 -0.308442 C -3.161985 -1.811131 0.429772 N -0.913737 -2.102741 -0.680766 C 2.290728 -0.463815 -0.459245 C 0.870606 2.600705 1.568733 N 0.922644 2.121302 -0.655308 C 0.014122 0.065797 3.236957 H 1.164862 2.728744 2.601434 C 0.401274 -2.811750 1.036731 H 1.042986 0.236434 3.612688 C -3.390011 -0.396809 -0.150122 H 1.262992 -3.148100 1.598032 H -0.345403 -0.855547 3.727800 C -3.756747 -1.887914 1.854046 C -0.902777 -2.596628 1.541626 H -0.602011 0.898207 3.630216 H -3.647500 -2.897548 2.273072 H -1.221569 -2.738578 2.563103 C -2.615679 1.745104 -0.972196 H -4.825508 -1.645009 1.825960 C 0.340724 -2.523143 -0.339019 C 1.846617 -4.147899 -1.474493 H -3.267655 -1.174088 2.530136 C -0.417243 2.821969 1.029102 H 2.313637 -4.487074 -0.537192 C -4.704981 -0.030637 -0.480552 H -1.292653 3.149497 1.571599 H 2.551003 -4.334349 -2.300916 H -5.529273 -0.721527 -0.307633 C -0.346947 2.538876 -0.339448 H 0.951848 -4.763968 -1.652413 C 2.290817 -0.460800 -0.469669 C -2.309513 0.509985 -0.337720 C -3.856353 -2.880725 -0.433143 C 0.029016 0.063538 3.252105 C -3.156436 -1.804562 0.420722 H -3.477633 -2.836141 -1.464440 H 1.056130 0.234333 3.623898 C 0.874270 2.593884 1.563594 H -4.948092 -2.743928 -0.451199 H -0.325769 -0.856679 3.742462 H 1.169779 2.719870 2.593641 H -3.647314 -3.884636 -0.028521 H -0.585635 0.890636 3.650960 C -3.380220 -0.393581 -0.157585 C -3.925675 2.093634 -1.317272 C -2.625857 1.746073 -0.964506 C -3.752619 -1.880176 1.839138 H -4.147059 3.049736 -1.798270 C 1.850792 -4.150985 -1.476179 H -3.646277 -2.887699 2.257441 C 3.372868 0.419914 -0.185040 H 2.315308 -4.491365 -0.542819 H -4.818483 -1.636048 1.809348 C 1.441617 -2.660990 -1.394346 H 2.554754 -4.327796 -2.299850 H -3.265172 -1.168916 2.515177 C -1.809412 4.128008 -1.568133 H 0.959081 -4.762799 -1.658612 C -4.690612 -0.027579 -0.490412 H -2.257332 4.530971 -0.647338 C -3.849987 -2.880900 -0.459587 H -5.513617 -0.716603 -0.321007 H -2.524705 4.273988 -2.392236 H -3.459319 -2.829552 -1.481521 C 2.284547 -0.462227 -0.466613 H -0.907646 4.718202 -1.797923 H -4.936863 -2.737894 -0.488076 C 0.021766 0.065579 3.249205 C 3.147920 1.800600 0.487544 H -3.648441 -3.883056 -0.057700 H 1.047041 0.230576 3.621473 C -4.972963 1.212538 -1.046107 C -3.934989 2.095755 -1.305954 H -0.338880 -0.847978 3.741891 H -6.001051 1.488899 -1.294521 H -4.156139 3.050243 -1.780102 H -0.585864 0.896345 3.644267 C 2.609383 -1.734801 -1.019013 C 3.374164 0.420436 -0.194261 C -2.615126 1.744365 -0.963699 C -1.438170 2.639569 -1.398915 C 1.445027 -2.661298 -1.388608 C 1.847625 -4.145186 -1.455745 C -0.927547 2.108272 -2.757228 C -1.820237 4.131829 -1.562874 H 2.314883 -4.477132 -0.523578 H -0.047694 2.674291 -3.111314 H -2.267312 4.534378 -0.646394 H 2.547151 -4.327306 -2.278608 H -1.720961 2.198243 -3.514597 H -2.533633 4.268615 -2.384919 H 0.958558 -4.758801 -1.629968 H -0.691744 1.028981 -2.688945 H -0.921699 4.718547 -1.794722 C -3.840911 -2.870016 -0.467461 C 3.696286 1.742685 1.927711 C 3.148913 1.804918 0.471011 H -3.450461 -2.817884 -1.486825 H 3.575163 2.714798 2.432060 C -4.980134 1.212684 -1.037329 H -4.925418 -2.728918 -0.497094 H 4.768554 1.497254 1.918768 H -6.004893 1.487774 -1.281635 H -3.639488 -3.870322 -0.067663 H 3.177811 0.974762 2.522692 C 2.615203 -1.735676 -1.017313 C -3.919514 2.094205 -1.307141 C 0.917540 -2.232055 -2.780357 C -1.446877 2.641241 -1.387137 H -4.138464 3.047421 -1.778672 H 0.081406 -2.869797 -3.104196 C -0.926382 2.104587 -2.743214 C 3.365131 0.417703 -0.198611 H 1.728761 -2.289848 -3.523604 H -0.050014 2.670994 -3.092902 C 1.440070 -2.660349 -1.378750 H 0.516191 -1.202923 -2.756436 H -1.713908 2.183011 -3.501709 C -1.811950 4.125359 -1.550769 C 3.934625 -2.109005 -1.266675 H -0.683262 1.031505 -2.658920 H -2.260727 4.522834 -0.635834 H 4.171868 -3.090017 -1.684406 C 3.716874 1.766066 1.907942 H -2.521088 4.266168 -2.372384 C 4.700571 0.028968 -0.445708 H 3.595435 2.740517 2.398844 H -0.915088 4.712339 -1.776634 H 5.533987 0.698461 -0.215465 H 4.786452 1.527648 1.885026 C 3.143142 1.797425 0.466966 C 4.976519 -1.224836 -0.979467 280

Appendix

C -4.963022 1.213258 -1.044352 H -3.482308 -2.823980 -1.456223 C -0.481215 -2.084310 0.399222 H -5.984516 1.488407 -1.290851 H -4.950394 -2.719433 -0.444023 C 2.487074 -1.799096 -2.822899 C 2.605930 -1.733285 -1.014170 H -3.653147 -3.857023 -0.012932 H 2.091649 -2.829025 -2.886137 C -1.439327 2.638851 -1.381806 C -3.889620 2.105501 -1.337013 H 3.567196 -1.897332 -2.656520 C -0.920860 2.109776 -2.735918 H -4.100513 3.061617 -1.820663 H 2.355210 -1.359803 -3.821082 H -0.046886 2.676591 -3.082809 C 3.363148 0.404835 -0.186487 C 0.539748 2.838502 -0.894430 H -1.706951 2.191986 -3.491888 C 1.417409 -2.658881 -1.385676 C 1.555715 -4.229055 1.807976 H -0.678779 1.038799 -2.658305 C -1.765769 4.118676 -1.574325 H 1.389162 -4.458339 0.751127 C 3.708149 1.753804 1.899639 H -2.220236 4.526922 -0.659972 H 0.890699 -4.867237 2.397035 H 3.589367 2.725055 2.391946 H -2.471027 4.270168 -2.405014 H 2.590820 -4.478940 2.064752 H 4.774676 1.513069 1.877352 H -0.859951 4.704054 -1.795392 C 4.125703 1.647064 2.281284 H 3.200953 0.993601 2.501686 C 3.149658 1.775199 0.494473 H 3.323672 1.509196 3.010972 C 0.908811 -2.236689 -2.761726 C -4.942016 1.230676 -1.077159 H 4.555921 2.644427 2.409573 H 0.073158 -2.868417 -3.074658 H -5.965643 1.510972 -1.336612 H 4.913184 0.918789 2.499939 H 1.711908 -2.300993 -3.503770 C 2.586622 -1.739564 -1.018406 C 0.500274 4.124247 -0.351585 H 0.520750 -1.209519 -2.735664 C -1.406254 2.635162 -1.399911 H -0.225218 4.851779 -0.703494 C 3.925501 -2.108228 -1.259302 C -0.889443 2.096345 -2.745193 C -1.831361 -2.197283 -0.009138 H 4.160750 -3.085941 -1.666854 H -0.006563 2.656366 -3.098950 C 1.261230 -2.753443 2.103114 C 4.688687 0.028343 -0.456573 H -1.676052 2.180394 -3.508719 C 0.271571 3.197184 -3.317558 H 5.515274 0.696356 -0.231521 H -0.657934 1.017292 -2.669779 H 1.281053 2.809999 -3.482452 C 4.963936 -1.224150 -0.980322 C 3.687297 1.697895 1.930724 H 0.355184 4.276089 -3.161977 H 5.992259 -1.518423 -1.169501 H 3.577050 2.665427 2.444687 H -0.327447 3.021118 -4.217919 C 3.874256 2.915412 -0.314628 H 4.755714 1.438781 1.926679 C -2.119476 -2.098826 -1.504653 H 3.505336 2.985207 -1.343784 H 3.157596 0.931436 2.516298 C 1.399405 4.499826 0.627524 H 4.953341 2.739751 -0.349209 C 0.891149 -2.230615 -2.763519 H 1.364176 5.499348 1.051409 H 3.700462 3.881934 0.169690 H 0.050415 -2.862186 -3.084120 C -0.192082 -2.508431 1.711367 Li 1.588662 0.889894 -1.950332 H 1.697251 -2.292405 -3.510951 C -0.371424 2.546785 -2.085676 H 0.496237 -1.199944 -2.740864 C -1.780403 3.133422 -1.922977 C 3.904958 -2.112439 -1.290674 H -2.414412 2.819188 -2.758730 Li1 with cc-pVDZ basis sets on all H 4.133373 -3.089890 -1.719296 H -1.759505 4.226269 -1.916664 light atoms. SCF energy = - C 4.684466 0.016405 -0.470925 H -2.248100 2.799349 -0.993034 1803.0416112 H 5.520316 0.684544 -0.249860 C -1.720170 -3.439973 -2.132392 C 4.950639 -1.232350 -1.015566 H -1.921395 -3.447582 -3.209012 Th -0.052025 -0.017493 0.721556 H 5.981506 -1.527036 -1.225828 H -2.297028 -4.247781 -1.672601 C 1.683241 2.142916 0.515896 C 3.896286 2.896983 -0.254590 H -0.659118 -3.647904 -1.968799 C -1.690514 -2.142083 0.464513 H 3.552256 2.982173 -1.297334 C 1.551354 -2.488808 3.585626 N -0.932301 -2.103858 -0.680386 H 4.983319 2.729774 -0.266684 H 2.618685 -2.630417 3.782260 N 0.947512 2.119507 -0.651948 H 3.708753 3.863972 0.236509 H 1.002870 -3.179062 4.233195 C 0.394880 -2.804397 1.034323 Li 1.610530 0.873746 -1.958451 H 1.293281 -1.463053 3.858406 H 1.268846 -3.138786 1.591919 C -1.208473 -2.853203 2.603855 C -0.907585 -2.585876 1.546600 H -0.971275 -3.152939 3.619750 H -1.225584 -2.721603 2.576735 Li 1 with THF. SCF energy = - C -2.843813 -2.540311 0.885018 C 0.321092 -2.519762 -0.344817 2267.8507749 H -3.875638 -2.611668 0.555248 C -0.411149 2.820576 1.019438 C -2.532437 -2.833092 2.204969 H -1.301160 3.149117 1.552249 Th 1.221440 -0.659327 -0.969726 H -3.318899 -3.092549 2.908064 C -0.321593 2.536742 -0.350710 C -1.291871 -0.988132 -2.090331 C -3.591562 -1.845747 -1.849334 C -2.293941 0.516669 -0.342394 C 3.229487 -0.024796 0.748861 H -3.970149 -0.948807 -1.354669 C -3.161791 -1.784143 0.434486 N 2.188608 -0.527436 1.479167 H -4.219206 -2.693461 -1.556770 C 0.875425 2.587273 1.568335 N -1.258277 0.255592 -1.501259 H -3.696458 -1.713891 -2.930425 H 1.164532 2.709097 2.608512 C 3.190908 -2.244037 0.394564 Li -2.088315 0.415508 0.336904 C -3.373054 -0.381163 -0.162277 H 3.421256 -3.235991 0.034186 O -1.552734 1.332949 1.958402 C -3.739157 -1.823883 1.856471 C 3.863437 -1.051933 0.048463 C -1.887538 2.710474 2.171529 H -3.644191 -2.828697 2.298280 H 4.702333 -0.963294 -0.625247 H -2.954318 2.837618 1.963482 H -4.807313 -1.563013 1.839993 C 2.188993 -1.879976 1.297777 H -1.307424 3.329213 1.476008 H -3.232285 -1.104145 2.518850 C -0.037834 0.326131 -3.403231 C -1.502533 3.001636 3.605942 C -4.680691 -0.009419 -0.510231 H 0.590876 0.682913 -4.204484 H -1.321230 4.065441 3.776457 H -5.513758 -0.696371 -0.341332 C -0.515927 1.066331 -2.326895 H -2.289496 2.668519 4.292671 C 2.275931 -0.473929 -0.447146 C 1.476830 1.876586 -0.461958 C -0.255586 2.141702 3.757060 C -0.017622 0.069728 3.226561 C 3.606210 1.427582 0.853454 H 0.601821 2.637133 3.290235 H 1.002547 0.264720 3.615088 C -0.535353 -0.985400 -3.253957 H -0.004921 1.916690 4.796265 H -0.368416 -0.844898 3.735556 H -0.352719 -1.819396 -3.913738 C -0.623480 0.895555 2.975228 H -0.648772 0.900168 3.601925 C 2.420090 2.318915 0.495913 H 0.236396 0.426029 2.490649 C -2.587032 1.750714 -0.980464 C 4.737823 1.748978 -0.128851 H -1.139336 0.156481 3.600611 C 1.814689 -4.141174 -1.461394 H 5.631106 1.153177 0.088956 O -4.033574 0.854988 0.413678 H 2.286154 -4.479461 -0.526919 H 5.005319 2.806730 -0.052200 C -6.149210 0.068899 0.983665 H 2.512133 -4.336549 -2.290476 H 4.429304 1.556393 -1.161226 H -6.101654 -1.005245 0.785937 H 0.918191 -4.755572 -1.630648 C 2.368220 3.600485 1.037725 H -6.981196 0.248400 1.668475 C -3.859113 -2.856349 -0.424446 H 3.095918 3.916584 1.777832 C -6.275992 0.855938 -0.332266 281

Appendix

H -7.060849 1.614584 -0.282569 C -3.281129 3.020398 -0.597151 H -2.923901 4.498524 -1.525522 H -6.511653 0.191449 -1.166423 H -3.059735 3.962923 -1.109697 H -1.351415 4.953250 -0.852084 C -4.826203 0.549148 1.555447 H -4.256963 3.116133 -0.111996 C 3.077309 1.879936 0.286063 H -4.290264 -0.196426 2.145545 H -3.352085 2.223435 -1.343742 C -4.832591 0.932766 -1.625722 H -4.960941 1.458281 2.161845 C -3.013492 -3.553094 0.936309 H -5.793432 1.082279 -2.107710 C -4.900894 1.507739 -0.509791 H -2.824878 -4.421795 0.298049 C 2.628734 -1.672831 -0.981438 H -4.935728 2.580254 -0.271291 H -4.056305 -3.603865 1.262095 C -1.602414 2.808535 -1.078020 H -4.473425 1.387405 -1.506761 H -2.372019 -3.638139 1.818778 C -1.106055 2.786709 -2.529862 C -3.731404 -0.963065 2.074101 H -0.293754 3.498790 -2.697894 H -4.210093 -1.870720 2.427352 H -1.931823 2.984702 -3.217524 Li1 with THF PCM. SCF energy = C -3.472825 1.411453 2.208281 H -0.707477 1.784280 -2.765866 -1803.348361 H -3.747125 2.352169 2.674553 C 3.773025 1.789768 1.648093 C -4.005821 0.236385 2.710983 H 3.680237 2.729787 2.202693 Th 0.021493 0.046788 -0.879929 H -4.664589 0.259528 3.574216 H 4.837623 1.581715 1.508889 C -0.864300 2.567482 -0.215981 C -2.120523 3.881509 1.424848 H 3.351651 0.983094 2.256350 C 0.859803 -2.551912 -0.279679 H -1.422309 3.667856 2.238090 C 1.097623 -2.944659 -2.486656 N -0.264475 -2.277079 0.458372 H -3.097600 4.125291 1.851821 H 0.383420 -3.766391 -2.591755 N 0.243296 2.282172 0.528685 H -1.763690 4.769965 0.893896 H 1.924191 -3.081499 -3.187564 C -0.897381 -2.610594 -1.687098 Li -0.514118 -1.438999 2.246379 H 0.536695 -2.037122 -2.770865 H -1.504876 -2.703862 -2.574778 C 3.814231 -1.883169 -1.695949 C 0.509050 -2.738804 -1.611501 H 4.035176 -2.814554 -2.204516 H 1.177885 -2.949267 -2.432527 Li1 with Li+ frozen. SCF energy = - C 4.498427 0.365009 -1.057887 C -1.336628 -2.354473 -0.394708 1803.2311668 H 5.247522 1.149466 -1.069212 C 0.902996 2.685204 -1.600414 C 4.788519 -0.836235 -1.690881 Th -0.000392 -0.002026 0.794890 H 1.522744 2.808513 -2.476269 H 5.739750 -0.980848 -2.194570 C 1.615099 2.158936 0.467919 C 1.322145 2.388276 -0.302195 C 3.660215 3.076660 -0.482287 C -1.622163 -2.166538 0.462634 C 2.229955 -0.188426 0.493292 H 3.248801 3.122699 -1.494047 N -0.753638 -2.156212 -0.598860 C 2.197023 -2.719324 0.386568 H 4.750826 3.033809 -0.547357 N 0.762083 2.150396 -0.604805 C -0.504194 2.796508 -1.546606 H 3.397935 4.005019 0.035251 C 0.381229 -2.809353 1.251953 H -1.161480 3.021946 -2.374071 Li 0.078982 -0.081959 -3.291348 H 1.181857 -3.131318 1.902489 C 2.626524 -1.419652 1.060991 C 3.260444 -3.061621 -0.663004 C -0.956548 -2.563076 1.622014 H 3.017128 -3.994825 -1.182728 H -1.375357 -2.660870 2.611478 Li1’ SCF energy -1803.2758329 H 4.231732 -3.184176 -0.175384 C 0.449600 -2.581087 -0.124824 H 3.353695 -2.260601 -1.402391 C -0.396314 2.801932 1.231869 Th -0.002887 0.000012 -0.946433 C 3.512586 -1.482537 2.138196 H -1.208506 3.118736 1.870784 C -1.092907 2.456751 -0.319309 H 3.790090 -2.437491 2.573066 C -0.446000 2.573739 -0.145631 C 1.101472 -2.458002 -0.330826 C -2.207723 0.172500 0.514035 C -2.313486 0.446351 -0.345302 N 0.008525 -2.249260 0.465199 C -0.010906 0.063982 -3.430029 C -3.085550 -1.887433 0.272402 N 0.008460 2.248531 0.465081 H -1.044490 0.266330 -3.759760 C 0.935784 2.554731 1.620674 C -0.709860 -2.712412 -1.634867 H 0.287095 -0.887663 -3.891227 H 1.338446 2.644976 2.617838 H -1.356194 -2.887028 -2.482420 H 0.617337 0.852686 -3.867273 C -3.283537 -0.532812 -0.405322 C 0.704052 -2.714470 -1.641427 C 2.888346 0.961006 0.989226 C -3.796094 -1.851669 1.629212 H 1.342283 -2.892926 -2.494274 C -3.745050 -2.182192 -0.997395 H -3.709473 -2.812915 2.147248 C -1.092856 -2.456817 -0.319359 H -3.556269 -1.304681 -1.622517 H -4.858692 -1.637302 1.485402 C 0.704022 2.715218 -1.641200 H -4.757765 -2.099525 -0.592116 H -3.382270 -1.069616 2.274039 H 1.342268 2.894371 -2.493890 H -3.701923 -3.078837 -1.625097 C -4.518876 -0.308043 -1.036755 C 1.101415 2.457994 -0.330730 C 2.080316 -3.907451 1.351104 H -5.262189 -1.097391 -1.080363 C 2.220523 -0.000041 0.467276 H 1.389728 -3.688002 2.170315 C 2.312499 -0.474924 -0.349732 C 2.470286 -2.488116 0.286097 H 3.050135 -4.176884 1.777641 C 0.060617 0.046094 3.308382 C -0.709895 2.713118 -1.634674 H 1.701535 -4.783268 0.814593 H 1.103031 0.188002 3.639252 H -1.356214 2.888394 -2.482102 C 3.776530 0.892091 2.060384 H -0.300220 -0.861736 3.807516 C 2.682549 -1.196081 1.058794 H 4.255603 1.788464 2.440301 H -0.510014 0.889119 3.725578 C 3.548853 -2.562184 -0.798800 C -2.607490 1.387408 1.114304 C -2.652237 1.721751 -0.923372 H 3.447081 -3.478413 -1.390518 C -2.733095 -2.265178 0.150114 C 2.255105 -4.161814 -0.667448 H 4.541157 -2.562522 -0.338069 C 3.741365 2.318392 -0.887721 H 2.718987 -4.100540 0.320067 H 3.488312 -1.698660 -1.467497 H 3.588954 1.483362 -1.578527 H 3.030196 -4.455326 -1.380258 C 3.389005 -1.197484 2.261364 H 4.752853 2.238172 -0.478600 H 1.497581 -4.951271 -0.642875 H 3.705278 -2.130053 2.716953 H 3.674943 3.256171 -1.450333 C -3.656113 -3.053592 -0.549168 C -2.196760 -0.000091 0.499470 C -2.207857 2.700379 0.449907 H -3.230188 -3.060581 -1.555786 C -0.159274 0.000330 -3.444246 C 4.066600 -0.324906 2.654996 H -4.745375 -3.005017 -0.628672 H -1.236798 0.001191 -3.687837 H 4.746565 -0.372802 3.500845 H -3.402333 -4.001696 -0.063955 H 0.267297 -0.883662 -3.936056 C -2.867046 -0.990295 0.978137 C -3.910747 1.933622 -1.545233 H 0.268633 0.883803 -3.935840 C 2.716625 2.284705 0.251248 H -4.136980 2.900311 -1.987593 C 2.682523 1.195963 1.058877 C 2.943368 3.516915 1.137284 C 3.283418 0.552071 -0.443365 C -3.545446 -2.559767 -0.759064 H 2.723154 4.424470 0.565785 C 1.614157 -2.818269 -1.048494 H -3.492520 -1.695724 -1.427746 H 3.981042 3.586571 1.476334 C -2.156758 4.214169 -0.800455 H -4.532395 -2.560692 -0.286982 H 2.287321 3.496417 2.011400 H -2.601966 4.262718 0.196229 H -3.450273 -3.475299 -1.352919 282

Appendix

C 2.561382 -3.752478 1.147455 H -3.148206 0.479724 -4.174357 Th 0.370857 -0.000022 0.000000 H 1.845519 -3.719213 1.973374 H -4.333165 -0.511262 -3.304857 Si 4.593228 -0.000139 3.560501 H 3.567910 -3.889075 1.554686 C 3.034448 -1.066459 -2.177816 N -1.031774 -2.247534 0.000000 H 2.330555 -4.630438 0.536419 C -1.708294 -3.121279 0.757491 N -1.031574 2.247616 0.000000 C 3.388956 1.197289 2.261460 C 3.709447 0.140933 -1.937772 C -0.243203 -2.454827 1.097706 H 3.705177 2.129835 2.717134 H 3.177766 1.079348 -2.075014 C 1.074877 -2.708926 0.705904 C -2.658676 1.196120 1.090285 C -3.972677 -2.050803 1.109941 H 1.927400 -2.876648 1.345398 C -2.454402 -2.487237 0.313523 H -4.219018 -2.824845 1.829125 C -0.242983 2.454843 1.097705 C 3.548844 2.562492 -0.798428 C 0.845953 -2.909536 0.193709 C 1.075120 2.708819 0.705904 H 3.488473 1.699093 -1.467302 H 0.962116 -3.672607 -0.561791 H 1.927660 2.876459 1.345397 H 4.541099 2.562848 -0.337593 C 1.940313 3.793572 -0.523012 C -0.866509 -2.499941 2.479805 H 3.447030 3.478826 -1.389976 H 2.373729 4.496694 0.194364 C -0.866286 2.500006 2.479806 C -2.454419 2.487084 0.313671 H 1.978718 4.254460 -1.516131 C -1.014076 0.000039 2.628429 C 3.708578 -0.000116 2.883094 H 2.558158 2.891087 -0.522599 H 0.083129 -0.000011 2.642294 H 4.246174 -0.000144 3.827018 C -4.936387 -1.114823 0.768311 C 3.166570 -0.000152 2.431402 C -2.658631 -1.196343 1.090249 H -5.915785 -1.140763 1.237271 C -1.679979 -1.225835 2.664820 C 2.470173 2.488088 0.286342 C -4.083200 1.952625 -2.112937 C -1.679869 1.225973 2.664816 C 2.561061 3.752286 1.147956 H -5.118223 1.638356 -2.277943 C 2.221119 -0.000111 1.649200 H 2.330229 4.630343 0.537062 H -3.790056 2.579822 -2.960359 C -1.739023 3.755737 2.541151 H 3.567532 3.888889 1.555330 H -4.038054 2.565251 -1.208356 H -1.113701 4.639484 2.386088 H 1.845105 3.718801 1.973785 C 1.747678 -1.046070 4.088344 H -2.221850 3.849975 3.519412 C -3.545536 2.559833 -0.758828 H 2.267762 -0.474631 4.863168 H -2.504727 3.744683 1.761909 H -3.450356 3.475450 -1.352551 H 2.196644 -2.043480 4.057698 C 0.208569 -2.603213 3.564387 H -4.532450 2.560733 -0.286677 H 0.697720 -1.157382 4.373553 H 0.758760 -3.543659 3.462210 H -3.492699 1.695888 -1.427643 C 0.975223 1.735562 3.758376 H -0.260615 -2.592214 4.552416 C -2.535774 -3.752608 1.174453 H 1.186690 1.329820 4.742119 H 0.931913 -1.785391 3.513477 H -2.311123 -4.629817 0.560042 C 1.882118 -0.380533 2.714007 C -3.060559 1.208128 2.809381 H -3.537835 -3.890170 1.592193 C -1.738733 1.280170 -1.928060 H -3.622092 2.133097 2.841011 H -1.811171 -3.719745 1.992727 C -3.139220 0.748907 -2.012337 C 0.208801 2.603176 3.564386 C -3.362164 -1.197536 2.294465 C 3.781944 -2.243722 -2.018432 H 0.932064 1.785282 3.513480 H -3.678291 -2.130089 2.750165 H 3.301686 -3.199044 -2.213727 H -0.260384 2.592224 4.552415 C -3.362187 1.197243 2.294512 C 1.607435 -1.080580 -2.523269 H 0.759085 3.543567 3.462208 H -3.678317 2.129772 2.750260 H 1.269060 -2.074431 -2.840035 C -1.739362 -3.755594 2.541141 C -3.679359 -0.000163 2.917313 H 1.389115 -0.370229 -3.327976 H -2.505064 -3.744465 1.761897 H -4.214031 -0.000186 3.862878 C -1.814719 -4.094641 -0.420433 H -2.222200 -3.849792 3.519401 C -2.535696 3.752322 1.174801 H -1.605232 -3.586361 -1.366226 H -1.114121 -4.639397 2.386075 H -1.811025 3.719322 1.993008 H -2.827641 -4.504306 -0.475315 C -3.734149 0.000160 2.898734 H -3.537720 3.889838 1.592646 H -1.115313 -4.929425 -0.302994 H -4.813748 0.000210 3.013624 H -2.311079 4.629618 0.560503 C -0.326760 4.757343 -0.186813 C -3.060669 -1.207867 2.809380 Li 0.025053 -0.000090 2.666843 H -1.353406 4.585396 0.148021 H -3.622283 -2.132788 2.841008 H -0.364145 5.119577 -1.218760 C -0.243203 -2.454827 -1.097706 H 0.118627 5.548269 0.424270 C 1.074877 -2.708926 -0.705904 Complex 2 C 0.311203 3.585942 2.394649 H 1.927400 -2.876648 -1.345398 H 0.003722 4.623287 2.314591 C -0.242983 2.454843 -1.097705 K2 SCF energy = -2054.9820159 C 3.370797 -0.175242 2.416846 C 1.075120 2.708819 -0.705904 Th 0.167155 -0.216775 -0.582474 H 3.519298 0.237569 1.415116 H 1.927660 2.876459 -1.345397 K -2.055997 0.893635 2.068541 H 3.917704 -1.121318 2.489521 C -0.866509 -2.499941 -2.479805 N -0.088709 -1.506596 1.710081 H 3.800389 0.523352 3.141114 C -0.866286 2.500006 -2.479806 N -1.340852 1.954856 -0.806460 C -1.938687 -3.903249 2.055580 C -1.014076 0.000039 -2.628429 C 0.893117 1.456394 1.321489 H -1.139013 -4.638281 2.188294 H 0.083129 -0.000011 -2.642294 C -2.343833 -0.980383 -0.380430 H -2.887370 -4.448235 2.033281 C -1.679979 -1.225835 -2.664820 C 0.535620 2.821055 1.250634 H -1.932029 -3.237343 2.922865 C -1.679869 1.225973 -2.664816 C -0.736097 1.311204 -2.893340 C -4.659407 -0.184561 -0.220979 C -1.739023 3.755737 -2.541151 H -0.757513 0.850856 -3.870305 H -5.441370 0.496372 -0.540362 H -1.113701 4.639484 -2.386088 C 0.310200 2.093606 -2.351994 C 0.493343 3.030693 3.651606 H -2.221850 3.849975 -3.519412 H 1.237967 2.352493 -2.841032 H 0.304723 3.620661 4.543937 H -2.504727 3.744683 -1.761909 C 1.875673 -2.124210 0.760890 C 5.040105 0.170047 -1.550172 C 0.208569 -2.603213 -3.564387 H 2.924739 -2.162995 0.511002 H 5.525398 1.126287 -1.377128 H 0.758760 -3.543659 -3.462210 C -0.115901 2.494306 -1.087534 C 5.752382 -1.008202 -1.386533 H -0.260615 -2.592214 -4.552416 C -0.334023 -2.523362 0.827708 H 6.794100 -0.987526 -1.085006 H 0.931913 -1.785391 -3.513477 C -2.708947 -2.002758 0.522781 C 5.109544 -2.215988 -1.630253 C -3.060559 1.208128 -2.809381 C 1.199779 0.972352 2.612578 H 5.654931 -3.149636 -1.525022 H -3.622092 2.133097 -2.841011 C 0.498480 3.466968 -0.123947 C 0.208801 2.603176 -3.564386 C -3.394782 -0.139585 -0.807261 H 0.932064 1.785282 -3.513480 Complex 3 C 1.264677 -1.303411 1.704612 H -0.260384 2.592224 -4.552415 H 0.759085 3.543567 -3.462208 C -3.315589 -0.111399 -3.267454 3PBE0 SCF energy = -2491.665441 H -2.621678 -0.957018 -3.261630 C -1.739362 -3.755594 -2.541141 H -2.505064 -3.744465 -1.761897 283

Appendix

H -2.222200 -3.849792 -3.519401 H 2.643558 0.077582 0.001670 H -4.582427 0.257063 2.608463 H -1.114121 -4.639397 -2.386075 C 2.689053 -1.626235 1.310316 H -3.488599 -0.776474 3.553704 C -3.734149 0.000160 -2.898734 C 2.688031 -1.752909 -1.149739 C -2.559855 1.756817 -3.780681 H -4.813748 0.000210 -3.013624 C 2.553426 -1.930268 -3.691250 H -1.777103 2.523166 -3.766812 C -3.060669 -1.207867 -2.809380 H 2.393282 -1.341695 -4.607587 H -3.540915 2.242227 -3.869392 H -3.622283 -2.132788 -2.841008 H 3.537649 -2.419919 -3.769021 H -2.407949 1.129517 -4.667342 Si 4.593228 -0.000139 -3.560501 H 1.769527 -2.699925 -3.641557 C -2.938789 3.754508 0.006764 C 3.166570 -0.000152 -2.431402 C 3.592856 0.359519 2.562223 H -3.067654 4.835426 0.008710 C 2.221119 -0.000111 -1.649200 H 3.485408 0.982941 3.463910 C -2.842580 3.079793 -1.209674 H 4.566787 1.211449 4.433174 H 4.585335 -0.115896 2.594225 H -2.885171 3.643268 -2.136461 H 4.566787 1.211449 -4.433174 H 3.550319 1.023032 1.685641 C 1.107727 0.241261 -2.469150 H 5.867851 -0.003033 2.785646 C 2.852295 -3.139317 -1.061506 C 0.709249 -1.082881 -2.729285 H 4.563770 -1.208884 -4.437008 H 2.892207 -3.750590 -1.963072 H 1.347191 -1.938746 -2.902247 H 4.563770 -1.208884 4.437008 C 3.592212 0.078367 -2.623949 C 1.108144 0.232188 2.469288 H 5.867851 -0.003033 -2.785646 H 3.548214 0.839567 -1.830945 C 0.709791 -1.093045 2.724035 H 4.584915 -0.396792 -2.598830 H 1.347821 -1.949579 2.893561 H 3.485789 0.592351 -3.592398 C 2.495928 0.874682 -2.514931 3PBE SCF energy = -2491.4473907 C 2.551900 -1.509428 3.855103 C 2.496198 0.865806 2.517365 H 1.767879 -2.279475 3.894632 C 2.625659 1.021979 0.001486 Th 0.000001 0.349698 -0.005068 H 3.535990 -1.986618 3.991839 H 2.625009 -0.079960 -0.000430 Si -3.519179 4.621954 -0.200192 H 2.390091 -0.817316 4.695595 C 2.678344 1.693124 -1.231086 N 0.000018 -0.910248 2.273086 C 2.951340 -3.753912 0.188509 C 2.678415 1.688835 1.236402 N -0.000025 -1.150543 -2.197446 H 3.081824 -4.837746 0.244851 C 2.559013 1.743686 3.786620 C -1.106957 -0.099416 2.434737 C 2.853172 -3.013216 1.367860 H 2.407263 1.113184 4.671023 C -0.709326 1.240752 2.612348 H 2.893189 -3.527148 2.328054 H 3.539877 2.229122 3.877177 H -1.350668 2.109407 2.732319 Si 3.519211 4.621926 -0.200245 H 1.775997 2.509786 3.775351 C -1.107746 -0.363900 -2.448154 C 2.412885 3.171217 -0.136829 C 3.593371 -0.207617 -2.616146 C -0.709777 0.948333 -2.773844 C 1.640940 2.202726 -0.093443 H 3.489014 -0.763128 -3.556923 H -1.350777 1.798510 -2.988001 H 3.448246 5.401920 1.081541 H 4.582377 0.266601 -2.607146 C -2.496927 -0.723688 2.530014 H 4.940693 4.178742 -0.405486 H 3.539313 -0.925336 -1.789591 C -2.497257 -0.994998 -2.467246 H 3.137537 5.529746 -1.334172 C 2.841754 3.075980 1.220304 C -2.640262 -1.025626 0.048580 H -3.448019 5.402074 1.081506 H 2.883796 3.636264 2.149043 H -2.643558 0.077596 0.001716 H -3.137656 5.529656 -1.334265 C 3.593865 -0.216575 2.614740 C -2.412863 3.171236 -0.136791 H -4.940695 4.178768 -0.405186 H 3.540018 -0.930973 1.785300 C -2.689037 -1.626238 1.310338 H 4.582781 0.257892 2.607846 C -2.688069 -1.752879 -1.149719 H 3.489273 -0.775812 3.553275 C -1.640925 2.202739 -0.093417 3TPSS SCF energy = -2493.9263496 C 2.558920 1.757088 -3.781051 C -2.553511 -1.930203 -3.691236 H 1.776078 2.523343 -3.767085 H -2.393379 -1.341619 -4.607567 Th 0.000086 -0.354462 -0.001070 H 3.539908 2.242614 -3.869924 H -3.537741 -2.419842 -3.768995 Si -3.497525 -4.656708 -0.005571 H 2.406956 1.129745 -4.667672 H -1.769621 -2.699871 -3.641570 N -0.000312 1.040792 -2.256703 C 2.938122 3.754956 0.006264 C -3.592823 0.359494 2.562289 N 0.000084 1.032480 2.260065 H 3.066802 4.835896 0.008153 H -3.485365 0.982901 3.463985 C -1.108282 0.241131 -2.469028 C 2.841816 3.080186 -1.210137 H -4.585299 -0.115926 2.594295 C -0.709681 -1.082964 -2.729210 H 2.884146 3.643640 -2.136948 H -3.550302 1.023023 1.685717 H -1.347542 -1.938905 -2.902090 Si 3.498374 -4.656147 -0.005773 C -2.852343 -3.139286 -1.061501 C -1.107805 0.231986 2.469424 C 2.409858 -3.193589 -0.004928 H -2.892280 -3.750548 -1.963075 C -0.709178 -1.093175 2.724120 C 1.647268 -2.219584 -0.004304 C -3.592247 0.078432 -2.623888 H -1.347031 -1.949824 2.893731 H 3.074632 -5.624763 -1.055421 H -3.548225 0.839619 -1.830874 C -2.496564 0.874382 -2.514596 H 4.905726 -4.247996 -0.281686 H -4.584957 -0.396712 -2.598762 C -2.495966 0.865356 2.517705 H 3.460606 -5.342645 1.316377 H -3.485832 0.592429 -3.592331 C -2.625853 1.021585 0.001848 H -3.073737 -5.625196 -1.055318 C -2.551832 -1.509466 3.855122 H -2.624995 -0.080354 -0.000099 H -3.459479 -5.343266 1.316541 H -1.767805 -2.279508 3.894626 C -2.409268 -3.193957 -0.004781 H -4.904983 -4.248791 -0.281295 H -3.535916 -1.986664 3.991871 C -2.678883 1.692758 -1.230695

H -2.390012 -0.817364 4.695622 C -2.678518 1.688393 1.236794

C -2.951363 -3.753898 0.188508 C -1.646848 -2.219818 -0.004199 3TPSSh SCF energy = -2493.767592 H -3.081853 -4.837732 0.244838 C -2.558763 1.743186 3.786995 C -2.853163 -3.013219 1.367866 H -2.406776 1.112685 4.671358 Th 0.000071 -0.357356 -0.001054 H -2.893161 -3.527164 2.328055 H -3.539704 2.228441 3.877704 Si -3.509309 -4.640887 -0.005701 C 1.106990 -0.099407 2.434724 H -1.775888 2.509428 3.775640 N -0.000259 1.038239 -2.253000 C 0.709350 1.240758 2.612341 C -3.593886 -0.208052 -2.615676 N 0.000069 1.029825 2.256417 H 1.350688 2.109417 2.732302 H -3.489602 -0.763521 -3.556486 C -1.104017 0.242764 -2.463009 C 1.107707 -0.363922 -2.448170 H -4.582950 0.266041 -2.606511 C -0.708083 -1.078346 -2.719612 C 0.709759 0.948320 -2.773852 H -3.539612 -0.925790 -1.789151 H -1.345549 -1.931971 -2.889825 H 1.350772 1.798484 -2.988019 C -2.842102 3.075510 1.220766 C -1.103616 0.233522 2.463429 C 2.496965 -0.723669 2.529984 H -2.884089 3.635757 2.149530 C -0.707672 -1.088631 2.714609 C 2.497207 -0.995043 -2.467273 C -3.593425 -0.217226 2.615201 H -1.345142 -1.942926 2.881660 C 2.640256 -1.025639 0.048551 H -3.539568 -0.931588 1.785731 C -2.489361 0.873207 -2.507431 284

Appendix

C -2.488847 0.864083 2.510481 H 3.472524 -5.327806 1.313148 C -1.444181 -2.495937 -2.479371 C -2.622712 1.019870 0.001790 H -3.093887 -5.607855 -1.056834 C -1.424261 2.501969 -2.479046 H -2.627450 -0.078912 -0.000346 H -3.471587 -5.328322 1.313291 C -1.582767 0.003688 -2.630976 C -2.413690 -3.186265 -0.004821 H -4.912545 -4.223989 -0.276888 H -0.485624 -0.000333 -2.641237 C -2.669908 1.689765 -1.227098 C -2.253318 -1.219129 -2.665669 C -2.669533 1.685289 1.233134 C -2.243705 1.231761 -2.665559 C -1.648785 -2.220431 -0.004146 Complex 4 C -2.291788 3.761429 -2.538905 C -2.552922 1.738888 3.775746 H -1.662799 4.642509 -2.383183 4PBE0 SCF energy = -2727.4040732 H -2.402705 1.109686 4.658271 H -2.775196 3.858607 -3.516679 H -3.531506 2.223474 3.865264 Th -0.167344 -0.002635 0.000000 H -3.056938 3.752472 -1.759079 H -1.771535 2.503127 3.766299 Si 4.032438 -0.006100 3.597977 C -0.369780 -2.603544 -3.564334 C -3.582266 -0.206748 -2.607314 N -1.606219 -2.240362 0.000000 H 0.174954 -3.547470 -3.463174 H -3.479416 -0.759869 -3.546758 N -1.587842 2.247263 0.000000 H -0.839110 -2.588998 -4.552346 H -4.569687 0.265026 -2.596225 C -0.819732 -2.453764 1.097455 H 0.357846 -1.789574 -3.511321 H -3.526887 -0.924400 -1.784071 C 0.496213 -2.719987 0.705891 C -3.624617 1.219757 -2.809372 C -2.824290 3.069511 1.217603 H 1.347495 -2.891639 1.345853 H -4.182707 2.146917 -2.839492 H -2.862209 3.628742 2.144116 C -0.799608 2.454135 1.097406 C -0.349462 2.601360 -3.564381 C -3.581895 -0.216016 2.606664 C 0.518588 2.709337 0.705934 H 0.370730 1.780762 -3.511583 H -3.526792 -0.930325 1.780514 H 1.371160 2.874243 1.346081 H -0.819564 2.591546 -4.552112 H -4.569267 0.255940 2.597854 C -1.444181 -2.495937 2.479371 H 0.203721 3.540270 -3.462513 H -3.478608 -0.772874 3.543841 C -1.424261 2.501969 2.479046 C -2.321842 -3.748329 -2.540045 C -2.553805 1.752571 -3.769537 C -1.582767 0.003688 2.630976 H -3.087126 -3.733680 -1.760432 H -1.772598 2.516983 -3.757489 H -0.485624 -0.000333 2.641237 H -2.805682 -3.841143 -3.518024 H -3.532531 2.237241 -3.857199 C 2.592771 -0.009346 2.457044 H -1.699966 -4.634494 -2.384608 H -2.403498 1.126570 -4.654332 C -2.253318 -1.219129 2.665669 C -4.303079 0.014479 -2.898567 C -2.917156 3.747132 0.006800 C -2.243705 1.231761 2.665559 H -5.382829 0.018715 -3.012288 H -3.039217 4.826262 0.008829 C 1.650432 -0.009799 1.669493 C -3.634126 -1.196088 -2.809477 C -2.824902 3.073884 -1.206513 C -2.291788 3.761429 2.538905 H -4.199542 -2.118792 -2.839763 H -2.863588 3.636375 -2.131023 H -1.662799 4.642509 2.383183 Si 4.032438 -0.006100 -3.597977 C 1.103559 0.242873 -2.463108 H -2.775196 3.858607 3.516679 C 2.592771 -0.009346 -2.457044 C 0.707729 -1.078277 -2.719670 H -3.056938 3.752472 1.759079 C 1.650432 -0.009799 -1.669493 H 1.345264 -1.931838 -2.889947 C -0.369780 -2.603544 3.564334 C 3.618509 -1.049692 -5.105860 C 1.103894 0.233688 2.463319 H 0.174954 -3.547470 3.463174 H 3.395484 -2.081818 -4.816385 C 0.708175 -1.088524 2.714540 H -0.839110 -2.588998 4.552346 H 2.745080 -0.648748 -5.630565 H 1.345790 -1.942724 2.881520 H 0.357846 -1.789574 3.511321 H 4.459847 -1.066448 -5.807976 C 2.488835 0.873459 -2.507706 C -3.624617 1.219757 2.809372 C 4.394149 1.760818 -4.127008 C 2.489037 0.864453 2.510202 H -4.182707 2.146917 2.839492 H 5.250221 1.794304 -4.810459 C 2.622550 1.020198 0.001492 C -0.349462 2.601360 3.564381 H 3.531493 2.199085 -4.639637 H 2.627462 -0.078583 -0.000619 H 0.370730 1.780762 3.511583 H 4.626234 2.385404 -3.258243 C 2.669463 1.690069 -1.227418 H -0.819564 2.591546 4.552112 C 5.516798 -0.726118 -2.700855 C 2.669446 1.685654 1.232813 H 0.203721 3.540270 3.462513 H 5.747530 -0.140483 -1.805226 C 2.553128 1.739297 3.775440 C -2.321842 -3.748329 2.540045 H 5.319356 -1.756230 -2.387563 H 2.403107 1.110093 4.657997 H -3.087126 -3.733680 1.760432 H 6.400333 -0.727144 -3.349285 H 3.531649 2.224031 3.864833 H -2.805682 -3.841143 3.518024 H 1.771625 2.503419 3.766066 H -1.699966 -4.634494 2.384608 4PBE SCF energy = -2727.1373764 C 3.581841 -0.206384 -2.607702 C -4.303079 0.014479 2.898567 H 3.478930 -0.759539 -3.547120 H -5.382829 0.018715 3.012288 Th -0.002159 0.182958 0.000000 H 4.569214 0.265494 -2.596751 C -3.634126 -1.196088 2.809477 Si -0.005385 -4.095099 3.525255 H 3.526642 -0.924021 -1.784435 H -4.199542 -2.118792 2.839763 N -2.248534 1.627362 0.000000 C 2.824000 3.069898 1.217227 C 3.618509 -1.049692 5.105860 N 2.254755 1.611136 0.000000 H 2.861964 3.629158 2.143721 H 3.395484 -2.081818 4.816385 C -2.468995 0.832125 1.107322 C 3.582255 -0.215482 2.606281 H 2.745080 -0.648748 5.630565 C -2.747430 -0.491068 0.709771 H 3.527161 -0.929818 1.780153 H 4.459847 -1.066448 5.807976 H -2.926870 -1.348586 1.351537 H 4.569556 0.256620 2.597344 C 4.394149 1.760818 4.127008 C 2.469492 0.814328 1.107270 H 3.479161 -0.772335 3.543483 H 5.250221 1.794304 4.810459 C 2.738453 -0.510886 0.709797 C 2.553030 1.752801 -3.769840 H 3.531493 2.199085 4.639637 H 2.912183 -1.369539 1.351733 H 1.771748 2.517133 -3.757712 H 4.626234 2.385404 3.258243 C -2.514388 1.462204 2.496992 H 3.531696 2.237568 -3.857636 C 5.516798 -0.726118 2.700855 C 2.519689 1.444485 2.496735 H 2.402676 1.126764 -4.654602 H 5.747530 -0.140483 1.805226 C 0.003191 1.601675 2.643020 C 2.916603 3.747502 0.006394 H 5.319356 -1.756230 2.387563 H -0.000718 0.495829 2.639366 H 3.038510 4.826649 0.008379 H 6.400333 -0.727144 3.349285 C -0.007855 -2.611087 2.432191 C 2.824270 3.074211 -1.206889 C -0.819732 -2.453764 -1.097455 C -1.229064 2.275149 2.690663 H 2.862741 3.636685 -2.131418 C 0.496213 -2.719987 -0.705891 C 1.240146 2.266499 2.690513 Si 3.510014 -4.640418 -0.005875 H 1.347495 -2.891639 -1.345853 C -0.008226 -1.636433 1.664126 C 2.414179 -3.185958 -0.004946 C -0.799608 2.454135 -1.097406 C 3.787288 2.319696 2.552227 C 1.649134 -2.220235 -0.004233 C 0.518588 2.709337 -0.705934 H 4.674315 1.688185 2.390434 H 3.094632 -5.607490 -1.056928 H 1.371160 2.874243 -1.346081 H 3.889588 2.804992 3.536528 H 4.913163 -4.223324 -0.277217 285

Appendix

H 3.773069 3.091104 1.768574 C -1.038777 -3.726957 -5.067371 C -2.468037 0.833164 -1.107675 C -2.627153 0.382464 3.591481 H -2.077750 -3.482156 -4.794348 C -2.738470 -0.489158 -0.709447 H -3.575252 -0.168608 3.485915 H -0.622381 -2.872492 -5.624622 H -2.914730 -1.343827 -1.347995 H -2.619209 0.857412 4.584726 H -1.057023 -4.599962 -5.741078 C 2.468559 0.811675 -1.107641 H -1.805155 -0.347338 3.544401 C 1.774708 -4.493462 -4.027955 C 2.727662 -0.512955 -0.709464 C 1.226232 3.654809 2.856388 H 1.805875 -5.377753 -4.686320 H 2.896920 -1.369031 -1.348081 H 2.159582 4.216615 2.895672 H 2.228876 -3.647331 -4.568285 C -2.511891 1.467389 -2.495670 C 2.625032 0.364257 3.591466 H 2.392955 -4.703644 -3.140584 C 2.518113 1.445718 -2.495535 H 1.797258 -0.359013 3.544232 C -0.750629 -5.549917 -2.574834 C 0.003809 1.609047 -2.627814 H 2.620986 0.839709 4.584515 H -0.174261 -5.751001 -1.657719 H -0.000847 0.507155 -2.622999 H 3.568757 -0.194168 3.485456 H -1.789978 -5.333688 -2.280898 C -1.226582 2.283196 -2.679676 C -3.775753 2.346359 2.552960 H -0.748526 -6.462976 -3.193462 C 1.239926 2.272648 -2.679606 H -3.756372 3.117832 1.769474 C 3.789897 2.320074 -2.558011 H -3.874368 2.832110 3.537408 H 4.672510 1.687342 -2.404758 H -4.667252 1.721139 2.391298 4TPSS SCF energy = -2729.9842788 H 3.882795 2.804966 -3.539038 C 0.012817 4.336365 2.955959 H 3.779760 3.086652 -1.775410 Th -0.002511 0.202846 0.000000 H 0.016627 5.421583 3.087043 C -2.615974 0.385112 -3.592947 Si -0.006585 -4.117415 3.480755 C -1.205356 3.663327 2.856570 H -3.559765 -0.165789 -3.489824 N -2.250440 1.630929 0.000000 H -2.134720 4.231690 2.896042 H -2.603144 0.858762 -4.582276 N 2.257844 1.611314 0.000000 C -1.038777 -3.726957 5.067371 H -1.792752 -0.336269 -3.535754 C -2.468037 0.833164 1.107675 H -2.077750 -3.482156 4.794348 C 1.227796 3.659831 -2.843587 C -2.738470 -0.489158 0.709447 H -0.622381 -2.872492 5.624622 H 2.157989 4.217873 -2.884932 H -2.914730 -1.343827 1.347995 H -1.057023 -4.599962 5.741078 C 2.612899 0.362709 -3.592945 C 2.468559 0.811675 1.107641 C 1.774708 -4.493462 4.027955 H 1.783236 -0.351280 -3.535278 C 2.727662 -0.512955 0.709464 H 1.805875 -5.377753 4.686320 H 2.604181 0.836719 -4.582172 H 2.896920 -1.369031 1.348081 H 2.228876 -3.647331 4.568285 H 3.551721 -0.196588 -3.489797 C -2.511891 1.467389 2.495670 H 2.392955 -4.703644 3.140584 C -3.776038 2.352739 -2.558388 C 2.518113 1.445718 2.495535 C -0.750629 -5.549917 2.574834 H -3.759519 3.119222 -1.775800 C 0.003809 1.609047 2.627814 H -0.174261 -5.751001 1.657719 H -3.864517 2.838365 -3.539453 H -0.000847 0.507155 2.622999 H -1.789978 -5.333688 2.280898 H -4.664113 1.727638 -2.405370 C -0.009447 -2.615906 2.417976 H -0.748526 -6.462976 3.193462 C 0.015546 4.341977 -2.940274 C -1.226582 2.283196 2.679676 C -2.468995 0.832125 -1.107322 H 0.020169 5.422976 -3.068767 C 1.239926 2.272648 2.679606 C -2.747430 -0.491068 -0.709771 C -1.202500 3.670232 -2.843642 C -0.009731 -1.633275 1.664669 H -2.926870 -1.348586 -1.351537 H -2.127845 4.236270 -2.885047 C 3.789897 2.320074 2.558011 C 2.469492 0.814328 -1.107270 Si -0.006585 -4.117415 -3.480755 H 4.672510 1.687342 2.404758 C 2.738453 -0.510886 -0.709797 C -0.009447 -2.615906 -2.417976 H 3.882795 2.804966 3.539038 H 2.912183 -1.369539 -1.351733 C -0.009731 -1.633275 -1.664669 H 3.779760 3.086652 1.775410 C -2.514388 1.462204 -2.496992 C -0.779463 -3.695768 -5.156193 C -2.615974 0.385112 3.592947 C 2.519689 1.444485 -2.496735 H -1.814613 -3.347355 -5.038001 H -3.559765 -0.165789 3.489824 C 0.003191 1.601675 -2.643020 H -0.213594 -2.903367 -5.664996 H -2.603144 0.858762 4.582276 H -0.000718 0.495829 -2.639366 H -0.791925 -4.577746 -5.813122 H -1.792752 -0.336269 3.535754 C -1.229064 2.275149 -2.690663 C 1.775104 -4.702997 -3.731736 C 1.227796 3.659831 2.843587 C 1.240146 2.266499 -2.690513 H 1.806238 -5.605871 -4.359051 H 2.157989 4.217873 2.884932 C 3.787288 2.319696 -2.552227 H 2.380320 -3.928873 -4.223208 C 2.612899 0.362709 3.592945 H 4.674315 1.688185 -2.390434 H 2.249086 -4.941742 -2.769918 H 1.783236 -0.351280 3.535278 H 3.889588 2.804992 -3.536528 C -1.013222 -5.473065 -2.629216 H 2.604181 0.836719 4.582172 H 3.773069 3.091104 -1.768574 H -0.592823 -5.711412 -1.642805 H 3.551721 -0.196588 3.489797 C -2.627153 0.382464 -3.591481 H -2.054843 -5.157095 -2.481902 C -3.776038 2.352739 2.558388 H -3.575252 -0.168608 -3.485915 H -1.018380 -6.394131 -3.230306 H -3.759519 3.119222 1.775800 H -2.619209 0.857412 -4.584726 H -3.864517 2.838365 3.539453 H -1.805155 -0.347338 -3.544401 H -4.664113 1.727638 2.405370 C 1.226232 3.654809 -2.856388 4TPSSh SCF energy = -2729.8089524 C 0.015546 4.341977 2.940274 H 2.159582 4.216615 -2.895672 H 0.020169 5.422976 3.068767 Th -0.002672 0.196979 0.000000 C 2.625032 0.364257 -3.591466 C -1.202500 3.670232 2.843642 Si -0.006870 -4.100920 3.498125 H 1.797258 -0.359013 -3.544232 H -2.127845 4.236270 2.885047 N -2.246598 1.625435 0.000000 H 2.620986 0.839709 -4.584515 C -0.779463 -3.695768 5.156193 N 2.254257 1.604945 0.000000 H 3.568757 -0.194168 -3.485456 H -1.814613 -3.347355 5.038001 C -2.462071 0.831879 1.103488 C -3.775753 2.346359 -2.552960 H -0.213594 -2.903367 5.664996 C -2.729324 -0.487374 0.707881 H -3.756372 3.117832 -1.769474 H -0.791925 -4.577746 5.813122 H -2.903210 -1.339674 1.346027 H -3.874368 2.832110 -3.537408 C 1.775104 -4.702997 3.731736 C 2.462552 0.809450 1.103452 H -4.667252 1.721139 -2.391298 H 1.806238 -5.605871 4.359051 C 2.717891 -0.512206 0.707903 C 0.012817 4.336365 -2.955959 H 2.380320 -3.928873 4.223208 H 2.884401 -1.365968 1.346132 H 0.016627 5.421583 -3.087043 H 2.249086 -4.941742 2.769918 C -2.504570 1.463294 2.488553 C -1.205356 3.663327 -2.856570 C -1.013222 -5.473065 2.629216 C 2.511057 1.440745 2.488381 H -2.134720 4.231690 -2.896042 H -0.592823 -5.711412 1.642805 C 0.003969 1.604082 2.624716 Si -0.005385 -4.095099 -3.525255 H -2.054843 -5.157095 2.481902 H -0.000882 0.505347 2.625562 C -0.007855 -2.611087 -2.432191 H -1.018380 -6.394131 3.230306 C -0.010020 -2.609899 2.423997 C -0.008226 -1.636433 -1.664126 286

Appendix

C -1.222693 2.277079 2.670713 H 0.021018 5.410507 -3.040418 C 0.375343 -0.670839 2.711089 C 1.236599 2.266099 2.670641 C -1.198801 3.661207 -2.825908 H -0.550567 -1.198437 2.877111 C -0.010287 -1.636695 1.666716 H -2.121774 4.226417 -2.863314 C 2.105693 -2.590826 -2.533601 C 3.778971 2.311888 2.551919 Si -0.006870 -4.100920 -3.498125 C 2.074218 -2.673475 2.462283 H 4.659613 1.680339 2.400202 C -0.010020 -2.609899 -2.423997 C 2.218018 -2.801021 -0.037454 H 3.870947 2.796029 3.530602 C -0.010287 -1.636695 -1.666716 H 1.128532 -2.671303 -0.041473 H 3.770673 3.076517 1.770867 C -0.786255 -3.667815 -5.161856 C 2.881298 -2.901219 -1.260384 C -2.607619 0.383574 3.581474 H -1.819680 -3.324955 -5.035815 C 2.865925 -2.942241 1.189592 H -3.550176 -0.164729 3.479873 H -0.226406 -2.870446 -5.664130 C 2.924735 -2.861965 3.720840 H -2.592687 0.854958 4.569118 H -0.798400 -4.541695 -5.825325 H 2.319126 -2.640431 4.604213 H -1.787893 -0.337932 3.523149 C 1.771312 -4.675788 -3.760310 H 3.279369 -3.894700 3.803510 C 1.225163 3.650377 2.825850 H 1.803535 -5.571113 -4.393888 H 3.783205 -2.186144 3.723270 H 2.153186 4.207259 2.863187 H 2.369796 -3.896531 -4.246297 C 0.902735 -3.527687 -2.660930 C 2.604543 0.360336 3.581491 H 2.248423 -4.919956 -2.804270 H 0.377598 -3.343696 -3.603344 H 1.778096 -0.353487 3.522811 C -1.002807 -5.462779 -2.655382 H 1.239827 -4.568271 -2.658786 H 2.593989 0.832182 4.569000 H -0.577750 -5.706819 -1.675181 H 0.186784 -3.389990 -1.846682 H 3.541928 -0.196719 3.479793 H -2.042099 -5.151227 -2.501014 C 4.216591 -3.263464 1.175438 C -3.764551 2.345850 2.552481 H -1.008175 -6.376827 -3.262489 H 4.763814 -3.381725 2.102024 H -3.749668 3.110447 1.771491 C 0.870430 -3.615329 2.544896 H -3.851872 2.830684 3.531240 H 0.164383 -3.458635 1.725138 H -4.650882 1.722245 2.401016 Complex 5 H 1.211277 -4.654436 2.518900 C 0.016200 4.331305 2.918674 H 0.333221 -3.459735 3.485778 5PBE0 SCF energy = -3198.6406204 H 0.021018 5.410507 3.040418 C 2.971612 -2.738123 -3.786998 C -1.198801 3.661207 2.825908 Th 1.125054 -0.012220 0.001567 H 3.830026 -2.062893 -3.756782 H -2.121774 4.226417 2.863314 Si -3.108305 3.446348 0.075696 H 3.327240 -3.767735 -3.899069 C -0.786255 -3.667815 5.161856 N 2.576382 -0.158418 -2.227937 H 2.376828 -2.487640 -4.669990 H -1.819680 -3.324955 5.035815 N 2.550454 -0.231922 2.240344 C 4.880776 -3.418781 -0.031042 H -0.226406 -2.870446 5.664130 C 1.938345 1.033258 -2.428369 H 5.936698 -3.671373 -0.028648 H -0.798400 -4.541695 5.825325 C 0.585696 0.817275 -2.710421 C 4.231769 -3.222952 -1.239902 C 1.771312 -4.675788 3.760310 H -0.173953 1.564232 -2.881247 H 4.790638 -3.310252 -2.162959 H 1.803535 -5.571113 4.393888 C 1.911028 0.953375 2.473175 Si -3.600341 -2.884750 0.098004 H 2.369796 -3.896531 4.246297 C 0.555784 0.728905 2.734569 C -1.951179 -2.065151 0.001445 H 2.248423 -4.919956 2.804270 H -0.206890 1.468008 2.923575 C -0.885252 -1.453883 -0.022590 C -1.002807 -5.462779 2.655382 C 2.737112 2.322243 -2.448995 C -4.322927 2.154094 -0.631455 H -0.577750 -5.706819 1.675181 C 2.708516 2.241482 2.544136 C -4.061435 1.863289 -2.106409 H -2.042099 -5.151227 2.501014 C 2.890622 2.408524 0.050626 C -5.804884 2.409001 -0.375323 H -1.008175 -6.376827 3.262489 H 1.803414 2.556327 0.047189 H -4.037569 1.251395 -0.068656 C -2.462071 0.831879 -1.103488 C -1.482779 2.574927 0.038622 H -3.007571 1.631234 -2.290461 C -2.729324 -0.487374 -0.707881 C 3.562495 2.380357 -1.171123 H -4.655290 1.004621 -2.445253 H -2.903210 -1.339674 -1.346027 C 3.548465 2.340998 1.278389 H -4.337712 2.714459 -2.739413 C 2.462552 0.809450 -1.103452 C -0.486504 1.855429 0.021757 H -6.030836 2.498099 0.691740 C 2.717891 -0.512206 -0.707903 C 3.572191 2.168211 3.805606 H -6.156728 3.321505 -0.868971 H 2.884401 -1.365968 -1.346132 H 2.925514 2.080711 4.683296 H -6.407991 1.579110 -0.767115 C -2.504570 1.463294 -2.488553 H 4.177431 3.073635 3.919641 C -3.507642 3.823824 1.906431 C 2.511057 1.440745 -2.488381 H 4.230509 1.296494 3.784274 C -4.659399 4.803645 2.118584 C 0.003969 1.604082 -2.624716 C 1.813483 3.538797 -2.533241 C -2.274372 4.306295 2.664688 H -0.000882 0.505347 -2.625562 H 1.250456 3.524638 -3.471501 H -3.802778 2.850751 2.328775 C -1.222693 2.277079 -2.670713 H 2.406439 4.457599 -2.508065 H -5.580467 4.499690 1.612837 C 1.236599 2.266099 -2.670641 H 1.093947 3.566294 -1.711102 H -4.887733 4.902607 3.187611 C 3.778971 2.311888 -2.551919 C 4.936461 2.311013 1.268770 H -4.395860 5.804114 1.756104 H 4.659613 1.680339 -2.400202 H 5.491951 2.256421 2.196389 H -1.442830 3.602046 2.578532 H 3.870947 2.796029 -3.530602 C 1.783645 3.455265 2.658840 H -1.925240 5.273123 2.280674 H 3.770673 3.076517 -1.770867 H 1.069334 3.512512 1.833320 H -2.501146 4.446444 3.729608 C -2.607619 0.383574 -3.581474 H 2.377720 4.373716 2.668662 C -2.974280 5.073293 -0.918599 H -3.550176 -0.164729 -3.479873 H 1.214749 3.411339 3.592716 C -4.322800 5.634136 -1.367318 H -2.592687 0.854958 -4.569118 C 3.614670 2.289719 -3.702439 C -2.016511 4.987610 -2.103295 H -1.787893 -0.337932 -3.523149 H 4.272460 1.417345 -3.702227 H -2.540623 5.784410 -0.197595 C 1.225163 3.650377 -2.825850 H 4.221419 3.197988 -3.779937 H -5.033400 5.745034 -0.543255 H 2.153186 4.207259 -2.863187 H 2.977829 2.231476 -4.589704 H -4.194462 6.622365 -1.827454 C 2.604543 0.360336 -3.581491 C 5.623076 2.333821 0.065021 H -4.788096 4.988837 -2.120719 H 1.778096 -0.353487 -3.522811 H 6.708535 2.311126 0.070867 H -1.026436 4.637482 -1.800334 H 2.593989 0.832182 -4.569000 C 4.950252 2.349629 -1.146626 H -2.389123 4.298187 -2.869358 H 3.541928 -0.196719 -3.479793 H 5.516300 2.324543 -2.069133 H -1.901618 5.970472 -2.578988 C -3.764551 2.345850 -2.552481 C 1.659452 -1.142922 -2.466024 C -4.419380 -2.151873 1.659156 H -3.749668 3.110447 -1.771491 C 0.406221 -0.583136 -2.734517 C -3.723133 -2.618767 2.933855 H -3.851872 2.830684 -3.531240 H -0.515839 -1.108408 -2.929355 C -5.932041 -2.319019 1.763259 H -4.650882 1.722245 -2.401016 C 1.630294 -1.223235 2.436959 H -4.212117 -1.076424 1.546693 C 0.016200 4.331305 -2.918674 H -2.637929 -2.483854 2.874272 287

Appendix

H -4.083802 -2.059725 3.806644 H 5.514130 2.494472 -2.044748 C -4.344696 -2.234028 1.688696 H -3.914013 -3.680387 3.129730 C 1.743689 -1.134810 -2.483620 C -3.709576 -2.856406 2.945510 H -6.454525 -1.893539 0.900709 C 0.469826 -0.607640 -2.780045 C -5.874685 -2.284643 1.769356 H -6.224759 -3.371974 1.842773 H -0.441676 -1.160854 -2.990692 H -4.043884 -1.168531 1.660470 H -6.314006 -1.811285 2.658540 C 1.634542 -1.213826 2.442120 H -2.613928 -2.945804 2.862632 C -3.259062 -4.753897 0.273606 C 0.356037 -0.678672 2.698644 H -3.927557 -2.248061 3.841056 C -2.576815 -5.339350 -0.959700 H -0.572086 -1.225660 2.842399 H -4.111444 -3.866731 3.136385 C -4.456320 -5.605643 0.686545 C 2.242851 -2.575551 -2.545175 H -6.354567 -1.773580 0.919692 H -2.529521 -4.786640 1.097702 C 2.115286 -2.661771 2.478026 H -6.246728 -3.322823 1.791937 H -1.696778 -4.759357 -1.254339 C 2.319156 -2.774677 -0.035961 H -6.233361 -1.792639 2.692181 H -2.251034 -6.370671 -0.772228 H 1.220627 -2.655114 -0.063635 C -3.205566 -4.809936 0.191631 H -3.258735 -5.369144 -1.817321 C 3.010654 -2.868944 -1.252385 C -2.608858 -5.384315 -1.101543 H -4.910905 -5.260835 1.620116 C 2.945999 -2.914276 1.214576 C -4.377860 -5.663400 0.699489 H -5.237635 -5.608636 -0.080414 C 2.948182 -2.831785 3.764589 H -2.413474 -4.848523 0.965256 H -4.149912 -6.648969 0.837943 H 2.315748 -2.620775 4.641007 H -1.753225 -4.789142 -1.458520 C -4.600634 -2.382391 -1.451323 H 3.325684 -3.863829 3.857226 H -2.257681 -6.420297 -0.943291 C -5.788988 -3.292541 -1.755171 H 3.798180 -2.133199 3.783556 H -3.355424 -5.417355 -1.912474 C -3.738326 -2.198622 -2.696899 C 1.066904 -3.560388 -2.695686 H -4.663900 -5.378756 1.723890 H -4.998604 -1.390969 -1.181223 H 0.541783 -3.384724 -3.648789 H -5.272532 -5.573864 0.063193 H -6.445511 -3.439341 -0.892040 H 1.443428 -4.595521 -2.700413 H -4.097134 -6.732110 0.716539 H -6.398524 -2.872227 -2.565434 H 0.333098 -3.457715 -1.881760 C -4.626239 -2.404180 -1.469432 H -5.454302 -4.281391 -2.088026 C 4.309573 -3.224076 1.226398 C -5.785319 -3.355608 -1.805390 H -2.922684 -1.492992 -2.517269 H 4.843214 -3.341540 2.170443 C -3.777260 -2.127525 -2.717441 H -3.293881 -3.146802 -3.020756 C 0.925596 -3.639575 2.535201 H -5.075961 -1.440971 -1.152480 H -4.342037 -1.819946 -3.532134 H 0.233710 -3.502034 1.689987 H -6.445751 -3.541606 -0.944392 H 1.294490 -4.677349 2.522790 H -6.409208 -2.932344 -2.613509 H 0.355911 -3.492770 3.467478 H -5.416591 -4.331875 -2.161608 5PBE SCF energy = -3198.27317 C 3.139945 -2.693056 -3.792360 H -2.980571 -1.395870 -2.514581 H 3.983831 -1.988544 -3.743858 H -3.294953 -3.048402 -3.087471 Th 1.132422 -0.010587 -0.013929 H 3.530223 -3.718550 -3.902649 H -4.407672 -1.737207 -3.537234 Si -3.173007 3.381242 0.041530 H 2.550431 -2.454865 -4.691470 N 2.636275 -0.113651 -2.228995 C 5.005333 -3.367481 0.025188 N 2.552221 -0.196723 2.271924 H 6.071874 -3.608617 0.049038 5TPSS SCF energy = -3201.8824173 C 1.953731 1.068093 -2.435507 C 4.374129 -3.175767 -1.204684 C 0.604149 0.804666 -2.745588 Th 1.131501 -0.033204 0.006992 H 4.957269 -3.254617 -2.123096 H -0.184830 1.529110 -2.928946 Si -3.330341 3.249852 0.093764 Si -3.568653 -2.926493 0.061099 C 1.877659 0.986566 2.493336 N 2.562526 0.040526 -2.239392 C -1.919082 -2.103731 -0.070118 C 0.512665 0.731573 2.735909 N 2.571622 -0.124994 2.248404 C -0.829877 -1.507316 -0.085577 H -0.274680 1.459934 2.911241 C 1.770050 1.158663 -2.418514 C -4.330339 2.147717 -0.906428 C 2.716007 2.388408 -2.442719 C 0.446483 0.775777 -2.704296 C -4.306618 2.334714 -2.431340 C 2.661114 2.292803 2.580939 H -0.404885 1.423421 -2.862041 C -5.771743 2.041116 -0.396802 C 2.857714 2.461197 0.074553 C 1.783497 0.979290 2.510717 H -3.830376 1.182359 -0.696855 H 1.756254 2.562872 0.064642 C 0.459710 0.581296 2.773576 H -3.280938 2.328399 -2.833189 C -1.524689 2.539591 -0.008589 H -0.388038 1.219535 2.981595 H -4.860794 1.517167 -2.927770 C 3.539922 2.468077 -1.152165 C 2.413559 2.542915 -2.418364 H -4.783678 3.281102 -2.737431 C 3.514447 2.418595 1.314949 C 2.428133 2.359215 2.608268 H -5.819822 1.794927 0.675529 C -0.503092 1.832909 -0.026420 C 2.572560 2.582273 0.099281 H -6.335537 2.975705 -0.555972 C 3.520940 2.222296 3.858412 H 1.470495 2.582169 0.102014 H -6.311348 1.244115 -0.941958 H 2.865004 2.111552 4.735816 C -1.723899 2.339080 0.078502 C -3.615056 3.521697 1.917399 H 4.111148 3.144696 3.988280 C 3.238447 2.676848 -1.132963 C -4.935212 4.215159 2.282341 H 4.201812 1.358126 3.832194 C 3.245351 2.587422 1.331391 C -2.460669 4.163630 2.704303 C 1.749280 3.584251 -2.524936 C -0.698339 1.643676 0.061630 H -3.679275 2.461959 2.236886 H 1.200183 3.572665 -3.480695 C 3.313349 2.366234 3.874111 H -5.801935 3.824400 1.730878 H 2.320768 4.524365 -2.473141 H 2.687089 2.181218 4.755246 H -5.146396 4.096960 3.360850 H 1.006252 3.582441 -1.710431 H 3.804294 3.340265 4.001972 H -4.876778 5.299600 2.090464 C 4.912083 2.445253 1.312934 H 4.075635 1.580862 3.826117 H -1.495708 3.681182 2.486724 H 5.468184 2.411850 2.250577 C 1.340452 3.651810 -2.478365 H -2.360381 5.236192 2.462354 C 1.713021 3.501557 2.697563 H 0.781553 3.584937 -3.420641 H -2.642858 4.095896 3.792037 H 1.011008 3.563627 1.852140 H 1.822553 4.636191 -2.436410 C -3.009174 5.134401 -0.738959 H 2.299701 4.433265 2.732389 H 0.625403 3.574281 -1.651435 C -4.364639 5.834236 -0.927818 H 1.122408 3.436580 3.625995 C 4.632834 2.748168 1.315261 C -2.190666 5.181146 -2.038032 C 3.606409 2.393685 -3.700629 H 5.197476 2.754201 2.242352 H -2.443963 5.702541 0.025749 H 4.297698 1.537885 -3.703251 C 1.352668 3.457654 2.755292 H -4.938389 5.910912 0.007927 H 4.187876 3.328532 -3.769513 H 0.627903 3.429595 1.933664 H -4.220811 6.859651 -1.313625 H 2.972387 2.320741 -4.597965 H 1.829817 4.445085 2.772910 H -4.996424 5.303544 -1.659281 C 5.608982 2.498948 0.104906 H 0.804417 3.325140 3.696849 H -1.209313 4.690394 -1.937468 H 6.702433 2.519412 0.117158 C 3.291556 2.641785 -3.685522 H -2.735371 4.684071 -2.856918 C 4.937880 2.493580 -1.118658 H 4.053467 1.854711 -3.699504 H -2.008806 6.223663 -2.357329 288

Appendix

H 3.782465 3.622384 -3.744856 H -3.918129 7.017837 0.874060 H 0.933877 3.506325 1.841642 H 2.660005 2.521828 -4.574110 H -4.183983 6.238520 -0.692211 H 2.204222 4.423022 2.684156 C 5.306811 2.886976 0.102623 H -0.813677 4.939208 0.514709 H 1.070471 3.418977 3.605211 H 6.388159 3.012436 0.104143 H -1.616690 5.770984 -0.827818 C 3.580956 2.379749 -3.695913 C 4.626013 2.836112 -1.113065 H -1.453657 6.586166 0.737357 H 4.264498 1.526852 -3.685432 H 5.185398 2.909373 -2.040453 C -3.987802 -3.036533 1.848439 H 4.160904 3.306720 -3.766509 C 1.760877 -1.055165 -2.497453 C -3.117158 -3.893011 2.787711 H 2.953111 2.302280 -4.588794 C 0.440381 -0.642347 -2.754565 C -5.484797 -3.272050 2.124564 C 5.558514 2.507253 0.104656 H -0.416351 -1.270327 -2.957329 H -3.777064 -1.978656 2.083517 H 6.644198 2.530973 0.119752 C 1.767218 -1.234172 2.430551 H -2.046747 -3.712894 2.622537 C 4.893537 2.497072 -1.116615 C 0.449400 -0.836722 2.722491 H -3.341230 -3.666944 3.841595 H 5.467751 2.499952 -2.034807 H -0.408349 -1.475033 2.883749 H -3.302802 -4.966061 2.638310 C 1.699035 -1.120446 -2.473263 C 2.391526 -2.441585 -2.596483 H -6.122286 -2.595109 1.541398 C 0.429043 -0.591820 -2.748305 C 2.395174 -2.625470 2.427503 H -5.788258 -4.302286 1.893293 H -0.476745 -1.140921 -2.952811 C 2.545462 -2.664536 -0.089491 H -5.707674 -3.098790 3.188908 C 1.662223 -1.220146 2.441995 H 1.443509 -2.653604 -0.088214 C -3.119325 -4.989387 -0.527543 C 0.384705 -0.711720 2.718648 C 3.213483 -2.675366 -1.323971 C -2.639323 -5.098312 -1.988222 H -0.521532 -1.272618 2.883408 C 3.215042 -2.766216 1.139951 C -4.276195 -5.973427 -0.266001 C 2.194745 -2.557738 -2.547288 C 3.274879 -2.736198 3.692435 H -2.275707 -5.298925 0.113840 C 2.164802 -2.657053 2.464935 H 2.646750 -2.611565 4.582810 H -1.798461 -4.423120 -2.191092 C 2.317567 -2.756608 -0.043102 H 3.755923 -3.721880 3.748528 H -2.312289 -6.125258 -2.213043 H 1.223760 -2.652547 -0.046739 H 4.044866 -1.957027 3.706201 H -3.446739 -4.852610 -2.691948 C 2.984499 -2.845093 -1.270355 C 1.306434 -3.531634 -2.732932 H -4.578613 -5.987074 0.788655 C 2.970470 -2.892153 1.187325 H 0.744704 -3.391424 -3.665352 H -5.162570 -5.727607 -0.865295 C 3.025618 -2.820811 3.731129 H 1.777187 -4.521903 -2.762903 H -3.973357 -6.997034 -0.536235 H 2.410329 -2.625314 4.614659 H 0.595633 -3.504344 -1.899132 C -4.624714 -2.164170 -1.102048 H 3.417016 -3.841413 3.807363 C 4.601031 -2.937768 1.114906 C -5.890438 -2.929112 -1.539444 H 3.859411 -2.113993 3.734194 H 5.163135 -3.016780 2.040193 C -3.944423 -1.522329 -2.327051 C 1.014769 -3.537560 -2.674715 C 1.309965 -3.722619 2.487811 H -4.948891 -1.337533 -0.444589 H 0.481791 -3.365445 -3.615683 H 0.594814 -3.635578 1.661693 H -6.425771 -3.382913 -0.695875 H 1.385475 -4.567227 -2.675951 H 1.781347 -4.712128 2.443829 H -6.589647 -2.249610 -2.050619 H 0.300374 -3.420361 -1.855282 H 0.753093 -3.651039 3.430869 H -5.642117 -3.730807 -2.248259 C 4.332757 -3.182447 1.172349 C 3.268760 -2.459430 -3.867678 H -3.078918 -0.916882 -2.033234 H 4.881881 -3.292398 2.099237 H 4.037552 -1.680023 -3.826533 H -3.597896 -2.286065 -3.037421 C 0.989512 -3.648992 2.540847 H 3.751160 -3.437714 -3.995542 H -4.656215 -0.875193 -2.863383 H 0.284283 -3.510663 1.716428 H 2.638764 -2.271986 -4.745636 H 1.369496 -4.674925 2.511294 C 5.276856 -2.993400 -0.103404 H 0.444063 -3.514746 3.480955 H 6.357078 -3.128078 -0.109028 5TPSSh SCF energy = -3201.669287 C 3.069216 -2.676854 -3.809020 C 4.599540 -2.848059 -1.313460 H 3.906133 -1.974504 -3.775823 Th 1.131197 -0.009278 0.004031 H 5.160388 -2.858548 -2.242832 H 3.456911 -3.695706 -3.919799 Si -3.193533 3.385696 0.067194 Si -3.421539 -3.170843 0.015219 H 2.464802 -2.444883 -4.691223 N 2.593425 -0.105757 -2.223873 C -1.777931 -2.329878 -0.039859 C 5.002911 -3.318522 -0.038446 N 2.552907 -0.189210 2.248714 C -0.723246 -1.679386 -0.041669 H 6.064877 -3.545965 -0.036770 C 1.916597 1.074394 -2.427072 C -4.010194 3.106242 -1.699465 C 4.346396 -3.136786 -1.250752 C 0.568604 0.817063 -2.718085 C -3.150711 3.862309 -2.730842 H 4.906066 -3.211734 -2.174813 H -0.211657 1.540936 -2.894101 C -5.502774 3.435627 -1.891146 Si -3.558302 -2.966561 0.074217 C 1.863242 0.977120 2.488768 H -3.886659 2.028230 -1.904059 C -1.913559 -2.133366 -0.011270 C 0.513627 0.697361 2.748863 H -2.084698 3.623123 -2.623778 C -0.847734 -1.511095 -0.030398 H -0.276287 1.405177 2.944150 H -3.456452 3.601519 -3.755875 C -4.307812 2.240227 -0.991929 C 2.685706 2.387719 -2.443260 H -3.263458 4.950298 -2.625068 C -3.873871 2.197852 -2.465281 C 2.618175 2.296790 2.568255 H -6.145457 2.818912 -1.250070 C -5.825069 2.447684 -0.878438 C 2.815644 2.460340 0.066817 H -5.720676 4.489833 -1.673319 H -4.079525 1.251312 -0.564041 H 1.721645 2.563450 0.054107 H -5.802451 3.249257 -2.934248 H -2.799905 2.007111 -2.560429 C -1.557361 2.529115 0.050460 C -4.492385 2.310286 1.310093 H -4.406093 1.400764 -3.001565 C 3.501440 2.468009 -1.153153 C -5.720794 3.113250 1.782846 H -4.099121 3.140887 -2.977510 C 3.468191 2.424963 1.304381 C -3.735969 1.755364 2.532699 H -6.176960 2.349982 0.153657 C -0.548587 1.817713 0.030292 H -4.858921 1.445161 0.730137 H -6.133784 3.432046 -1.247855 C 3.479293 2.255940 3.844139 H -6.320323 3.505236 0.951751 H -6.355464 1.695116 -1.478083 H 2.828059 2.146981 4.716728 H -6.378145 2.477906 2.396123 C -3.794540 3.426909 1.888864 H 4.050622 3.183873 3.958861 H -5.417718 3.963860 2.409359 C -5.006670 4.334512 2.153829 H 4.169062 1.408133 3.826520 H -2.909151 1.102702 2.229993 C -2.658567 3.801053 2.853251 C 1.723608 3.584784 -2.536029 H -3.318995 2.569340 3.144700 H -4.091360 2.389858 2.111457 H 1.172922 3.554812 -3.481976 H -4.418040 1.179347 3.177525 H -5.862155 4.102677 1.512086 H 2.290473 4.520226 -2.500861 C -2.999463 5.043316 0.712223 H -5.337320 4.234437 3.196372 H 0.994998 3.584525 -1.721064 C -4.121698 6.051003 0.388467 H -4.747961 5.388903 1.998860 C 4.860776 2.455012 1.306379 C -1.640526 5.612108 0.258973 H -1.789926 3.149835 2.722899 H 5.409954 2.425598 2.239271 H -2.956140 4.939220 1.811204 H -2.325500 4.834090 2.689823 C 1.642954 3.483490 2.674032 H -5.107962 5.711088 0.726590 H -2.995253 3.729166 3.896287 289

Appendix

C -2.986381 5.179141 -0.584161 C -0.229564 0.482884 -2.756947 C -5.862441 -0.646466 1.526051 C -4.286402 5.812134 -1.108695 H 0.823767 0.734464 -2.742000 H -5.720723 0.028895 0.677427 C -1.867604 5.338032 -1.624039 C 1.325577 2.340787 -0.043154 H -6.162013 -0.057093 2.401041 H -2.680813 5.750278 0.307446 C -3.473544 0.761069 2.139882 H -6.683755 -1.319620 1.271224 H -5.105447 5.758355 -0.384690 H -4.383568 1.252102 1.827112 C -4.929385 -2.437883 2.960847 H -4.124796 6.871644 -1.348661 C -2.950848 3.309091 0.825044 H -5.793828 -3.056118 2.707372 H -4.621750 5.319780 -2.028634 C -2.910966 -0.158795 -2.708061 H -5.173055 -1.870770 3.865710 H -0.913128 4.959530 -1.248008 H -3.956215 -0.430134 -2.658446 H -4.097096 -3.109932 3.182685 H -2.099786 4.794889 -2.547655 C -1.108702 -0.441167 2.878020 C 7.304218 1.839724 -0.706111 H -1.737792 6.396286 -1.889320 H -0.173682 -0.919857 3.139776 H 6.976955 2.829052 -0.355438 C -4.422463 -2.197667 1.603294 C -3.335629 3.015169 -1.313618 H 8.323277 1.696562 -0.328232 C -3.754142 -2.624597 2.918739 C -2.209754 -1.218869 2.554267 C -1.237468 3.812925 2.581095 C -5.946205 -2.372021 1.683899 H -2.127848 -2.297525 2.564480 H -0.940532 3.672511 3.628029 H -4.223381 -1.122358 1.472445 C -4.608556 -1.486056 1.799428 H -1.398190 4.881152 2.419038 H -2.668586 -2.482662 2.882347 C 3.909077 -1.922460 -0.680360 H -0.423327 3.490622 1.928949 H -4.143442 -2.039311 3.762423 H 3.285132 -2.534443 -0.012763 C -3.614627 3.548143 3.230092 H -3.945464 -3.681546 3.140049 C -2.526153 3.057096 2.258755 H -4.582094 3.080715 3.032293 H -6.452371 -1.977681 0.796441 C -3.573303 2.288458 -2.611537 H -3.742736 4.627902 3.122693 H -6.232725 -3.424468 1.792940 C 4.219883 -0.437630 1.831515 H -3.328560 3.340094 4.267324 H -6.345702 -1.835632 2.555354 H 5.281434 -0.720411 1.811149 C -3.392283 3.227349 -3.810883 C -3.199508 -4.833813 0.309825 C -2.484488 -2.613120 -2.636330 H -2.404429 3.693559 -3.818403 C -2.460772 -5.450856 -0.887802 C -4.900027 -3.377949 0.076370 H -4.137362 4.025894 -3.774993 C -4.401062 -5.705339 0.706893 H -5.695778 -3.922440 0.565307 H -3.530539 2.679281 -4.748904 H -2.498090 -4.839588 1.159208 C -1.683153 -4.846891 0.975420 C 3.277676 -3.490733 -2.553744 H -1.576951 -4.866874 -1.163691 H -2.535380 -4.195518 1.190726 H 2.624734 -4.090898 -1.908218 H -2.131634 -6.472511 -0.654797 H -1.747070 -5.729130 1.623687 H 2.855832 -3.543750 -3.564655 H -3.111326 -5.512505 -1.768175 H -1.803455 -5.182165 -0.057757 C 3.903251 -1.641521 4.026276 H -4.898307 -5.338822 1.610674 C 4.952323 0.926000 -0.633531 H 3.321321 -2.418564 4.536168 H -5.150188 -5.751440 -0.090679 H 4.583140 1.903689 -0.295093 H 4.952592 -1.968246 4.058289 H -4.073990 -6.735093 0.905416 C -4.344603 -3.657569 -1.185971 C 0.330734 -3.928553 3.084110 C -4.541923 -2.510476 -1.510067 H -4.617075 -4.472652 -1.842022 H 1.293057 -3.446189 3.279409 C -5.713519 -3.452319 -1.833897 C 3.456151 -1.531766 2.573363 H 0.373247 -4.945033 3.493026 C -3.657360 -2.323103 -2.752092 H 2.382917 -1.306768 2.526352 H -0.440978 -3.387008 3.639850 H -4.969862 -1.523652 -1.269611 H 3.589704 -2.499859 2.078917 C 1.292702 -5.146505 0.476977 H -6.385822 -3.600866 -0.982647 C -3.376870 4.521736 0.328439 H 1.136687 -5.269443 -0.599283 H -6.310914 -3.047332 -2.661709 H -3.497104 5.440692 0.885808 H 1.235051 -6.138994 0.939481 H -5.351972 -4.437848 -2.149379 C 4.933118 0.942778 -2.163333 H 2.302222 -4.755843 0.636022 H -2.862775 -1.594854 -2.566429 H 5.247509 -0.039443 -2.535942 C 5.307766 -3.959783 -1.155989 H -3.185713 -3.265803 -3.054122 H 3.909953 1.106719 -2.522055 H 6.329856 -4.356175 -1.164537 H -4.258706 -1.969874 -3.600974 C 6.386287 0.771218 -0.121464 H 4.739670 -4.573785 -0.442974 H 6.417721 0.832836 0.970131 C 5.317340 -2.511815 -0.676391 H 6.778381 -0.216117 -0.390754 H 5.962871 -1.929624 -1.346063 Complex Th6 C 4.083566 0.892477 2.575094 H 5.764210 -2.452769 0.322552 H 4.657109 1.678432 2.071665 C 0.492441 5.198499 -0.677305 Th6a SCF energy = -3944.7163881 H 3.032028 1.207904 2.531621 H 0.274778 5.019670 -1.736356 Th -1.579397 0.135738 -0.075167 C -1.348799 -3.636356 -2.572505 H 0.755837 6.257236 -0.567477 Ni 1.504043 0.357066 0.026388 H -0.737483 -3.613748 -3.482938 H -0.428635 5.005115 -0.119966 P 3.646776 -0.231001 0.067731 H -1.776601 -4.637725 -2.482774 C 4.529728 0.782031 4.026942 Si -0.019934 -4.028078 1.231272 H -0.701027 -3.462317 -1.709824 H 5.606518 0.561939 4.061858 Si 1.910979 4.099593 -0.114059 C 3.271664 -2.047990 -2.066240 H 4.391583 1.745430 4.531204 N -3.304314 -1.823184 -0.352585 H 2.248464 -1.662891 -2.015813 C 2.517798 4.632169 1.589493 N -2.915304 2.358962 -0.175496 H 3.812171 -1.429930 -2.791304 H 1.721131 4.574931 2.337312 C 0.694495 -1.257279 0.228676 C -3.296996 -2.901625 -3.910063 H 2.877881 5.667023 1.557085 C 0.121117 -2.329404 0.512009 H -4.156557 -2.234180 -4.005228 H 3.343264 3.995939 1.925612 C -2.548207 1.179515 -2.703986 H -3.673124 -3.927460 -3.887354 C 4.678923 -4.083639 -2.535962 C -0.619438 -0.858347 -2.757366 H -2.665823 -2.792278 -4.798700 H 5.307406 -3.553286 -3.266063 H 0.138227 -1.629425 -2.745962 C -3.618122 4.335711 -1.044877 H 4.653604 -5.133322 -2.849925 C 0.185293 1.757268 0.025134 H -3.979391 5.076859 -1.743422 C 3.772325 -0.315053 4.757732 C -1.176616 0.949732 2.807356 C 7.290910 1.818940 -2.225883 H 4.131764 -0.409097 5.788718 H -0.293919 1.538357 3.015404 H 7.700699 0.860882 -2.577317 H 2.709571 -0.039470 4.819307 C -1.966539 -1.195938 -2.719970 H 7.942733 2.603727 -2.626079 C 3.323686 4.370226 -1.328837 C -3.379189 -2.701718 -1.415496 C -5.010698 1.756799 -2.644646 H 4.273070 3.984413 -0.948062 C -2.366438 1.567841 2.433480 H -5.228931 1.213182 -3.571879 H 3.448075 5.446184 -1.498818 C -1.178520 1.492078 -2.706894 H -5.695786 2.604966 -2.578084 H 3.123134 3.898392 -2.296175 H -0.863739 2.525492 -2.636898 H -5.219697 1.100973 -1.794601 Th C -4.249765 -2.259321 0.551538 C 5.874561 1.987624 -2.751158 6a THF PCM SCF energy = - C -3.425060 -0.625049 2.188321 H 5.860997 1.916240 -3.845162 3944.789102 H 5.514306 2.992031 -2.500016 290

Appendix

Th -1.595337 0.133490 -0.077070 H -0.823213 -3.595192 -3.531654 H -0.363722 5.136354 0.082367 Ni 1.499354 0.372227 0.018603 H -1.862666 -4.626289 -2.539041 C 4.531614 0.631360 4.069468 P 3.650609 -0.221663 0.070615 H -0.766309 -3.475700 -1.757298 H 5.610501 0.420134 4.080941 Si -0.002134 -4.038844 1.165086 C 3.276034 -1.958486 -2.130885 H 4.389949 1.570788 4.616337 Si 1.914406 4.106082 -0.129782 H 2.256669 -1.563017 -2.079211 C 2.627078 4.596906 1.544554 N -3.314105 -1.841290 -0.336654 H 3.829911 -1.324820 -2.831711 H 1.872602 4.526866 2.334813 N -2.895948 2.391287 -0.148581 C -3.380745 -2.853759 -3.918272 H 2.992348 5.630055 1.513301 C 0.692355 -1.246170 0.208018 H -4.230775 -2.171839 -3.997768 H 3.465235 3.947171 1.817707 C 0.123291 -2.324719 0.476232 H -3.769518 -3.875188 -3.904501 C 4.667321 -3.989610 -2.657818 C -2.556535 1.207505 -2.687507 H -2.756353 -2.742124 -4.811135 H 5.303464 -3.438971 -3.365771 C -0.662042 -0.862937 -2.774254 C -3.642298 4.361714 -0.990386 H 4.635454 -5.028127 -3.006807 H 0.083494 -1.645708 -2.782264 H -4.022201 5.102504 -1.680466 C 3.791931 -0.503438 4.759997 C 0.169335 1.760108 0.013242 C 7.366492 1.824968 -2.105797 H 4.165286 -0.639449 5.781425 C -1.150571 0.947024 2.810080 H 7.760698 0.862260 -2.461869 H 2.727697 -0.240394 4.845183 H -0.272348 1.540732 3.021323 H 8.043545 2.600800 -2.481059 C 3.248326 4.359798 -1.431054 C -2.014626 -1.178980 -2.724509 C -5.008962 1.824267 -2.640089 H 4.199904 3.918555 -1.125436 C -3.429157 -2.689175 -1.418761 H -5.218680 1.282370 -3.569788 H 3.410029 5.434291 -1.577377 C -2.349460 1.557709 2.451917 H -5.682891 2.682611 -2.589076 H 2.962069 3.925397 -2.394551 C -1.182447 1.496036 -2.708785 H -5.242858 1.172374 -1.793440 H -0.846234 2.523153 -2.655506 C 5.965507 2.034025 -2.656310 C -4.255795 -2.268509 0.573806 H 5.970943 1.980201 -3.751385 Th6a hexane PCM SCF energy = - C -3.393167 -0.644180 2.212498 H 5.626195 3.043740 -2.396239 3944.7207344 C -0.250846 0.471025 -2.773427 C -5.849844 -0.686977 1.631532 Th -1.586358 0.136390 -0.078573 H 0.806413 0.705203 -2.781872 H -5.752987 -0.003693 0.782729 Ni 1.503000 0.354831 0.019014 C 1.302099 2.358118 -0.055752 H -6.114849 -0.106736 2.523089 P 3.648251 -0.236002 0.069577 C -3.454378 0.742999 2.172218 H -6.676243 -1.366241 1.410898 Si -0.026699 -4.033619 1.203667 H -4.375455 1.225943 1.879156 C -4.850125 -2.488598 3.003935 Si 1.922336 4.094237 -0.122633 C -2.950049 3.321665 0.866215 H -5.714992 -3.113330 2.767975 N -3.323326 -1.819150 -0.343962 C -2.940666 -0.126070 -2.696232 H -5.072627 -1.936446 3.923240 N -2.891973 2.377661 -0.168264 H -3.990328 -0.379124 -2.641476 H -4.002959 -3.152324 3.191919 C 0.689432 -1.257931 0.217241 C -1.070010 -0.442993 2.874174 C 7.345667 1.825016 -0.586429 C 0.112576 -2.329970 0.494860 H -0.129596 -0.913490 3.131141 H 7.026455 2.814727 -0.229378 C -2.545480 1.191940 -2.699391 C -3.331349 3.048605 -1.278138 H 8.352781 1.657631 -0.187171 C -0.642978 -0.870862 -2.763445 C -2.168194 -1.228651 2.559492 C -1.233759 3.809309 2.625491 H 0.105033 -1.651377 -2.758121 H -2.077306 -2.306300 2.571627 H -0.930649 3.647859 3.667016 C 0.184180 1.754373 0.012085 C -4.577388 -1.515965 1.846619 H -1.406253 4.879529 2.489092 C -1.158605 0.947812 2.805200 C 3.903941 -1.886094 -0.736827 H -0.418844 3.508377 1.963871 H -0.274185 1.533921 3.012531 H 3.271505 -2.515885 -0.094528 C -3.605207 3.521783 3.278047 C -1.994347 -1.191516 -2.719973 C -2.519009 3.049767 2.294889 H -4.570457 3.048997 3.081501 C -3.416620 -2.688669 -1.412103 C -3.563755 2.334109 -2.586760 H -3.739424 4.602592 3.187388 C -2.349170 1.568769 2.438183 C 4.211779 -0.496660 1.829029 H -3.310358 3.301071 4.309898 C -1.172145 1.486595 -2.710586 H 5.275156 -0.769402 1.798179 C -3.360642 3.280987 -3.776995 H -0.842466 2.515625 -2.648487 C -2.550111 -2.591659 -2.650667 H -2.362543 3.725061 -3.781094 C -4.265621 -2.249067 0.565604 C -4.944800 -3.359467 0.084001 H -4.089383 4.094316 -3.735731 C -3.414232 -0.622400 2.199575 H -5.748240 -3.890768 0.576267 H -3.509282 2.743323 -4.719275 C -0.236302 0.465044 -2.765098 C -1.669248 -4.853833 0.910347 C 3.270825 -3.385091 -2.663878 H 0.820216 0.703149 -2.759773 H -2.514747 -4.201416 1.148131 H 2.609781 -3.999916 -2.040037 C 1.323068 2.340498 -0.055056 H -1.724278 -5.746003 1.545731 H 2.853329 -3.401570 -3.677737 C -3.459640 0.764241 2.151530 H -1.796384 -5.170234 -0.128004 C 3.925488 -1.795643 3.969767 H -4.371629 1.256766 1.846459 C 4.976339 0.948686 -0.576583 H 3.355063 -2.598616 4.451704 C -2.934382 3.319841 0.838192 H 4.612674 1.921737 -0.217804 H 4.977695 -2.114119 3.975081 C -2.924983 -0.142307 -2.702627 C -4.417571 -3.625042 -1.195361 C 0.363281 -3.980628 3.014858 H -3.973610 -0.399848 -2.650147 H -4.719758 -4.417405 -1.866891 H 1.333156 -3.515141 3.212260 C -1.093261 -0.443110 2.874706 C 3.461642 -1.627361 2.527559 H 0.394242 -5.007199 3.399165 H -0.158198 -0.923218 3.133560 H 2.386365 -1.409684 2.502720 H -0.397471 -3.439761 3.586057 C -3.318081 3.035062 -1.302811 H 3.599405 -2.572151 1.991313 C 1.300055 -5.138090 0.367167 C -2.197812 -1.218588 2.557457 C -3.402864 4.534208 0.387131 H 1.133908 -5.231511 -0.710686 H -2.118084 -2.297298 2.570528 H -3.538912 5.442038 0.959885 H 1.243292 -6.141554 0.805778 C -4.603960 -1.481012 1.823047 C 4.987401 1.001871 -2.106085 H 2.311348 -4.752753 0.528201 C 3.909972 -1.920727 -0.693249 H 5.285074 0.021501 -2.495479 C 5.289165 -3.917145 -1.271037 H 3.283728 -2.538115 -0.032862 H 3.976124 1.199415 -2.481614 H 6.308606 -4.319967 -1.287845 C -2.506233 3.059633 2.269469 C 6.397558 0.763931 -0.038195 H 4.712449 -4.550153 -0.581947 C -3.556823 2.313956 -2.604870 H 6.407001 0.811213 1.054221 C 5.307615 -2.486591 -0.741764 C 4.215552 -0.460004 1.833146 H 6.779582 -0.225553 -0.313498 H 5.963881 -1.887622 -1.385276 H 5.277598 -0.740228 1.811274 C 4.067109 0.799262 2.628875 H 5.745334 -2.467229 0.262528 C -2.528425 -2.603253 -2.638159 H 4.623902 1.613998 2.153406 C 0.496880 5.260559 -0.580838 C -4.933011 -3.357586 0.088685 H 3.010309 1.099488 2.615875 H 0.156969 5.061798 -1.603409 H -5.730721 -3.895478 0.582194 C -1.425028 -3.628056 -2.615720 H 0.829226 6.304642 -0.533979 291

Appendix

C -1.696247 -4.844028 0.956900 C 3.283618 -3.471352 -2.582734 H -0.696815 1.694791 -3.031300 H -2.542452 -4.187667 1.180851 H 2.628951 -4.077286 -1.944204 C -3.455096 -3.005444 -1.411624 H -1.758884 -5.727465 1.603687 H 2.864515 -3.514906 -3.595219 C -1.064992 0.524318 2.705183 H -1.824270 -5.175429 -0.076622 C 3.903742 -1.688366 4.014208 H -0.297354 1.243729 2.947352 C 4.960191 0.924818 -0.615777 H 3.323981 -2.472059 4.516321 C 4.280610 1.851595 -0.553776 H 4.591045 1.901447 -0.273816 H 4.953842 -2.012919 4.040946 H 3.636485 2.544187 0.005193 C -4.391502 -3.635321 -1.180844 C 0.338562 -3.950439 3.053872 C -4.144933 2.203027 1.418117 H -4.677033 -4.443496 -1.840206 H 1.307019 -3.478979 3.245061 C -2.295251 -1.144669 -2.529226 C 3.454609 -1.563854 2.563018 H 0.373575 -4.970697 3.454138 C -2.718616 1.002072 -2.393955 H 2.380773 -1.341152 2.520033 H -0.423735 -3.404808 3.618528 C 1.378937 -2.269391 -0.231650 H 3.590788 -2.526118 2.058152 C 1.273393 -5.151670 0.427880 C -2.655540 -2.827571 2.307031 C -3.369719 4.532984 0.348725 H 1.110570 -5.260385 -0.648947 C 4.008983 0.426697 1.986915 H -3.494852 5.447684 0.912327 H 1.211091 -6.148824 0.879757 H 5.082090 0.600956 2.146120 C 4.952679 0.949234 -2.145754 H 2.286183 -4.769174 0.586129 C -4.757619 -3.545593 1.008083 H 5.263612 -0.033075 -2.520583 C 5.309069 -3.954403 -1.183155 H -5.295045 -3.735740 1.928964 H 3.933439 1.121636 -2.511724 H 6.331165 -4.350743 -1.192318 C 0.110306 2.406734 -0.112110 C 6.389659 0.763666 -0.092837 H 4.738414 -4.574965 -0.477871 C -4.354457 2.253129 -1.020472 H 6.412474 0.823163 0.998988 C 5.317862 -2.511158 -0.689533 C 6.355588 -1.053883 0.461535 H 6.780388 -0.224370 -0.361318 H 5.966462 -1.923188 -1.350978 H 6.181473 -1.084378 1.540934 C 4.076240 0.861518 2.591139 H 5.760494 -2.462333 0.311769 H 6.902230 -0.126325 0.259056 H 4.645999 1.654927 2.095299 C 0.508643 5.218586 -0.648800 C -5.529591 2.176259 1.517617 H 3.023329 1.173082 2.554663 H 0.241480 5.025564 -1.693768 H -6.009716 2.107766 2.485337 C -1.403339 -3.638821 -2.585296 H 0.806513 6.271041 -0.569580 C -1.476932 -3.796542 2.401691 H -0.796399 -3.617174 -3.498516 H -0.391825 5.061990 -0.048465 H -1.835499 -4.828790 2.353469 H -1.841125 -4.636157 -2.498923 C 4.525268 0.736346 4.040919 H -0.949231 -3.663052 3.351820 H -0.749410 -3.476125 -1.725074 H 5.602474 0.517945 4.071222 H -0.764214 -3.637680 1.590126 C 3.276849 -2.033018 -2.082305 H 4.385671 1.693873 4.555917 C 5.284031 -1.124001 -1.810402 H 2.253646 -1.647520 -2.032801 C 2.564324 4.608453 1.573675 H 4.330833 -1.165318 -2.350720 H 3.820478 -1.409184 -2.799937 H 1.780042 4.550365 2.334688 H 5.790425 -0.205891 -2.132695 C -3.350838 -2.877699 -3.908610 H 2.931305 5.640982 1.542766 C 5.731707 2.262205 -0.309016 H -4.202360 -2.199102 -3.997758 H 3.390599 3.962821 1.889274 H 5.983033 2.186027 0.754681 H -3.738729 -3.899234 -3.887638 C 4.684750 -4.064633 -2.566312 H 6.400855 1.575646 -0.841627 H -2.722325 -2.772874 -4.799607 H 5.315456 -3.526726 -3.288891 C 5.659110 3.812912 -2.281004 C -3.610224 4.352902 -1.026222 H 4.660250 -5.111225 -2.890600 H 6.317223 3.158899 -2.871133 H -3.977686 5.094544 -1.721403 C 3.771011 -0.370319 4.760525 H 5.844454 4.836681 -2.625430 C 7.316351 1.812420 -2.186808 H 4.132367 -0.475117 5.789856 C 3.248743 1.620399 2.562056 H 7.723608 0.852721 -2.536576 H 2.707809 -0.097606 4.826478 H 2.182485 1.511236 2.325611 H 7.975440 2.594788 -2.579868 C 3.312752 4.359970 -1.363256 H 3.576230 2.551429 2.088748 C -5.000350 1.799102 -2.646829 H 4.265042 3.964194 -1.001015 C -3.220635 2.047689 2.619412 H -5.217382 1.256453 -3.574755 H 3.442555 5.435786 -1.530272 C 3.900691 2.019389 -2.026849 H -5.676334 2.655132 -2.587783 H 3.091139 3.893242 -2.328499 H 2.837249 1.787346 -2.152813 H -5.223855 1.146935 -1.797662 H 4.452843 1.303254 -2.645151 C 5.905339 1.989902 -2.723224 C -4.767063 -3.459357 -1.408139 H 5.899903 1.920530 -3.817436 Th6b SCF energy = -3944.7258168 H -5.312967 -3.582500 -2.335363 H 5.549433 2.996182 -2.473296 C -6.311844 2.205947 0.374658 Th -1.491362 -0.036367 -0.082325 C -5.861179 -0.638679 1.574076 H -7.393272 2.181500 0.467304 Ni 1.581443 -0.273886 -0.141428 H -5.735218 0.038189 0.724136 C 6.008423 3.675761 -0.807870 P 3.731032 0.213130 0.152650 H -6.142430 -0.050449 2.455702 H 5.412073 4.392479 -0.225347 Si 2.075634 -3.977286 -0.427024 H -6.688782 -1.309916 1.334737 H 7.060419 3.931137 -0.635026 Si 0.293657 4.245023 -0.312546 C -4.909040 -2.438413 2.984429 C -5.400096 -3.737007 -0.205664 N -3.062109 -0.381608 2.128304 H -5.777728 -3.054412 2.740053 H -6.428004 -4.086865 -0.214120 N -3.243948 -0.235344 -2.172065 H -5.139503 -1.875107 3.895066 C -2.694119 -2.600098 -2.667329 C -2.815228 -2.865504 -0.185471 H -4.074302 -3.112045 3.191782 C -3.647373 2.201020 -2.368973 H -1.743307 -2.625155 -0.181954 C 7.316402 1.830133 -0.667060 C -5.736303 2.218861 -0.885018 C -3.442962 -3.098233 1.032390 H 6.989638 2.819882 -0.317047 H -6.373503 2.184804 -1.759479 C -0.904193 -0.876164 2.615421 H 8.331431 1.681808 -0.280446 C 3.611727 -0.855687 2.720066 H 0.008839 -1.428919 2.772531 C -1.214998 3.811174 2.592559 H 2.556871 -1.067269 2.498300 C 0.764945 1.333530 -0.103166 H -0.914689 3.661746 3.637083 H 4.177637 -1.712151 2.338894 C -3.589319 2.290092 0.143251 H -1.375450 4.880927 2.439975 C -1.466969 -3.490381 -2.861929 H -2.506917 2.437891 0.053142 H -0.403305 3.492587 1.935527 H -0.744415 -3.360046 -2.053782 C -2.165637 -1.393674 2.294423 C -3.590309 3.548684 3.246632 H -0.966295 -3.245241 -3.804411 C 0.254622 -1.657504 -0.203545 H -4.559226 3.083369 3.050826 H -1.768334 -4.541217 -2.902856 C 5.029536 -1.065106 -0.303835 H -3.716254 4.629367 3.145245 C 0.767473 -5.311928 -0.173502 H 4.507067 -1.992116 -0.039791 H -3.300215 3.335107 4.281532 H 0.511823 -5.424307 0.884116 C -2.414425 0.778865 2.430920 C -3.360752 3.254410 -3.800945 H 1.170160 -6.271473 -0.520474 C -1.109644 -0.490947 -2.892466 H -2.366148 3.706090 -3.806612 H -0.154402 -5.113826 -0.726428 H -0.174455 -0.941793 -3.188378 H -4.094583 4.063259 -3.763686 C 4.208423 3.427651 -2.524004 C -1.385001 0.893285 -2.808667 H -3.505926 2.710879 -4.740542 H 3.962843 3.506335 -3.589611 292

Appendix

H 3.564324 4.147074 -2.002151 Ni 1.567597 -0.267341 -0.130150 C 6.071694 3.666290 -0.612970 C -3.521351 -2.988243 3.559712 P 3.733186 0.200719 0.142457 H 5.488570 4.353359 0.016725 H -4.382791 -2.316668 3.530894 Si 2.052736 -3.974389 -0.422850 H 7.128608 3.886211 -0.422769 H -2.929020 -2.744304 4.446449 Si 0.297570 4.258092 -0.273150 C -5.424741 -3.696946 -0.183628 H -3.873113 -4.020048 3.662864 N -3.107325 -0.365908 2.166031 H -6.459882 -4.024760 -0.191007 C 3.418492 -4.383994 0.833666 N -3.237328 -0.236827 -2.223301 C -2.697259 -2.622600 -2.653552 H 4.354421 -3.839667 0.687779 C -2.816077 -2.893642 -0.166123 C -3.586031 2.213953 -2.418483 H 3.645847 -5.454864 0.770125 H -1.743920 -2.659497 -0.162221 C -5.702021 2.237540 -0.973547 H 3.061714 -4.179655 1.848835 C -3.453407 -3.094232 1.054333 H -6.322277 2.202010 -1.860127 C 6.165495 -2.308263 -2.189535 C -0.940502 -0.841911 2.628357 C 3.660263 -0.980983 2.673466 H 5.639371 -3.244839 -1.962511 H -0.023704 -1.386716 2.790134 H 2.598978 -1.183792 2.476446 H 6.344522 -2.304672 -3.271020 C 0.747771 1.339373 -0.089540 H 4.215108 -1.821880 2.245570 C -2.298842 3.255341 2.764593 C -3.575351 2.325085 0.099000 C -1.470164 -3.515933 -2.833745 H -1.703553 3.168590 3.679045 H -2.491822 2.474508 0.031032 H -0.751625 -3.378964 -2.023272 H -2.886086 4.175801 2.826585 C -2.201647 -1.371431 2.323376 H -0.964846 -3.280244 -3.775861 H -1.610028 3.338031 1.922929 C 0.238049 -1.647707 -0.175388 H -1.772930 -4.566666 -2.866130 C 7.482337 -2.283106 -1.430409 C 5.001720 -1.072529 -0.404097 C 0.748050 -5.307594 -0.142410 H 8.059338 -1.396500 -1.730693 H 4.469442 -2.005742 -0.185185 H 0.505297 -5.407413 0.919629 H 8.091411 -3.156008 -1.691218 C -2.462126 0.803484 2.437907 H 1.151991 -6.268857 -0.483415 C -4.632921 2.013100 -3.526433 C -1.087095 -0.531044 -2.871199 H -0.179354 -5.116801 -0.688682 H -4.076847 1.938712 -4.465486 H -0.153133 -0.998353 -3.143874 C 4.272118 3.567906 -2.344330 H -5.315238 2.865902 -3.605202 C -1.343020 0.858120 -2.806678 H 4.031894 3.719346 -3.403316 H -5.213108 1.096021 -3.403152 H -0.637429 1.647388 -3.018002 H 3.639763 4.264076 -1.778248 C -1.168218 5.317560 0.208036 C -3.461077 -3.015194 -1.392968 C -3.534896 -2.995496 3.584706 H -2.151319 4.928613 -0.066479 C -1.108631 0.558762 2.703567 H -4.402613 -2.331701 3.569889 H -1.046863 6.289862 -0.285111 H -0.343566 1.284622 2.933864 H -2.941422 -2.759080 4.472739 H -1.164536 5.496489 1.286673 C 4.305403 1.866597 -0.481095 H -3.879515 -4.030722 3.675304 C 3.808932 -0.735344 4.225170 H 3.678014 2.539746 0.119078 C 3.422226 -4.390603 0.803385 H 4.880023 -0.617048 4.444634 C -4.157243 2.232692 1.363687 H 4.345608 -3.825597 0.656816 H 3.490956 -1.662610 4.715880 C -2.291765 -1.165233 -2.534877 H 3.664458 -5.455354 0.701316 C 2.727583 -4.154349 -2.184214 C -2.686266 0.991667 -2.430494 H 3.079132 -4.222992 1.829954 H 1.892547 -4.114233 -2.892073 C 1.361345 -2.263518 -0.212933 C 6.095713 -2.217772 -2.375871 H 3.238313 -5.114815 -2.317976 C -2.671731 -2.813822 2.333076 H 5.563710 -3.161201 -2.195299 H 3.423182 -3.353347 -2.445887 C 4.040842 0.327942 1.980903 H 6.259291 -2.151314 -3.457740 C -2.878735 3.496322 -2.607150 H 5.116818 0.495275 2.125740 C -2.331976 3.281238 2.741553 H -2.100445 3.642485 -1.858546 C -4.779107 -3.511052 1.030444 H -1.756267 3.198231 3.668485 H -3.559032 4.351881 -2.565063 H -5.323207 -3.682574 1.951173 H -2.911643 4.207507 2.782419 H -2.404907 3.484008 -3.593829 C 0.095482 2.414028 -0.100960 H -1.625413 3.348873 1.913396 C -3.567593 -2.699948 -3.921670 C -4.316949 2.277218 -1.081302 C 7.423175 -2.250380 -1.635971 H -3.876245 -3.735030 -4.102227 C 6.338695 -1.122394 0.340774 H 8.004207 -1.352528 -1.891147 H -2.997100 -2.361489 -4.791395 H 6.179683 -1.212041 1.419197 H 8.018657 -3.112601 -1.956939 H -4.457307 -2.071719 -3.833501 H 6.895257 -0.192696 0.182730 C -4.554274 2.065465 -3.596053 C 7.235179 -2.237004 0.068582 C -5.544608 2.199131 1.433930 H -3.981987 1.990457 -4.525236 H 8.184911 -2.185708 0.613721 H -6.045539 2.132907 2.391293 H -5.212189 2.936944 -3.674877 H 6.747454 -3.171246 0.381115 C -1.478460 -3.764734 2.428818 H -5.164554 1.164771 -3.500216 C -4.003472 1.882469 3.925771 H -1.822974 -4.802161 2.388421 C -1.174392 5.336798 0.202055 H -4.661055 1.011078 3.885018 H -0.950493 -3.618622 3.376632 H -2.148035 4.960081 -0.119270 H -4.600845 2.774574 4.142174 H -0.769452 -3.600641 1.615088 H -1.020422 6.311411 -0.277347 H -3.301197 1.737174 4.751530 C 5.233213 -1.048170 -1.915875 H -1.212988 5.504889 1.281510 C 3.440586 1.734460 4.069968 H 4.272777 -1.048275 -2.445522 C 3.900027 -0.917392 4.176060 H 4.495589 1.958362 4.284705 H 5.746362 -0.119598 -2.192835 H 4.976876 -0.805349 4.367967 H 2.859669 2.582238 4.451984 C 5.765516 2.228281 -0.212820 H 3.595756 -1.863162 4.639470 C 0.653590 4.617188 -2.124468 H 6.017745 2.074200 0.841602 C 2.666084 -4.144257 -2.194578 H 1.392646 3.925391 -2.535192 H 6.418002 1.566891 -0.795140 H 1.818098 -4.095551 -2.886539 H 1.045827 5.636578 -2.220980 C 5.729094 3.909153 -2.073801 H 3.169253 -5.107000 -2.340342 H -0.249461 4.550463 -2.736896 H 6.376262 3.283846 -2.705470 H 3.362554 -3.345910 -2.463540 C 3.048600 0.453917 4.789952 H 5.932396 4.950544 -2.348287 C -2.775878 3.487662 -2.634766 H 1.969570 0.283686 4.666332 C 3.292948 1.497109 2.620100 H -2.003052 3.603017 -1.875304 H 3.229903 0.549587 5.866624 H 2.220367 1.389102 2.412734 H -3.430669 4.362863 -2.595335 C 1.734641 4.831304 0.748477 H 3.603030 2.446933 2.173594 H -2.288788 3.468454 -3.614529 H 1.581893 4.551675 1.795857 C -3.263133 2.081555 2.590597 C -3.566588 -2.743491 -3.908953 H 1.809485 5.924065 0.695968 C 3.934550 2.135827 -1.941257 H -3.876293 -3.781190 -4.070818 H 2.688397 4.410321 0.419962 H 2.867034 1.936121 -2.086961 H -2.990922 -2.423213 -4.782182 H 4.475256 1.451276 -2.603376 H -4.457323 -2.114344 -3.839761 Th6b THF PCM SCF energy = - C -4.784704 -3.438633 -1.387595 C 7.196866 -2.291266 -0.133519 3944.7391883 H -5.333984 -3.553948 -2.313924 H 8.154378 -2.282179 0.400085 C -6.303918 2.224913 0.274699 H 6.701805 -3.236824 0.129619 Th -1.511531 -0.028022 -0.074276 H -7.386953 2.198789 0.345204 C -4.077706 1.947237 3.880993 293

Appendix

H -4.743812 1.082193 3.845630 H -1.834448 -4.814568 2.367569 C -1.169005 5.327754 0.197243 H -4.671929 2.848170 4.065696 H -0.946669 -3.643170 3.357678 H -2.147544 4.941477 -0.096578 H -3.394823 1.813966 4.724900 H -0.770940 -3.621879 1.595218 H -1.034512 6.299232 -0.294149 C 3.526288 1.556086 4.125196 C 5.265792 -1.074301 -1.872337 H -1.185060 5.506529 1.275699 H 4.586753 1.773615 4.317505 H 4.311782 -1.088822 -2.412848 C 3.829186 -0.860167 4.191105 H 2.954099 2.387411 4.553538 H 5.777992 -0.148145 -2.159985 H 4.902329 -0.749450 4.404176 C 0.721104 4.645470 -2.067091 C 5.749813 2.242333 -0.231700 H 3.513050 -1.799278 4.660054 H 1.475832 3.960475 -2.459802 H 5.993581 2.115470 0.828593 C 2.701955 -4.145531 -2.197448 H 1.113250 5.667235 -2.134887 H 6.414347 1.573181 -0.791415 H 1.861291 -4.103658 -2.898615 H -0.161130 4.583496 -2.709871 C 5.711871 3.878773 -2.132307 H 3.213381 -5.104676 -2.337982 C 3.155401 0.248528 4.806659 H 6.369095 3.244455 -2.744446 H 3.394420 -3.342005 -2.460586 H 2.073289 0.082211 4.705533 H 5.909580 4.914824 -2.430019 C -2.826736 3.492816 -2.624401 H 3.367079 0.303612 5.880653 C 3.261632 1.538332 2.594540 H -2.047978 3.623301 -1.873407 C 1.702254 4.808182 0.851696 H 2.193300 1.435096 2.364720 H -3.492544 4.359659 -2.582580 H 1.496425 4.527918 1.890001 H 3.586000 2.481252 2.143224 H -2.349809 3.474629 -3.609391 H 1.800595 5.899383 0.805939 C -3.228551 2.067806 2.605058 C -3.586636 -2.715633 -3.909962 H 2.659774 4.367731 0.562197 C 3.931579 2.093992 -1.971833 H -3.899388 -3.751018 -4.081318 H 2.866793 1.880496 -2.117878 H -3.015582 -2.386765 -4.783022 H 4.481497 1.398932 -2.615396 H -4.474454 -2.084065 -3.826949 Th6b hexane PCM SCF energy = - C -4.788731 -3.444180 -1.388513 C 7.212371 -2.273263 -0.041565 3944.7257224 H -5.339421 -3.563748 -2.313411 H 8.163018 -2.249556 0.503838 C -6.300629 2.224306 0.333664 H 6.718770 -3.216039 0.233868 Th -1.499491 -0.030923 -0.080880 H -7.382696 2.200194 0.418555 C -4.024168 1.917803 3.905525 Ni 1.573363 -0.271456 -0.146139 C 6.045868 3.673442 -0.663740 H -4.686309 1.049816 3.867902 P 3.729500 0.201883 0.143336 H 5.451470 4.369745 -0.055012 H -4.618876 2.814757 4.108320 Si 2.064458 -3.975231 -0.434252 H 7.098944 3.909013 -0.470672 H -3.329602 1.776983 4.738581 Si 0.299419 4.251681 -0.297033 C -5.420980 -3.711450 -0.182970 C 3.465274 1.613524 4.103289 N -3.076363 -0.369805 2.144119 H -6.452729 -4.049911 -0.187041 H 4.522443 1.829730 4.315011 N -3.246851 -0.233421 -2.191268 C -2.711036 -2.609332 -2.657679 H 2.888642 2.452138 4.511110 C -2.825174 -2.871553 -0.173653 C -3.617742 2.209895 -2.392321 C 0.696298 4.632561 -2.099032 H -1.752630 -2.635656 -0.173979 C -5.715702 2.236306 -0.921959 H 1.450190 3.949155 -2.496394 C -3.452708 -3.089742 1.047613 H -6.346908 2.201923 -1.800743 H 1.080889 5.656054 -2.182115 C -0.914543 -0.859843 2.617989 C 3.619346 -0.941101 2.684972 H -0.193452 4.559629 -2.730175 H -0.000445 -1.410763 2.775026 H 2.562181 -1.144411 2.467079 C 3.076159 0.315538 4.792860 C 0.758326 1.336652 -0.104857 H 4.180262 -1.788384 2.277613 H 1.995733 0.151296 4.673022 C -3.575235 2.309702 0.121942 C -1.487788 -3.505812 -2.848539 H 3.266436 0.382795 5.870148 H -2.492191 2.456632 0.039548 H -0.763990 -3.373958 -2.041797 C 1.719316 4.819558 0.801062 C -2.177362 -1.380336 2.306345 H -0.987073 -3.267872 -3.792737 H 1.535868 4.538688 1.843293 C 0.244904 -1.654155 -0.197076 H -1.793647 -4.555584 -2.883113 H 1.807330 5.911557 0.753159 C 5.014500 -1.071489 -0.363805 C 0.759144 -5.311084 -0.171346 H 2.675882 4.387827 0.495688 H 4.484477 -2.003513 -0.134776 H 0.506221 -5.416934 0.887684 C -2.427042 0.793485 2.432113 H 1.164468 -6.271381 -0.513318 C -1.107385 -0.514728 -2.884681 Th H -0.163996 -5.118235 -0.723970 6a’ SCF energy = -3893.3270459 H -0.174332 -0.976535 -3.169991 C 4.259800 3.519133 -2.405354 C -1.369216 0.872774 -2.811232 Th 1.746835 -0.144330 -0.090908 H 4.026035 3.645027 -3.469101 H -0.670679 1.666075 -3.030912 Pt -1.382202 -0.344282 0.009771 H 3.617570 4.222806 -1.860134 C -3.471214 -3.005057 -1.397627 P -3.653010 0.241261 0.059348 C -3.521661 -2.982997 3.576532 C -1.075899 0.541071 2.700843 Si 0.065935 4.249382 1.140899 H -4.383120 -2.311206 3.556772 H -0.307553 1.262173 2.935323 Si -1.710889 -4.230948 -0.102516 H -2.924231 -2.743938 4.461207 C 4.295930 1.859945 -0.503900 N 3.376800 1.884080 -0.345932 H -3.873645 -4.015034 3.676136 H 3.656221 2.537909 0.077532 N 3.151247 -2.298425 -0.099484 C 3.418190 -4.387658 0.812254 C -4.140682 2.222035 1.393364 C -0.602937 1.455116 0.196732 H 4.346037 -3.828048 0.673063 C -2.303240 -1.154765 -2.529822 C -0.068138 2.545287 0.451424 H 3.658219 -5.454187 0.725250 C -2.705954 0.997662 -2.410790 C 2.812199 -1.182831 -2.664029 H 3.062933 -4.208436 1.832670 C 1.368892 -2.267216 -0.231293 C 0.804169 0.775423 -2.799282 C 6.139385 -2.248343 -2.298821 C -2.661826 -2.816637 2.320516 H 0.014369 1.514290 -2.811345 H 5.608464 -3.190200 -2.107530 C 4.015514 0.358442 1.983002 C 0.057207 -1.882226 -0.015364 H 6.316745 -2.202784 -3.379618 H 5.089891 0.524839 2.141529 C 1.237588 -0.909171 2.770116 C -2.300609 3.270575 2.751257 C -4.772598 -3.522666 1.028475 H 0.369040 -1.527091 2.951009 H -1.713182 3.184861 3.670780 H -5.309932 -3.703156 1.951394 C 2.135832 1.166957 -2.736926 H -2.883151 4.194534 2.803971 C 0.105870 2.411179 -0.112744 C 3.464381 2.737962 -1.428558 H -1.604701 3.345083 1.914682 C -4.332641 2.269964 -1.047618 C 2.466784 -1.487074 2.466486 C 7.457409 -2.260930 -1.541553 C 6.341712 -1.100434 0.399125 C 1.456033 -1.550695 -2.704157 H 8.038722 -1.366134 -1.807125 H 6.168762 -1.171488 1.476836 H 1.180861 -2.595104 -2.630913 H 8.060828 -3.126388 -1.837939 H 6.895120 -0.170103 0.231911 C 4.287548 2.362188 0.572915 C -4.598276 2.040194 -3.556823 C -5.526399 2.194696 1.482248 C 3.448548 0.741131 2.213214 H -4.036782 1.963048 -4.492419 H -6.014012 2.127057 2.446274 C 0.469700 -0.581450 -2.795626 H -5.268172 2.902712 -3.635626 C -1.478981 -3.780998 2.410836 H -0.572560 -0.873978 -2.804761 H -5.193200 1.131337 -3.443176 294

Appendix

C -1.075497 -2.492041 -0.067755 H 6.190936 0.286778 2.572364 Si -1.821748 4.168582 0.241748 C 3.553412 -0.642381 2.201487 H 6.719381 1.540477 1.436077 N 3.082844 0.327046 -2.312164 H 4.495528 -1.102445 1.941609 C 4.841722 2.631754 3.005983 N 3.483403 0.173593 2.003176 C 3.167083 -3.235689 0.914437 H 5.689663 3.280726 2.774648 C 0.003399 1.825078 0.182538 C 3.120587 0.168528 -2.682570 H 5.066924 2.099237 3.936357 C 3.126203 2.798860 -0.017235 H 4.152150 0.483775 -2.609767 H 3.972150 3.272076 3.171467 H 2.040632 2.631671 0.057240 C 1.109636 0.479934 2.796050 C -7.259208 -1.898641 -0.730759 C -0.644044 -1.489131 0.055812 H 0.143527 0.926616 2.993405 H -6.927515 -2.870918 -0.339098 C 3.530043 -2.370832 -0.300714 C 3.618734 -2.961716 -1.215712 H -8.289009 -1.757061 -0.382623 H 2.443746 -2.456823 -0.173869 C 2.193506 1.294020 2.503682 C 1.433102 -3.776947 2.641157 C 1.554392 -0.785571 2.706878 H 2.065056 2.367609 2.475154 H 1.102483 -3.620028 3.675481 H 0.805407 -1.523620 2.952410 C 4.615575 1.637595 1.857625 H 1.647203 -4.840852 2.516357 C 1.401896 0.617739 2.783950 C -3.915232 1.916851 -0.716589 H 0.622730 -3.512134 1.959175 H 0.516830 1.149785 3.097562 H -3.287283 2.534944 -0.057548 C 3.778950 -3.395319 3.339758 C 2.862697 -1.011321 2.256937 C 2.695174 -2.971935 2.331627 H 4.731221 -2.892529 3.155637 C 2.224336 1.379939 -2.439944 C 3.877791 -2.247103 -2.515975 H 3.954589 -4.470683 3.258544 C 2.363032 -0.804732 -2.558994 C -4.233285 0.468199 1.814162 H 3.458752 -3.178029 4.365064 C -1.116389 2.457386 0.223453 H -5.298613 0.736007 1.784019 C 3.779458 -3.210973 -3.704660 C -0.071868 -2.597157 0.081088 C 2.600275 2.603128 -2.666207 H 2.811968 -3.716872 -3.740523 C 0.923991 0.919445 -2.677049 C 4.931504 3.478828 0.086093 H 4.554377 -3.977690 -3.628322 H 0.026263 1.508901 -2.779572 H 5.702005 4.051378 0.583401 H 3.930216 -2.671924 -4.645875 C 4.336656 -2.392001 0.836367 C 1.739121 5.047069 0.885303 C -3.282694 3.480572 -2.585613 C 2.626305 1.164033 2.377059 H 2.576955 4.396072 1.152667 H -2.623531 4.070838 -1.936861 C 3.855193 2.913453 1.161223 H 1.799974 5.959350 1.490568 H -2.861261 3.536458 -3.596472 C 1.012834 -0.488082 -2.752861 H 1.885931 5.327054 -0.161176 C -3.922270 1.711813 3.989413 H 0.195701 -1.171611 -2.927538 C -4.923360 -0.951839 -0.635885 H -3.346019 2.503915 4.482142 C 3.676710 3.003747 -1.277178 H -4.548412 -1.914104 -0.259223 H -4.975590 2.025173 4.025656 C 4.046467 -2.321685 -1.594887 C 4.406549 3.715766 -1.197987 C -0.307081 4.169354 2.989762 C 2.781744 2.787954 -2.489216 H 4.682159 4.518832 -1.867282 H -1.282648 3.707035 3.170502 C 3.685380 -2.283497 2.210243 C -3.484409 1.587162 2.535106 H -0.329525 5.183782 3.405025 C 5.425597 -2.388206 -1.742162 H -2.407859 1.380203 2.481707 H 0.444284 3.602646 3.549192 H 5.875566 -2.350990 -2.725914 H -3.640034 2.544979 2.027379 C -1.238327 5.348059 0.344658 C 3.093405 -2.116218 -2.766270 C 3.627597 -4.446514 0.447007 H -1.070250 5.440390 -0.733084 C 5.711644 -2.455295 0.652120 H 3.745276 -5.355948 1.020295 H -1.192700 6.353117 0.780321 H 6.380116 -2.470388 1.503360 C -4.867251 -1.012252 -2.162851 H -2.247155 4.954259 0.502168 C 3.150076 2.581935 2.469066 H -5.190385 -0.046928 -2.570823 C -5.311984 3.953907 -1.185967 C -1.653708 -5.046857 -0.778451 H -3.832884 -1.167985 -2.491168 H -6.333514 4.351795 -1.194869 H -2.603895 -4.584817 -0.496263 C -6.369621 -0.799010 -0.160119 H -4.744669 4.563816 -0.468769 H -1.755141 -6.132681 -0.663309 H -6.424286 -0.825307 0.932158 C -5.324231 2.504466 -0.710551 H -1.468469 -4.834556 -1.835940 H -6.767069 0.174051 -0.470772 H -5.968244 1.923082 -1.382763 C 2.813975 -3.502861 2.488771 C -4.081779 -0.847953 2.579296 H -5.772636 2.443892 0.287597 H 2.398613 -3.449018 3.500121 H -4.652314 -1.646555 2.092188 C -0.309155 -5.393878 -0.570289 H 3.405295 -4.419618 2.410720 H -3.027374 -1.152650 2.532232 H -0.018669 -5.237371 -1.614960 H 1.983235 -3.565960 1.786449 C 1.429558 3.587693 -2.641775 H -0.619586 -6.439771 -0.461873 C 1.654838 3.823009 -2.488953 H 0.836283 3.526237 -3.562389 H 0.581435 -5.226634 0.042549 H 1.041587 3.718329 -3.389941 H 1.822858 4.604421 -2.566514 C -4.519766 -0.717820 4.031798 H 2.075892 4.832597 -2.480519 H 0.773930 3.409103 -1.785887 H -5.598453 -0.507923 4.071093 H 1.002444 3.707584 -1.620182 C -3.287242 2.035058 -2.107117 H -4.368471 -1.671675 4.550212 C -0.656328 -4.817507 2.084367 H -2.268755 1.636338 -2.069225 C -2.393089 -4.677680 1.595874 H 0.140279 -4.530622 2.775541 H -3.844923 1.427610 -2.828581 H -1.612793 -4.635376 2.362280 H -0.828084 -5.894621 2.195678 C 3.429491 2.898732 -3.927375 H -2.806189 -5.692910 1.588554 H -1.569209 -4.294725 2.383180 H 4.312940 2.259604 -3.995119 H -3.190895 -3.986652 1.887756 C 4.724980 -2.175263 3.329973 H 3.769774 3.937161 -3.913443 C -4.679931 4.083018 -2.564061 H 5.375743 -1.310821 3.181343 H 2.820631 2.754849 -4.826520 H -5.311042 3.561987 -3.298618 H 5.335318 -3.082544 3.388662 C 3.911698 -4.273629 -0.920199 H -4.647974 5.134857 -2.870229 H 4.211697 -2.052163 4.288012 H 4.307400 -5.017498 -1.596751 C -3.768333 0.398326 4.739386 C 5.012044 3.377976 -1.347100 C -7.208881 -1.928386 -2.249754 H -4.119874 0.503553 5.772078 H 5.491871 3.541966 -2.304102 H -7.624540 -0.989363 -2.643081 H -2.702061 0.136096 4.795124 C 2.105034 -3.274882 -2.877277 H -7.839011 -2.736429 -2.638243 C -3.088570 -4.454416 -1.362604 H 1.445293 -3.327736 -2.009402 C 5.292642 -1.657560 -2.504182 H -4.006840 -3.955892 -1.041426 H 2.644622 -4.221794 -2.967067 H 5.524906 -1.122523 -3.432911 H -3.311207 -5.521048 -1.482106 H 1.480074 -3.152952 -3.767586 H 6.008190 -2.475644 -2.394748 H -2.807014 -4.054855 -2.342261 C 5.748693 3.529852 -0.181945 H 5.441595 -0.977990 -1.660113 H 6.792745 3.820964 -0.247448 C -5.777983 -2.091221 -2.736480 Th6b’ SCF energy = -3893.3367821 C 5.187080 3.292113 1.063935 H -5.739814 -2.057152 -3.831623 H 5.801208 3.389884 1.950677 H -5.407611 -3.081034 -2.443642 Th 1.664985 0.094583 -0.022607 C -3.247134 4.324268 1.462127 C 5.912807 0.841835 1.668315 Pt -1.439411 0.306561 0.096687 H -4.140640 3.778135 1.148645 H 5.839953 0.140858 0.831698 Si -0.233312 -4.431232 0.290309 H -3.523277 5.379361 1.573235 295

Appendix

H -2.948810 3.947639 2.446280 H -5.521402 -0.430630 4.220430 H -3.177650 5.474665 1.131774 C 6.242578 -2.476485 -0.627014 C -3.742500 -1.582078 4.580845 C -1.444969 -3.577174 -2.613888 H 7.319241 -2.527247 -0.757055 H -5.056809 -2.902196 3.509396 H -0.863718 -3.551397 -3.543721 C 3.556573 2.912237 -3.804016 H -3.454533 -3.571892 3.786383 H -1.902295 -4.566230 -2.533723 H 4.377901 2.192662 -3.845218 C -5.017843 -3.143707 -3.437072 H -0.763613 -3.445679 -1.769743 H 3.958184 3.923293 -3.928287 H -3.198924 -2.417270 -4.353453 C -3.411141 -2.747019 -3.866634 H 2.885252 2.710982 -4.643861 H -2.949681 -3.424360 -2.932267 H -4.250945 -2.050156 -3.916581 C 4.107353 2.625228 3.663383 H -5.040821 -4.205449 -1.566985 H -3.819873 -3.760500 -3.855771 H 3.570070 2.340241 4.572563 H -6.638203 -3.720030 -2.123889 H -2.806478 -2.635759 -4.773285 H 4.504789 3.635101 3.809272 H -7.718101 1.920242 -1.991745 C -3.398829 4.422849 -0.819620 H 4.938808 1.929305 3.527447 H -7.799288 3.594006 -1.453047 H -3.758436 5.192476 -1.487555 C -0.529408 5.435210 0.768809 H -4.087216 -1.927947 5.562088 C -4.927740 1.930844 -2.432586 H -0.277244 5.333527 1.828585 H -2.661562 -1.404158 4.670308 H -5.194328 1.417910 -3.364646 H -0.927639 6.445371 0.614972 H -5.637551 -2.399193 -3.957641 H -5.581959 2.798628 -2.322531 H 0.394600 5.345162 0.189288 H -5.062231 -4.060516 -4.036038 H -5.129956 1.260976 -1.591902 C 1.268343 -5.453125 -0.215136 C -5.719578 -0.547570 1.705810 H 1.285279 -5.610185 -1.297215 H -5.583880 0.143941 0.869295 H 1.178712 -6.438264 0.258085 Complex Th7 H -5.970454 0.029010 2.604324 H 2.230801 -5.028815 0.078169 H -6.570591 -1.187422 1.462920 Th7a SCF energy = -3933.8922108 C 2.012829 3.571423 2.719171 C -4.799002 -2.403390 3.064810 H 1.240986 3.498020 1.950888 Th -1.468473 0.136763 -0.022497 H -5.691245 -2.987019 2.826049 H 2.400290 4.594295 2.729990 Ni 1.622256 0.256273 -0.018277 H -4.993781 -1.851594 3.990743 H 1.545414 3.374863 3.689729 Si -0.005341 -4.108564 1.123154 H -3.982398 -3.107151 3.242135 C 3.841095 -1.996319 -4.097892 Si 2.147471 3.986246 -0.075518 C -0.917930 3.733258 2.709983 H 3.121099 -1.812494 -4.900370 N -3.265171 -1.758353 -0.286135 H -0.591278 3.557204 3.742583 H 4.379017 -2.921234 -4.331476 N -2.733061 2.403404 -0.022181 H -1.048681 4.809817 2.579111 H 4.547798 -1.163417 -4.081172 C 0.766978 -1.336135 0.169165 H -0.136878 3.401429 2.023073 C -2.380041 4.626717 -1.497042 C 0.168115 -2.396553 0.443698 C -3.279726 3.528731 3.432674 H -1.511154 4.700040 -2.159847 C -2.488901 1.276493 -2.589198 H -4.268073 3.097696 3.256648 H -2.887163 5.598485 -1.497011 C -0.631082 -0.820246 -2.756756 H -3.375709 4.614397 3.355583 H -3.061455 3.884279 -1.919220 H 0.100754 -1.615287 -2.789526 H -2.966478 3.285691 4.454328 P -3.720278 -0.236058 0.090672 C 0.351004 1.697576 0.060672 C -3.301297 3.377447 -3.617455 C -4.967577 1.129596 -0.215172 C -0.943900 0.864818 2.865382 H -2.299423 3.811754 -3.647291 C -4.257895 -0.880746 1.751206 H -0.035902 1.419413 3.057427 H -4.018090 4.198344 -3.537200 C -4.069873 -1.636030 -1.086792 C -1.986588 -1.115259 -2.681807 H -3.488499 2.857769 -4.563112 H -4.534250 1.939282 0.386162 C -3.404074 -2.607130 -1.366641 C 0.408509 -4.070218 2.965201 C -4.963435 1.610354 -1.665153 C -2.124457 1.529967 2.546980 H 1.392044 -3.624395 3.140652 C -6.404145 0.918849 0.268727 C -1.110516 1.544910 -2.631054 H 0.430796 -5.098171 3.346078 H -5.337205 -1.079700 1.698264 H -0.759744 2.565611 -2.547030 H -0.326455 -3.519348 3.560203 C -4.009145 0.188910 2.817127 C -4.194014 -2.186434 0.638814 C 1.244504 -5.247818 0.296811 C -3.558915 -2.180601 2.139985 C -3.262223 -0.620988 2.285382 H 1.049592 -5.336691 -0.776455 H -3.460532 -2.434331 -0.638890 C -0.197470 0.507350 -2.737419 H 1.169268 -6.250030 0.735192 C -3.480605 -1.390634 -2.478238 H 0.863488 0.724541 -2.752170 H 2.270985 -4.894154 0.432096 C -5.507999 -2.137714 -1.184513 C 1.507066 2.245850 -0.030559 C 0.748329 5.144837 -0.562511 H -3.933125 1.773737 -2.001407 C -3.266632 0.766751 2.271841 H 0.490554 5.001636 -1.617968 H -5.388067 0.829668 -2.308734 H -4.169856 1.294418 2.001961 H 1.049892 6.191244 -0.434229 C -5.796498 2.874396 -1.838989 C -2.704166 3.328822 1.001467 H -0.159997 4.966170 0.020093 C -7.236626 2.184343 0.086656 C -2.895452 -0.048963 -2.613037 C 2.826606 4.453065 1.620009 H -6.874592 0.101189 -0.289401 H -3.946850 -0.287773 -2.534527 H 2.053238 4.401310 2.392284 H -6.423396 0.630309 1.323577 C -0.919503 -0.528878 2.900356 H 3.219339 5.476335 1.602336 H -2.937260 0.429678 2.814879 H 0.007407 -1.043737 3.118714 H 3.641164 3.781876 1.911831 H -4.532125 1.118307 2.566610 C -3.169009 3.101067 -1.129348 C 3.528056 4.244014 -1.329396 C -4.432015 -0.281090 4.202326 C -2.055673 -1.262487 2.595579 H 4.476101 3.817847 -0.990627 H -3.775222 -2.968004 1.409534 H -2.009023 -2.343133 2.577161 H 3.682226 5.319612 -1.475587 H -2.473812 -2.019025 2.116058 C -4.485645 -1.433555 1.916321 H 3.280705 3.805049 -2.301362 C -3.986739 -2.649348 3.525847 C -2.240761 3.027490 2.413504 P 3.723320 -0.394501 -0.063253 H -4.012124 -0.569725 -2.972490 C -3.473316 2.415100 -2.435502 C 4.425910 -0.918277 1.554481 H -2.437292 -1.074811 -2.373540 C -2.547851 -2.516738 -2.614635 C 4.072931 -1.773216 -1.228297 C -3.586254 -2.634713 -3.351097 C -4.896119 -3.271361 0.159300 C 5.007526 0.828512 -0.567661 H -5.920805 -2.341811 -0.190082 H -5.692738 -3.802109 0.661749 C 3.551681 -1.172975 2.606283 H -6.137291 -1.359884 -1.635021 C -1.702074 -4.866434 0.901918 C 5.799436 -1.019799 1.780291 C -5.595431 -3.389399 -2.051301 H -2.524925 -4.194092 1.162314 C 3.339085 -1.785774 -2.413782 H -5.339250 3.694854 -1.270001 H -1.773894 -5.763289 1.528953 C 5.028532 -2.762206 -1.018506 H -5.788649 3.182412 -2.891044 H -1.866904 -5.169761 -0.134981 C 5.297081 1.877589 0.304541 C -7.222794 2.667189 -1.354721 C -4.392299 -3.536953 -1.127484 C 5.675720 0.769487 -1.786532 H -8.264510 2.000450 0.420477 H -4.713024 -4.326181 -1.793261 H 2.484704 -1.087221 2.429177 H -6.834795 2.975653 0.735567 C -3.106249 4.566574 0.548790 C 4.036334 -1.533260 3.855435 H -4.212168 0.498727 4.940641 H 6.498640 -0.787867 0.983402 296

Appendix

C 6.282385 -1.389814 3.024772 H -1.650361 -5.143843 -0.327834 C 5.693333 0.922870 -1.703229 H 2.570110 -1.033589 -2.567531 C -4.229636 -3.655095 -1.144499 H 2.354509 -1.072439 2.356002 C 3.579245 -2.746692 -3.383544 H -4.529881 -4.437573 -1.828402 C 3.826894 -1.726350 3.786966 H 5.598116 -2.782884 -0.095977 C -3.364667 4.468959 0.718287 H 6.431695 -0.827402 1.086648 C 5.255962 -3.735008 -1.981688 H -3.496451 5.347938 1.335200 C 6.109793 -1.596073 3.056595 H 4.790017 1.934263 1.263039 C -1.333909 -3.502217 -2.727029 H 2.619063 -0.664290 -2.609245 C 6.233776 2.839664 -0.030663 H -0.779760 -3.404760 -3.667936 C 3.461955 -2.460904 -3.424951 H 5.471609 -0.038600 -2.480116 H -1.742695 -4.514526 -2.682865 H 5.351759 -2.773238 -0.075153 C 6.611837 1.738100 -2.124863 H -0.636586 -3.377388 -1.895717 C 4.979481 -3.644059 -1.992933 C 5.400856 -1.646905 4.065887 C -3.373272 -2.716745 -3.884682 H 5.019779 1.882196 1.470966 H 3.342743 -1.722877 4.668654 H -4.242006 -2.054092 -3.887287 C 6.486626 2.777286 0.197573 H 7.352961 -1.467489 3.185674 H -3.737448 -3.747140 -3.899588 H 5.400569 0.196692 -2.453621 H 3.005642 -2.738440 -4.304891 H -2.800243 -2.547711 -4.802654 C 6.691035 1.842758 -2.000388 C 4.540291 -3.724097 -3.169202 C -3.671290 4.345521 -0.651187 C 5.177814 -1.914947 4.035351 H 5.999193 -4.505245 -1.801611 H -4.108682 5.101387 -1.288808 H 3.094056 -1.967678 4.550374 C 6.894944 2.773664 -1.249913 C -5.047223 1.846492 -2.345706 H 7.169003 -1.737253 3.246387 H 6.447596 3.646889 0.662674 H -5.286481 1.340089 -3.288150 H 2.927366 -2.371960 -4.365379 H 7.123364 1.676823 -3.080194 H -5.738666 2.683888 -2.226319 C 4.306696 -3.539050 -3.201081 H 5.780881 -1.927257 5.043145 H -5.226389 1.152687 -1.519259 H 5.635194 -4.488850 -1.807364 H 4.723217 -4.483439 -3.922618 C -5.637456 -0.822754 1.795980 C 7.093290 2.769678 -1.051952 H 7.628006 3.528540 -1.514894 H -5.566304 -0.112832 0.966650 H 6.793518 3.498791 0.948159 H -5.892560 -0.273176 2.709563 H 7.158996 1.826949 -2.979644 Th7a THF PCM SCF energy = - H -6.458550 -1.507109 1.571416 H 5.507009 -2.304685 4.993243 3933.908275 C -4.580976 -2.646160 3.096629 H 4.435518 -4.298925 -3.965033 H -5.441101 -3.278343 2.863176 H 7.876507 3.484233 -1.283071 Th -1.488694 0.137641 0.007919 H -4.791716 -2.122296 4.034958 Ni 1.601280 0.402800 0.049790 H -3.719041 -3.300208 3.248233 Si 0.300329 -4.132517 0.845120 C -1.040108 3.707980 2.790372 Th7a hexane PCM SCF energy = - Si 2.110995 4.072953 -0.244502 H -0.672793 3.518844 3.806189 3933.8979791 N -3.161572 -1.855298 -0.275630 H -1.237330 4.778960 2.700459 Th -1.482663 0.140911 0.006834 N -2.823329 2.366064 0.066220 H -0.261149 3.443540 2.071452 Ni 1.603795 0.384334 0.030966 C 0.810028 -1.231880 0.169173 C -3.365607 3.365484 3.573634 Si 0.257223 -4.140737 0.788061 C 0.288463 -2.347832 0.353749 H -4.334398 2.883662 3.420460 Si 2.113960 4.056734 -0.310762 C -2.584086 1.298590 -2.523298 H -3.519368 4.446452 3.527845 N -3.193837 -1.816831 -0.269984 C -0.639708 -0.714130 -2.767293 H -3.005168 3.115975 4.577680 N -2.810235 2.363372 0.105599 H 0.126292 -1.474648 -2.833116 C -3.487749 3.390678 -3.492754 C 0.803268 -1.244537 0.139580 C 0.265167 1.787777 0.096281 H -2.501674 3.859840 -3.522886 C 0.258297 -2.351833 0.312127 C -0.927703 0.838165 2.902393 H -4.232762 4.182863 -3.384779 C -2.616350 1.324887 -2.497792 H -0.049567 1.435654 3.103551 H -3.666860 2.888160 -4.449002 C -0.684277 -0.694608 -2.781711 C -1.981977 -1.067809 -2.682597 C 0.881088 -4.233767 2.634407 H 0.077841 -1.458703 -2.855021 C -3.292478 -2.671563 -1.380856 H 1.871119 -3.783551 2.753300 C 0.277576 1.779594 0.069322 C -2.145567 1.445937 2.610319 H 0.944036 -5.285719 2.937263 C -0.870109 0.800177 2.897798 C -1.220500 1.625660 -2.585121 H 0.190803 -3.731535 3.320546 H 0.022708 1.381305 3.082741 H -0.909526 2.658790 -2.501134 C 1.538930 -5.030941 -0.246805 C -2.027319 -1.042077 -2.683058 C -4.044181 -2.350195 0.660720 H 1.229790 -5.007083 -1.296741 C -3.333548 -2.637948 -1.371677 C -3.169439 -0.759791 2.323666 H 1.618975 -6.080251 0.060920 C -2.081498 1.430713 2.628878 C -0.266662 0.630644 -2.728611 H 2.529339 -4.570826 -0.175969 C -1.251899 1.646734 -2.574105 H 0.780693 0.901001 -2.768433 C 0.719210 5.286522 -0.617549 H -0.936775 2.677538 -2.475899 C 1.395305 2.379311 -0.012475 H 0.215721 5.027274 -1.555009 C -4.062802 -2.316951 0.676939 C -3.252780 0.627966 2.342703 H 1.114948 6.304554 -0.715164 C -3.147973 -0.755115 2.339646 H -4.190625 1.108694 2.103959 H -0.033846 5.282107 0.176543 C -0.304458 0.648470 -2.737512 C -2.851691 3.253586 1.121528 C 2.977483 4.635358 1.329600 H 0.744194 0.913776 -2.779479 C -2.932919 -0.043083 -2.574824 H 2.271979 4.661355 2.167183 C 1.411220 2.360690 -0.051883 H -3.972799 -0.326768 -2.491971 H 3.383417 5.644936 1.196568 C -3.204660 0.632777 2.368971 C -0.828154 -0.552342 2.911662 H 3.801740 3.968891 1.597781 H -4.135709 1.132653 2.143725 H 0.124152 -1.020566 3.123720 C 3.303890 4.098341 -1.696885 C -2.785753 3.253546 1.159853 C -3.337617 3.056590 -1.010184 H 4.151747 3.425984 -1.539586 C -2.972187 -0.014296 -2.554037 C -1.924700 -1.341089 2.602505 H 3.691112 5.113092 -1.846516 H -4.011525 -0.294941 -2.456235 H -1.816057 -2.417159 2.563935 H 2.790366 3.795193 -2.616259 C -0.796185 -0.592300 2.895855 C -4.349320 -1.638709 1.960827 P 3.707692 -0.228446 -0.017794 H 0.151725 -1.078893 3.084935 C -2.334747 2.940874 2.512298 C 4.334160 -0.903974 1.573451 C -3.320518 3.074567 -0.960347 C -3.614057 2.391414 -2.335161 C 3.975540 -1.587154 -1.229342 C -1.910198 -1.360298 2.597526 C -2.481713 -2.494673 -2.650788 C 5.079501 0.923310 -0.454081 H -1.820474 -2.437664 2.544224 C -4.708034 -3.453441 0.165707 C 3.409068 -1.223626 2.562507 C -4.348434 -1.607056 1.980971 H -5.467270 -4.032702 0.673618 C 5.692025 -1.090300 1.835619 C -2.250869 2.927846 2.540789 C -1.364979 -4.979573 0.713792 C 3.292166 -1.499352 -2.440997 C -3.637850 2.419348 -2.279580 H -2.173046 -4.402972 1.174215 C 4.819296 -2.672541 -1.014204 C -2.537197 -2.464315 -2.651199 H -1.304924 -5.955035 1.211129 C 5.485058 1.866870 0.490156 297

Appendix

C -4.727176 -3.422993 0.191373 C 3.389155 -1.330029 2.524088 C 3.490945 0.989407 2.573046 H -5.476232 -4.007241 0.707771 C 5.678655 -1.113003 1.841472 H 2.792018 0.159491 2.632061 C -1.412395 -4.978980 0.657731 C 3.332128 -1.456128 -2.478984 C 4.109629 1.269988 1.355440 H -2.226033 -4.385580 1.086160 C 4.812050 -2.677030 -1.042860 C -2.657776 -2.766694 -2.400829 H -1.367901 -5.939518 1.184922 C 5.423923 1.875915 0.549307 C -3.243943 2.353929 2.326722 H -1.684889 -5.176425 -0.381381 C 5.767508 0.908451 -1.616849 C 5.593228 1.265486 -1.869304 C -4.263307 -3.624103 -1.122911 H 2.334819 -1.203217 2.301257 H 6.378032 0.942674 -1.192854 H -4.568964 -4.409519 -1.800554 C 3.800789 -1.857254 3.739911 C -5.240494 2.415096 -1.502272 C -3.262192 4.485242 0.765750 H 6.422164 -0.807507 1.112692 H -5.752889 2.364948 -2.454409 H -3.351305 5.368937 1.383030 C 6.090043 -1.643246 3.054041 C -2.976042 2.143128 -2.670369 C -1.398252 -3.479920 -2.747324 H 2.673330 -0.608623 -2.643700 C -5.370453 2.508533 0.904760 H -0.859500 -3.385864 -3.697827 C 3.510380 -2.401198 -3.476733 H -5.982056 2.530423 1.797626 H -1.812900 -4.489431 -2.696903 H 5.321367 -2.801340 -0.093692 C -2.793189 -2.531988 2.567638 H -0.685849 -3.360710 -1.928099 C 4.979367 -3.632477 -2.035729 C 3.755870 1.759829 3.694538 C -3.447635 -2.675244 -3.873297 H 4.898738 1.897791 1.499388 H 3.273001 1.523887 4.637479 H -4.313468 -2.009278 -3.858643 C 6.433573 2.790821 0.305414 C 2.257570 4.551431 -0.962028 H -3.818385 -3.703229 -3.887201 H 5.524629 0.170277 -2.373255 H 3.135471 3.951230 -0.707635 H -2.888204 -2.504930 -4.799590 C 6.772852 1.834179 -1.865872 H 2.522701 5.611418 -0.867693 C -3.600072 4.373131 -0.596101 C 5.151737 -2.015548 4.006741 H 2.007276 4.356108 -2.009222 H -4.020032 5.145871 -1.224432 H 3.062878 -2.142733 4.483093 C -2.326577 3.557784 2.516212 C -5.072346 1.879432 -2.253016 H 7.149567 -1.760764 3.258017 H -1.837630 3.513325 3.494466 H -5.344161 1.385016 -3.193364 H 2.998365 -2.287588 -4.427145 H -2.904085 4.485373 2.466005 H -5.756015 2.717577 -2.100055 C 4.334682 -3.495247 -3.255284 H -1.549265 3.593667 1.752734 H -5.226877 1.176878 -1.429032 H 5.618385 -4.490408 -1.852155 C 5.150777 -1.064862 0.113111 C -5.620929 -0.765073 1.826650 C 7.111596 2.774386 -0.906583 C 5.931469 1.910226 -3.047772 H -5.536711 -0.047971 1.004927 H 6.689710 3.524387 1.063315 H 6.974608 2.107865 -3.273282 H -5.866413 -0.220637 2.746242 H 7.296668 1.812626 -2.816288 C -1.531102 -3.801305 -2.442999 H -6.454185 -1.431360 1.593133 H 5.475456 -2.423793 4.958813 H -0.962685 -3.707368 -3.374020 C -4.592730 -2.616078 3.112247 H 4.468870 -4.242888 -4.030313 H -1.950614 -4.810767 -2.402990 H -5.467759 -3.228590 2.882066 H 7.900336 3.493887 -1.100601 H -0.836542 -3.676834 -1.608795 H -4.784586 -2.094326 4.055906 C 1.333301 4.478625 1.949357 H -3.744288 -3.290156 3.251554 H 0.516130 4.318354 2.658118 C -0.940853 3.674451 2.800258 Th7b SCF energy = -3933.9050410 H 1.671526 5.516330 2.054239 H -0.562011 3.480497 3.811319 H 2.160835 3.818517 2.225765 Th -1.400816 -0.068366 0.000015 H -1.121250 4.748290 2.711234 C -4.204669 2.294327 3.518045 Ni 1.631439 -0.450502 0.014351 H -0.177491 3.397340 2.069708 H -4.878418 1.438330 3.438443 P 3.745734 0.120084 -0.032260 C -3.259797 3.363122 3.618906 H -4.795065 3.213508 3.593639 Si 0.811041 4.160579 0.171544 H -4.238491 2.898776 3.475746 H -3.628442 2.186458 4.441483 Si 2.148268 -4.101408 0.161566 H -3.398123 4.446247 3.578189 C -4.845367 -3.303533 -1.154583 N -2.947572 -0.303196 -2.215826 H -2.890576 3.104362 4.617643 H -5.372761 -3.457832 -2.087841 N -3.109976 -0.112686 2.118035 C -3.536910 3.424324 -3.434118 C -1.988090 3.295932 -2.834349 C 0.257246 -1.784436 0.124605 H -2.551784 3.893964 -3.481884 H -1.280415 3.341709 -2.004996 C -2.884220 -2.775679 0.084844 H -4.278460 4.216516 -3.304860 H -2.524298 4.247677 -2.886963 H -1.794787 -2.630322 0.107473 H -3.737254 2.928045 -4.389559 H -1.416102 3.175731 -3.759838 C 0.907147 1.209125 -0.018525 C 0.836861 -4.259683 2.578391 C -5.532648 -3.427688 0.043524 C -3.255258 2.422862 -0.186994 H 1.834677 -3.827973 2.698971 H -6.586400 -3.689215 0.027285 H -2.163428 2.504397 -0.131099 H 0.883205 -5.313740 2.876730 C -4.909160 -3.196308 1.260639 C -1.131423 0.808337 2.731401 H 0.155339 -3.751617 3.269228 H -5.485673 -3.268385 2.174604 H -0.358039 1.531453 2.943441 C 1.494414 -5.037071 -0.306861 C 5.427098 -1.895707 -0.972469 C -1.003680 -0.597441 2.800930 H 1.191102 -4.998579 -1.357928 H 4.837384 -1.807224 -1.879913 H -0.118087 -1.149417 3.076172 H 1.566878 -6.090595 -0.012089 C 4.972784 2.357986 1.274743 C -2.452781 1.060420 2.340075 H 2.487001 -4.583394 -0.227648 H 5.450716 2.605961 0.333466 C -2.099745 -1.357661 -2.388993 C 0.710142 5.234766 -0.743552 C 3.527356 -4.197477 1.430788 C -2.242075 0.827083 -2.506564 H 0.274987 4.981013 -1.716217 H 4.347429 -3.512583 1.202868 C 1.363803 -2.422792 0.143035 H 1.075333 6.267252 -0.798798 H 3.931150 -5.215877 1.468670 C 0.403709 2.354542 0.000631 H -0.094375 5.187767 -0.002969 H 3.143140 -3.951027 2.426669 C -0.814696 -0.900247 -2.704877 C 2.937779 4.668992 1.268073 C -5.983604 2.513042 -0.337347 H 0.072484 -1.493690 -2.863132 H 2.213049 4.710346 2.088120 H -7.066659 2.558041 -0.397589 C -3.986193 2.452368 0.999504 H 3.337093 5.678762 1.118016 C 4.940975 2.289796 -3.943294 C -2.255592 -1.120214 2.450969 H 3.761770 4.018546 1.572861 H 5.208046 2.786181 -4.870831 C 3.272760 1.386251 -2.468450 C 3.337834 4.065281 -1.737514 C 3.612910 2.022537 -3.653571 H 2.235257 1.177866 -2.229029 H 4.194385 3.412738 -1.549304 H 2.834992 2.307653 -4.354927 C -3.563383 -2.857156 1.295295 H 3.710599 5.082364 -1.906545 C -3.491299 -2.903252 -3.678010 C 4.256843 1.006322 -1.561438 H 2.848812 3.730940 -2.659381 H -4.309725 -2.179345 -3.692782 C -0.907664 0.506655 -2.782089 P 3.706282 -0.243495 -0.019681 H -3.903897 -3.913351 -3.770351 H -0.107012 1.190589 -3.018465 C 4.321055 -0.954779 1.561700 H -2.857066 -2.717128 -4.549554 C -3.498197 -2.967300 -1.147591 C 3.988479 -1.576256 -1.255369 C -3.692509 -2.563790 3.806481 C -3.854384 2.356234 -1.443703 C 5.082327 0.918624 -0.406122 H -3.107593 -2.290014 4.689334 298

Appendix

H -4.098991 -3.567514 3.968941 C -0.926612 -0.509402 2.766669 H -3.927679 3.918195 3.775734 H -4.518032 -1.853994 3.712650 H -0.122087 -1.190831 2.997201 H -2.875961 2.728669 4.558094 C 4.624785 2.837852 3.606638 C -3.529615 2.966499 1.156527 C -3.738808 2.574322 -3.801922 H 4.826117 3.448595 4.480798 C -3.831912 -2.402859 1.415673 H -3.154067 2.312440 -4.688519 C 0.879420 -5.421733 0.612054 C 3.520909 -1.036972 -2.568527 H -4.151075 3.577080 -3.953988 H 0.557356 -5.327079 1.653521 H 2.826911 -0.205693 -2.657870 H -4.562353 1.861261 -3.715187 H 1.326340 -6.415745 0.489859 C 4.121545 -1.295742 -1.336630 C 4.666338 -2.906266 -3.552048 H -0.009686 -5.371160 -0.024139 C -2.686788 2.763755 2.408805 H 4.880163 -3.532606 -4.412065 C -0.569582 5.360200 -0.285614 C -3.184902 -2.378951 -2.353227 C 0.863460 5.441701 -0.594800 H -0.651523 5.476198 -1.369963 C 5.568181 -1.246745 1.896401 H 0.526570 5.339195 -1.631033 H -0.309088 6.341301 0.129497 H 6.362626 -0.977135 1.208186 H 1.315154 6.435026 -0.484550 H -1.554806 5.088282 0.100740 C -5.218319 -2.487937 1.458169 H -0.015413 5.394216 0.055995 C -1.657592 -3.536515 2.764256 H -5.743347 -2.447603 2.404018 C -0.556329 -5.358769 0.299754 H -0.923755 -3.478627 1.957795 C -2.976872 -2.164690 2.655783 H -0.681096 -5.465062 1.380753 H -2.059390 -4.553343 2.798764 C -5.318587 -2.585633 -0.950680 H -0.273776 -6.341276 -0.097361 H -1.139556 -3.344355 3.709596 H -5.920545 -2.620672 -1.849775 H -1.524625 -5.092490 -0.130721 C -3.802496 2.031877 -3.954992 C -2.835182 2.536890 -2.566211 C -1.706636 3.550235 -2.762336 H -3.133030 1.849115 -4.800367 C 3.799915 -1.828811 -3.672176 H -0.971642 3.496245 -1.956432 H -4.351009 2.959174 -4.151590 H 3.331441 -1.608771 -4.626080 H -2.116934 4.563751 -2.794861 H -4.509471 1.200924 -3.899401 C 2.239126 -4.521390 1.082523 H -1.188362 3.364115 -3.708446 C 5.223649 3.140227 2.393203 H 3.123324 -3.920255 0.851888 C -3.824179 -2.072109 3.928452 H 5.893325 3.990738 2.314139 H 2.511620 -5.581765 1.018315 H -3.170094 -1.875932 4.782848 C 7.220169 -2.939193 0.239339 H 1.941558 -4.307001 2.113762 H -4.353306 -3.012004 4.116447 H 8.023867 -3.666576 0.288486 C -2.223251 -3.549498 -2.534983 H -4.551976 -1.259784 3.866547 C 5.924792 -1.188154 1.262595 H -1.731331 -3.489766 -3.510663 C 5.247118 -3.187390 -2.324069 H 5.732786 -0.550803 2.118541 H -2.768002 -4.496580 -2.485739 H 5.914662 -4.036791 -2.219545 C 6.453566 -2.822050 -0.912472 H -1.448616 -3.554917 -1.767725 C 7.227366 2.939077 -0.316019 H 6.655181 -3.457786 -1.768765 C 5.156314 1.067872 -0.145082 H 8.032817 3.663246 -0.381537 C 2.785818 -4.497328 -1.564960 C 5.888724 -1.857605 3.098163 C 5.907564 1.188627 -1.310469 H 1.955284 -4.523677 -2.278590 H 6.925497 -2.080391 3.329116 H 5.698510 0.550587 -2.161954 H 3.273803 -5.478743 -1.576017 C -1.557077 3.795542 2.446949 C 6.482647 2.825698 0.851070 H 3.507523 -3.753055 -1.909919 H -0.982134 3.696424 3.373154 H 6.703521 3.461309 1.702721 C 6.951418 -2.121543 1.324374 H -1.975315 4.805841 2.415069 C 2.781532 4.504005 1.571384 H 7.544958 -2.204535 2.229302 H -0.868905 3.674005 1.606969 H 1.955551 4.521230 2.290834 C 1.428701 -4.509187 -1.867654 H 3.265412 5.487561 1.585159 Th7b THF PCM SCF energy = - H 0.640922 -4.347294 -2.608934 H 3.509246 3.759645 1.904763 3933.9215973 H 1.754586 -5.553555 -1.941737 C 6.935171 2.119767 -1.394727 H 2.275936 -3.864951 -2.121386 H 7.511816 2.198569 -2.310917 Th -1.400620 0.072251 -0.010411 C -4.137276 -2.359210 -3.552854 Ni 1.630697 0.467844 -0.036082 H -4.844700 -1.529515 -3.487941 P 3.749875 -0.113954 0.022033 H -4.693885 -3.299021 -3.626820 Th7b hexane PCM SCF energy = - Si 0.838221 -4.162901 -0.117284 H -3.556276 -2.238147 -4.471640 3933.9110391 Si 2.135156 4.121409 -0.154425 C -4.880562 3.290660 1.167703 Th -1.403882 0.072085 -0.001034 N -2.977439 0.295092 2.231875 H -5.406939 3.441571 2.102233 Ni 1.627243 0.459679 -0.013787 N -3.121454 0.099866 -2.150375 C -1.967611 -3.296091 2.838765 P 3.743540 -0.115549 0.029142 C 0.250882 1.795726 -0.128544 H -1.248262 -3.331697 2.019026 Si 0.830489 -4.161724 -0.139267 C -2.916836 2.786171 -0.078857 H -2.485856 -4.257695 2.889125 Si 2.139833 4.111375 -0.141814 H -1.827193 2.644471 -0.104320 H -1.410565 -3.160123 3.770812 N -2.969370 0.295613 2.219052 C 0.911580 -1.197451 0.004176 C -5.573241 3.409183 -0.029003 N -3.099907 0.106022 -2.136543 C -3.216087 -2.468055 0.165642 H -6.628872 3.662605 -0.009637 C 0.251230 1.791844 -0.113843 H -2.122414 -2.527219 0.122851 C -4.951109 3.182153 -1.248592 C -2.899728 2.775467 -0.085877 C -1.116227 -0.776070 -2.741138 H -5.531929 3.250083 -2.160303 H -1.809563 2.634488 -0.103685 H -0.327901 -1.482141 -2.954628 C 5.455136 1.901039 0.933146 C 0.907128 -1.203465 0.021555 C -1.017383 0.632255 -2.803412 H 4.885320 1.816768 1.853568 C -3.232568 -2.442146 0.171820 H -0.142664 1.202070 -3.076731 C 4.981144 -2.384346 -1.223438 H -2.139466 -2.512277 0.126561 C -2.435837 -1.059173 -2.364121 H 5.447313 -2.617101 -0.272652 C -1.106101 -0.793193 -2.731084 C -2.131108 1.352682 2.394734 C 3.513513 4.224572 -1.425207 H -0.323723 -1.507834 -2.938542 C -2.262603 -0.835159 2.502016 H 4.326019 3.527081 -1.205672 C -0.992187 0.613916 -2.796879 C 1.356251 2.439181 -0.147270 H 3.926280 5.240007 -1.445333 H -0.110254 1.174719 -3.065848 C 0.426563 -2.350349 0.001722 H 3.126432 3.997778 -2.424880 C -2.428339 -1.060229 -2.352374 C -0.841106 0.898618 2.696896 C -5.946611 -2.603315 0.284674 C -2.125169 1.353147 2.392044 H 0.042507 1.495986 2.859838 H -7.028997 -2.671983 0.332511 C -2.258507 -0.833003 2.503871 C -3.933766 -2.503059 -1.030259 C 4.888390 -2.172371 4.009028 C 1.357655 2.431681 -0.131033 C -2.282845 1.128258 -2.461791 H 5.142216 -2.642551 4.953729 C 0.417057 -2.354359 0.010045 C 3.246209 -1.271987 2.503237 C 3.567926 -1.873984 3.711731 C -0.838260 0.900084 2.707299 H 2.214909 -1.039655 2.259063 H 2.782710 -2.107917 4.423657 H 0.045724 1.496921 2.870459 C -3.601025 2.855969 -1.288098 C -3.515056 2.907863 3.688623 C -3.952316 -2.475741 -1.021969 C 4.239405 -0.958007 1.580566 H -4.334810 2.185752 3.714778 299

Appendix

C -2.252246 1.123639 -2.456619 H 5.201749 -2.736064 4.893568 C -0.562680 0.699098 -2.764207 C 3.269909 -1.345064 2.482990 C 3.608622 -1.969889 3.674816 H 0.479347 0.985761 -2.827811 H 2.233438 -1.128264 2.246550 H 2.831106 -2.237331 4.383513 C 1.160871 2.485270 -0.105432 C -3.574219 2.853013 -1.299570 C -3.524670 2.898231 3.675678 C -3.273273 0.528912 2.431832 C 4.253509 -0.987915 1.566084 H -4.341058 2.172006 3.690166 H -4.231392 0.998265 2.262401 C -0.925226 -0.507518 2.780308 H -3.941061 3.907082 3.763840 C -2.977472 3.185701 1.243738 H -0.122057 -1.188628 3.016344 H -2.892654 2.716706 4.549836 C -3.209225 -0.028813 -2.514511 C -3.520318 2.961320 1.144505 C -3.693054 2.565636 -3.812498 H -4.238079 -0.336378 -2.389641 C -3.844830 -2.380088 1.422979 H -3.103057 2.298419 -4.694006 C -0.796336 -0.614409 2.798975 C 3.490417 -1.001376 -2.571406 H -4.103417 3.568145 -3.972314 H 0.181670 -1.063627 2.910799 H 2.792349 -0.171407 -2.638147 H -4.516357 1.852345 -3.725784 C -3.576124 3.023010 -0.861677 C 4.106220 -1.275519 -1.350710 C 4.627890 -2.854359 -3.593473 C -1.896456 -1.418224 2.543618 C -2.685663 2.761491 2.402101 H 4.832079 -3.468988 -4.464246 H -1.766362 -2.488482 2.448634 C -3.201152 -2.365333 -2.343889 C 0.868712 5.433859 -0.579642 C -4.360762 -1.735906 2.060675 C 5.588621 -1.257810 1.870680 H 0.538302 5.340586 -1.618705 C -2.398878 2.854278 2.605471 H 6.374111 -0.953479 1.186566 H 1.317678 6.427177 -0.458789 C -3.925144 2.380451 -2.178016 C -5.231059 -2.453963 1.468290 H -0.015030 5.381497 0.063940 C -2.726152 -2.463488 -2.657983 H -5.753283 -2.409810 2.415420 C -0.555666 -5.361979 0.297104 C -4.802058 -3.499478 0.238783 C -2.982289 -2.156104 2.659492 H -0.662137 -5.470236 1.379998 H -5.519070 -4.108000 0.771808 C -5.337040 -2.547092 -0.940065 H -0.281254 -6.344561 -0.105447 C -1.547401 -5.119009 0.765551 H -5.940387 -2.574806 -1.838409 H -1.532003 -5.095680 -0.114887 H -2.041382 -4.786432 1.683911 C -2.798271 2.533002 -2.570341 C -1.666769 3.543792 -2.760228 H -1.479617 -6.212645 0.807103 C 3.758283 -1.777293 -3.688665 H -0.936300 3.488252 -1.950450 H -2.200296 -4.841283 -0.066570 H 3.277750 -1.545880 -4.633913 H -2.074085 4.558434 -2.794933 C -4.389434 -3.665317 -1.096849 C 2.256009 -4.538956 1.025363 H -1.143538 3.355918 -3.703478 H -4.714274 -4.438403 -1.779405 H 3.137208 -3.938612 0.782558 C -3.823554 -2.054872 3.935339 C -3.461458 4.419832 0.871558 H 2.524413 -5.599243 0.944237 H -3.164698 -1.866007 4.787715 H -3.531992 5.299330 1.496827 H 1.984358 -4.335318 2.065705 H -4.363537 -2.988472 4.125081 C -1.572080 -3.457655 -2.785735 C -2.263415 -3.554732 -2.525991 H -4.539967 -1.232475 3.874176 H -1.063536 -3.358801 -3.752706 H -1.768951 -3.503609 -3.501067 C 5.223686 -3.150700 -2.376750 H -1.965815 -4.474490 -2.715969 H -2.826655 -4.491131 -2.478323 H 5.893647 -4.000413 -2.291725 H -0.839989 -3.319190 -1.987329 H -1.490516 -3.576589 -1.757440 C 7.215375 2.944848 -0.278756 C -3.662997 -2.680126 -3.858325 C 5.147679 1.069455 -0.128956 H 8.018689 3.672040 -0.336737 H -4.542199 -2.033205 -3.814399 C 5.925686 -1.891278 3.055807 C 5.907463 1.194549 -1.287948 H -4.012712 -3.715384 -3.873383 H 6.967680 -2.097878 3.278504 H 5.705478 0.558349 -2.142463 H -3.131588 -2.489363 -4.797013 C -1.560423 3.797590 2.449429 C 6.462741 2.826267 0.882340 C -3.840062 4.318293 -0.479656 H -0.994721 3.702719 3.381930 H 6.675164 3.460664 1.737041 H -4.275882 5.097307 -1.088595 H -1.981469 4.806460 2.410053 C 2.786410 4.496800 1.583658 C -5.343301 1.802863 -2.106977 H -0.863127 3.675763 1.617070 H 1.959498 4.519330 2.301732 H -5.639513 1.317058 -3.044559 C 1.386524 -4.490945 -1.904481 H 3.275018 5.477957 1.596973 H -6.040783 2.620749 -1.912674 H 0.581621 -4.335903 -2.628380 H 3.509573 3.749713 1.919862 H -5.447833 1.083881 -1.289271 H 1.726482 -5.529558 -1.994338 C 6.933305 2.128174 -1.361543 C -5.667630 -0.935125 2.006004 H 2.218571 -3.832454 -2.170900 H 7.515871 2.211852 -2.273542 H -5.657658 -0.197619 1.198229 C -4.153235 -2.322630 -3.542907 H -5.875763 -0.421427 2.952333 H -4.842556 -1.478437 -3.471282 H -6.490206 -1.624609 1.804609 H -4.727895 -3.251399 -3.621332 Th7a’ SCF energy = -3882.5011521 C -4.502574 -2.782807 3.174756 H -3.571064 -2.207359 -4.461716 H -5.365415 -3.422983 2.976563 Th -1.660859 0.144604 -0.004815 C -4.869477 3.290637 1.145897 H -4.658683 -2.294354 4.142662 Pt 1.470184 0.338174 -0.006118 H -5.401974 3.441454 2.076870 H -3.623354 -3.426977 3.246194 Si 0.174592 -4.400646 0.605108 C -1.983990 -3.298271 2.835060 C -1.112414 3.645887 2.848555 Si 1.855436 4.178796 -0.394981 H -1.267619 -3.337753 2.012869 H -0.699126 3.442232 3.844163 N -3.310139 -1.860861 -0.247428 H -2.511182 -4.255212 2.883556 H -1.336327 4.713603 2.791502 N -3.037958 2.300953 0.184923 H -1.422722 -3.170986 3.766053 H -0.359368 3.417954 2.090973 C 0.690574 -1.471367 0.088885 C -5.552367 3.412585 -0.055323 C -3.397900 3.231586 3.714320 C 0.185250 -2.593015 0.234123 H -6.607482 3.668775 -0.043456 H -4.362746 2.735602 3.584608 C -2.883325 1.317205 -2.448890 C -4.922285 3.185202 -1.270105 H -3.577195 4.309204 3.695340 C -0.913247 -0.652461 -2.811256 H -5.495629 3.255264 -2.186270 H -2.997329 2.969496 4.700100 H -0.136288 -1.399242 -2.907681 C 5.437019 1.899458 0.954018 C -3.890994 3.405197 -3.318521 C 0.032627 1.883900 0.014807 H 4.859267 1.810370 1.869047 H -2.922504 3.905561 -3.388580 C -0.923282 0.774237 2.846387 C 4.969385 -2.363178 -1.262540 H -4.651350 4.172433 -3.153412 H -0.042004 1.382937 2.994292 H 5.445783 -2.607017 -0.319490 H -4.106241 2.917972 -4.275344 C -2.245054 -1.032240 -2.685151 C 3.514543 4.215664 -1.415749 C 1.073899 -4.654184 2.242247 C -3.482807 -2.661985 -1.360083 H 4.332678 3.525324 -1.196533 H 2.118796 -4.337117 2.173666 C -2.168752 1.363912 2.655686 H 3.921281 5.233284 -1.444106 H 1.056182 -5.715286 2.517571 C -1.528626 1.672927 -2.562242 H 3.125742 3.980435 -2.412662 H 0.596669 -4.091344 3.052307 H -1.235344 2.709781 -2.460152 C -5.962197 -2.559981 0.296236 C 1.131303 -5.297797 -0.742770 C -4.131774 -2.398307 0.722185 H -7.045180 -2.617358 0.346128 H 0.614559 -5.251163 -1.705925 C -3.169332 -0.854191 2.371484 C 4.935391 -2.248364 3.961232 H 1.254489 -6.353968 -0.475685 300

Appendix

H 2.124544 -4.854753 -0.868884 C -2.340168 1.279985 2.408820 C 3.206947 4.310894 -1.446500 C 0.437799 5.333053 -0.842709 C -2.358444 -0.911417 2.484808 H 4.000742 3.582926 -1.260156 H 0.005998 5.061430 -1.812070 C 1.092248 2.559496 -0.097142 H 3.656632 5.309908 -1.479215 H 0.786794 6.370153 -0.911197 C 0.369274 -2.592191 0.006221 H 2.776497 4.101155 -2.431700 H -0.365285 5.283340 -0.100325 C -1.030354 0.890436 2.710072 C -5.951904 -2.793449 0.221967 C 2.680683 4.820851 1.170389 H -0.175141 1.528006 2.871679 H -7.030660 -2.909752 0.260211 H 1.952084 4.897439 1.984341 C -3.938015 -2.585366 -1.074996 C 5.087352 -2.232199 3.919190 H 3.099019 5.818882 0.996126 C -2.440263 1.118781 -2.442089 H 5.390185 -2.726745 4.836704 H 3.490525 4.164485 1.499157 C 3.356423 -1.495342 2.422510 C 3.744595 -2.132548 3.591933 C 3.076573 4.139766 -1.821890 H 2.307409 -1.410890 2.158315 H 2.991374 -2.550000 4.252684 H 3.909319 3.459356 -1.624534 C -3.866995 2.741749 -1.264826 C -3.824235 2.726032 3.710954 H 3.484972 5.140598 -2.003626 C 4.308771 -0.951972 1.565729 H -4.599586 1.956006 3.712639 H 2.577065 3.809688 -2.739367 C -1.041774 -0.520977 2.757719 H -4.294557 3.709523 3.813514 P 3.716755 -0.249081 -0.010110 H -0.198578 -1.160460 2.969795 H -3.184257 2.565995 4.583427 C 4.319454 -0.920475 1.592100 C -3.822289 2.818041 1.181032 C -3.962241 2.488799 -3.782181 C 4.099723 -1.598007 -1.196457 C -3.858805 -2.515413 1.372241 H -3.355148 2.269916 -4.665351 C 5.011775 0.991662 -0.401847 C 3.505804 -1.101428 -2.542131 H -4.432067 3.466744 -3.930090 C 3.408706 -1.597305 2.399616 H 2.756954 -0.318997 -2.625927 H -4.740211 1.725115 -3.706909 C 5.642688 -0.809768 2.015575 C 4.151385 -1.289981 -1.321260 C 4.732229 -2.931373 -3.501100 C 3.339510 -1.679225 -2.359678 C -2.978341 2.653524 2.436871 H 4.957956 -3.571701 -4.347786 C 5.119453 -2.522943 -0.990489 C -3.180869 -2.419318 -2.387389 C 0.583545 5.553524 -0.524706 C 5.225758 2.030450 0.504142 C 5.658461 -1.051329 1.905551 H 0.200705 5.443449 -1.544053 C 5.751630 0.965358 -1.579521 H 6.413806 -0.612683 1.261733 H 1.032335 6.550564 -0.441273 H 2.380121 -1.687396 2.065168 C -5.239027 -2.664130 1.402622 H -0.266142 5.507775 0.164167 C 3.811834 -2.152632 3.604019 H -5.771380 -2.661829 2.345078 C -0.670726 -5.560397 0.233544 H 6.366958 -0.282931 1.403911 C -3.019602 -2.268406 2.620157 H -0.876156 -5.625234 1.305422 C 6.042703 -1.359840 3.224335 C -5.317153 -2.732358 -1.007753 H -0.388775 -6.563105 -0.109240 H 2.525629 -0.974752 -2.501224 H -5.909315 -2.782658 -1.912470 H -1.598596 -5.283767 -0.273255 C 3.604041 -2.653565 -3.309564 C -3.070460 2.492684 -2.537713 C -2.003890 3.575873 -2.705092 H 5.713454 -2.484174 -0.083599 C 3.803346 -1.908702 -3.628718 H -1.274961 3.554413 -1.892055 C 5.374897 -3.506738 -1.933849 H 3.298236 -1.746175 -4.575574 H -2.474308 4.563183 -2.726978 H 4.644981 2.069109 1.420896 C 2.124326 -4.778428 1.115288 H -1.465082 3.435669 -3.647863 C 6.172526 3.006533 0.248827 H 3.016051 -4.175719 0.919928 C -3.878245 -2.216070 3.887335 H 5.602092 0.166049 -2.297123 H 2.401209 -5.837613 1.053491 H -3.238347 -2.002374 4.748209 C 6.688932 1.955875 -1.843122 H 1.794471 -4.572548 2.138551 H -4.375116 -3.175653 4.065123 C 5.128778 -2.031779 4.021603 C -2.171555 -3.548020 -2.574127 H -4.631132 -1.427204 3.822743 H 3.091851 -2.681782 4.220406 H -1.673800 -3.454309 -3.544456 C 5.360740 -3.140882 -2.283109 H 7.075568 -1.261453 3.543231 H -2.677724 -4.517156 -2.543745 H 6.078488 -3.947596 -2.172798 H 3.006190 -2.703701 -4.214147 H -1.403338 -3.529864 -1.800111 C 6.976615 3.169931 -0.375774 C 4.621646 -3.571351 -3.096832 C 5.054008 1.154253 -0.165005 H 7.723740 3.952587 -0.457775 H 6.166795 -4.227843 -1.757832 C 6.044409 -1.689990 3.072989 C 5.808743 1.292302 -1.325423 C 6.907006 2.973691 -0.929614 H 7.097696 -1.759125 3.325849 H 5.659542 0.610354 -2.155271 H 6.331863 3.803585 0.968121 C -1.914775 3.752555 2.495671 C 6.228350 3.037705 0.786750 H 7.255389 1.924097 -2.768438 H -1.343520 3.678779 3.426697 H 6.387590 3.717314 1.617921 H 5.442586 -2.459788 4.968326 H -2.393621 4.735729 2.469135 C 2.577255 4.618277 1.574253 H 4.823051 -4.342323 -3.833657 H -1.211933 3.681827 1.661896 H 1.773095 4.654486 2.317093 H 7.644018 3.743268 -1.134525 C 1.410744 -4.735716 -1.858756 H 3.082037 5.591198 1.572042 H 0.644917 -4.568387 -2.621811 H 3.297083 3.859018 1.889501 Th7b’ SCF energy = -3882.5127809 H 1.743175 -5.777713 -1.935765 C 6.761237 2.297759 -1.429746 H 2.261975 -4.084991 -2.081551 H 7.340273 2.393347 -2.342816 Th -1.594302 0.085816 0.004210 C -4.121589 -2.413861 -3.595916 Pt 1.482266 0.425428 -0.001158 H -4.856635 -1.609409 -3.520752 Complex An6 (PBE functional) P 3.739863 -0.117058 0.030763 H -4.642710 -3.372155 -3.692348 Si 0.765830 -4.396666 -0.125938 H -3.537636 -2.254237 -4.506895 Hf6a SCF energy = -3584.6509688 Si 1.873551 4.236876 -0.128727 C -5.184112 3.087657 1.183337 Hf -1.641051 0.132627 -0.078740 N -3.128444 0.182074 2.217470 H -5.723448 3.205401 2.115056 Ni 1.460095 0.356410 0.027878 N -3.231140 0.047990 -2.146846 C -1.973137 -3.366550 2.796780 P 3.616490 -0.245017 0.072329 C -0.010476 1.902680 -0.081496 H -1.247949 -3.370252 1.980773 Si -0.100415 -4.033538 1.235199 C -3.192661 2.668331 -0.050264 H -2.460170 -4.344879 2.837760 Si 1.902382 4.130669 -0.119037 H -2.093728 2.592836 -0.067942 H -1.426369 -3.219091 3.733580 N -3.395625 -1.805114 -0.364514 C 0.783221 -1.421204 0.018446 C -5.869567 3.193035 -0.017687 N -2.940131 2.396124 -0.182968 C -3.232128 -2.523154 0.126347 H -6.935111 3.401642 -0.004768 C 0.632604 -1.249350 0.232515 H -2.135801 -2.545261 0.092326 C -5.227956 3.013262 -1.234118 C 0.035532 -2.328260 0.513020 C -1.175711 -0.720739 -2.717651 H -5.801005 3.073982 -2.151058 C -2.581308 1.205868 -2.728184 H -0.346259 -1.384448 -2.911516 C 5.272043 2.042894 0.887660 C -0.671852 -0.877075 -2.774153 C -1.146793 0.691221 -2.765817 H 4.690064 1.946852 1.799395 H 0.078777 -1.665265 -2.761166 H -0.292841 1.306800 -3.002987 C 5.077264 -2.321354 -1.199816 C 0.145767 1.763896 0.022770 C -2.486710 -1.071827 -2.369143 H 5.576947 -2.496366 -0.253342 301

Appendix

C -1.236151 0.954524 2.827520 H 7.713872 0.824803 -2.596926 H 2.669149 -0.055469 4.859939 H -0.341825 1.535399 3.045519 H 7.975019 2.576888 -2.640440 C 3.303406 4.380852 -1.368826 C -2.033976 -1.196100 -2.742873 C -5.051663 1.832379 -2.681867 H 4.256450 3.964964 -1.009424 C -3.477826 -2.693357 -1.437344 H -5.278026 1.290099 -3.616384 H 3.451669 5.461796 -1.532595 C -2.424844 1.593175 2.445775 H -5.724948 2.699289 -2.617754 H 3.070020 3.919894 -2.341834 C -1.197612 1.497810 -2.725599 H -5.279171 1.175993 -1.827774 H -0.864197 2.533223 -2.658662 C 5.887338 1.977922 -2.765835 C -4.353711 -2.240553 0.549776 H 5.871169 1.907783 -3.867298 Hf6b SCF energy = -3584.7093695 C -3.517480 -0.602313 2.194512 H 5.536756 2.993340 -2.511725 C -0.257111 0.466107 -2.770814 C -5.968757 -0.596953 1.511204 Hf 1.335040 0.063798 -0.022854 H 0.807792 0.701544 -2.754934 H -5.812283 0.079469 0.656754 Ni -1.495569 0.290732 0.057794 C 1.285144 2.372411 -0.045842 H -6.272258 0.001409 2.387749 Si -0.009752 -4.196800 0.602013 C -3.547485 0.794755 2.142309 H -6.800087 -1.266807 1.249317 Si -2.008088 4.026807 0.148981 H -4.457640 1.299657 1.826129 C -5.059480 -2.405686 2.969070 N 2.931155 0.369525 -2.045008 C -2.970289 3.355826 0.827414 H -5.933917 -3.019847 2.708803 N 3.330495 0.402527 1.671670 C -2.968864 -0.136542 -2.733356 H -5.306665 -1.828536 3.875103 C -0.152169 1.647431 0.144072 H -4.026093 -0.391878 -2.692506 H -4.230463 -3.089461 3.202007 C 2.791750 3.104979 -0.023690 C -1.186470 -0.446017 2.901483 C 7.327749 1.807224 -0.709773 H 1.763635 2.728116 0.006837 H -0.253788 -0.939423 3.174329 H 7.010298 2.805530 -0.352250 C -0.644132 -1.300134 0.072725 C -3.345885 3.066728 -1.335705 H 8.352497 1.649676 -0.331448 C 3.706012 -2.290745 -0.376397 C -2.303819 -1.215196 2.571287 C -1.265048 3.841510 2.621010 H 2.629379 -2.219931 -0.171230 H -2.235649 -2.302130 2.588532 H -0.981823 3.691946 3.677878 C 1.598534 -0.849157 2.480486 C -4.716281 -1.454486 1.798274 H -1.415021 4.919104 2.462224 H 0.982446 -1.692237 2.776818 C 3.874882 -1.957707 -0.681963 H -0.438552 3.514709 1.974517 C 1.230359 0.520610 2.572607 H 3.240108 -2.566707 -0.009359 C -3.670174 3.598214 3.238520 H 0.290276 0.910028 2.952867 C -2.565030 3.093526 2.273678 H -4.645773 3.138187 3.024791 C 2.918302 -0.878025 1.971456 C -3.593636 2.339303 -2.640785 H -3.785886 4.686577 3.130507 C 2.040288 1.406387 -2.233390 C 4.194975 -0.458262 1.856040 H -3.398860 3.383782 4.285834 C 2.252319 -0.800931 -2.335645 H 5.262373 -0.748724 1.830093 C -3.388903 3.281126 -3.848760 C -1.240357 2.332183 0.187535 C -2.575996 -2.614058 -2.663634 H -2.385384 3.730293 -3.853548 C 0.014626 -2.378829 0.173225 C -5.012860 -3.364717 0.068444 H -4.122967 4.099663 -3.815020 C 0.751608 0.889796 -2.507435 H -5.817177 -3.909139 0.559308 H -3.536248 2.731809 -4.792797 H -0.166562 1.449631 -2.654061 C -1.772792 -4.866628 0.989620 C 3.236799 -3.528648 -2.574302 C 4.583321 -2.260826 0.698909 H -2.631107 -4.221896 1.234703 H 2.570134 -4.130514 -1.931614 C 2.352542 1.260924 2.120344 H -1.818566 -5.766199 1.627216 H 2.818439 -3.574583 -3.595020 C 3.459704 3.268377 1.181965 H -1.911047 -5.185698 -0.053781 C 3.863643 -1.673152 4.062522 C 0.887830 -0.520558 -2.571859 C 4.950792 0.912615 -0.635736 H 3.269600 -2.452471 4.571076 H 0.095609 -1.231092 -2.787542 H 4.587644 1.897702 -0.286864 H 4.917569 -2.009513 4.099332 C 3.382856 3.292607 -1.264273 C -4.455960 -3.650249 -1.200358 C 0.259347 -3.946284 3.100959 C 4.116220 -2.320849 -1.703370 H -4.736066 -4.470755 -1.858315 H 1.225344 -3.456962 3.299865 C 2.558419 2.831208 -2.464999 C 3.420423 -1.557323 2.598402 H 0.308142 -4.972370 3.503971 C 3.978862 -1.981302 2.073819 H 2.341129 -1.325133 2.547523 H -0.519435 -3.409925 3.665673 C 5.480689 -2.488288 -1.958554 H 3.551581 -2.531557 2.098868 C 1.217890 -5.161105 0.470268 H 5.861130 -2.516447 -2.980887 C -3.374702 4.584434 0.320000 H 1.062280 -5.278550 -0.613762 C 3.039593 -2.045927 -2.750085 H -3.488889 5.511437 0.879227 H 1.156410 -6.161906 0.930934 C 5.947130 -2.426457 0.430281 C 4.926518 0.937487 -2.174808 H 2.235045 -4.771822 0.632890 H 6.683204 -2.410097 1.235758 H 5.226397 -0.054376 -2.556129 C 5.269671 -4.017975 -1.157553 C 2.739162 2.714298 2.411370 H 3.897602 1.119050 -2.531359 H 6.296136 -4.423605 -1.161915 C -1.517216 -4.991999 -0.224965 C 6.392586 0.739857 -0.123320 H 4.690613 -4.633225 -0.442903 H -2.463146 -4.546878 0.118741 H 6.426952 0.796827 0.975993 C 5.287506 -2.561213 -0.671272 H -1.535888 -6.067306 0.022946 H 6.776021 -0.257064 -0.399906 H 5.945816 -1.978748 -1.340648 H -1.465445 -4.896981 -1.320640 C 4.067033 0.879522 2.606529 H 5.732458 -2.507874 0.336971 C 3.377536 -3.273756 2.650543 H 4.653943 1.666876 2.104258 C 0.482348 5.262892 -0.651802 H 2.968113 -3.099811 3.659147 H 3.011071 1.206162 2.558676 H 0.224785 5.079375 -1.708096 H 4.159249 -4.045561 2.725240 C -1.449337 -3.663574 -2.601013 H 0.776932 6.322197 -0.558126 H 2.577532 -3.668666 2.012313 H -0.831116 -3.648605 -3.515618 H -0.430632 5.095173 -0.060513 C 1.381920 3.802610 -2.682430 H -1.896013 -4.664824 -2.514092 C 4.508368 0.762519 4.069985 H 0.809473 3.531173 -3.584554 H -0.797166 -3.501301 -1.729973 H 5.591087 0.535376 4.109742 H 1.765647 4.825872 -2.815268 C 3.238350 -2.077993 -2.079048 H 4.372064 1.732525 4.578295 H 0.695568 3.799558 -1.823320 H 2.210924 -1.681555 -2.032836 C 2.552560 4.644231 1.587663 C -0.235465 -4.406800 2.474832 H 3.791368 -1.457877 -2.804561 H 1.763998 4.588663 2.354292 H 0.628642 -4.059691 3.059486 C -3.398265 -2.889114 -3.948416 H 2.925408 5.681956 1.556618 H -0.382248 -5.477325 2.699085 H -4.251702 -2.202456 -4.043809 H 3.382041 3.991798 1.904850 H -1.126742 -3.861140 2.820878 H -3.794119 -3.915280 -3.927253 C 4.641921 -4.137022 -2.549172 C 5.043847 -1.467199 3.066133 H -2.760132 -2.788440 -4.841793 H 5.282638 -3.608216 -3.280972 H 5.549356 -0.575488 2.670241 C -3.609701 4.401882 -1.062343 H 4.609509 -5.193502 -2.865570 H 5.792149 -2.249445 3.271164 H -3.957218 5.155250 -1.765920 C 3.737667 -0.338812 4.800677 H 4.566459 -1.200812 4.022396 C 7.311383 1.792130 -2.239268 H 4.095684 -0.437334 5.839631 302

Appendix

C 4.678905 3.818760 -1.296137 C -3.805391 -2.386372 3.757869 H 3.290865 -2.566356 -0.009002 H 5.197562 3.986623 -2.241777 H -3.957967 -0.925452 -2.954304 C -2.520345 3.086220 2.277556 C 2.100790 -3.255185 -2.908262 H -2.355032 -1.343111 -2.327902 C -3.550422 2.331249 -2.636483 H 1.514700 -3.428432 -1.995813 C -3.486983 -3.020031 -3.145803 C 4.243970 -0.456910 1.856166 H 2.686860 -4.161169 -3.126422 H -5.791050 -2.498671 0.040011 H 5.311724 -0.746010 1.829657 H 1.397877 -3.093815 -3.741651 H -6.071661 -1.653750 -1.491529 C -2.526488 -2.620810 -2.660404 C 5.335949 4.098894 -0.093474 C -5.465396 -3.708531 -1.735965 C -4.961041 -3.374883 0.072794 H 6.348619 4.509655 -0.120873 H -5.554330 3.397654 -1.755822 H -5.764421 -3.920384 0.563993 C 4.751601 3.801379 1.142906 H -6.040152 2.625129 -3.272760 C -1.718608 -4.872772 0.992194 H 5.327320 3.954299 2.057560 C -7.385990 2.263550 -1.598783 H -2.577622 -4.229161 1.237775 C -3.401301 4.204577 1.422650 H -8.316466 1.804403 0.316054 H -1.762921 -5.772473 1.629709 H -4.283379 3.585659 1.200030 H -6.924126 2.894202 0.416698 H -1.856973 -5.191899 -0.051175 H -3.730893 5.256849 1.458236 H -4.108363 0.891472 4.892123 C 4.996807 0.915213 -0.635827 H -3.038996 3.929377 2.426437 H -5.407492 -0.141752 4.273631 H 4.632578 1.899797 -0.286662 C 6.379146 -2.571636 -0.890382 C -3.581465 -1.214084 4.715424 C -4.404406 -3.659561 -1.196317 H 7.445484 -2.696926 -1.095117 H -4.874033 -2.674374 3.779846 H -4.683793 -4.480348 -1.854229 C 3.401674 2.781928 -3.755093 H -3.237037 -3.271327 4.093400 C 3.471185 -1.557041 2.598785 H 4.272670 2.122683 -3.628552 C -4.913572 -3.576927 -3.157922 H 2.391571 -1.326219 2.548467 H 3.750688 3.791243 -4.026996 H -3.119553 -2.883800 -4.177616 H 3.603336 -2.531050 2.099075 H 2.793716 2.398459 -4.589637 H -2.817089 -3.756596 -2.666816 C -3.332881 4.576319 0.324450 C 3.664817 2.674242 3.645071 H -4.875271 -4.464998 -1.184784 H -3.447971 5.503112 0.883840 H 3.139572 2.212511 4.495884 H -6.505955 -4.075693 -1.758202 C 4.971739 0.940229 -2.174883 H 3.955383 3.695540 3.940753 H -7.866935 1.402307 -2.101104 H 5.272692 -0.051208 -2.556467 H 4.573562 2.089926 3.439285 H -8.022891 3.141510 -1.800243 H 3.942417 1.120523 -2.530904 C -0.758646 5.396187 0.554562 H -3.909224 -1.481076 5.734497 C 6.439073 0.744232 -0.124144 H -0.523737 5.430726 1.628995 H -2.497873 -0.997631 4.777331 H 6.473911 0.801120 0.975158 H -1.202077 6.368038 0.276641 H -5.566691 -2.896956 -3.738203 H 6.823640 -0.252168 -0.401034 H 0.187238 5.284759 0.002420 H -4.940712 -4.552867 -3.671794 C 4.114696 0.880625 2.606872 C 1.477860 -5.225817 0.033880 H 4.700354 1.668782 2.104401 H 1.361616 -5.523541 -1.019637 Th6a SCF energy = -3944.384093 H 3.058295 1.205925 2.559579 H 1.500007 -6.149072 0.638072 C -1.398462 -3.668898 -2.598461 H 2.453847 -4.731437 0.135842 Th -1.593761 0.126769 -0.075658 H -0.780714 -3.653037 -3.513370 C 1.502190 3.559566 2.754475 Ni 1.507150 0.354488 0.029451 H -1.843820 -4.670725 -2.511434 H 0.754649 3.517543 1.952046 P 3.664331 -0.244198 0.072766 H -0.746067 -3.505894 -1.727725 H 1.795914 4.609501 2.908053 Si -0.047172 -4.037581 1.237041 C 3.287460 -2.077409 -2.078634 H 1.030788 3.197492 3.683161 Si 1.944558 4.129324 -0.117250 H 2.259553 -1.682285 -2.031868 C 3.657822 -1.725913 -4.127540 N -3.346008 -1.813172 -0.360786 H 3.839329 -1.456506 -2.804349 H 2.863138 -1.458723 -4.841397 N -2.895773 2.388621 -0.178984 C -3.349042 -2.896766 -3.944810 H 4.190228 -2.603996 -4.527998 C 0.681805 -1.252348 0.234313 H -4.203399 -2.211184 -4.039702 H 4.360330 -0.882589 -4.058084 C 0.086247 -2.332049 0.514990 H -3.743578 -3.923438 -3.923569 C -2.647598 4.368433 -1.601703 C -2.536695 1.199114 -2.724513 H -2.711480 -2.795178 -4.838492 H -1.799623 4.458732 -2.299981 C -0.624612 -0.881391 -2.771666 C -3.568332 4.393626 -1.057797 H -3.210938 5.316375 -1.629802 H 0.127027 -1.668626 -2.759141 H -3.917156 5.146631 -1.761116 H -3.301793 3.565913 -1.970285 C 0.191029 1.760300 0.025155 C 7.355482 1.797915 -2.240426 P -3.647363 -0.273893 0.077235 C -1.188469 0.948849 2.830496 H 7.759025 0.831142 -2.598394 C -4.982417 1.008668 -0.358486 H -0.294776 1.530837 3.048119 H 8.017920 2.583563 -2.641836 C -4.150810 -0.783117 1.821609 C -1.986313 -1.202154 -2.739749 C -5.007823 1.822473 -2.676902 C -3.970516 -1.813907 -0.961315 C -3.427609 -2.701397 -1.433677 H -5.233958 1.280012 -3.611369 H -4.561348 1.917446 0.108291 C -2.378163 1.586029 2.449412 H -5.682179 2.688518 -2.612356 C -5.066059 1.286448 -1.869164 C -1.153371 1.492817 -2.722580 H -5.234072 1.165701 -1.822772 C -6.393606 0.801706 0.223968 H -0.821241 2.528646 -2.655689 C 5.930941 1.981954 -2.766267 H -5.231933 -1.016211 1.799279 C -4.303086 -2.249935 0.553928 H 5.914316 1.911920 -3.867729 C -3.921192 0.392646 2.788827 C -3.468127 -0.610819 2.198438 H 5.579193 2.996896 -2.511867 C -3.406849 -2.030352 2.319596 C -0.211580 0.462317 -2.768378 C -5.919747 -0.608503 1.516344 H -3.327443 -2.548855 -0.441190 H 0.853031 0.699108 -2.752998 H -5.764557 0.068216 0.661894 C -3.400361 -1.689711 -2.387457 C 1.329596 2.370273 -0.043951 H -6.223576 -0.010627 2.393107 C -5.401927 -2.371196 -0.984497 C -3.499937 0.786215 2.146410 H -6.750353 -1.279385 1.254791 H -4.056498 1.461018 -2.279644 H -4.410890 1.289994 1.830738 C -5.007446 -2.416243 2.973552 H -5.467786 0.396272 -2.384738 C -2.926653 3.348169 0.831523 H -5.881229 -3.031487 2.713648 C -5.987060 2.473533 -2.180959 C -2.922544 -0.143788 -2.729647 H -5.254917 -1.839511 3.879774 C -7.309867 1.992046 -0.095620 H -3.979427 -0.400475 -2.688304 H -4.177444 -3.098988 3.206001 H -6.843278 -0.116501 -0.191690 C -1.136969 -0.451636 2.904273 C 7.372586 1.812856 -0.710937 H -6.353194 0.666617 1.315998 H -0.203524 -0.943885 3.176601 H 7.054041 2.810716 -0.353143 H -2.850303 0.668864 2.751494 C -3.302951 3.058840 -1.331443 H 8.397721 1.656569 -0.333137 H -4.478263 1.285879 2.461104 C -2.253501 -1.222199 2.574542 C -1.221144 3.835819 2.624331 C -4.315756 0.036010 4.226586 H -2.183938 -2.309048 2.591629 H -0.937206 3.686496 3.681041 H -3.609352 -2.892366 1.662427 C -4.666038 -1.464473 1.802696 H -1.372568 4.913240 2.465743 H -2.319626 -1.841021 2.266115 C 3.924530 -1.956472 -0.681850 H -0.394553 3.510145 1.977392 303

Appendix

C -3.625652 3.589391 3.243003 C 0.264904 -1.663905 -0.204031 H -1.730660 -4.569386 -2.947771 H -4.600771 3.128146 3.029704 C 5.080527 -1.056563 -0.284883 C 0.793670 -5.358100 -0.186734 H -3.742804 4.677618 3.135172 H 4.561749 -1.989519 -0.002615 H 0.509571 -5.459467 0.871849 H -3.353547 3.375185 4.290158 C -2.429402 0.780514 2.444548 H 1.213962 -6.324947 -0.514020 C -3.347486 3.273469 -3.844452 C -1.115776 -0.480082 -2.918242 H -0.120444 -5.170949 -0.769443 H -2.344542 3.723914 -3.849685 H -0.169055 -0.916483 -3.225688 C 4.210065 3.428942 -2.589234 H -4.082575 4.091067 -3.810254 C -1.413023 0.907809 -2.833483 H 3.966276 3.484772 -3.664305 H -3.494599 2.724073 -4.788478 H -0.731959 1.722239 -3.066100 H 3.550225 4.154778 -2.080386 C 3.287511 -3.528008 -2.574053 C -3.434633 -3.056239 -1.422269 C -3.530926 -3.009004 3.582790 H 2.621931 -4.130796 -1.931105 C -1.071041 0.529278 2.731995 H -4.404388 -2.342346 3.536402 H 2.868704 -3.574359 -3.594569 H -0.301855 1.255393 2.981926 H -2.945307 -2.745840 4.477265 C 3.915277 -1.672472 4.062672 C 4.295700 1.877959 -0.578539 H -3.875372 -4.049509 3.698040 H 3.322478 -2.452605 4.571431 H 3.638690 2.576010 -0.026075 C 3.449274 -4.400727 0.853604 H 4.969648 -2.007495 4.098922 C -4.185040 2.207379 1.436368 H 4.381667 -3.833641 0.716594 C 0.313402 -3.950082 3.102632 C -2.294850 -1.158976 -2.538476 H 3.699433 -5.473578 0.789521 H 1.278874 -3.459553 3.301116 C -2.753576 1.000687 -2.401444 H 3.076848 -4.203014 1.871904 H 0.363703 -4.976151 3.505503 C 1.390762 -2.297160 -0.238185 C 6.236396 -2.326612 -2.163400 H -0.465782 -3.414779 3.667793 C -2.649175 -2.855006 2.326711 H 5.713443 -3.271021 -1.925292 C 1.272189 -5.163382 0.471328 C 4.029293 0.469124 2.008942 H 6.419334 -2.334744 -3.251724 H 1.116192 -5.280901 -0.612638 H 5.109941 0.651575 2.161849 C -2.333072 3.273104 2.794464 H 1.212211 -6.164313 0.931910 C -4.733619 -3.647632 1.009685 H -1.733163 3.186989 3.714586 H 2.288928 -4.772822 0.633491 H -5.270355 -3.858630 1.935251 H -2.932469 4.193846 2.861458 C 5.321705 -4.014908 -1.158367 C 0.082182 2.409987 -0.121034 H -1.640620 3.366214 1.947382 H 6.348683 -4.419230 -1.163283 C -4.410536 2.249605 -1.019166 C 7.559566 -2.282008 -1.396630 H 4.743785 -4.630976 -0.443501 C 6.414294 -1.020518 0.485339 H 8.136275 -1.391376 -1.712380 C 5.337926 -2.558180 -0.671928 H 6.240023 -1.032262 1.572690 H 8.178094 -3.161534 -1.643811 H 5.995162 -1.974801 -1.341562 H 6.957063 -0.086335 0.262892 C -4.708342 1.966634 -3.536659 H 5.783309 -2.504389 0.336101 C -5.579162 2.196822 1.543785 H -4.154712 1.884518 -4.484796 C 0.522820 5.259798 -0.649182 H -6.057301 2.137383 2.521438 H -5.408200 2.813326 -3.625575 H 0.264968 5.076074 -1.705370 C -1.458913 -3.824757 2.443451 H -5.277478 1.037279 -3.392117 H 0.816102 6.319467 -0.555531 H -1.815923 -4.865506 2.406205 C -1.208892 5.339241 0.186226 H -0.389653 5.090850 -0.057461 H -0.934698 -3.676115 3.401507 H -2.198657 4.948633 -0.090046 C 4.556904 0.764017 4.070096 H -0.737150 -3.673116 1.628868 H -1.085881 6.317218 -0.310737 H 5.639931 0.538248 4.109291 C 5.336895 -1.137912 -1.799595 H -1.206329 5.520035 1.271655 H 4.419617 1.733790 4.578584 H 4.377493 -1.198146 -2.342293 C 3.827834 -0.669918 4.278195 C 2.594927 4.643518 1.589187 H 5.836195 -0.213102 -2.139303 H 4.904658 -0.543779 4.502577 H 1.806816 4.586859 2.356200 C 5.750815 2.310379 -0.334909 H 3.509103 -1.598182 4.783024 H 2.966438 5.681721 1.558076 H 6.001505 2.255913 0.737973 C 2.779020 -4.185532 -2.191465 H 3.425395 3.992106 1.905889 H 6.434023 1.617170 -0.856675 H 1.946186 -4.145490 -2.912523 C 4.693418 -4.134595 -2.549688 C 5.664183 3.839305 -2.346409 H 3.293972 -5.152513 -2.319459 H 5.333099 -3.604891 -3.281745 H 6.336547 3.180917 -2.929492 H 3.482417 -3.380255 -2.448240 H 4.662195 -5.191080 -2.866192 H 5.838623 4.867124 -2.707688 C -2.965636 3.507407 -2.646136 C 3.787968 -0.338378 4.801043 C 3.259341 1.675271 2.569547 H -2.182649 3.685344 -1.898737 H 4.146624 -0.436563 5.839808 H 2.187011 1.557786 2.329427 H -3.670057 4.352945 -2.613961 H 2.719119 -0.056403 4.860866 H 3.586633 2.607060 2.080548 H -2.493514 3.490764 -3.641597 C 3.344644 4.381433 -1.367704 C -3.250756 2.049445 2.642081 C -3.562931 -2.726749 -3.946833 H 4.298394 3.966718 -1.008821 C 3.914888 2.017529 -2.064089 H -3.858153 -3.771001 -4.139862 H 3.491449 5.462583 -1.531422 H 2.847432 1.768246 -2.189245 H -2.997510 -2.367603 -4.820538 H 3.111363 3.920289 -2.340649 H 4.481622 1.292054 -2.671692 H -4.467844 -2.109613 -3.846925 C -4.737783 -3.562693 -1.421921 C 7.308866 -2.211614 0.110655 Th6b SCF energy = -3944.3923986 H -5.279015 -3.707484 -2.357506 H 8.263980 -2.143529 0.659527 C -6.373796 2.230389 0.398275 H 6.824018 -3.150034 0.441281 Th -1.497620 -0.029179 -0.081620 H -7.462201 2.219111 0.498282 C -4.033968 1.868170 3.959176 Ni 1.586836 -0.270293 -0.144452 C 6.015176 3.727615 -0.861387 H -4.693291 0.989390 3.912324 P 3.750609 0.227509 0.157080 H 5.406592 4.452114 -0.287145 H -4.637328 2.761960 4.187791 Si 2.106282 -4.008367 -0.428940 H 7.071345 3.998261 -0.689963 H -3.323589 1.717159 4.786424 Si 0.260036 4.254446 -0.336179 C -5.369236 -3.864749 -0.213856 C 3.446754 1.811882 4.086320 N -3.076459 -0.394666 2.132327 H -6.390265 -4.255230 -0.225738 H 4.506873 2.045755 4.303498 N -3.264991 -0.256144 -2.168706 C -2.679722 -2.626938 -2.685624 H 2.856001 2.667833 4.456243 C -2.801139 -2.888954 -0.184884 C -3.709782 2.190165 -2.381719 C 0.615620 4.623985 -2.163836 H -1.727497 -2.614494 -0.178124 C -5.801480 2.231169 -0.872993 H 1.369466 3.935921 -2.572847 C -3.427396 -3.148228 1.039760 H -6.448557 2.200081 -1.749617 H 0.994837 5.655004 -2.268279 C -0.899914 -0.877861 2.641277 C 3.637748 -0.813697 2.763951 H -0.292300 4.538287 -2.779390 H 0.023475 -1.425223 2.807338 H 2.578331 -1.038471 2.538163 C 3.056234 0.531571 4.827663 C 0.759599 1.331826 -0.109643 H 4.216827 -1.676852 2.396132 H 1.970920 0.353861 4.702972 C -3.632357 2.281773 0.148273 C -1.436197 -3.509745 -2.894840 H 3.235566 0.643517 5.910639 H -2.541299 2.426249 0.050205 H -0.709182 -3.381947 -2.080691 C 1.715216 4.861021 0.718540 C -2.163810 -1.409801 2.306416 H -0.935812 -3.248078 -3.841438 H 1.565996 4.596514 1.777528 304

Appendix

H 1.791658 5.959641 0.647561 H 6.801403 -0.137942 -0.189903 H 6.050965 -1.894115 -1.176459 H 2.673411 4.430596 0.390740 C 3.859825 0.772878 2.695121 H 5.734444 -2.483581 0.463720 H 4.423412 1.607975 2.247105 C 0.639709 5.351126 -0.119400 Pa6a SCF energy = -3978.081366 H 2.791203 1.045623 2.605222 H -0.329562 5.052573 -0.549616 C -1.501718 -3.548457 -2.765702 H 0.970693 6.282973 -0.609633 Pa -1.624638 0.138727 -0.060651 H -0.899593 -3.486249 -3.688897 H 0.474345 5.572022 0.945880 Ni 1.443009 0.298386 0.019288 H -1.979985 -4.538783 -2.743051 C 4.237046 0.627534 4.173752 P 3.595494 -0.285997 0.105530 H -0.829096 -3.468690 -1.899350 H 5.327126 0.454403 4.259194 Si -0.129708 -4.166796 0.923293 C 3.408312 -2.067979 -2.117905 H 4.026835 1.571105 4.706039 Si 1.956941 4.012655 -0.354297 H 2.363108 -1.717294 -2.137849 C 3.415742 4.442056 0.778873 N -3.343836 -1.747624 -0.393547 H 3.984506 -1.401572 -2.781618 H 3.120295 4.349229 1.836624 N -2.784814 2.438635 -0.033524 C -3.434322 -2.612473 -4.024417 H 3.723536 5.487040 0.604906 C 0.600652 -1.310404 0.129803 H -4.264374 -1.892445 -4.060988 H 4.295843 3.801236 0.615473 C 0.024611 -2.418270 0.315681 H -3.865462 -3.623860 -4.071816 C 4.929756 -4.055499 -2.542377 C -2.495384 1.349288 -2.578632 H -2.801711 -2.469461 -4.915880 H 5.602811 -3.477834 -3.204969 C -0.634270 -0.773686 -2.735596 C -3.437439 4.494899 -0.800295 H 4.963453 -5.100548 -2.894515 H 0.095464 -1.580081 -2.781823 H -3.787774 5.286026 -1.459880 C 3.491494 -0.536318 4.829881 C 0.138122 1.695049 0.102031 C 7.312311 2.035541 -1.908351 H 3.803570 -0.652032 5.881751 C -0.989608 0.809238 2.777789 H 7.808131 1.121897 -2.288865 H 2.407665 -0.311001 4.845093 H -0.081034 1.360364 3.012638 H 7.935085 2.888120 -2.228285 C 2.496020 4.061787 -2.172669 C -2.003398 -1.060220 -2.703387 C -4.952187 2.030017 -2.521612 H 3.193775 3.250152 -2.424293 C -3.477716 -2.581202 -1.506938 H -5.191615 1.520415 -3.471063 H 2.985874 5.023247 -2.401860 C -2.175953 1.492546 2.475083 H -5.605124 2.910286 -2.431254 H 1.617112 3.969008 -2.831855 C -1.106865 1.606879 -2.540489 H -5.192842 1.354542 -1.686122 H -0.750413 2.630142 -2.433782 C 5.911273 2.140464 -2.513990 Pa6b SCF energy = -3978.0829293 C -4.306684 -2.187198 0.514935 H 5.964858 2.140744 -3.616269 C -3.334380 -0.661664 2.165138 H 5.462270 3.107188 -2.220357 Pa -1.527984 -0.041374 -0.080106 C -0.187030 0.552413 -2.647077 C -5.827566 -0.569775 1.656109 Ni 1.526829 -0.274955 -0.139709 H 0.882946 0.762232 -2.629922 H -5.713960 0.143379 0.825040 P 3.691556 0.224539 0.150529 C 1.266926 2.317211 -0.002182 H -6.055870 -0.007975 2.578315 Si 2.042590 -4.009709 -0.371388 C -3.332341 0.734036 2.171940 H -6.690813 -1.209300 1.422026 Si 0.220042 4.259965 -0.341373 H -4.246217 1.273944 1.937085 C -4.865265 -2.465611 2.961717 N -3.000054 -0.363278 2.050795 C -2.755892 3.354856 1.019295 H -5.763565 -3.055729 2.727088 N -3.154120 -0.267131 -2.097109 C -2.916300 0.020285 -2.629357 H -5.046940 -1.929031 3.907380 C -2.776788 -2.855524 -0.184162 H -3.979099 -0.210964 -2.606881 H -4.033609 -3.169162 3.111257 H -1.711756 -2.535252 -0.159989 C -0.959187 -0.589279 2.741066 C 7.238889 1.970229 -0.382054 C -3.408187 -3.148355 1.028082 H -0.027250 -1.115920 2.939420 H 6.840713 2.928382 0.003354 C -0.847941 -0.903205 2.605029 C -3.212402 3.169633 -1.140705 H 8.247989 1.854501 0.049585 H 0.058140 -1.475290 2.781705 C -2.111020 -1.319853 2.409806 C -0.995215 3.713077 2.798068 C 0.700086 1.328124 -0.115075 H -2.067632 -2.405985 2.361652 H -0.696355 3.485004 3.836377 C -3.522894 2.276826 0.136841 C -4.579164 -1.464447 1.817966 H -1.141520 4.800260 2.721720 H -2.424456 2.365416 0.028760 C 3.938869 -1.968729 -0.675401 H -0.181771 3.429734 2.116227 C -2.118274 -1.405505 2.253344 H 3.278105 -2.614588 -0.064788 C -3.380534 3.442490 3.459115 C 0.201824 -1.649672 -0.184494 C -2.308177 3.000114 2.428160 H -4.366969 3.007745 3.242814 C 5.016262 -1.066841 -0.292238 C -3.482794 2.500286 -2.466898 H -3.488124 4.537097 3.433118 H 4.491280 -1.997824 -0.015124 C 4.094407 -0.530136 1.909793 H -3.081219 3.150468 4.479704 C -2.323960 0.799663 2.374191 H 5.175750 -0.763516 1.928202 C -3.252344 3.473205 -3.644274 C -1.016545 -0.493092 -2.880572 C -2.589824 -2.459210 -2.733671 H -2.234369 3.888619 -3.639354 H -0.070100 -0.929947 -3.187885 C -5.021116 -3.253773 -0.009861 H -3.959473 4.313768 -3.580413 C -1.312541 0.890776 -2.802273 H -5.837930 -3.788716 0.470829 H -3.420415 2.959865 -4.604942 H -0.631831 1.703376 -3.041555 C -1.834189 -4.939436 0.708096 C 3.506716 -3.500845 -2.656508 C -3.370477 -3.074028 -1.431581 H -2.658275 -4.291718 1.044653 H 2.818865 -4.150918 -2.087382 C -0.978092 0.504910 2.683260 H -1.869876 -5.878259 1.287039 H 3.168955 -3.527234 -3.707129 H -0.190488 1.209632 2.935500 H -2.037593 -5.182359 -0.344639 C 3.724395 -1.836364 4.057371 C 4.244024 1.870523 -0.591716 C 4.925672 0.928589 -0.505661 H 3.148567 -2.662336 4.509952 H 3.587862 2.573916 -0.044886 H 4.493650 1.889741 -0.171261 H 4.791821 -2.118389 4.136696 C -4.068133 2.265872 1.429467 C -4.492897 -3.502345 -1.300919 C 0.315345 -4.214796 2.771139 C -2.187373 -1.175518 -2.482226 H -4.818444 -4.274625 -1.995353 H 1.317137 -3.796875 2.953996 C -2.646881 0.993015 -2.351932 C 3.348219 -1.694735 2.576889 H 0.316725 -5.264735 3.110720 C 1.319888 -2.299839 -0.207172 H 2.261381 -1.522310 2.478196 H -0.404516 -3.666542 3.399143 C -2.652114 -2.829802 2.318183 H 3.559957 -2.642540 2.054768 C 1.125623 -5.261482 0.018449 C 3.982649 0.475612 1.999885 C -3.151488 4.609970 0.582291 H 0.942426 -5.269899 -1.067571 H 5.066035 0.646812 2.145412 H -3.223355 5.512538 1.186611 H 1.038860 -6.298508 0.385226 C -4.685241 -3.717060 0.978071 C 5.009310 0.993182 -2.040168 H 2.159147 -4.923373 0.191947 H -5.226709 -3.952812 1.895211 H 5.427210 0.046068 -2.425230 C 5.444167 -3.961401 -1.103662 C 0.043404 2.416895 -0.126753 H 3.998632 1.092413 -2.472880 H 6.482689 -4.329626 -1.040133 C -4.311463 2.279535 -1.022834 C 6.338703 0.821983 0.097685 H 4.836066 -4.619970 -0.454478 C 6.347386 -1.040772 0.483023 H 6.299477 0.836149 1.197942 C 5.368149 -2.521898 -0.576099 H 6.168932 -1.057098 1.569580 305

Appendix

H 6.895281 -0.107929 0.267431 C -4.622632 1.875586 -3.519303 C 3.319590 0.685459 2.198195 C -5.458450 2.346827 1.549237 H -4.073478 1.736988 -4.463476 C 0.222551 -0.566902 -2.693678 H -5.930429 2.335021 2.531897 H -5.321671 2.716550 -3.656358 H -0.847975 -0.775643 -2.684463 C -1.496417 -3.832043 2.493919 H -5.192467 0.957685 -3.315900 C -1.260316 -2.302087 -0.040325 H -1.885123 -4.862046 2.484363 C -1.266884 5.342493 0.137055 C 3.312399 -0.710592 2.229363 H -0.986333 -3.666306 3.456889 H -2.249420 4.919425 -0.116178 H 4.225985 -1.256820 2.006000 H -0.757029 -3.730298 1.687638 H -1.165435 6.299982 -0.402592 C 2.733578 -3.329346 1.066720 C 5.277820 -1.144895 -1.806283 H -1.264445 5.569613 1.213690 C 2.947601 -0.037691 -2.647297 H 4.320127 -1.200070 -2.352611 C 3.777814 -0.645761 4.278067 H 4.010757 0.192158 -2.610301 H 5.781675 -0.221050 -2.141591 H 4.856461 -0.528711 4.498589 C 0.946378 0.632026 2.764897 C 5.700648 2.294798 -0.342449 H 3.451499 -1.567476 4.790048 H 0.015240 1.165346 2.951719 H 5.944894 2.244472 0.732056 C 2.734002 -4.204229 -2.125073 C 3.208223 -3.169764 -1.094047 H 6.381899 1.593771 -0.856191 H 1.907775 -4.191755 -2.854564 C 2.101579 1.351184 2.445175 C 5.637647 3.812024 -2.362481 H 3.267662 -5.163562 -2.232092 H 2.062990 2.437694 2.386417 H 6.306711 3.143603 -2.937887 H 3.424512 -3.390232 -2.388779 C 4.566085 1.479891 1.836096 H 5.823266 4.835799 -2.729635 C -2.897210 3.481517 -2.711788 C -3.983660 1.961393 -0.666364 C 3.230303 1.694913 2.555638 H -2.117575 3.705206 -1.973850 H -3.324677 2.612576 -0.059326 H 2.156117 1.591969 2.317608 H -3.615029 4.316429 -2.717246 C 2.269322 -2.968353 2.470519 H 3.569918 2.619333 2.061304 H -2.426510 3.425041 -3.706586 C 3.506068 -2.518975 -2.425653 C -3.126947 2.069434 2.620395 C -3.470205 -2.679426 -3.945374 C -4.098332 0.513965 1.915385 C 3.869923 2.007552 -2.079112 H -3.768742 -3.714715 -4.177873 H -5.182442 0.732865 1.945320 H 2.800517 1.767870 -2.206754 H -2.896856 -2.293017 -4.802112 C 2.625244 2.442234 -2.754564 H 4.431299 1.274641 -2.682426 H -4.373494 -2.062643 -3.828636 C 5.013680 3.255936 0.000710 C -4.644189 -3.649493 -1.454930 C 7.238476 -2.233912 0.106522 H 5.824016 3.795842 0.486699 H -5.156194 -3.831896 -2.400668 H 8.191460 -2.172417 0.659863 C 1.814624 4.950135 0.673480 C -6.259405 2.410028 0.408609 H 6.748234 -3.171844 0.430478 H 2.632001 4.303832 1.028798 H -7.345429 2.470592 0.517110 C -3.902013 1.856647 3.937890 H 1.848943 5.897496 1.238408 C 5.979481 3.706782 -0.875049 H -4.584448 0.997532 3.862555 H 2.030254 5.176119 -0.380604 H 5.373286 4.439540 -0.308791 H -4.480181 2.755790 4.207543 C -4.936702 -0.948709 -0.496099 H 7.036803 3.969847 -0.698928 H -3.188292 1.656640 4.751756 H -4.488538 -1.905517 -0.170321 C -5.284789 -3.972612 -0.256485 C 3.422388 1.838210 4.071251 C 4.503904 3.491331 -1.300084 H -6.283486 -4.416401 -0.285605 H 4.485545 2.061477 4.284628 H 4.836673 4.259686 -1.995413 C -2.596622 -2.629104 -2.674106 H 2.842237 2.703100 4.437159 C -3.361027 1.687320 2.577152 C -3.619376 2.166830 -2.383159 C 0.629248 4.635347 -2.157478 H -2.273035 1.530310 2.466426 C -5.699699 2.352307 -0.867159 H 1.372739 3.930260 -2.555645 H -3.591519 2.633087 2.059270 H -6.354728 2.347554 -1.738722 H 1.040672 5.655939 -2.240894 C 3.139230 -4.586889 0.648947 C 3.581506 -0.797612 2.765491 H -0.264805 4.583048 -2.796390 H 3.207434 -5.482592 1.263763 H 2.519542 -1.013843 2.544212 C 3.019734 0.566941 4.821566 C -5.036342 -1.007680 -2.029900 H 4.150822 -1.668699 2.401443 H 1.932435 0.399475 4.700268 H -5.469370 -0.063792 -2.406099 C -1.368584 -3.530646 -2.892294 H 3.202513 0.684026 5.903428 H -4.029418 -1.093307 -2.474044 H -0.650372 -3.432622 -2.066883 C 1.648919 4.862993 0.750963 C -6.344081 -0.862639 0.123593 H -0.853816 -3.256885 -3.827836 H 1.474080 4.595549 1.805251 H -6.292104 -0.881545 1.223252 H -1.681573 -4.583331 -2.971928 H 1.728504 5.961626 0.684369 H -6.822134 0.092667 -0.154032 C 0.742415 -5.372094 -0.124759 H 2.613860 4.431430 0.444614 C -3.839453 -0.787298 2.695982 H 0.475128 -5.486924 0.936817 H -4.396636 -1.628800 2.251822 H 1.168315 -6.331438 -0.466642 U6a SCF energy = -4013.6300788 H -2.768394 -1.046349 2.595443 H -0.182333 -5.190576 -0.692059 C 1.535663 3.529939 -2.798306 C 4.180769 3.414134 -2.608733 U 1.644188 -0.141700 -0.073378 H 0.943587 3.467291 -3.727893 H 3.940632 3.468349 -3.684707 Ni -1.461245 -0.285969 0.000338 H 2.012468 4.520822 -2.770085 H 3.527041 4.148441 -2.104425 P -3.614845 0.279701 0.105372 H 0.854002 3.449134 -1.939078 C -3.565775 -2.908573 3.558547 Si 0.104209 4.188237 0.882204 C -3.469861 2.075256 -2.114068 H -4.425945 -2.230733 3.456979 Si -1.927969 -4.003697 -0.400267 H -2.419129 1.742039 -2.147373 H -2.997886 -2.613780 4.454593 N 3.344608 1.742066 -0.393079 H -4.042741 1.403002 -2.774804 H -3.931271 -3.936507 3.714319 N 2.765628 -2.425651 0.000257 C 3.489806 2.601691 -4.030950 C 3.376096 -4.378444 0.928222 C -0.618252 1.324450 0.099139 H 4.322207 1.883830 -4.056213 H 4.302708 -3.800048 0.800242 C -0.053807 2.435825 0.288970 H 3.918872 3.614201 -4.069680 H 3.640124 -5.448430 0.872327 C 2.525006 -1.366309 -2.579977 H 2.871643 2.459168 -4.932578 H 2.988588 -4.180628 1.940827 C 0.670567 0.759462 -2.777786 C 3.436953 -4.488437 -0.732996 C 6.174673 -2.335275 -2.171520 H -0.058603 1.565941 -2.831411 H 3.800438 -5.286257 -1.377220 H 5.648113 -3.278994 -1.939153 C -0.142377 -1.660588 0.070950 C -7.325177 -2.078488 -1.877209 H 6.361352 -2.339399 -3.259239 C 0.964304 -0.768001 2.798832 H -7.836304 -1.169059 -2.247462 C -2.195642 3.278659 2.801374 H 0.047619 -1.311922 3.018964 H -7.941157 -2.937003 -2.194409 H -1.595688 3.161847 3.718243 C 2.039860 1.041910 -2.739068 C 4.977644 -2.052634 -2.454635 H -2.784323 4.204180 2.893066 C 3.493960 2.566384 -1.512949 H 5.239499 -1.559471 -3.406770 H -1.504731 3.381254 1.954185 C 2.151729 -1.458616 2.521515 H 5.626748 -2.932190 -2.334944 C 7.495177 -2.298256 -1.399922 C 1.136238 -1.619769 -2.572512 H 5.201155 -1.363343 -1.625559 H 8.076027 -1.408103 -1.709366 H 0.774560 -2.641393 -2.462129 C -5.929918 -2.163413 -2.499054 H 8.111750 -3.178707 -1.648711 C 4.295123 2.192350 0.525543 H -5.995964 -2.159000 -3.600656 306

Appendix

H -5.465999 -3.126053 -2.215344 U 1.504007 0.060193 -0.027085 C -3.457723 4.174791 1.530652 C 5.810421 0.578286 1.678947 Ni -1.536704 0.305329 0.083583 H -4.352416 3.583493 1.284813 H 5.690448 -0.144745 0.857241 Si -0.142173 -4.194063 0.594066 H -3.764927 5.231898 1.604622 H 6.041048 0.026607 2.606651 Si -2.066217 4.016113 0.251464 H -3.103048 3.855287 2.523955 H 6.675075 1.211370 1.433164 N 2.802449 0.384788 -2.275868 C 6.218229 -2.439672 -0.949529 C 4.862754 2.492564 2.967109 N 3.347250 0.321516 1.855093 H 7.285358 -2.531211 -1.167756 H 5.764599 3.073768 2.724472 C -0.195228 1.662177 0.178663 C 3.215021 2.936429 -3.826209 H 5.042972 1.965327 3.918279 C 2.759926 2.879851 -0.030660 H 4.089513 2.270076 -3.796441 H 4.036431 3.203639 3.110707 H 1.708273 2.519059 0.036122 H 3.552998 3.967792 -4.016882 C -7.235229 -2.019785 -0.351538 C -0.692620 -1.296516 0.076210 H 2.575932 2.630661 -4.669128 H -6.820663 -2.974707 0.024491 C 3.527815 -2.223847 -0.400878 C 3.765280 2.739945 3.657547 H -8.240694 -1.918776 0.092114 H 2.443278 -2.283543 -0.176585 H 3.275118 2.341004 4.559180 C 0.943507 -3.669016 2.819695 C 1.582962 -0.875526 2.676316 H 4.056668 3.782292 3.865559 H 0.628552 -3.435813 3.852051 H 0.940737 -1.701152 2.969428 H 4.670415 2.145439 3.464599 H 1.082051 -4.757631 2.748884 C 1.264287 0.505003 2.776448 C -0.803517 5.359801 0.702962 H 0.143938 -3.380534 2.123465 H 0.336267 0.925069 3.155113 H -0.558871 5.345578 1.775782 C 3.322402 -3.424223 3.514946 C 2.887602 -0.945593 2.141268 H -1.240371 6.346728 0.471579 H 4.316112 -2.999241 3.312972 C 1.901293 1.420330 -2.400368 H 0.135808 5.263251 0.137074 H 3.418976 -4.519780 3.489596 C 2.109579 -0.782572 -2.538446 C 1.301653 -5.271970 -0.009438 H 3.011722 -3.130384 4.531575 C -1.314927 2.311649 0.233406 H 1.153101 -5.553096 -1.063683 C 3.301605 -3.511886 -3.591219 C -0.029774 -2.375975 0.192470 H 1.304492 -6.203026 0.582994 H 2.283410 -3.926799 -3.602081 C 0.607876 0.908522 -2.641606 H 2.297323 -4.815537 0.077141 H 4.006356 -4.351681 -3.498816 H -0.315528 1.471145 -2.741805 C 1.564102 3.542523 2.781122 H 3.491079 -3.014322 -4.556212 C 4.430942 -2.236582 0.671357 H 0.786333 3.429038 2.014388 C -3.597043 3.509214 -2.644467 C 2.396926 1.208023 2.306198 H 1.857507 4.602272 2.834007 H -2.912338 4.167146 -2.080594 C 3.446597 3.129891 1.160854 H 1.133044 3.258125 3.755167 H -3.271960 3.545445 -3.698757 C 0.742220 -0.498535 -2.734924 C 3.522562 -1.877046 -4.227943 C -3.723818 1.821368 4.061690 H -0.058301 -1.208645 -2.921561 H 2.731640 -1.686472 -4.969477 H -3.153523 2.653519 4.509921 C 3.272679 3.190321 -1.292327 H 4.065517 -2.784893 -4.538014 H -4.793765 2.090157 4.152358 C 3.937593 -2.247266 -1.742315 H 4.214677 -1.022282 -4.237754 C -0.356036 4.257191 2.725522 C 2.413468 2.851643 -2.510635 C -2.702176 4.425940 -1.486601 H -1.360333 3.843440 2.904451 C 3.888964 -2.095137 2.095480 H -1.853603 4.538376 -2.180650 H -0.357618 5.310431 3.054735 C 5.305550 -2.368524 -2.002580 H -3.260881 5.377055 -1.478424 H 0.357366 3.713500 3.364859 H 5.673701 -2.383305 -3.028694 H -3.360115 3.641235 -1.885248 C -1.138108 5.278114 -0.046051 C 2.883631 -2.060373 -2.834936 P -3.700347 -0.253508 0.087649 H -0.950588 5.266154 -1.131311 C 5.793429 -2.352341 0.375592 C -5.032078 1.041390 -0.328152 H -1.045463 6.320557 0.303447 H 6.534062 -2.357644 1.175843 C -4.220026 -0.793530 1.818505 H -2.174700 4.950224 0.128927 C 2.790218 2.669926 2.463457 C -4.030735 -1.770731 -0.982860 C -5.522049 3.934851 -1.066839 C -1.674721 -4.947348 -0.228677 H -4.609554 1.939621 0.157092 H -6.564738 4.288166 -0.988726 H -2.609756 -4.502963 0.144246 C -5.110453 1.349428 -1.833243 H -4.915030 4.598627 -0.421892 H -1.701420 -6.029329 -0.012116 C -6.446027 0.828986 0.245682 C -5.419169 2.494064 -0.547981 H -1.641638 -4.821637 -1.321945 H -5.302363 -1.019847 1.786466 H -6.099860 1.859733 -1.143845 C 3.248302 -3.416383 2.545544 C -3.987830 0.361788 2.809396 H -5.772895 2.445053 0.495680 H 2.888934 -3.336470 3.584399 C -3.486194 -2.054190 2.296343 C -0.587651 -5.323185 -0.191626 H 3.989474 -4.229334 2.499783 H -3.392698 -2.519548 -0.477088 H 0.364174 -5.017341 -0.654496 H 2.401897 -3.693252 1.906500 C -3.454416 -1.617579 -2.403764 H -0.920698 -6.264847 -0.661334 C 1.238430 3.845953 -2.586926 C -5.464563 -2.320462 -1.023407 H -0.385165 -5.528999 0.870111 H 0.637936 3.667828 -3.493982 H -4.098960 1.529475 -2.236551 C -4.204527 -0.649101 4.178377 H 1.621954 4.877176 -2.627181 H -5.512612 0.470857 -2.367981 H -5.295847 -0.489766 4.274313 H 0.579801 3.751296 -1.711807 C -6.027730 2.544421 -2.125609 H -3.977549 -1.590809 4.707056 C -0.357196 -4.434636 2.465310 C -7.358413 2.027326 -0.054555 C -3.366336 -4.462740 0.747606 H 0.521328 -4.124148 3.048603 H -6.897505 -0.080102 -0.187700 H -3.056555 -4.380758 1.802188 H -0.535322 -5.504141 2.670826 H -6.409599 0.673875 1.335159 H -3.667697 -5.508040 0.564553 H -1.228177 -3.868625 2.829407 H -2.915101 0.631757 2.781630 H -4.254108 -3.827444 0.605188 C 5.004563 -1.742212 3.103208 H -4.537966 1.264463 2.496291 C -5.026579 4.042455 -2.511153 H 5.530838 -0.825268 2.802696 C -4.391196 -0.019410 4.238397 H -5.699145 3.457724 -3.168017 H 5.729598 -2.566758 3.195593 H -3.691285 -2.902004 1.621939 H -5.079544 5.088301 -2.858543 H 4.559378 -1.574320 4.096244 H -2.397594 -1.870636 2.250793 C -3.467519 0.522957 4.829562 C 4.527688 3.805885 -1.352891 C -3.894153 -2.435260 3.725463 H -3.771238 0.633028 5.884494 H 4.979566 4.057376 -2.313480 H -4.004235 -0.836340 -2.954812 H -2.380875 0.311064 4.834556 C 1.936242 -3.271543 -2.895566 H -2.407344 -1.279162 -2.331024 C -2.489193 -4.049836 -2.212129 H 1.338101 -3.359066 -1.978393 C -3.547107 -2.928360 -3.194870 H -3.200317 -3.245790 -2.450263 H 2.513334 -4.198837 -3.032596 H -5.857162 -2.469850 -0.003183 H -2.969480 -5.016157 -2.441229 H 1.242841 -3.171047 -3.746009 H -6.129602 -1.588288 -1.515368 H -1.619887 -3.941652 -2.881643 C 5.220453 4.090368 -0.174468 C -5.532904 -3.639323 -1.806675 H 6.201366 4.569571 -0.231664 H -5.595063 3.459379 -1.681047 U6b SCF energy = -4013.6313541 C 4.694890 3.752993 1.075254 H -6.076509 2.717220 -3.214534 H 5.276574 3.962671 1.974028 C -7.429217 2.326674 -1.552654 307

Appendix

H -8.366832 1.834861 0.350574 H 1.774852 5.954173 1.151972 H -3.391166 3.516189 -3.709424 H -6.972050 2.919074 0.475286 H 1.918129 5.218624 -0.464645 C -3.667477 1.803049 4.053611 H -4.181555 0.821885 4.921200 C -4.942013 -1.004288 -0.451604 H -3.136050 2.670284 4.482637 H -5.484235 -0.191269 4.277309 H -4.479653 -1.964043 -0.154460 H -4.748578 2.005571 4.177932 C -3.667025 -1.283273 4.706601 C 4.466216 3.516876 -1.317008 C -0.433714 4.353663 2.683549 H -4.964939 -2.716027 3.736707 H 4.790430 4.282700 -2.019079 H -1.447993 3.971569 2.874947 H -3.333898 -3.330606 4.046893 C -3.343988 1.688133 2.558223 H -0.399381 5.406581 3.012031 C -4.977080 -3.476004 -3.223726 H -2.252995 1.603358 2.411106 H 0.268197 3.787648 3.315993 H -3.176557 -2.769147 -4.222344 H -3.652028 2.615637 2.047840 C -1.244315 5.356834 -0.089455 H -2.882895 -3.681017 -2.733070 C 3.141406 -4.567383 0.735599 H -1.061940 5.336775 -1.175611 H -4.947755 -4.411746 -1.272735 H 3.213599 -5.449279 1.369801 H -1.146189 6.400988 0.253276 H -6.575281 -4.000635 -1.840441 C -5.107897 -1.039676 -1.980934 H -2.281356 5.033899 0.092291 H -7.909998 1.475684 -2.072348 H -5.530912 -0.080404 -2.325970 C -5.586727 3.872296 -1.029300 H -8.063765 3.209506 -1.740164 H -4.122669 -1.144829 -2.467131 H -6.632037 4.211128 -0.926335 H -4.000994 -1.567668 5.719024 C -6.318087 -0.924027 0.235663 H -4.974081 4.544805 -0.398785 H -2.582386 -1.074990 4.776937 H -6.210292 -0.979101 1.330552 C -5.452425 2.433632 -0.511576 H -5.624597 -2.777592 -3.788259 H -6.797603 0.043335 0.012630 H -6.143677 1.791124 -1.084937 H -5.009202 -4.438700 -3.761904 C -3.669735 -0.812087 2.697656 H -5.774800 2.384012 0.542313 H -4.192683 -1.685404 2.272406 C -0.567957 -5.344276 -0.317620 Np6a SCF energy = -4051.1276833 H -2.590287 -1.011306 2.559999 H 0.221946 -5.171341 -1.066220 C 1.522300 3.477925 -2.847973 H -1.001776 -6.343140 -0.496815 Np 1.674553 -0.142076 -0.083669 H 0.935000 3.389741 -3.778461 H -0.079817 -5.348016 0.666569 Ni -1.439487 -0.279156 -0.074902 H 1.986453 4.475204 -2.836908 C -3.993501 -0.690695 4.190949 P -3.605385 0.238936 0.096955 H 0.838442 3.404810 -1.989270 H -5.088643 -0.596194 4.322453 Si -0.000323 4.265679 0.834422 C -3.531994 2.040269 -2.124359 H -3.694098 -1.615679 4.713076 Si -1.920907 -4.031638 -0.448147 H -2.474329 1.732395 -2.179462 C -3.305848 -4.466176 0.773121 N 3.336579 1.757758 -0.400304 H -4.103592 1.358349 -2.776027 H -2.939426 -4.403614 1.810634 N 2.757031 -2.424826 0.036612 C 3.499782 2.555693 -4.051276 H -3.665201 -5.494554 0.601157 C -0.647998 1.370023 0.038907 H 4.343711 1.850819 -4.056015 H -4.168871 -3.788478 0.680738 C -0.175791 2.517494 0.239038 H 3.912978 3.574227 -4.104787 C -5.126527 3.985905 -2.484347 C 2.571569 -1.400875 -2.549563 H 2.892047 2.386371 -4.955272 H -5.805049 3.390849 -3.125681 C 0.696395 0.697315 -2.784231 C 3.464315 -4.491392 -0.644006 H -5.202583 5.030511 -2.831127 H -0.040458 1.495730 -2.850936 H 3.849326 -5.297444 -1.265001 C -3.307721 0.525836 4.815699 C -0.143872 -1.673924 0.047098 C -7.412888 -2.065148 -1.748492 H -3.583708 0.621581 5.879574 C 0.921124 -0.719608 2.747969 H -7.919640 -1.133685 -2.066185 H -2.210615 0.380346 4.786775 H 0.000971 -1.264955 2.948483 H -8.062326 -2.899957 -2.061935 C -2.571559 -4.084347 -2.226280 C 2.061110 0.996249 -2.749501 C 5.025642 -2.055014 -2.352547 H -3.380111 -3.357945 -2.392672 C 3.479951 2.566572 -1.530485 H 5.311090 -1.575717 -3.305020 H -2.954417 -5.089575 -2.470062 C 2.122100 -1.407095 2.531342 H 5.682987 -2.922521 -2.195512 H -1.759766 -3.852758 -2.935181 C 1.185849 -1.672419 -2.561331 H 5.211414 -1.346362 -1.530401 H 0.836151 -2.697203 -2.440544 C -6.049886 -2.162541 -2.434981 Np6b SCF energy = -4051.1297292 C 4.267068 2.235674 0.522501 H -6.162860 -2.127605 -3.532221 C 3.283651 0.734950 2.187668 H -5.600950 -3.145264 -2.198273 Np -1.556635 -0.064927 -0.077741 C 0.262981 -0.635024 -2.699129 C 5.780607 0.637190 1.701911 Ni 1.541128 -0.299592 -0.133218 H -0.805199 -0.855911 -2.698971 H 5.667136 -0.100624 0.892260 P 3.719085 0.203584 0.148479 C -1.230498 -2.340043 -0.105546 H 6.011075 0.102269 2.639534 Si 2.013027 -4.012398 -0.360114 C 3.285797 -0.659723 2.256765 H 6.642280 1.271452 1.448981 Si 0.298433 4.300188 -0.342697 H 4.209827 -1.202954 2.071396 C 4.808240 2.554984 2.967301 N -3.020773 -0.355186 2.101441 C 2.718735 -3.306470 1.122278 H 5.709918 3.139611 2.732085 N -3.185851 -0.248808 -2.148837 C 2.980819 -0.069691 -2.637604 H 4.979596 2.034689 3.923891 C -2.809795 -2.829082 -0.187934 H 4.041068 0.172890 -2.596169 H 3.976055 3.261998 3.096281 H -1.745066 -2.503418 -0.164496 C 0.899028 0.680805 2.693576 C -7.246610 -2.055748 -0.228215 C -3.436610 -3.132124 1.024820 H -0.039195 1.212654 2.844704 H -6.825956 -3.026783 0.096134 C -0.851556 -0.908596 2.571135 C 3.233172 -3.182248 -1.033445 H -8.226377 -1.956154 0.269826 H 0.052277 -1.489909 2.726209 C 2.058332 1.398219 2.396414 C 0.914303 -3.612125 2.867542 C 0.699249 1.330086 -0.101527 H 2.016416 2.482250 2.316614 H 0.591259 -3.358510 3.892521 C -3.495103 2.278328 0.139920 C 4.530617 1.533432 1.838896 H 1.054001 -4.702164 2.821514 H -2.393417 2.321662 0.029887 C -4.013836 1.916374 -0.665834 H 0.118656 -3.337782 2.159970 C -2.141901 -1.398825 2.261657 H -3.348619 2.573047 -0.071974 C 3.289192 -3.349591 3.575866 C 0.179227 -1.640899 -0.183433 C 2.242881 -2.917394 2.515196 H 4.283370 -2.926027 3.374128 C 5.035259 -1.100234 -0.278881 C 3.560411 -2.540642 -2.362605 H 3.389199 -4.445062 3.572368 H 4.503126 -2.025570 0.003801 C -4.027580 0.468680 1.923878 H 2.970017 -3.037056 4.584281 C -2.325876 0.797310 2.393224 H -5.120358 0.623385 1.990836 C 3.402500 -3.544020 -3.525838 C -1.020220 -0.494838 -2.846044 C 2.626669 2.405833 -2.779440 H 2.391411 -3.974601 -3.561522 H -0.073675 -0.944412 -3.133173 C 4.971576 3.305026 -0.008827 H 4.117793 -4.371903 -3.409125 C -1.301329 0.891722 -2.764620 H 5.766649 3.866530 0.477996 H 3.609385 -3.049640 -4.488806 H -0.605821 1.699200 -2.975543 C 1.717603 5.003204 0.594988 C -3.693560 3.473554 -2.648649 C -3.402538 -3.054750 -1.435117 H 2.530996 4.348513 0.942904 H -3.006205 4.139231 -2.097520 C -0.970273 0.499546 2.657002 308

Appendix

H -0.173112 1.200861 2.886519 H -3.024640 -2.618201 4.455103 N -3.242402 -1.884032 -0.400527 C 4.273511 1.837787 -0.615105 H -3.959869 -3.935875 3.708240 N -2.901769 2.348179 -0.191653 H 3.618517 2.549827 -0.078023 C 3.332975 -4.384057 0.951839 C 0.707141 -1.333144 0.264917 C -4.039125 2.295842 1.432921 H 4.261857 -3.807271 0.833776 C 0.318240 -2.481382 0.582281 C -2.219069 -1.161228 -2.496174 H 3.595236 -5.454551 0.898067 C -2.482542 1.172405 -2.704296 C -2.652422 1.000735 -2.362928 H 2.935499 -4.186359 1.960625 C -0.502418 -0.840513 -2.706710 C 1.299322 -2.295259 -0.200847 C 6.190346 -2.394423 -2.141961 H 0.273761 -1.602714 -2.682940 C -2.680445 -2.822042 2.317616 H 5.654242 -3.331259 -1.903425 C 0.143471 1.729957 0.102717 C 4.007217 0.474607 1.994769 H 6.381389 -2.409881 -3.228771 C -1.198153 0.916284 2.792174 H 5.092490 0.632612 2.140749 C -2.149356 3.275948 2.798928 H -0.325932 1.522065 3.030264 C -4.709631 -3.710055 0.974807 H -1.547596 3.151766 3.713711 C -1.851382 -1.207254 -2.717843 H -5.247210 -3.952741 1.892429 H -2.720486 4.212641 2.888558 C -3.261769 -2.774455 -1.474132 C 0.126364 2.457214 -0.130133 H -1.460587 3.362805 1.948087 C -2.404175 1.522669 2.419479 C -4.284013 2.318598 -1.018660 C 7.507936 -2.361862 -1.365175 C -1.112814 1.511651 -2.661812 C 6.363449 -1.076855 0.501403 H 8.098043 -1.480039 -1.680798 H -0.818513 2.558187 -2.583008 H 6.180808 -1.081603 1.587381 H 8.117499 -3.250142 -1.602990 C -4.196194 -2.356782 0.493621 H 6.919056 -0.150065 0.278880 C -4.609706 1.940517 -3.518244 C -3.426052 -0.697514 2.132521 C -5.425009 2.432761 1.553889 H -4.065556 1.793863 -4.464170 C -0.136901 0.514727 -2.686337 H -5.895624 2.443814 2.537261 H -5.285835 2.801030 -3.648453 H 0.919193 0.788901 -2.651416 C -1.527892 -3.829153 2.486260 H -5.203175 1.036623 -3.320329 C 1.188960 2.463344 0.062200 H -1.920460 -4.857717 2.474723 C -1.186985 5.369607 0.160784 C -3.502034 0.697241 2.101983 H -1.013409 -3.667882 3.447689 H -2.166451 4.947158 -0.105472 H -4.431072 1.176370 1.801323 H -0.791365 -3.728499 1.677273 H -1.087406 6.339765 -0.355999 C -2.962509 3.299732 0.828184 C 5.302660 -1.192944 -1.791179 H -1.187281 5.570090 1.242570 C -2.823791 -0.182929 -2.727817 H 4.347420 -1.244372 -2.342057 C 3.785391 -0.616770 4.285697 H -3.872443 -0.475166 -2.727739 H 5.816014 -0.276313 -2.131777 H 4.865628 -0.512700 4.504885 C -1.101439 -0.481798 2.836939 C 5.731524 2.260277 -0.370672 H 3.445654 -1.527473 4.808380 H -0.154124 -0.950444 3.102550 H 5.974033 2.225275 0.704881 C 2.715397 -4.200384 -2.109755 C -3.326511 3.008206 -1.336775 H 6.410609 1.548519 -0.872435 H 1.894301 -4.176015 -2.844704 C -2.193537 -1.278959 2.493768 C 5.674786 3.748131 -2.412939 H 3.240421 -5.164247 -2.218305 H -2.093706 -2.363715 2.491604 H 6.340699 3.068691 -2.979002 H 3.415583 -3.391599 -2.363464 C -4.598942 -1.582987 1.733996 H 5.864721 4.765697 -2.794723 C -2.843041 3.495874 -2.697983 C 3.982827 -1.922404 -0.651724 C 3.271428 1.710979 2.534881 H -2.057577 3.691182 -1.957757 H 3.371910 -2.531409 0.042493 H 2.195791 1.621631 2.298413 H -3.539039 4.349096 -2.693859 C -2.591511 3.021297 2.278657 H 3.624766 2.624253 2.029710 H -2.373819 3.437218 -3.693430 C -3.531380 2.273981 -2.643925 C -3.104484 2.083853 2.626593 C -3.503862 -2.671357 -3.951885 C 4.251727 -0.314986 1.816600 C 3.899078 1.955533 -2.104289 H -3.801126 -3.707799 -4.180727 H 5.331186 -0.557160 1.782691 H 2.828124 1.721043 -2.228392 H -2.930935 -2.287287 -4.810082 C -2.338688 -2.645650 -2.675998 H 4.456407 1.211837 -2.697962 H -4.407025 -2.054361 -3.836694 C -4.794028 -3.511894 0.002898 C -4.672159 -3.639208 -1.457447 C 7.245989 -2.280776 0.139556 H -5.575743 -4.095984 0.484822 H -5.182797 -3.825762 -2.403124 H 8.197273 -2.221910 0.696009 C -1.501360 -4.994821 0.987352 C -6.224587 2.524351 0.414267 H 6.746484 -3.211284 0.470732 H -2.368239 -4.340808 1.171018 H -7.307308 2.627318 0.523778 C -3.885098 1.896875 3.944708 H -1.597047 -5.889864 1.625615 C 6.016683 3.662844 -0.924156 H -4.587741 1.054071 3.872302 H -1.568594 -5.318285 -0.061998 H 5.414263 4.406719 -0.368465 H -4.441138 2.811275 4.209291 C 4.898898 1.009243 -0.737864 H 7.075246 3.923465 -0.752110 H -3.176986 1.683616 4.760225 H 4.487927 1.980148 -0.403569 C -5.310200 -3.966392 -0.258927 C 3.465443 1.869400 4.048718 C -4.197766 -3.776025 -1.253705 H -6.306097 -4.416467 -0.287297 H 4.531639 2.080195 4.259612 H -4.426913 -4.608762 -1.916101 C -2.630446 -2.615140 -2.680981 H 2.897428 2.746654 4.403900 C 3.539323 -1.423868 2.606652 C -3.597983 2.196310 -2.381354 C 0.679169 4.673792 -2.164183 H 2.449725 -1.243707 2.571079 C -5.668011 2.447486 -0.861874 H 1.417474 3.970464 -2.574853 H 3.704922 -2.406633 2.135238 H -6.322980 2.472352 -1.733201 H 1.087833 5.695060 -2.252093 C -3.400421 4.519537 0.326234 C 3.587100 -0.783926 2.774989 H -0.225006 4.620873 -2.788487 H -3.552608 5.436722 0.892516 H 2.521690 -0.986770 2.557503 C 3.044396 0.613083 4.813945 C 4.835640 0.996708 -2.275685 H 4.143236 -1.667805 2.421300 H 1.954960 0.459564 4.694051 H 5.197418 0.020753 -2.644503 C -1.403664 -3.519690 -2.894935 H 3.228530 0.740555 5.894354 H 3.788800 1.096679 -2.611996 H -0.687423 -3.423631 -2.067489 C 1.743551 4.896895 0.730917 C 6.360728 0.934270 -0.259266 H -0.885728 -3.248201 -3.829409 H 1.583623 4.626662 1.786809 H 6.419026 1.007672 0.838156 H -1.718991 -4.571790 -2.973659 H 1.822436 5.995703 0.666474 H 6.800006 -0.039540 -0.534778 C 0.706048 -5.369567 -0.128788 H 2.703830 4.466017 0.409116 C 4.076613 1.039318 2.525819 H 0.426096 -5.485229 0.929314 H 4.618656 1.835016 1.987489 H 1.132571 -6.329731 -0.467581 Pu6a SCF energy = -4090.6041606 H 3.006724 1.317832 2.490198 H -0.211408 -5.183584 -0.706317 C -1.174976 -3.652972 -2.594719 C 4.216100 3.353224 -2.653179 Pu -1.679224 0.117471 -0.098094 H -0.532652 -3.602658 -3.491558 H 3.975633 3.393581 -3.729641 Ni 1.462824 0.340513 0.023169 H -1.586619 -4.671229 -2.533336 H 3.565860 4.097112 -2.158534 P 3.651363 -0.196221 0.032437 H -0.554378 -3.477809 -1.703095 C -3.593506 -2.907469 3.557783 Si 0.154543 -4.166057 1.334893 C 3.370959 -2.141055 -2.047003 H -4.452257 -2.227439 3.460362 Si 1.809986 4.218151 0.028839 H 2.321733 -1.805163 -2.031652 309

Appendix

H 3.898347 -1.527036 -2.796434 H 1.649717 4.644956 2.506106 C 5.754508 2.079502 -0.433842 C -3.117894 -2.936050 -3.983683 H 2.800257 5.761083 1.724849 H 5.985841 2.097652 0.644628 H -3.992913 -2.279370 -4.093592 H 3.278919 4.075332 2.059950 H 6.408770 1.313223 -0.885636 H -3.477116 -3.976030 -3.982387 C 4.890571 -4.143230 -2.400104 C 5.777626 3.446301 -2.559583 H -2.462036 -2.802161 -4.859738 H 5.511001 -3.618576 -3.152094 H 6.419216 2.707741 -3.077718 C -3.632077 4.335906 -1.056721 H 4.916988 -5.214265 -2.663379 H 6.013386 4.431013 -2.997880 H -3.992011 5.084305 -1.759611 C 3.843757 -0.122499 4.762960 C 3.290368 1.769701 2.485123 C 7.151581 2.015145 -2.412799 H 4.226099 -0.171987 5.796608 H 2.212767 1.731305 2.245108 H 7.611348 1.073722 -2.770367 H 2.765203 0.115385 4.835474 H 3.695093 2.638136 1.941276 H 7.747866 2.838778 -2.840637 C 3.219718 4.482365 -1.207372 C -2.952786 2.186717 2.608579 C -4.972037 1.722536 -2.704063 H 4.174383 4.068226 -0.849562 C 3.925289 1.749314 -2.167598 H -5.166777 1.172868 -3.641387 H 3.362752 5.565974 -1.358181 H 2.845942 1.556179 -2.287416 H -5.674436 2.567011 -2.650130 H 2.990522 4.032242 -2.186357 H 4.454286 0.949889 -2.712754 H -5.188580 1.058371 -1.853132 C -4.870761 -3.447377 -1.325468 C 5.704920 2.093489 -2.904901 Pu6b SCF energy = -4090.6079354 H -5.422293 -3.604111 -2.253170 H 5.666885 2.006607 -4.004469 C -6.043197 2.672016 0.365442 H 5.288669 3.084544 -2.652981 Pu -1.623990 -0.083051 -0.073918 H -7.124874 2.794228 0.465238 C -5.872592 -0.764146 1.430354 Ni 1.481038 -0.314821 -0.148402 C 6.102930 3.434298 -1.064710 H -5.722565 -0.080810 0.580117 P 3.668069 0.129531 0.172087 H 5.528359 4.234313 -0.559872 H -6.206088 -0.176855 2.303547 Si 1.892884 -4.118659 -0.443085 H 7.170158 3.659971 -0.896485 H -6.679983 -1.457922 1.155131 Si 0.592015 4.432413 -0.403942 C -5.494063 -3.714886 -0.105305 C -4.925190 -2.539907 2.904235 N -2.990566 -0.272744 2.178332 H -6.521260 -4.089046 -0.098402 H -5.776426 -3.183647 2.637100 N -3.205095 -0.185005 -2.184005 C -2.802818 -2.601814 -2.630413 H -5.200831 -1.967034 3.804745 C -2.910481 -2.768071 -0.123095 C -3.401869 2.288259 -2.408966 H -4.076010 -3.193998 3.149828 H -1.823635 -2.524086 -0.135230 C -5.477001 2.585486 -0.905864 C 7.208393 2.051739 -0.884443 C -3.523278 -3.016095 1.112550 H -6.123430 2.623105 -1.782840 H 6.837653 3.032295 -0.529344 C -0.816177 -0.893587 2.533214 C 3.476016 -0.726471 2.838063 H 8.251099 1.965121 -0.533538 H 0.073492 -1.504249 2.648729 H 2.401453 -0.883160 2.628390 C -1.330743 3.805974 2.683870 C 0.755746 1.388933 -0.169419 H 3.986065 -1.652733 2.524108 H -1.078165 3.640098 3.745987 C -3.314167 2.377899 0.114927 C -1.635558 -3.580676 -2.850906 H -1.511701 4.881766 2.544398 H -2.212093 2.402330 0.014450 H -0.889795 -3.503019 -2.047772 H -0.471839 3.521484 2.061100 C -2.137902 -1.341978 2.312043 H -1.131325 -3.364533 -3.806880 C -3.740403 3.472091 3.219249 C 0.147731 -1.686721 -0.195557 H -2.011160 -4.615052 -2.889175 H -4.696357 2.993631 2.962748 C 4.937397 -1.242846 -0.173435 C 0.548777 -5.430801 -0.161872 H -3.881293 4.559935 3.136788 H 4.370274 -2.128057 0.163451 H 0.293869 -5.520792 0.905235 H -3.496565 3.235211 4.268404 C -2.239785 0.858947 2.404931 H 0.936754 -6.408852 -0.495844 C -3.337383 3.218011 -3.851456 C -1.044741 -0.608479 -2.815799 H -0.377333 -5.225412 -0.718278 H -2.345637 3.692853 -3.845776 H -0.128244 -1.133933 -3.067235 C 4.305768 3.098400 -2.791866 H -4.093431 4.017138 -3.829230 C -1.216245 0.796450 -2.751516 H 4.075586 3.086671 -3.871289 H -3.457902 2.662442 -4.795533 H -0.452662 1.545347 -2.940935 H 3.683774 3.895512 -2.346573 C 3.455355 -3.613264 -2.468519 C -3.559897 -2.962515 -1.350052 C -3.589643 -2.812130 3.653164 H 2.813677 -4.216237 -1.801684 C -0.881926 0.520983 2.592441 H -4.422315 -2.096163 3.594831 H 3.050901 -3.732439 -3.488598 H -0.050003 1.199360 2.756789 H -2.978519 -2.557685 4.533008 C 4.014835 -1.472941 4.064173 C 4.283057 1.701326 -0.670127 H -3.992129 -3.826860 3.804185 H 3.464635 -2.260638 4.607642 H 3.648902 2.463542 -0.179185 C 3.238445 -4.541929 0.827432 H 5.083015 -1.762158 4.090314 C -3.871313 2.409514 1.403967 H 4.205699 -4.054243 0.639445 C 0.406616 -4.024850 3.212616 C -2.299807 -1.173158 -2.493391 H 3.408164 -5.632199 0.812633 H 1.366602 -3.538576 3.448270 C -2.567202 1.014301 -2.393895 H 2.908029 -4.267527 1.842578 H 0.418544 -5.034892 3.656534 C 1.215799 -2.397012 -0.251359 C 6.042832 -2.683638 -1.957545 H -0.395409 -3.455230 3.707764 C -2.716100 -2.747329 2.384172 H 5.473650 -3.585184 -1.666043 C 1.528079 -5.286738 0.663903 C 3.960069 0.473688 2.004610 H 6.231379 -2.768990 -3.041594 H 1.421761 -5.437476 -0.421980 H 5.051569 0.582106 2.148500 C -1.937912 3.332887 2.746193 H 1.466778 -6.274921 1.150938 C -4.837167 -3.495086 1.106217 H -1.336364 3.198415 3.659655 H 2.529380 -4.871708 0.859597 H -5.361682 -3.689564 2.042447 H -2.462066 4.298016 2.819020 C 5.494949 -3.921677 -1.011253 C 0.407551 2.597717 -0.207263 H -1.250241 3.368503 1.890110 H 6.542335 -4.268665 -0.986261 C -4.094588 2.433817 -1.051472 C 7.362299 -2.652902 -1.183740 H 4.942631 -4.531366 -0.271241 C 6.265992 -1.223673 0.607261 H 7.982332 -1.812220 -1.550213 C 5.426498 -2.443912 -0.600632 H 6.083369 -1.163789 1.691647 H 7.939897 -3.574412 -1.369273 H 6.055849 -1.859804 -1.295975 H 6.854092 -0.330486 0.336433 C -4.411062 2.150105 -3.566873 H 5.859281 -2.314153 0.405516 C -5.255851 2.568306 1.512099 H -3.863826 1.996041 -4.509739 C 0.384201 5.336887 -0.511990 H -5.734103 2.591037 2.491402 H -5.018697 3.063400 -3.674126 H 0.147722 5.163052 -1.574596 C -1.591595 -3.791886 2.507443 H -5.073914 1.286848 -3.411728 H 0.665733 6.397792 -0.398316 H -2.017985 -4.806972 2.507986 C -0.875167 5.486961 0.176208 H -0.536342 5.149667 0.061175 H -1.038759 -3.650391 3.450436 H -1.856973 5.097119 -0.129974 C 4.550835 0.987582 3.982821 H -0.879416 -3.712949 1.674437 H -0.758205 6.490400 -0.268294 H 5.643193 0.809738 4.006822 C 5.200742 -1.432247 -1.677095 H -0.880952 5.607207 1.269591 H 4.381263 1.966457 4.463237 H 4.243478 -1.478086 -2.224676 C 3.682086 -0.502330 4.340392 C 2.441500 4.718129 1.744541 H 5.748788 -0.556837 -2.068371 H 4.766199 -0.443980 4.557233 310

Appendix

H 3.295684 -1.369693 4.902817 H -0.187003 -0.998075 3.157185 H 6.983224 3.018295 -0.392219 C 2.537114 -4.339354 -2.211439 C -3.403603 3.035726 -1.255581 H 8.370743 1.917572 -0.412710 H 1.696995 -4.283476 -2.922925 C -2.216550 -1.337874 2.521556 C -1.361614 3.745041 2.735346 H 3.020283 -5.323473 -2.332532 H -2.107150 -2.422000 2.507264 H -1.095077 3.570728 3.792481 H 3.262537 -3.560610 -2.488536 C -4.602018 -1.663680 1.720685 H -1.539802 4.822591 2.605480 C -2.522917 3.517911 -2.679349 C 4.028052 -1.868469 -0.701849 H -0.512717 3.461015 2.097742 H -1.729033 3.612048 -1.927515 H 3.413211 -2.491814 -0.023854 C -3.766794 3.413770 3.303820 H -3.132908 4.434397 -2.658619 C -2.632604 2.968314 2.342414 H -4.726094 2.937007 3.056349 H -2.047928 3.440226 -3.670544 C -3.647618 2.325200 -2.572875 H -3.907879 4.502641 3.237354 C -3.714034 -2.640817 -3.874486 C 4.304831 -0.348058 1.834414 H -3.506626 3.163369 4.345507 H -4.079002 -3.663326 -4.064677 H 5.383471 -0.594631 1.808378 C -3.533192 3.305427 -3.761518 H -3.142612 -2.316524 -4.757918 C -2.367474 -2.587298 -2.729045 H -2.554450 3.805730 -3.789328 H -4.574094 -1.965948 -3.755100 C -4.783120 -3.562816 -0.052829 H -4.307651 4.083602 -3.687357 C 7.106751 -2.475420 0.313846 H -5.561371 -4.160776 0.417500 H -3.680694 2.768768 -4.712425 H 8.061058 -2.415716 0.865124 C -1.428664 -5.013561 0.889689 C 3.424325 -3.472384 -2.570559 H 6.578536 -3.368024 0.699800 H -2.302304 -4.372837 1.087829 H 2.777511 -4.080975 -1.913469 C -3.742374 2.076791 3.929017 H -1.524750 -5.932078 1.493532 H 2.998712 -3.544000 -3.586480 H -4.477722 1.260465 3.885113 H -1.481697 -5.298268 -0.171737 C 4.025338 -1.566535 4.044075 H -4.261170 3.021737 4.159519 C 4.998341 1.047671 -0.668195 H 3.464214 -2.367602 4.555876 H -3.044436 1.863858 4.753356 H 4.603222 2.015452 -0.305051 H 5.092402 -1.858742 4.081432 C 3.489691 1.984737 3.991269 C -4.196937 -3.788523 -1.313809 C 0.432815 -4.072228 3.167143 H 4.564995 2.150264 4.196297 H -4.437370 -4.594557 -2.004328 H 1.383988 -3.581717 3.428177 H 2.966706 2.904553 4.305687 C 3.575306 -1.476186 2.580352 H 0.446537 -5.090571 3.591563 C 0.902034 4.862286 -2.227043 H 2.486945 -1.293339 2.529861 H -0.382907 -3.519710 3.659154 H 1.604462 4.160302 -2.698941 H 3.748427 -2.445500 2.084365 C 1.612159 -5.267695 0.610467 H 1.330094 5.877091 -2.296492 C -3.491217 4.513520 0.436389 H 1.526154 -5.394615 -0.480210 H -0.030311 4.852329 -2.810943 H -3.658404 5.411815 1.028005 H 1.555578 -6.267480 1.073761 C 3.004958 0.786684 4.810620 C 4.945090 1.083650 -2.206233 H 2.604262 -4.844020 0.832862 H 1.909206 0.683132 4.695229 H 5.282005 0.109431 -2.601992 C 5.482553 -3.887126 -1.164381 H 3.195079 0.952867 5.884738 H 3.903217 1.222288 -2.543890 H 6.521207 -4.260176 -1.174001 C 2.081339 5.010764 0.619765 C 6.453826 0.926593 -0.180258 H 4.929689 -4.511293 -0.437066 H 1.957993 4.740061 1.680288 H 6.503833 0.971174 0.919192 C 5.459568 -2.425215 -0.694228 H 2.168122 6.108915 0.553333 H 6.871245 -0.050930 -0.476360 H 6.093635 -1.828976 -1.374973 H 3.025930 4.573380 0.261528 C 4.124006 0.987619 2.578290 H 5.909637 -2.346924 0.310128 H 4.681036 1.794537 2.072822 C 0.365573 5.293264 -0.524708 Am6a SCF energy = -4132.1441824 H 3.056297 1.272916 2.531198 H 0.100741 5.110718 -1.579025 C -1.172602 -3.560447 -2.672558 H 0.632403 6.359162 -0.423603 Am -1.672060 0.115242 -0.058924 H -0.550033 -3.489762 -3.581640 H -0.534157 5.095360 0.077533 Ni 1.525298 0.343298 -0.014229 H -1.553123 -4.590482 -2.605943 C 4.570150 0.893063 4.041940 P 3.729570 -0.166115 0.050361 H -0.539637 -3.368017 -1.792860 H 5.661135 0.709728 4.081301 Si 0.213789 -4.179126 1.283453 C 3.389053 -2.015531 -2.095419 H 4.395312 1.858860 4.546270 Si 1.823228 4.200061 -0.018138 H 2.349846 -1.650364 -2.052710 C 2.464314 4.692739 1.695857 N -3.239431 -1.916032 -0.418038 H 3.924448 -1.389661 -2.829407 H 1.678817 4.598100 2.461788 N -2.951797 2.362326 -0.131429 C -3.161780 -2.894758 -4.023753 H 2.807225 5.741083 1.685810 C 0.753829 -1.331524 0.240166 H -4.059429 -2.265326 -4.109651 H 3.313053 4.058163 1.997564 C 0.373012 -2.481019 0.561493 H -3.484545 -3.946700 -4.029140 C 4.845775 -4.041697 -2.548457 C -2.591508 1.235343 -2.721819 H -2.526936 -2.727492 -4.909239 H 5.465454 -3.506030 -3.293271 C -0.580887 -0.738863 -2.861818 C -3.733471 4.358629 -0.940607 H 4.839777 -5.102896 -2.850077 H 0.210899 -1.485592 -2.888850 H -4.117111 5.114843 -1.621929 C 3.844273 -0.235563 4.776771 C 0.193181 1.696752 0.100224 C 7.288598 2.042790 -2.298830 H 4.206084 -0.314939 5.815941 C -1.244245 0.861720 2.848881 H 7.725808 1.098852 -2.677389 H 2.765220 0.004021 4.834605 H -0.376728 1.470770 3.096646 H 7.910218 2.860828 -2.700550 C 3.209772 4.491015 -1.272655 C -1.921065 -1.131792 -2.785311 C -5.083502 1.755566 -2.572976 H 4.170141 4.076345 -0.931278 C -3.261848 -2.769798 -1.511599 H -5.313052 1.225929 -3.513633 H 3.346778 5.576382 -1.415179 C -2.451531 1.464149 2.472265 H -5.795596 2.586639 -2.463900 H 2.969870 4.048050 -2.252359 C -1.229226 1.597876 -2.779443 H -5.247305 1.066264 -1.730573 H -0.948091 2.649867 -2.718444 C 5.848591 2.173200 -2.798581 Am6b SCF energy = -4132.1454156 C -4.182149 -2.411369 0.466619 H 5.816145 2.117548 -3.900336 C -3.451290 -0.762809 2.152802 H 5.457500 3.168393 -2.523436 Am -1.576737 -0.056612 -0.081064 C -0.241734 0.622064 -2.871773 C -5.886216 -0.861062 1.416317 Ni 1.557458 -0.305405 -0.170844 H 0.809016 0.915674 -2.899805 H -5.736416 -0.158109 0.582267 P 3.734221 0.171136 0.187564 C 1.237745 2.432743 0.019081 H -6.237918 -0.297073 2.297625 Si 1.951257 -4.223377 -0.498544 C -3.543344 0.631604 2.145305 H -6.679750 -1.561080 1.117601 Si 0.610805 4.448220 -0.477525 H -4.474209 1.105672 1.840356 C -4.927598 -2.648545 2.868287 N -3.036375 -0.317404 2.222735 C -3.019779 3.280120 0.903585 H -5.767221 -3.298303 2.579992 N -3.324262 -0.198307 -2.186614 C -2.910755 -0.124760 -2.736032 H -5.219687 -2.096935 3.776722 C -2.886538 -2.826989 -0.122734 H -3.951991 -0.436861 -2.669494 H -4.072334 -3.295958 3.110508 H -1.805993 -2.585628 -0.151611 C -1.136503 -0.536304 2.885839 C 7.333547 2.038522 -0.769659 C -3.484840 -3.062350 1.122718 311

Appendix

C -0.831881 -0.868248 2.552635 C 3.504365 -0.638785 2.861874 H -0.112588 4.665226 -2.880818 H 0.074266 -1.456481 2.661770 H 2.432668 -0.803154 2.642631 C 3.002159 0.904504 4.803348 C 0.834714 1.408634 -0.181689 H 4.022838 -1.567684 2.569878 H 1.908401 0.793226 4.677805 C -3.449590 2.355423 0.153955 C -1.644074 -3.539641 -2.872114 H 3.179819 1.089538 5.876442 H -2.352551 2.417105 0.039718 H -0.889463 -3.445129 -2.078741 C 2.135922 5.076917 0.459407 C -2.147790 -1.354078 2.329601 H -1.159468 -3.300885 -3.832828 H 2.064017 4.835502 1.531685 C 0.261150 -1.707574 -0.240382 H -1.987010 -4.585363 -2.913769 H 2.202663 6.173746 0.358413 C 5.001627 -1.210063 -0.115245 C 0.599319 -5.531441 -0.264037 H 3.069883 4.642813 0.070831 H 4.435937 -2.087447 0.247131 H 0.259561 -5.577796 0.781798 C -2.312923 0.832503 2.436716 H 1.011733 -6.520241 -0.529529 Complex An7 (PBE functional) C -1.151239 -0.554706 -2.841261 H -0.278147 -5.345811 -0.900983 H -0.228387 -1.057981 -3.115738 C 4.336077 3.082123 -2.832719 Hf7a SCF energy = -3573.8993164 C -1.359686 0.840897 -2.767843 H 4.104580 3.047992 -3.911254 H -0.622912 1.613547 -2.970143 H 3.700820 3.876117 -2.399906 Hf -1.538702 0.138290 0.004599 C -3.565813 -2.989974 -1.338210 C -3.516263 -2.903906 3.668256 Ni 1.565029 0.381596 0.014485 C -0.940519 0.537492 2.624708 H -4.369519 -2.211023 3.640052 Si 0.193602 -4.159553 0.727318 H -0.131292 1.242628 2.793434 H -2.897306 -2.649375 4.542635 Si 2.085366 4.083265 -0.391439 C 4.338076 1.725620 -0.686904 H -3.885967 -3.933469 3.803304 N -3.302682 -1.779348 -0.278864 H 3.698231 2.492731 -0.211116 C 3.275227 -4.612659 0.800423 N -2.826740 2.395031 0.140933 C -3.990281 2.346005 1.449719 H 4.211615 -4.053747 0.658426 C 0.746918 -1.239661 0.121853 C -2.392726 -1.154224 -2.500806 H 3.518414 -5.687973 0.756072 C 0.179865 -2.355095 0.284768 C -2.714113 1.015235 -2.385211 H 2.895631 -4.393891 1.811739 C -2.670592 1.373295 -2.496588 C 1.233035 -2.522625 -0.297100 C 6.114400 -2.694047 -1.858035 C -0.767273 -0.695466 -2.813619 C -2.666860 -2.784653 2.386694 H 5.548065 -3.590035 -1.544526 H -0.016161 -1.479466 -2.897853 C 3.993494 0.550911 2.015967 H 6.305986 -2.807145 -2.938934 C 0.241974 1.783955 0.054744 H 5.082187 0.669535 2.173852 C -2.058799 3.317549 2.753975 C -0.888136 0.764310 2.920582 C -4.806395 -3.519467 1.136093 H -1.438318 3.204720 3.657550 H 0.024663 1.327566 3.106813 H -5.318350 -3.706418 2.080574 H -2.603238 4.271550 2.827754 C -2.125970 -1.020340 -2.709072 C 0.489044 2.613847 -0.236838 H -1.385768 3.364841 1.886751 C -3.459612 -2.606442 -1.391759 C -4.246240 2.387475 -1.001669 C 7.431740 -2.637770 -1.081950 C -2.096007 1.429318 2.665415 C 6.328582 -1.163175 0.666541 H 8.049984 -1.805425 -1.469694 C -1.291284 1.670647 -2.581810 H 6.143869 -1.071455 1.748372 H 8.012628 -3.562040 -1.241164 H -0.953574 2.701508 -2.477689 H 6.913112 -0.275984 0.369280 C -4.589153 2.140261 -3.518324 C -4.173132 -2.286970 0.685131 C -5.379090 2.442224 1.576427 H -4.050414 2.018978 -4.470866 C -3.219656 -0.746152 2.361106 H -5.844586 2.431501 2.561971 H -5.219400 3.041113 -3.597584 C -0.357308 0.647958 -2.760871 C -1.501436 -3.787283 2.478636 H -5.228298 1.257813 -3.373458 H 0.703967 0.893575 -2.807871 H -1.890611 -4.817324 2.469791 C -0.851094 5.464213 0.172396 C 1.374230 2.386636 -0.087736 H -0.941745 -3.639469 3.416559 H -1.836029 5.073979 -0.122796 C -3.244855 0.652339 2.401421 H -0.801745 -3.670219 1.639074 H -0.757263 6.484687 -0.237382 H -4.173286 1.177382 2.187750 C 5.265990 -1.439646 -1.613088 H -0.829443 5.543334 1.269600 C -2.756782 3.292082 1.205131 H 4.309096 -1.505483 -2.159274 C 3.690918 -0.388796 4.362754 C -3.056172 0.031759 -2.562280 H 5.808922 -0.571827 -2.027709 H 4.772099 -0.322231 4.591489 H -4.107684 -0.230388 -2.461163 C 5.806417 2.120970 -0.460569 H 3.301195 -1.248614 4.934168 C -0.845487 -0.638537 2.907951 H 6.040155 2.160965 0.616840 C 2.635046 -4.405058 -2.254099 H 0.099109 -1.150731 3.088180 H 6.466972 1.352969 -0.900548 H 1.811296 -4.330134 -2.982642 C -3.314137 3.138786 -0.933184 C 5.803366 3.455352 -2.609571 H 3.118080 -5.387910 -2.385140 C -1.985637 -1.384871 2.608880 H 6.453153 2.719219 -3.120832 H 3.369731 -3.623327 -2.496411 H -1.919053 -2.470740 2.546254 H 6.023356 4.437253 -3.061970 C -2.715995 3.527264 -2.631477 C -4.447387 -1.572203 1.997442 C 3.306636 1.849389 2.465201 H -1.916361 3.632214 -1.886409 C -2.233365 2.939265 2.592931 H 2.231540 1.795481 2.217501 H -3.344987 4.430256 -2.592425 C -3.673092 2.493067 -2.254923 H 3.708276 2.711861 1.909235 H -2.249925 3.473456 -3.628525 C -2.666034 -2.440540 -2.682949 C -3.050278 2.147515 2.641804 C -3.769381 -2.675917 -3.861549 C -4.848265 -3.397372 0.197164 C 3.978497 1.738379 -2.184686 H -4.109829 -3.709286 -4.038930 H -5.598178 -3.987115 0.720482 H 2.902494 1.526079 -2.301242 H -3.218883 -2.342474 -4.754882 C -1.513068 -4.958380 0.795176 H 4.521777 0.937868 -2.714523 H -4.644123 -2.021879 -3.734928 H -2.112573 -4.589959 1.642212 C -4.884164 -3.452661 -1.292183 C 7.172586 -2.420507 0.409828 H -1.391282 -6.047544 0.924646 H -5.456703 -3.586690 -2.210489 H 8.125465 -2.343471 0.961243 H -2.106302 -4.779270 -0.113698 C -6.185368 2.524795 0.441717 H 6.645028 -3.303101 0.819156 C -4.395633 -3.598466 -1.128680 H -7.269969 2.598162 0.556345 C -3.816445 2.032312 3.975493 H -4.716772 -4.386017 -1.807965 C 6.136747 3.468804 -1.116216 H -4.527818 1.194358 3.951601 C -3.179616 4.553691 0.806264 H 5.557051 4.270329 -0.619874 H -4.358739 2.964865 4.202909 H -3.230722 5.446813 1.426558 H 7.202394 3.708380 -0.957945 H -3.100223 1.848193 4.791079 C -1.541988 -3.487678 -2.786895 C -5.488422 -3.723570 -0.063826 C 3.489532 2.091405 3.969414 H -1.006082 -3.412091 -3.749201 H -6.521132 -4.081479 -0.040540 H 4.561551 2.267190 4.182992 H -1.977830 -4.495200 -2.721472 C -2.842075 -2.603179 -2.631037 H 2.957362 3.012957 4.262238 H -0.816012 -3.374981 -1.968995 C -3.568497 2.276292 -2.370117 C 0.818677 4.838008 -2.321227 C -3.596083 -2.629924 -3.908338 C -5.631737 2.477598 -0.836976 H 1.606572 4.220866 -2.777780 H -4.453877 -1.942543 -3.883604 H -6.289944 2.495676 -1.705665 H 1.095597 5.898758 -2.446455 H -3.990439 -3.656772 -3.922758 312

Appendix

H -3.037085 -2.466214 -4.844433 C 6.749016 1.750285 -1.985009 H 1.869007 -4.480391 1.986737 C -3.531211 4.457807 -0.560244 C 5.084464 -1.893296 4.128472 C -2.446465 -3.489445 -2.663704 H -3.921530 5.256865 -1.186706 H 2.972902 -2.075814 4.551701 H -1.933094 -3.317247 -3.623696 C -5.128775 1.980884 -2.202921 H 7.106953 -1.596369 3.422611 H -3.076677 -4.386235 -2.767045 H -5.435190 1.497576 -3.146941 H 2.939128 -2.586886 -4.310836 H -1.687180 -3.692977 -1.897894 H -5.794503 2.837924 -2.026021 C 4.338013 -3.697547 -3.091259 C 5.069577 1.070047 -0.107808 H -5.280660 1.270404 -1.375592 H 5.680843 -4.584614 -1.648969 C 5.919226 -1.980819 3.008398 C -5.711269 -0.697150 1.843972 C 7.109182 2.731173 -1.061103 H 6.974820 -2.167817 3.220451 H -5.607617 0.029227 1.022996 H 6.719903 3.560442 0.899286 C -1.647880 3.812056 2.567071 H -5.953448 -0.151526 2.772501 H 7.259409 1.691600 -2.949550 H -1.085845 3.603942 3.492223 H -6.561569 -1.349115 1.598227 H 5.395595 -2.272065 5.105014 H -2.095862 4.813561 2.657981 C -4.717114 -2.587302 3.132820 H 4.478114 -4.490525 -3.829603 H -0.937451 3.823834 1.727724 H -5.611086 -3.183468 2.898314 H 7.901149 3.445677 -1.296907 C 1.205701 -4.523326 -1.998158 H -4.898936 -2.061806 4.084546 H 0.394784 -4.331378 -2.716776 H -3.878418 -3.285007 3.270370 Hf7b SCF energy = -3573.9590612 H 1.516840 -5.575894 -2.112337 C -0.901026 3.662569 2.869246 H 2.059837 -3.880787 -2.262034 H -0.528098 3.450010 3.886646 Hf -1.253174 0.087117 0.007660 C -4.270482 -1.982586 -3.459127 H -1.060228 4.747706 2.789933 Ni 1.543579 0.445563 0.015778 H -4.945840 -1.150371 -3.214940 H -0.134526 3.378073 2.134014 P 3.662429 -0.136580 0.036561 H -4.869033 -2.873762 -3.707979 C -3.247557 3.390035 3.677060 Si 0.674220 -4.214853 -0.207458 H -3.688817 -1.707361 -4.352984 H -4.240988 2.944383 3.522653 Si 2.018739 4.144196 -0.077271 C -4.919017 3.532608 1.098493 H -3.364880 4.483010 3.641865 N -2.980978 0.289882 1.923255 H -5.479437 3.676476 2.023981 H -2.888298 3.115130 4.682960 N -3.080992 0.178646 -1.845402 C -2.025823 -3.270022 2.914222 C -3.571171 3.508718 -3.414766 C 0.147524 1.751255 -0.083286 H -1.328314 -3.425799 2.080114 H -2.571451 3.962313 -3.476278 C -2.935479 2.962746 -0.098138 H -2.573153 -4.208632 3.090942 H -4.299498 4.319975 -3.268346 H -1.873074 2.689863 -0.087276 H -1.437570 -3.041370 3.817848 H -3.798057 3.018163 -4.375232 C 0.778638 -1.205025 0.036805 C -5.561717 3.718672 -0.129983 C 0.984940 -4.334587 2.444391 C -3.350146 -2.502816 0.184893 H -6.608797 4.032273 -0.143219 H 2.016228 -3.949585 2.452666 H -2.261259 -2.372334 0.115738 C -4.912383 3.451278 -1.340228 H 1.012485 -5.399811 2.731121 C -1.119030 -0.798585 -2.503052 H -5.468394 3.532867 -2.275906 H 0.409880 -3.797950 3.217072 H -0.359563 -1.540458 -2.731397 C 5.360217 1.886760 0.996868 C 1.277514 -5.080763 -0.522492 C -0.957387 0.610073 -2.580058 H 4.782877 1.775929 1.918519 H 0.839038 -5.065167 -1.532277 H -0.056921 1.138621 -2.878058 C 4.875433 -2.379306 -1.319345 H 1.388218 -6.134970 -0.216063 C -2.455717 -1.026008 -2.099369 H 5.358793 -2.644173 -0.376807 H 2.279423 -4.627195 -0.580642 C -2.154243 1.368325 2.166811 C 3.386227 4.254878 -1.374474 C 0.662791 5.260068 -0.816247 C -2.267509 -0.845905 2.259868 H 4.193466 3.531501 -1.190534 H 0.206453 4.991974 -1.783228 C 1.213484 2.466736 -0.100802 H 3.823498 5.267573 -1.374812 H 1.028153 6.298396 -0.894005 C 0.348057 -2.390066 0.007926 H 2.974861 4.063669 -2.379181 H -0.133674 5.222814 -0.056320 C -0.862677 0.915962 2.524609 C -6.047318 -2.939765 0.362236 C 2.949050 4.719409 1.170559 H 0.015220 1.520476 2.729901 H -7.121729 -3.127469 0.433284 H 2.238111 4.775365 2.010642 C -4.080805 -2.569971 -0.994276 C 4.937509 -2.405103 3.907492 H 3.350214 5.731999 0.996116 C -2.205526 1.174860 -2.220837 H 5.223367 -2.925083 4.825016 H 3.783032 4.067101 1.469058 C 3.228913 -1.485350 2.462261 C 3.593011 -2.152985 3.633396 C 3.286227 4.052169 -1.852134 H 2.179018 -1.288314 2.233422 H 2.820643 -2.474633 4.336609 H 4.140981 3.383899 -1.671624 C -3.575249 3.043244 -1.326969 C -3.625934 2.697263 3.624970 H 3.674755 5.066493 -2.045085 C 4.205133 -1.058865 1.552813 H -4.446934 1.975853 3.502298 H 2.770093 3.711036 -2.764768 C -0.935960 -0.499582 2.582487 H -4.050113 3.688061 3.855043 P 3.679040 -0.258226 -0.009144 H -0.129365 -1.172937 2.854877 H -3.013242 2.383867 4.484822 C 4.286083 -0.907623 1.620617 C -3.580530 3.127462 1.118980 C -3.615745 2.433540 -3.795735 C 3.973932 -1.664089 -1.184393 C -3.930231 -2.510060 1.447098 H -3.006112 2.041888 -4.625128 C 5.071839 0.887702 -0.452406 C 3.392706 -0.969975 -2.604465 H -4.011607 3.415658 -4.101410 C 3.332519 -1.289343 2.573394 H 2.697436 -0.126342 -2.650029 H -4.457213 1.745358 -3.628413 C 5.648571 -1.022735 1.940781 C 4.017922 -1.273741 -1.384776 C 4.506828 -2.833443 -3.670568 C 3.287620 -1.630274 -2.407445 C -2.757185 2.764061 2.352674 H 4.697228 -3.441516 -4.558034 C 4.836662 -2.736477 -0.923650 C -3.316253 -2.280148 -2.283792 C 0.756470 5.507266 -0.463420 C 5.433509 1.886467 0.466513 C 5.557698 -1.306013 1.842092 H 0.425332 5.467682 -1.512587 C 5.740318 0.831042 -1.682806 H 6.335972 -0.951139 1.162590 H 1.226448 6.491852 -0.296553 H 2.274590 -1.195156 2.315659 C -5.304053 -2.757032 1.532023 H -0.136038 5.444912 0.178545 C 3.728222 -1.780755 3.818926 H -5.812517 -2.772518 2.497349 C -0.759718 -5.374628 0.227189 H 6.407514 -0.713343 1.218861 C -3.017434 -2.132899 2.610778 H -0.839598 -5.520463 1.315017 C 6.043173 -1.513762 3.186234 C -5.454710 -2.815142 -0.897261 H -0.545433 -6.358431 -0.224430 H 2.594016 -0.807493 -2.602012 H -6.077845 -2.876243 -1.790921 H -1.740488 -5.041529 -0.141941 C 3.475492 -2.632480 -3.359639 C -2.752948 2.572061 -2.524939 C -1.609898 3.562232 -2.809911 H 5.369819 -2.792193 0.027580 C 3.644568 -1.736754 -3.742759 H -0.906547 3.615957 -1.967778 C 5.012077 -3.749062 -1.870162 H 3.156532 -1.482887 -4.686938 H -2.022617 4.567808 -2.984984 H 4.920252 1.946476 1.429707 C 2.119943 -4.659400 0.929685 H -1.048969 3.261923 -3.710207 C 6.447912 2.794576 0.168699 H 3.016421 -4.068896 0.687421 C -3.821617 -1.831264 3.892298 H 5.480626 0.060246 -2.411271 H 2.364066 -5.729065 0.810396 H -3.141789 -1.494054 4.690327 313

Appendix

H -4.337764 -2.737498 4.248767 H -0.955470 -3.417546 -3.749338 C 3.525014 -2.631697 -3.359776 H -4.565457 -1.041317 3.713778 H -1.925710 -4.502006 -2.721609 H 5.419562 -2.788773 0.027443 C 5.112859 -3.157162 -2.455533 H -0.765452 -3.380171 -1.969132 C 5.063152 -3.746139 -1.870299 H 5.777546 -4.021980 -2.388348 C -3.546558 -2.638985 -3.908475 H 4.963399 1.949266 1.429570 C 7.137810 2.973403 -0.232937 H -4.405308 -1.952798 -3.883741 C 6.489877 2.799491 0.168562 H 7.941589 3.711600 -0.281382 H -3.939484 -3.666381 -3.922895 H 5.526398 0.063818 -2.411408 C 5.827515 1.222677 -1.276477 H -2.987788 -2.474497 -4.844570 C 6.792434 1.755621 -1.985146 H 5.623586 0.596359 -2.147060 C -3.491552 4.448830 -0.560381 C 5.132956 -1.890274 4.128335 C 6.386813 2.827295 0.936770 H -3.882983 5.247344 -1.186843 H 3.021650 -2.075731 4.551564 H 6.600609 3.451019 1.808207 C -5.085666 1.969685 -2.203058 H 7.155029 -1.590532 3.422474 C 2.695017 4.469899 1.661825 H -5.391408 1.485951 -3.147078 H 2.988587 -2.586850 -4.310973 H 1.871946 4.491246 2.394643 H -5.752587 2.825798 -2.026158 C 4.389017 -3.695562 -3.091396 H 3.208293 5.445593 1.696806 H -5.236562 1.258995 -1.375729 H 5.733080 -4.580759 -1.649106 H 3.409923 3.693733 1.971144 C -5.664432 -0.709157 1.843835 C 7.151234 2.737009 -1.061240 C 6.853461 2.170314 -1.337112 H -5.561791 0.017364 1.022859 H 6.760801 3.565735 0.899149 H 7.434839 2.275702 -2.256391 H -5.907370 -0.163871 2.772364 H 7.302908 1.697646 -2.949687 H -6.513824 -1.362305 1.598090 H 5.444614 -2.268609 5.104877 Th7a SCF energy = -3933.6325429 C -4.667647 -2.597923 3.132683 H 4.530222 -4.488344 -3.829740 H -5.560788 -3.195333 2.898177 H 7.942206 3.452615 -1.297044 Th -1.493032 0.132091 0.004462 H -4.850200 -2.072681 4.084409 Ni 1.610357 0.379717 0.014348 H -3.827980 -3.294460 3.270233 Si 0.245253 -4.163337 0.727181 C -0.860262 3.657254 2.869109 Th7b SCF energy = -3933.6436983 Si 2.125541 4.082106 -0.391576 H -0.487039 3.445214 3.886509 N -3.254341 -1.788001 -0.279001 H -1.020975 4.742168 2.789796 Th -1.408463 -0.060338 0.002455 N -2.784210 2.387036 0.140796 H -0.093367 3.373825 2.133877 Ni 1.638250 -0.447174 0.028343 C 0.794504 -1.242677 0.121716 C -3.206412 3.381454 3.676923 P 3.766714 0.132779 -0.031736 C 0.229004 -2.358900 0.284631 H -4.199221 2.934419 3.522516 Si 0.786508 4.176447 0.195511 C -2.626640 1.365519 -2.496725 H -3.325256 4.474264 3.641728 Si 2.173804 -4.129872 0.176876 C -0.720443 -0.700591 -2.813756 H -2.846770 3.107049 4.682823 N -2.952766 -0.317169 -2.222558 H 0.031760 -1.483544 -2.897990 C -3.530191 3.499686 -3.414903 N -3.138377 -0.124875 2.113236 C 0.285352 1.780233 0.054607 H -2.531103 3.954672 -3.476415 C 0.264744 -1.789997 0.137190 C -0.843338 0.759016 2.920445 H -4.259646 4.309928 -3.268483 C -2.874563 -2.796766 0.086157 H 0.068676 1.323542 3.106676 H -3.756394 3.008816 -4.375369 H -1.779684 -2.622518 0.110595 C -2.078687 -1.027356 -2.709209 C 1.036834 -4.337269 2.444254 C 0.900783 1.207842 -0.003374 C -3.410119 -2.615313 -1.391896 H 2.067585 -3.950832 2.452529 C -3.293215 2.419450 -0.199163 C -2.052134 1.422342 2.665278 H 1.065862 -5.402454 2.730984 H -2.192875 2.498540 -0.133394 C -1.247747 1.664790 -2.581947 H 0.461028 -3.801433 3.216935 C -1.162403 0.828132 2.760324 H -0.911473 2.696121 -2.477826 C 1.330446 -5.083037 -0.522629 H -0.393689 1.563493 2.983758 C -4.124083 -2.296834 0.684994 H 0.891949 -5.068052 -1.532414 C -1.016841 -0.583776 2.833092 C -3.172753 -0.754690 2.360969 H 1.442618 -6.137089 -0.216200 H -0.120246 -1.124296 3.123967 C -0.312349 0.643403 -2.761008 H 2.331723 -4.628075 -0.580779 C -2.490558 1.067752 2.346697 H 0.748584 0.890497 -2.808008 C 0.701329 5.256928 -0.816384 C -2.087932 -1.375718 -2.398643 C 1.416768 2.384489 -0.087873 H 0.245365 4.988199 -1.783365 C -2.246101 0.827452 -2.522438 C -3.199899 0.643764 2.401284 H 1.065246 6.295764 -0.894142 C 1.373397 -2.448165 0.161147 H -4.129060 1.167514 2.187613 H -0.095083 5.218565 -0.056457 C 0.381962 2.363643 0.014433 C -2.715501 3.284184 1.204994 C 2.988339 4.719452 1.170422 C -0.798831 -0.904323 -2.725225 C -3.010352 0.023447 -2.562417 H 2.277323 4.774418 2.010505 H 0.099439 -1.493178 -2.888142 H -4.061498 -0.240163 -2.461300 H 3.388093 5.732600 0.995979 C -4.039291 2.457800 0.989712 C -0.798736 -0.643771 2.907814 H 3.823228 4.068306 1.468921 C -2.265152 -1.129788 2.462976 H 0.146572 -1.154649 3.088043 C 3.326444 4.052682 -1.852271 C 3.270185 1.406944 -2.482647 C -3.272642 3.130112 -0.933321 H 4.182128 3.385603 -1.671761 H 2.228544 1.196618 -2.227531 C -1.937846 -1.391691 2.608743 H 3.713560 5.067546 -2.045222 C -3.556311 -2.901539 1.304843 H -1.869751 -2.477466 2.546117 H 2.810786 3.710831 -2.764905 C 4.270862 1.024338 -1.580041 C -4.399333 -1.582450 1.997305 P 3.725257 -0.257162 -0.009281 C -0.901771 0.509506 -2.806434 C -2.191593 2.932096 2.592794 C 4.333203 -0.905713 1.620480 H -0.098578 1.199718 -3.049575 C -3.630698 2.483894 -2.255060 C 4.022106 -1.662613 -1.184530 C -3.483676 -3.013979 -1.155703 C -2.616773 -2.448306 -2.683086 C 5.116459 0.890704 -0.452543 C -3.886316 2.361753 -1.470514 C -4.797670 -3.408175 0.197027 C 3.380172 -1.288760 2.573257 C 3.533148 1.022330 2.592322 H -5.546761 -3.998961 0.720345 C 5.695850 -1.018929 1.940644 H 2.830001 0.186703 2.660165 C -1.460303 -4.964539 0.795039 C 3.335747 -1.629753 -2.407582 C 4.146896 1.298275 1.360214 H -2.060321 -4.596953 1.642075 C 4.886328 -2.733799 -0.923787 C -2.641963 -2.796200 -2.416959 H -1.337001 -6.053532 0.924509 C 5.476739 1.889971 0.466376 C -3.305972 2.357150 2.332898 H -2.053786 -4.786255 -0.113835 C 5.785017 0.834974 -1.682943 C 5.613148 1.285208 -1.903070 C -4.344759 -3.608639 -1.128817 H 2.322113 -1.196046 2.315522 H 6.410473 0.961678 -1.230000 H -4.664801 -4.396636 -1.808102 C 3.776558 -1.779621 3.818789 C -5.281015 2.435515 -1.540126 C -3.140091 4.545203 0.806127 H 6.454362 -0.708480 1.218724 H -5.789037 2.391217 -2.503383 H -3.192440 5.438253 1.426421 C 6.091135 -1.509406 3.186097 C -2.995063 2.144061 -2.699234 C -1.491271 -3.493879 -2.787032 H 2.640999 -0.807939 -2.602149 C -5.431742 2.528563 0.881162 314

Appendix

H -6.054813 2.556221 1.775054 H -1.588539 5.122841 0.116389 H -1.296113 -6.094643 0.951611 C -2.793659 -2.554171 2.587543 C -1.643920 -3.555349 2.803009 H -2.019120 -4.853463 -0.114773 C 3.804794 1.807866 3.713340 H -0.902608 -3.501559 1.993452 C -4.269410 -3.631559 -1.115502 H 3.325502 1.575786 4.667587 H -2.041815 -4.580918 2.847902 H -4.588102 -4.419412 -1.795590 C 2.255619 4.578475 -0.927626 H -1.127983 -3.347630 3.754511 C -3.187776 4.521299 0.774629 H 3.138143 3.977441 -0.661608 C -3.819600 2.014849 -3.996600 H -3.271967 5.412835 1.393607 H 2.516558 5.645997 -0.825654 H -3.140087 1.825570 -4.841755 C -1.383888 -3.526839 -2.748252 H 2.018108 4.383676 -1.985047 H -4.374526 2.943576 -4.207659 H -0.839717 -3.437098 -3.704595 C -2.404940 3.583489 2.543417 H -4.528054 1.176067 -3.935875 H -1.818235 -4.536254 -2.700602 H -1.921658 3.539492 3.532583 C 5.268359 3.192903 2.382946 H -0.665025 -3.421045 -1.923815 H -3.002376 4.506925 2.494904 H 5.938515 4.051342 2.291942 C -3.416305 -2.652947 -3.888997 H -1.615953 3.640379 1.782808 C 7.276825 -2.941191 0.234083 H -4.275253 -1.966957 -3.870895 C 5.189064 -1.057635 0.108547 H 8.088048 -3.671235 0.282518 H -3.809012 -3.680249 -3.926119 C 5.940759 1.932405 -3.094826 C 5.962300 -1.188973 1.270026 H -2.839954 -2.474760 -4.811753 H 6.988725 2.131127 -3.332689 H 5.762735 -0.553438 2.134943 C -3.548885 4.404178 -0.589984 C -1.503269 -3.833510 -2.467807 C 6.510606 -2.817045 -0.928256 H -3.971628 5.184034 -1.219749 H -0.929157 -3.728486 -3.402642 H 6.719913 -3.450080 -1.794121 C -5.033206 1.902339 -2.276997 H -1.922277 -4.851209 -2.438048 C 2.832434 -4.512168 -1.557841 H -5.293729 1.395710 -3.222509 H -0.807196 -3.714204 -1.624816 H 2.004276 -4.534611 -2.284803 H -5.716073 2.754277 -2.145799 C 1.295556 4.501265 1.990649 H 3.325936 -5.498580 -1.571234 H -5.210492 1.207055 -1.441890 H 0.465897 4.341454 2.695833 H 3.560765 -3.758409 -1.890268 C -5.595586 -0.738741 1.883412 H 1.633640 5.546325 2.096259 C 6.997655 -2.126230 1.330944 H -5.529591 -0.021204 1.050962 H 2.125902 3.838733 2.279709 H 7.590698 -2.214076 2.244655 H -5.812137 -0.185115 2.813374 C -4.285091 2.272925 3.522082 H -6.445473 -1.404545 1.675212 H -4.952598 1.404723 3.425224 Pa7a SCF energy = -3967.328429 C -4.531596 -2.602050 3.156733 H -4.890449 3.190430 3.602623 H -5.417964 -3.220934 2.952840 H -3.713442 2.161201 4.456300 Pa -1.517367 0.124539 0.009626 H -4.698719 -2.069843 4.107441 C -4.828905 -3.395670 -1.162919 Ni 1.555920 0.378174 0.032750 H -3.672999 -3.277936 3.279018 H -5.353194 -3.569394 -2.103220 Si 0.263120 -4.190039 0.735488 C -0.846969 3.696820 2.826441 C -2.010250 3.313123 -2.868791 Si 1.996789 4.085525 -0.365447 H -0.466576 3.483656 3.840879 H -1.301471 3.370737 -2.031542 N -3.176062 -1.814793 -0.263161 H -1.034253 4.778475 2.758287 H -2.558716 4.265554 -2.929872 N -2.752646 2.375844 0.113493 H -0.074959 3.436660 2.089405 H -1.430126 3.191876 -3.797620 C 0.745773 -1.251578 0.117551 C -3.173014 3.346562 3.650283 C -5.518862 -3.540578 0.042026 C 0.231666 -2.392165 0.266046 H -4.156020 2.877029 3.500778 H -6.570811 -3.837579 0.024651 C -2.555792 1.323728 -2.449687 H -3.319619 4.436785 3.634450 C -4.899796 -3.286665 1.267453 C -0.617962 -0.721693 -2.712154 H -2.794705 3.065413 4.647327 H -5.478725 -3.376763 2.187194 H 0.141211 -1.497898 -2.793666 C -3.444015 3.426140 -3.453484 C 5.474771 -1.886572 -0.988483 C 0.207121 1.734976 0.100674 H -2.445319 3.884756 -3.485794 H 4.886020 -1.793038 -1.904808 C -0.762649 0.787394 2.832475 H -4.182364 4.235106 -3.348688 C 5.012137 2.395650 1.264547 H 0.139582 1.363388 3.029765 H -3.631522 2.916982 -4.412814 H 5.486630 2.639299 0.311825 C -1.973448 -1.062379 -2.624628 C 1.043006 -4.325105 2.461135 C 3.551076 -4.220844 1.465599 C -3.321799 -2.652699 -1.372278 H 2.071951 -3.934072 2.469088 H 4.366653 -3.515264 1.251783 C -1.980493 1.435763 2.583652 H 1.075323 -5.384928 2.766788 H 3.973752 -5.239343 1.494218 C -1.178537 1.637372 -2.471832 H 0.458959 -3.778226 3.219482 H 3.151894 -3.991614 2.467250 H -0.857797 2.672758 -2.369331 C 1.374605 -5.113974 -0.487492 C -6.038665 2.540467 -0.374165 C -4.064389 -2.309274 0.692653 H 0.943917 -5.131252 -1.500426 H -7.127972 2.597614 -0.444191 C -3.085071 -0.753006 2.308843 H 1.504711 -6.158030 -0.154979 C 4.934887 2.313550 -3.986553 C -0.224228 0.621602 -2.633144 H 2.367492 -4.641387 -0.548204 H 5.194240 2.811553 -4.923994 H 0.834184 0.880925 -2.659524 C 0.555375 5.241073 -0.782888 C 3.600524 2.045880 -3.679550 C 1.318431 2.378646 -0.037972 H 0.101898 4.972160 -1.750898 H 2.809658 2.332823 -4.377330 C -3.126335 0.642585 2.330529 H 0.908564 6.283856 -0.857600 C -3.481749 -2.929773 -3.703673 H -4.066586 1.155084 2.142173 H -0.241039 5.192539 -0.023824 H -4.312386 -2.208877 -3.710206 C -2.707610 3.283073 1.173698 C 2.879407 4.747942 1.174541 H -3.887485 -3.949348 -3.806162 C -2.923743 -0.020623 -2.498479 H 2.182181 4.813076 2.025199 H -2.846322 -2.728573 -4.579940 H -3.974289 -0.294947 -2.431655 H 3.271026 5.760134 0.977792 C -3.706969 -2.582917 3.830021 C -0.694650 -0.610036 2.789307 H 3.722351 4.105725 1.469235 H -3.127439 -2.289884 4.719053 H 0.257634 -1.110283 2.953635 C 3.172603 4.048915 -1.846094 H -4.104479 -3.596140 4.003413 C -3.278947 3.096074 -0.958816 H 4.039353 3.394833 -1.672071 H -4.546132 -1.880247 3.721425 C -1.832977 -1.375068 2.497439 H 3.543220 5.065978 -2.058677 C 4.674483 2.896167 3.610867 H -1.752718 -2.458773 2.430546 H 2.644911 3.689462 -2.744968 H 4.879959 3.519107 4.484611 C -4.315558 -1.594335 2.004037 P 3.677472 -0.230508 -0.012186 C 0.898836 -5.467331 0.611099 C -2.158941 2.939833 2.548531 C 4.315658 -0.870113 1.608830 H 0.556901 -5.374549 1.653669 C -3.582920 2.431227 -2.279843 C 3.992893 -1.629195 -1.190412 H 1.358333 -6.464036 0.495040 C -2.508560 -2.481631 -2.644243 C 5.040135 0.947373 -0.465454 H 0.014419 -5.422904 -0.043758 C -4.741925 -3.414482 0.203180 C 3.380788 -1.282778 2.566580 C -0.595786 5.389067 -0.274596 H -5.500621 -3.995628 0.723574 C 5.683371 -0.951663 1.916458 H -0.678513 5.498533 -1.366586 C -1.432740 -5.009814 0.802402 C 3.325280 -1.594111 -2.423767 H -0.329082 6.377987 0.136349 H -2.044042 -4.634318 1.637764 C 4.853303 -2.700812 -0.919124 315

Appendix

C 5.382499 1.954570 0.451507 C 5.578089 -1.253037 1.878303 H 0.479445 5.434535 -1.560853 C 5.707235 0.902512 -1.696908 H 6.367147 -0.927417 1.196581 H 1.283520 6.479766 -0.364939 H 2.319233 -1.215535 2.316949 C -5.168366 -2.599560 1.488172 H -0.070711 5.433380 0.134556 C 3.798722 -1.770651 3.806105 H -5.686569 -2.600346 2.447323 C -0.614135 -5.408400 0.251788 H 6.427947 -0.620213 1.189433 C -2.909690 -2.167895 2.661395 H -0.732315 -5.542797 1.337540 C 6.100644 -1.438772 3.156041 C -5.289643 -2.677025 -0.936433 H -0.344408 -6.389816 -0.174749 H 2.635765 -0.771372 -2.631073 H -5.900375 -2.738270 -1.837466 H -1.591454 -5.121744 -0.162591 C 3.528079 -2.594589 -3.374596 C -2.737953 2.548321 -2.573888 C -1.618450 3.581814 -2.794258 H 5.372663 -2.757406 0.039598 C 3.736475 -1.778490 -3.723969 H -0.890029 3.564346 -1.971827 C 5.044240 -3.711356 -1.864904 H 3.247522 -1.549764 -4.674152 H -2.047613 4.593357 -2.863721 H 4.870274 2.004601 1.415821 C 2.202152 -4.592016 1.053435 H -1.082781 3.372732 -3.734621 C 6.376881 2.883449 0.150339 H 3.097488 -3.992089 0.831011 C -3.751616 -2.003915 3.943685 H 5.463351 0.124743 -2.423360 H 2.468065 -5.660028 0.971509 H -3.087066 -1.762158 4.787371 C 6.695576 1.842561 -2.002520 H 1.909252 -4.391297 2.095833 H -4.285646 -2.936546 4.189194 C 5.160009 -1.848417 4.103946 C -2.249960 -3.565361 -2.606097 H -4.480266 -1.187025 3.837811 H 3.057037 -2.089533 4.542690 H -1.753356 -3.477018 -3.585792 C 5.230225 -3.145959 -2.409171 H 7.168110 -1.494941 3.383317 H -2.844897 -4.491821 -2.605447 H 5.913994 -3.994427 -2.326212 H 3.005570 -2.547588 -4.333344 H -1.472984 -3.650851 -1.836341 C 7.192345 2.985208 -0.274169 C 4.387882 -3.659100 -3.095404 C 5.117730 1.088128 -0.128735 H 7.998538 3.720264 -0.330315 H 5.711267 -4.546003 -1.635292 C 5.920787 -1.894705 3.068791 C 5.869530 1.234703 -1.302460 C 7.036635 2.832228 -1.080802 H 6.972047 -2.087720 3.296679 H 5.658702 0.605643 -2.169437 H 6.634355 3.655784 0.879350 C -1.552071 3.828947 2.507300 C 6.447455 2.846241 0.900210 H 7.205358 1.793082 -2.967874 H -0.984805 3.711433 3.444958 H 6.668344 3.472664 1.768015 H 5.489100 -2.223865 5.075849 H -2.000203 4.834633 2.503734 C 2.761764 4.486408 1.618279 H 4.539728 -4.450643 -3.832920 H -0.846283 3.754527 1.667411 H 1.939741 4.501440 2.352443 H 7.812905 3.562885 -1.319256 C 1.398008 -4.536726 -1.910054 H 3.260379 5.470010 1.643652 H 0.608148 -4.381725 -2.660533 H 3.488631 3.723615 1.932556 Pa7b SCF energy = -3967.3345561 H 1.738794 -5.583465 -1.987620 C 6.898396 2.178317 -1.373142 H 2.243965 -3.878707 -2.160604 H 7.474732 2.277593 -2.296337 Pa -1.436548 0.063447 0.003089 C -4.123069 -2.219307 -3.551070 Ni 1.573514 0.456099 -0.016266 H -4.807505 -1.369732 -3.414170 U7a SCF energy = -4002.8772072 P 3.704763 -0.112342 0.024726 H -4.710701 -3.141483 -3.689853 Si 0.793175 -4.197837 -0.147483 H -3.542584 -2.047360 -4.470612 U -1.536087 0.129132 0.002854 Si 2.087151 4.136083 -0.117375 C -4.815188 3.434493 1.137824 Ni 1.569259 0.372368 0.028616 N -2.898749 0.282215 2.132448 H -5.344980 3.629288 2.071227 Si 0.299698 -4.210352 0.707985 N -3.019477 0.121689 -2.051301 C -1.916862 -3.321684 2.879834 Si 1.966568 4.083642 -0.389179 C 0.192100 1.774946 -0.104959 H -1.195074 -3.391878 2.054809 N -3.166279 -1.815902 -0.262691 C -2.871958 2.748169 -0.082844 H -2.456735 -4.277822 2.958229 N -2.740675 2.362660 0.132684 H -1.778525 2.538749 -0.091675 H -1.354252 -3.168282 3.814825 C 0.761639 -1.260791 0.104453 C 0.851862 -1.209897 0.011483 C -5.480029 3.609641 -0.077657 C 0.269423 -2.408740 0.256556 C -3.174481 -2.425957 0.166703 H -6.519059 3.949642 -0.075599 C -2.576287 1.329449 -2.458110 H -2.068400 -2.443172 0.112245 C -4.851002 3.339534 -1.295034 C -0.639072 -0.712969 -2.743356 C -1.027003 -0.787126 -2.716471 H -5.408682 3.461442 -2.224531 H 0.121452 -1.487580 -2.826986 H -0.241176 -1.504783 -2.937436 C 5.418379 1.908970 0.970345 C 0.207641 1.708066 0.085228 C -0.911117 0.623332 -2.783004 H 4.847210 1.803220 1.896348 C -0.752436 0.765073 2.856230 H -0.023506 1.182904 -3.064808 C 4.967927 -2.358446 -1.285300 H 0.152858 1.340118 3.042420 C -2.348551 -1.061761 -2.299574 H 5.451482 -2.599645 -0.336552 C -1.993686 -1.053830 -2.656288 C -2.061436 1.361394 2.345870 C 3.451703 4.251945 -1.417708 C -3.320007 -2.648367 -1.376403 C -2.172258 -0.853047 2.446236 H 4.267473 3.539603 -1.229419 C -1.972600 1.412825 2.622185 C 1.290709 2.453058 -0.124387 H 3.876638 5.269879 -1.427390 C -1.200804 1.643509 -2.502829 C 0.384565 -2.385259 0.004052 H 3.040759 4.047204 -2.419926 H -0.878996 2.678814 -2.396621 C -0.772204 0.912018 2.699218 C -5.905964 -2.743398 0.312963 C -4.043460 -2.321599 0.699681 H 0.110070 1.518955 2.881469 H -6.989397 -2.876286 0.371374 C -3.073332 -0.773913 2.337342 C -3.904513 -2.509385 -1.028652 C 4.925843 -2.277482 3.972054 C -0.248784 0.632127 -2.668997 C -2.166353 1.147863 -2.407375 H 5.197077 -2.771077 4.908464 H 0.809375 0.893644 -2.698861 C 3.241915 -1.384032 2.482016 C 3.587217 -2.017249 3.677697 C 1.307727 2.371126 -0.055340 H 2.197085 -1.179839 2.235318 H 2.804788 -2.306369 4.384034 C -3.116477 0.622002 2.375416 C -3.524692 2.898236 -1.310682 C -3.517015 2.823649 3.689399 H -4.058117 1.134365 2.190973 C 4.231337 -0.999335 1.568240 H -4.335351 2.089617 3.650869 C -2.698434 3.261919 1.202459 C -0.843104 -0.500344 2.764629 H -3.941909 3.830888 3.829528 C -2.942268 -0.015723 -2.521327 H -0.029027 -1.173563 3.017666 H -2.891051 2.596477 4.566144 H -3.992223 -0.291896 -2.445745 C -3.487553 2.996114 1.148011 C -3.636270 2.519788 -3.827493 C -0.687460 -0.633907 2.820335 C -3.781975 -2.428791 1.431523 H -3.041445 2.210469 -4.700794 H 0.266631 -1.133730 2.979611 C 3.459786 -1.002423 -2.597612 H -4.050518 3.519271 -4.037823 C -3.274852 3.090290 -0.932583 H 2.743384 -0.177385 -2.656365 H -4.463998 1.805872 -3.704049 C -1.823493 -1.395757 2.536576 C 4.085983 -1.273644 -1.370820 C 4.624728 -2.852580 -3.632280 H -1.742555 -2.479756 2.465147 C -2.658087 2.760290 2.409915 H 4.835010 -3.467914 -4.510251 C -4.300483 -1.615008 2.015952 C -3.157327 -2.351933 -2.355088 C 0.817084 5.490661 -0.514399 C -2.144654 2.918473 2.576977 316

Appendix

C -3.599475 2.436270 -2.256060 C 4.027304 -1.612255 -1.188090 C -3.820650 -2.391760 1.472494 C -2.521643 -2.476540 -2.659121 C 5.044915 0.974528 -0.456530 C 3.465190 -1.010321 -2.603440 C -4.718714 -3.427892 0.209706 C 3.398517 -1.318747 2.550218 H 2.765966 -0.170383 -2.657147 H -5.470355 -4.015497 0.733008 C 5.697646 -0.899773 1.938801 C 4.088407 -1.300659 -1.379406 C -1.399011 -5.024193 0.777407 C 3.343922 -1.595963 -2.412958 C -2.613464 2.792834 2.393094 H -2.008404 -4.643622 1.611836 C 4.917262 -2.661574 -0.924742 C -3.261096 -2.329065 -2.325382 H -1.266916 -6.109248 0.928976 C 5.365945 1.991793 0.457035 C 5.605587 -1.308488 1.857908 H -1.984794 -4.867720 -0.140090 C 5.722959 0.930932 -1.682071 H 6.391020 -0.978695 1.173991 C -4.259135 -3.633889 -1.115165 H 2.338852 -1.286563 2.285833 C -5.202837 -2.585318 1.553216 H -4.579086 -4.421094 -1.795396 C 3.815722 -1.811956 3.787782 H -5.704194 -2.595745 2.521313 C -3.184111 4.500642 0.814186 H 6.440936 -0.533958 1.227198 C -2.930245 -2.131051 2.688946 H -3.267662 5.388141 1.438981 C 6.113782 -1.391703 3.177007 C -5.365065 -2.666839 -0.868740 C -1.391457 -3.515929 -2.766276 H 2.630644 -0.791541 -2.611614 H -5.989911 -2.740891 -1.759175 H -0.852891 -3.426513 -3.725802 C 3.559981 -2.593314 -3.364205 C -2.683524 2.552978 -2.589202 H -1.820177 -4.527445 -2.712883 H 5.449679 -2.702450 0.027685 C 3.723311 -1.786196 -3.734258 H -0.669085 -3.403452 -1.945650 C 5.121408 -3.669355 -1.870592 H 3.236948 -1.542689 -4.682054 C -3.442055 -2.662537 -3.892130 H 4.843835 2.041546 1.416067 C 2.146328 -4.580924 0.971260 H -4.305357 -1.982122 -3.868791 C 6.350997 2.931488 0.158813 H 3.039221 -3.984611 0.730366 H -3.828192 -3.692518 -3.919067 H 5.494705 0.145979 -2.405876 H 2.403034 -5.649802 0.872875 H -2.877091 -2.486278 -4.822279 C 6.701460 1.882065 -1.985077 H 1.882294 -4.388212 2.022800 C -3.548712 4.393372 -0.550991 C 5.174536 -1.847535 4.104780 C -2.394048 -3.567361 -2.598845 H -3.979604 5.176421 -1.171174 H 3.075118 -2.168661 4.507968 H -1.912501 -3.489502 -3.587001 C -5.049599 1.906916 -2.231701 H 7.179314 -1.415747 3.418612 H -3.016275 -4.475597 -2.590661 H -5.327543 1.410633 -3.177678 H 3.024685 -2.561757 -4.316504 H -1.607772 -3.680891 -1.842557 H -5.730433 2.756781 -2.078575 C 4.448899 -3.635773 -3.093157 C 5.146219 1.048204 -0.126774 H -5.211445 1.202059 -1.401371 H 5.811491 -4.486901 -1.647656 C 5.953906 -1.963904 3.039191 C -5.581136 -0.760036 1.893906 C 7.021897 2.881387 -1.066376 H 7.005993 -2.162480 3.258218 H -5.511087 -0.034871 1.068326 H 6.592085 3.711611 0.885129 C -1.488450 3.840856 2.501336 H -5.804878 -0.214759 2.827071 H 7.219715 1.833834 -2.945970 H -0.930593 3.712352 3.443276 H -6.428691 -1.425030 1.674225 H 5.502451 -2.226860 5.075582 H -1.918391 4.854401 2.495039 C -4.525021 -2.632956 3.158219 H 4.611081 -4.425118 -3.830862 H -0.778467 3.754626 1.666288 H -5.411655 -3.248245 2.945332 H 7.790600 3.620702 -1.302681 C 1.272534 -4.483405 -1.969292 H -4.695772 -2.108536 4.112601 H 0.467989 -4.320373 -2.702077 H -3.668555 -3.311870 3.278994 U7b SCF energy = -4002.882184 H 1.611802 -5.528938 -2.066847 C -0.827061 3.670542 2.843341 H 2.113729 -3.822422 -2.228531 H -0.440214 3.458899 3.855612 U -1.419513 0.060181 0.003148 C -4.248198 -2.165582 -3.500312 H -1.010038 4.752777 2.772719 Ni 1.603764 0.440459 -0.001138 H -4.912638 -1.304305 -3.340701 H -0.061194 3.404771 2.101774 P 3.727717 -0.145312 0.026010 H -4.856307 -3.074613 -3.635775 C -3.151441 3.337101 3.680597 Si 0.708838 -4.167627 -0.188689 H -3.683696 -1.996674 -4.430403 H -4.138029 2.873246 3.536960 Si 2.110581 4.112557 -0.109851 C -4.730985 3.560828 1.107363 H -3.291046 4.428106 3.661547 N -2.890233 0.315844 2.144328 H -5.253575 3.789198 2.037316 H -2.770669 3.057489 4.677116 N -3.045971 0.141270 -2.055851 C -1.947337 -3.295775 2.898615 C -3.484120 3.444823 -3.420695 C 0.212286 1.747639 -0.087950 H -1.239487 -3.377968 2.062817 H -2.486555 3.904877 -3.466779 C -2.822693 2.766131 -0.100558 H -2.497517 -4.244893 2.988930 H -4.221053 4.251908 -3.294375 H -1.740330 2.500492 -0.101241 H -1.369053 -3.145714 3.824586 H -3.688771 2.945687 -4.381805 C 0.836752 -1.202840 0.044018 C -5.380886 3.764350 -0.111937 C 1.089826 -4.367009 2.427031 C -3.235908 -2.377964 0.197368 H -6.400919 4.157534 -0.116230 H 2.122603 -3.986175 2.431166 H -2.129097 -2.379285 0.121518 C -4.760888 3.456219 -1.325182 H 1.113833 -5.429296 2.724730 C -1.079808 -0.838633 -2.690972 H -5.306753 3.603808 -2.258095 H 0.516204 -3.819588 3.192972 H -0.318181 -1.583948 -2.903669 C 5.446342 1.869313 0.972251 C 1.399334 -5.122903 -0.534173 C -0.915132 0.568478 -2.764828 H 4.871214 1.767565 1.896296 H 0.960367 -5.125648 -1.543763 H -0.009035 1.096778 -3.047906 C 4.948308 -2.403598 -1.301395 H 1.529376 -6.171497 -0.216323 C -2.414163 -1.062538 -2.287981 H 5.429186 -2.658993 -0.354990 H 2.393020 -4.652046 -0.596784 C -2.039013 1.383220 2.335817 C 3.476916 4.215213 -1.409609 C 0.514146 5.223667 -0.811996 C -2.179716 -0.824980 2.464094 H 4.289550 3.500511 -1.216502 H 0.066828 4.950732 -1.781747 C 1.309022 2.431448 -0.111114 H 3.906135 5.231290 -1.424680 H 0.856631 6.270159 -0.885234 C 0.310425 -2.354207 0.003255 H 3.066177 4.006737 -2.411157 H -0.283916 5.166654 -0.055130 C -0.751059 0.919273 2.681759 C -5.959137 -2.739878 0.391076 C 2.840996 4.765466 1.147303 H 0.140025 1.515898 2.853606 H -7.039272 -2.888580 0.468417 H 2.141766 4.831746 1.996192 C -3.984396 -2.477386 -0.984774 C 4.963536 -2.353762 3.944451 H 3.224349 5.779354 0.942887 C -2.159848 1.134829 -2.408763 H 5.239202 -2.858323 4.873678 H 3.688898 4.133090 1.448818 C 3.272789 -1.439267 2.475020 C 3.623822 -2.086727 3.661403 C 3.145065 4.053316 -1.868152 H 2.226755 -1.229541 2.238246 H 2.845002 -2.381252 4.369439 H 4.017438 3.407715 -1.690014 C -3.459816 2.944999 -1.331982 C -3.480857 2.870643 3.666353 H 3.506922 5.072883 -2.083924 C 4.257630 -1.047585 1.559245 H -4.317444 2.158278 3.616588 H 2.622577 3.685419 -2.766662 C -0.843209 -0.490989 2.768711 H -3.880767 3.887517 3.809338 P 3.694921 -0.218881 -0.008561 H -0.037902 -1.173597 3.023987 H -2.868172 2.622999 4.547016 C 4.332439 -0.858593 1.612959 C -3.428045 3.053069 1.126078 C -3.579782 2.541543 -3.844682 317

Appendix

H -2.995827 2.199121 -4.713046 H 0.288739 -1.108440 2.940405 C 3.086518 4.119735 -1.858528 H -3.955291 3.553169 -4.068582 C -3.301412 3.062177 -0.940205 H 3.965723 3.481792 -1.686853 H -4.434229 1.861424 -3.713420 C -1.798501 -1.406203 2.515524 H 3.438477 5.142639 -2.074864 C 4.588825 -2.879359 -3.649736 H -1.698561 -2.488163 2.434742 H 2.561693 3.748513 -2.754269 H 4.783934 -3.494742 -4.531153 C -4.271601 -1.669549 2.004926 P 3.681621 -0.180454 -0.011499 C 0.851197 5.475323 -0.511727 C -2.195136 2.901120 2.579744 C 4.329415 -0.814695 1.607732 H 0.517649 5.421505 -1.559548 C -3.621405 2.396481 -2.259047 C 4.041507 -1.561043 -1.196351 H 1.324184 6.461044 -0.360509 C -2.459548 -2.502069 -2.656218 C 5.002658 1.045663 -0.452300 H -0.039851 5.424495 0.133081 C -4.634847 -3.509185 0.210884 C 3.408105 -1.319931 2.534254 C -0.689995 -5.379312 0.235663 H -5.369213 -4.117641 0.734935 C 5.693909 -0.811128 1.939395 H -0.770911 -5.528186 1.323123 C -1.267342 -5.066419 0.819727 C 3.368167 -1.549302 -2.426692 H -0.439771 -6.355872 -0.213294 H -1.829570 -4.700608 1.693218 C 4.944645 -2.597850 -0.929058 H -1.680272 -5.083113 -0.139216 H -1.157147 -6.158836 0.930364 C 5.296940 2.067335 0.465351 C -1.528850 3.545244 -2.818837 H -1.886018 -4.865037 -0.067441 C 5.689200 1.017554 -1.673621 H -0.804144 3.514227 -1.993577 C -4.163705 -3.708099 -1.112372 H 2.349664 -1.328570 2.264025 H -1.924207 4.569419 -2.901733 H -4.458738 -4.506804 -1.790501 C 3.837652 -1.810988 3.768416 H -0.997621 3.307413 -3.754962 C -3.231771 4.474543 0.807567 H 6.427211 -0.413118 1.234886 C -3.753950 -1.953625 3.981614 H -3.328498 5.361753 1.430823 C 6.121723 -1.300952 3.174431 H -3.077058 -1.710265 4.814997 C -1.307330 -3.517839 -2.757512 H 2.645103 -0.754718 -2.629286 H -4.289543 -2.881498 4.240695 H -0.764126 -3.416057 -3.713254 C 3.606766 -2.539776 -3.379644 H -4.479856 -1.133803 3.879541 H -1.716529 -4.537676 -2.708125 H 5.469248 -2.634157 0.027870 C 5.191200 -3.191048 -2.429706 H -0.593287 -3.392350 -1.931162 C 5.171875 -3.598446 -1.877224 H 5.857515 -4.053814 -2.352583 C -3.371784 -2.706563 -3.892165 H 4.766964 2.105056 1.420553 C 7.228052 2.936955 -0.268434 H -4.249315 -2.044487 -3.871365 C 6.266191 3.025933 0.175801 H 8.036922 3.669151 -0.323259 H -3.736053 -3.744486 -3.920521 H 5.481454 0.229430 -2.400069 C 5.902228 1.189668 -1.298278 H -2.807771 -2.517841 -4.820436 C 6.651233 1.987902 -1.967887 H 5.691497 0.560153 -2.164951 C -3.590727 4.361693 -0.560748 C 5.195159 -1.799872 4.092628 C 6.479227 2.802432 0.904041 H -4.027597 5.140089 -1.182677 H 3.107062 -2.203608 4.480016 H 6.699852 3.429339 1.771536 C -5.063165 1.845764 -2.224452 H 7.186386 -1.289692 3.420701 C 2.787705 4.459535 1.625568 H -5.338608 1.343828 -3.168133 H 3.078531 -2.512722 -4.335956 H 1.966050 4.484555 2.359763 H -5.756519 2.684974 -2.068411 C 4.508851 -3.569947 -3.105082 H 3.296192 5.438118 1.648581 H -5.208116 1.138937 -1.392703 H 5.872433 -4.406352 -1.651889 H 3.506997 3.690111 1.941244 C -5.565590 -0.837653 1.868804 C 6.946515 2.990866 -1.044668 C 6.934681 2.129591 -1.367163 H -5.498636 -0.113478 1.042030 H 6.487152 3.809259 0.905022 H 7.514203 2.225551 -2.288693 H -5.807639 -0.293704 2.798220 H 7.176891 1.951708 -2.925252 H -6.399617 -1.517596 1.642918 H 5.531859 -2.177355 5.061137 Np7a SCF energy = -4040.3747108 C -4.482454 -2.681174 3.154970 H 4.688639 -4.353969 -3.844362 H -5.357554 -3.313802 2.944256 H 7.702784 3.745010 -1.274067 Np -1.567604 0.127054 0.006809 H -4.665587 -2.151755 4.104221 Ni 1.542271 0.368857 0.027976 H -3.614210 -3.343454 3.283962 Np7b SCF energy = -4040.3810601 Si 0.447131 -4.288411 0.707761 C -0.891232 3.671346 2.861996 Si 1.915494 4.138090 -0.373666 H -0.510057 3.457479 3.875892 Np -1.466572 0.081065 0.005633 N -3.131657 -1.853592 -0.265351 H -1.090206 4.751221 2.798135 Ni 1.584808 0.475719 -0.006699 N -2.764976 2.341516 0.128235 H -0.115022 3.423027 2.124944 P 3.735227 -0.081149 0.029941 C 0.790057 -1.298627 0.114930 C -3.219765 3.302245 3.673025 Si 0.907693 -4.233341 -0.159560 C 0.418341 -2.486522 0.275542 H -4.199136 2.827589 3.516313 Si 2.046177 4.139645 -0.124570 C -2.583314 1.303051 -2.457911 H -3.372044 4.391630 3.657466 N -2.925151 0.265092 2.182851 C -0.612124 -0.705839 -2.715874 H -2.847093 3.022259 4.672414 N -3.055039 0.089837 -2.098778 H 0.162049 -1.468409 -2.779787 C -3.526086 3.399946 -3.429543 C 0.170810 1.759515 -0.104440 C 0.205450 1.718263 0.106963 H -2.535818 3.874840 -3.482481 C -2.911632 2.718769 -0.084732 C -0.766453 0.772281 2.833843 H -4.275146 4.196354 -3.305338 H -1.818168 2.506247 -0.095129 H 0.129868 1.362858 3.012855 H -3.726211 2.891891 -4.386797 C 0.854608 -1.219827 0.022477 C -1.961522 -1.068389 -2.651743 C 1.289298 -4.478105 2.397765 C -3.150629 -2.433475 0.171658 C -3.256327 -2.693912 -1.375874 H 2.327417 -4.112536 2.373389 H -2.045086 -2.402456 0.114853 C -2.001060 1.397677 2.621071 H 1.305715 -5.542806 2.687064 C -1.023079 -0.792072 -2.675783 C -1.213255 1.641052 -2.506419 H 0.747717 -3.925697 3.183275 H -0.222743 -1.500900 -2.869767 H -0.910503 2.682462 -2.402395 C 1.488120 -5.202919 -0.582528 C -0.925026 0.620170 -2.742309 C -3.994549 -2.380941 0.696529 H 1.008593 -5.192995 -1.573471 H -0.040634 1.193949 -3.004098 C -3.060075 -0.805286 2.322098 H 1.621266 -6.255027 -0.277925 C -2.357895 -1.078028 -2.309568 C -0.244860 0.647626 -2.655759 H 2.482875 -4.740412 -0.681096 C -2.092738 1.347056 2.354394 H 0.809245 0.926095 -2.677291 C 0.447068 5.259780 -0.791806 C -2.178460 -0.857784 2.464271 C 1.263190 2.428800 -0.036292 H -0.006749 4.973869 -1.754643 C 1.269895 2.444220 -0.124797 C -3.131202 0.589271 2.376930 H 0.778362 6.309043 -0.875960 C 0.490958 -2.425184 0.001157 H -4.084241 1.083955 2.202760 H -0.342599 5.199896 -0.026513 C -0.782866 0.913143 2.662391 C -2.738214 3.241662 1.200027 C 2.787023 4.837917 1.156167 H 0.095764 1.530840 2.823384 C -2.928446 -0.047604 -2.528591 H 2.088771 4.898419 2.006410 C -3.877287 -2.553613 -1.021919 H -3.974484 -0.340627 -2.461850 H 3.156881 5.855881 0.947197 C -2.206367 1.122910 -2.415540 C -0.675997 -0.626413 2.793070 H 3.643765 4.218365 1.459202 C 3.290322 -1.382877 2.476108 318

Appendix

H 2.241263 -1.198385 2.233138 H 2.869782 -2.329452 4.369441 H -4.033877 1.091469 2.290521 C -3.567067 2.868924 -1.311581 C -3.553054 2.812882 3.690238 C -2.643861 3.245771 1.295136 C 4.272886 -0.972699 1.565790 H -4.369122 2.076347 3.655526 C -3.042218 0.025189 -2.490582 C -0.839443 -0.499770 2.733393 H -3.979743 3.819927 3.826098 H -4.085504 -0.262623 -2.375046 H -0.014102 -1.167578 2.961507 H -2.925903 2.590933 4.567583 C -0.660908 -0.709677 2.810319 C -3.524591 2.972203 1.146862 C -3.685491 2.493079 -3.829528 H 0.294073 -1.216258 2.942681 C -3.755073 -2.464537 1.437004 H -3.092198 2.185328 -4.704537 C -3.308764 3.106578 -0.811982 C 3.475506 -0.960639 -2.594399 H -4.101907 3.491985 -4.038245 C -1.804388 -1.457631 2.533244 H 2.746131 -0.146539 -2.644114 H -4.510751 1.776882 -3.704143 H -1.733417 -2.540786 2.435278 C 4.118069 -1.228020 -1.375389 C 4.659635 -2.786833 -3.649272 C -4.286492 -1.654441 2.036622 C -2.694875 2.744396 2.410739 H 4.871054 -3.394455 -4.532296 C -2.088971 2.860646 2.659593 C -3.133631 -2.388481 -2.349283 C 0.763288 5.478482 -0.528586 C -3.701981 2.468447 -2.126078 C 5.623958 -1.206287 1.873091 H 0.430123 5.416411 -1.576103 C -2.597358 -2.431523 -2.679734 H 6.407069 -0.861115 1.194186 H 1.218244 6.472950 -0.379500 C -4.701956 -3.474256 0.227693 C -5.133511 -2.690250 1.495888 H -0.126196 5.412534 0.117102 H -5.423281 -4.088460 0.763111 H -5.649423 -2.713802 2.456072 C -0.489773 -5.439417 0.276436 C -1.303229 -5.038960 0.715215 C -2.888117 -2.189279 2.667529 H -0.607767 -5.540884 1.365805 H -1.784958 -4.730373 1.656519 C -5.254485 -2.776146 -0.928473 H -0.217313 -6.432166 -0.121051 H -1.231562 -6.140074 0.727924 H -5.862551 -2.866500 -1.828960 H -1.467035 -5.165472 -0.147003 H -1.974808 -4.740851 -0.104170 C -2.784312 2.521656 -2.578342 C -1.668901 3.559491 -2.799881 C -4.262869 -3.659099 -1.105770 C 3.753151 -1.727062 -3.727094 H -0.941003 3.547311 -1.976853 H -4.581049 -4.444998 -1.788430 H 3.250621 -1.502103 -4.670982 H -2.102260 4.569210 -2.870200 C -3.101369 4.508166 0.934609 C 2.347337 -4.614233 1.008328 H -1.131834 3.351402 -3.739687 H -3.144435 5.389175 1.572533 H 3.231269 -4.005176 0.766011 C -3.730850 -2.054909 3.952541 C -1.455022 -3.451660 -2.835746 H 2.621667 -5.679473 0.919064 H -3.071043 -1.802255 4.796859 H -0.947617 -3.344367 -3.810518 H 2.075996 -4.417313 2.057177 H -4.240849 -3.002227 4.192587 H -1.867315 -4.469821 -2.778920 C -2.192877 -3.580989 -2.580031 H -4.479496 -1.255643 3.852655 H -0.709007 -3.337870 -2.036424 H -1.691708 -3.491612 -3.557382 C 5.282522 -3.076022 -2.433818 C -3.552173 -2.613313 -3.887186 H -2.763373 -4.522690 -2.571166 H 5.981230 -3.913225 -2.362104 H -4.423822 -1.946097 -3.825341 H -1.419511 -3.636150 -1.803262 C 7.178613 3.063244 -0.260513 H -3.923936 -3.648470 -3.917625 C 5.130756 1.137823 -0.119856 H 7.974556 3.809490 -0.314810 H -3.019383 -2.413615 -4.831564 C 5.977964 -1.853141 3.057364 C 5.881920 1.295542 -1.292519 C -3.526405 4.421343 -0.411148 H 7.032435 -2.030513 3.282956 H 5.680688 0.664535 -2.160339 H -3.949498 5.223931 -1.011477 C -1.593046 3.818031 2.501793 C 6.434252 2.912886 0.912816 C -5.143603 1.925909 -2.024447 H -1.020932 3.704514 3.437027 H 6.645387 3.541419 1.781477 H -5.474196 1.448703 -2.963332 H -2.045847 4.821654 2.498240 C 2.712759 4.496547 1.612470 H -5.821149 2.765265 -1.810122 H -0.890935 3.746849 1.658548 H 1.889585 4.500486 2.345396 H -5.246907 1.199620 -1.203548 C 1.468187 -4.564208 -1.937424 H 3.197827 5.486840 1.638444 C -5.562281 -0.790718 1.929838 H 0.657532 -4.411346 -2.665769 H 3.449574 3.743478 1.926984 H -5.486182 -0.051047 1.117838 H 1.811437 -5.609223 -2.025659 C 6.897692 2.253397 -1.360708 H -5.784008 -0.260896 2.872567 H 2.304376 -3.901838 -2.208600 H 7.473963 2.361591 -2.282895 H -6.413195 -1.447153 1.697432 C -4.099801 -2.297759 -3.548447 Pu7a SCF energy = -4079.8515155 C -4.510113 -2.680770 3.171463 H -4.807819 -1.466143 -3.422304 H -5.404621 -3.285371 2.960167 H -4.660680 -3.237884 -3.676704 Pu -1.562230 0.117768 0.026392 H -4.667440 -2.164252 4.132415 H -3.522893 -2.120476 -4.469302 Ni 1.590537 0.371459 -0.002510 H -3.658926 -3.368916 3.276935 C -4.851682 3.412591 1.137760 Si 0.428423 -4.312657 0.549313 C -0.759790 3.591155 2.930717 H -5.378748 3.610871 2.071963 Si 1.952939 4.119951 -0.561647 H -0.366289 3.352448 3.934366 C -1.870086 -3.324031 2.872485 N -3.198531 -1.824221 -0.258757 H -0.931581 4.676628 2.885778 H -1.153911 -3.376003 2.040966 N -2.756412 2.362745 0.221338 H -0.003838 3.335397 2.175026 H -2.390353 -4.291154 2.949219 C 0.820673 -1.314007 0.019543 C -3.084063 3.273065 3.776663 H -1.303017 -3.164377 3.803819 C 0.434895 -2.495828 0.171450 H -4.078671 2.828498 3.627865 C -5.519713 3.584746 -0.076216 C -2.684511 1.372320 -2.408867 H -3.205742 4.366277 3.779801 H -6.558465 3.925547 -0.072689 C -0.744190 -0.642399 -2.811676 H -2.704038 2.966148 4.765450 C -4.892803 3.312036 -1.293907 H 0.020731 -1.407987 -2.932889 C -3.665237 3.496389 -3.278675 H -5.451656 3.433003 -2.222823 C 0.243274 1.731763 0.086929 H -2.677381 3.969811 -3.374806 C 5.418212 1.961383 0.980779 C -0.716785 0.690487 2.870894 H -4.403664 4.291856 -3.097597 H 4.847680 1.846576 1.906115 H 0.195647 1.257081 3.048225 H -3.918267 3.009057 -4.234100 C 5.018466 -2.298583 -1.303523 C -2.090891 -0.999632 -2.678887 C 1.339471 -4.577932 2.192132 H 5.515302 -2.535964 -0.360676 C -3.353398 -2.643934 -1.376177 H 2.387929 -4.248104 2.131619 C 3.411245 4.261365 -1.423500 C -1.937231 1.350419 2.680359 H 1.329814 -5.650792 2.449830 H 4.235995 3.561384 -1.228484 C -1.317336 1.702458 -2.529174 H 0.852257 -4.031406 3.016388 H 3.822412 5.284818 -1.440011 H -1.003272 2.740378 -2.420729 C 1.390003 -5.205100 -0.815757 H 3.004674 4.044319 -2.424887 C -4.041974 -2.351928 0.712419 H 0.871485 -5.146301 -1.784965 C -5.867168 -2.861328 0.321726 C -3.052517 -0.822975 2.360659 H 1.505221 -6.270732 -0.554027 H -6.944629 -3.035628 0.381681 C -0.366848 0.707796 -2.752654 H 2.392884 -4.765974 -0.937300 C 4.990077 -2.261017 3.957326 H 0.686371 0.980294 -2.829657 C 0.490345 5.200511 -1.089023 H 5.270019 -2.758533 4.889048 C 1.291356 2.427882 -0.147469 H 0.103817 4.888507 -2.073151 C 3.647114 -2.020925 3.665804 C -3.090422 0.572279 2.443378 H 0.804297 6.254939 -1.174471 319

Appendix

H -0.340098 5.136499 -0.367705 C -0.763679 0.925616 2.625024 C -5.710893 -2.975743 0.316833 C 2.757831 4.895578 0.967077 H 0.099308 1.572626 2.747923 H -6.785689 -3.166611 0.374286 H 2.022915 4.996564 1.781661 C -3.722203 -2.644344 -1.023198 C 5.042319 -2.207825 3.926138 H 3.135589 5.902629 0.722265 C -2.255371 1.094269 -2.425990 H 5.346416 -2.709484 4.848029 H 3.601437 4.293853 1.335882 C 3.301512 -1.388912 2.458723 C 3.689102 -2.032708 3.635470 C 3.184305 4.025571 -1.992225 H 2.245474 -1.257986 2.213102 H 2.927665 -2.397619 4.329502 H 4.064434 3.415264 -1.741676 C -3.671745 2.763686 -1.281927 C -3.583744 2.750761 3.724916 H 3.530873 5.038201 -2.259262 C 4.262145 -0.907321 1.560503 H -4.371882 1.983711 3.717305 H 2.704852 3.588609 -2.883667 C -0.769078 -0.489652 2.690657 H -4.045074 3.743786 3.850191 P 3.744010 -0.202772 0.013997 H 0.087017 -1.130241 2.877565 H -2.934627 2.567836 4.595200 C 4.350605 -0.885357 1.627264 C -3.597420 2.871078 1.177851 C -3.813592 2.415058 -3.803911 C 4.107190 -1.548252 -1.203992 C -3.608059 -2.546649 1.437578 H -3.219088 2.148386 -4.691435 C 5.067959 1.037367 -0.361563 C 3.452468 -0.856381 -2.595965 H -4.278511 3.396610 -3.991323 C 3.411751 -1.453866 2.498454 H 2.687900 -0.074387 -2.630050 H -4.602332 1.658838 -3.678986 C 5.702010 -0.857500 2.006961 C 4.109085 -1.114709 -1.382914 C 4.715727 -2.609267 -3.682954 C 3.437259 -1.503870 -2.435494 C -2.743004 2.691594 2.433731 H 4.952328 -3.192127 -4.576253 C 5.008348 -2.591829 -0.957115 C -2.983121 -2.465514 -2.351922 C 0.632941 5.534801 -0.609369 C 5.290752 2.069812 0.564182 C 5.623101 -1.077507 1.866081 H 0.305078 5.446381 -1.656711 C 5.828582 1.007387 -1.538027 H 6.388633 -0.678662 1.196694 H 1.065578 6.541398 -0.476209 H 2.363443 -1.483889 2.192135 C -4.983467 -2.790485 1.492353 H -0.256786 5.460078 0.035326 C 3.812792 -1.983695 3.725925 H -5.501119 -2.820802 2.451224 C -0.234854 -5.507983 0.288102 H 6.447376 -0.411364 1.345318 C -2.752877 -2.255975 2.673491 H -0.366904 -5.559608 1.379409 C 6.100392 -1.385697 3.236055 C -5.096053 -2.885876 -0.931796 H 0.051972 -6.514994 -0.060156 H 2.712680 -0.705794 -2.619324 H -5.699741 -2.989814 -1.833557 H -1.207888 -5.261470 -0.161895 C 3.678922 -2.471209 -3.410951 C -2.895602 2.466973 -2.566090 C -1.828265 3.553814 -2.789531 H 5.528273 -2.651273 0.001376 C 3.761411 -1.591006 -3.741463 H -1.087480 3.563326 -1.977980 C 5.238035 -3.568884 -1.928713 H 3.246854 -1.373664 -4.680665 H -2.304709 4.545031 -2.841302 H 4.700095 2.109031 1.483225 C 2.618835 -4.669181 0.950277 H -1.296819 3.378854 -3.739112 C 6.264428 3.038102 0.326917 H 3.488306 -4.043782 0.697050 C -3.596940 -2.181291 3.961835 H 5.673780 0.211664 -2.269321 H 2.909683 -5.728707 0.846233 H -2.944381 -1.923492 4.810202 C 6.794993 1.987854 -1.780132 H 2.364190 -4.484741 2.005466 H -4.070747 -3.152089 4.181087 C 5.157322 -1.947718 4.099129 C -1.967402 -3.600389 -2.552931 H -4.374342 -1.407684 3.882377 H 3.069938 -2.426626 4.393860 H -1.467929 -3.497923 -3.529757 C 5.355067 -2.888998 -2.473833 H 7.154992 -1.355118 3.520802 H -2.477123 -4.576041 -2.528248 H 6.091996 -3.693996 -2.417365 H 3.153444 -2.421520 -4.367751 H -1.194173 -3.589217 -1.773413 C 7.032195 3.242395 -0.175705 C 4.579136 -3.508618 -3.157837 C 5.034682 1.261986 -0.083885 H 7.808924 4.009747 -0.210772 H 5.936738 -4.383066 -1.721186 C 6.008651 -1.730124 3.037390 C 5.804986 1.444782 -1.240505 C 7.019509 3.001642 -0.848891 H 7.070690 -1.857008 3.261607 H 5.638863 0.811819 -2.114206 H 6.430301 3.830260 1.061123 C -1.673865 3.799937 2.493125 C 6.267213 3.068304 0.981033 H 7.379169 1.951530 -2.702895 H -1.084826 3.715141 3.420784 H 6.442748 3.699635 1.855573 H 5.470805 -2.355539 5.063076 H -2.158208 4.788689 2.485164 C 2.592637 4.639933 1.555309 H 4.760454 -4.274615 -3.915411 H -0.981064 3.740566 1.641184 H 1.764093 4.646864 2.282265 H 7.778852 3.763892 -1.037654 C 1.675041 -4.652144 -1.973502 H 3.061075 5.638597 1.561927 H 0.844639 -4.519004 -2.683435 H 3.339945 3.907776 1.893436 Pu7b SCF energy = -4079.8594022 H 2.032080 -5.692795 -2.058708 C 6.795924 2.429707 -1.284280 H 2.494045 -3.980498 -2.273622 H 7.387895 2.557011 -2.194004 Pu -1.532692 0.076355 0.009565 C -3.944856 -2.456800 -3.557401 Ni 1.518268 0.473380 -0.000841 H -4.695391 -1.659401 -3.459155 Am7a SCF energy = -4121.3912053 P 3.683386 -0.008001 0.042691 H -4.455688 -3.427832 -3.662762 Si 1.150673 -4.302849 -0.187708 H -3.371233 -2.274671 -4.479312 Am -1.553716 0.111720 0.024011 Si 1.942522 4.229959 -0.176337 C -4.948220 3.231243 1.188135 Ni 1.631633 0.367117 -0.016668 N -2.903604 0.204713 2.241700 H -5.470990 3.400414 2.130229 Si 0.485767 -4.331983 0.550120 N -3.057050 0.016188 -2.133569 C -1.683059 -3.346256 2.855747 Si 1.996488 4.154220 -0.509881 C 0.135900 1.792994 -0.119739 H -0.969914 -3.358403 2.019482 N -3.222244 -1.857518 -0.257498 C -2.987464 2.650770 -0.064294 H -2.160037 -4.335948 2.925877 N -2.780458 2.386995 0.213022 H -1.883774 2.503151 -0.091524 H -1.116790 -3.171470 3.784843 C 0.879049 -1.326517 0.057079 C 0.901054 -1.267772 0.001552 C -5.644058 3.362048 -0.014998 C 0.507191 -2.512888 0.202546 C -2.998120 -2.507662 0.172820 H -6.700692 3.641874 0.004673 C -2.728829 1.391295 -2.443692 H -1.893479 -2.464010 0.118909 C -5.021254 3.126171 -1.241974 C -0.805389 -0.632588 -2.871664 C -0.962440 -0.750730 -2.652623 H -5.600100 3.214755 -2.162047 H -0.044111 -1.400764 -3.000349 H -0.119601 -1.415596 -2.819784 C 5.275923 2.089781 1.024673 C 0.305151 1.723210 0.067555 C -0.940692 0.664454 -2.717417 H 4.689163 1.955997 1.937307 C -0.787787 0.684875 2.921253 H -0.081711 1.287036 -2.948585 C 5.058047 -2.143421 -1.330278 H 0.119243 1.258391 3.104918 C -2.290507 -1.109817 -2.325819 H 5.567814 -2.372660 -0.392306 C -2.149552 -0.985990 -2.705383 C -2.100223 1.313367 2.382034 C 3.312649 4.361531 -1.468740 C -3.381045 -2.661594 -1.377877 C -2.106070 -0.891685 2.484149 H 4.149727 3.680436 -1.259665 C -2.007591 1.336508 2.696109 C 1.175129 2.538511 -0.159604 H 3.705032 5.392116 -1.497023 C -1.364872 1.714675 -2.600404 C 0.709435 -2.508824 -0.023811 H 2.916414 4.122403 -2.469240 H -1.042248 2.751928 -2.507248 320

Appendix

C -4.061462 -2.386509 0.706409 H 0.877987 -5.120016 -1.808103 H -0.161208 1.215075 -3.001713 C -3.100966 -0.848444 2.382454 H 1.508113 -6.286681 -0.614706 C -2.428639 -1.110626 -2.328128 C -0.422131 0.715851 -2.832193 H 2.418683 -4.789801 -0.975049 C -2.129258 1.324602 2.398339 H 0.630710 0.983808 -2.931190 C 0.535173 5.249220 -1.012273 C -2.182746 -0.868286 2.513824 C 1.328253 2.457039 -0.143418 H 0.126642 4.935620 -1.986830 C 1.216445 2.634501 -0.191653 C -3.152033 0.546895 2.450837 H 0.856431 6.300645 -1.106476 C 0.772497 -2.521000 -0.046351 H -4.096050 1.057196 2.269832 H -0.281612 5.195011 -0.274988 C -0.794581 0.909366 2.651330 C -2.698540 3.248149 1.292760 C 2.801160 4.888033 1.039346 H 0.079783 1.541857 2.773768 C -3.094605 0.044876 -2.507991 H 2.068034 4.961266 1.858594 C -3.866441 -2.603528 -0.983335 H -4.136332 -0.238461 -2.365018 H 3.176283 5.903012 0.825327 C -2.336394 1.080681 -2.441953 C -0.720837 -0.715386 2.883493 H 3.646945 4.276825 1.387405 C 3.334280 -1.448013 2.459424 H 0.236111 -1.212932 3.039442 C 3.229475 4.093442 -1.940510 H 2.280275 -1.325127 2.200874 C -3.329832 3.131917 -0.816608 H 4.104814 3.470388 -1.704410 C -3.674631 2.801513 -1.279779 C -1.852228 -1.472797 2.590355 H 3.583641 5.110469 -2.179351 C 4.307189 -0.951245 1.582162 H -1.771527 -2.556790 2.507534 H 2.748808 3.683015 -2.843733 C -0.832442 -0.498419 2.728476 C -4.318178 -1.697559 2.035032 P 3.789728 -0.197102 0.006387 H 0.006982 -1.159881 2.921959 C -2.154141 2.850848 2.656860 C 4.385467 -0.878924 1.623760 C -3.578467 2.917877 1.178782 C -3.727598 2.501944 -2.136917 C 4.154399 -1.543513 -1.210372 C -3.721355 -2.495190 1.474909 C -2.643923 -2.425758 -2.687616 C 5.115279 1.041485 -0.367350 C 3.512632 -0.924528 -2.574414 C -4.730546 -3.511689 0.211708 C 3.439028 -1.433573 2.496270 H 2.740578 -0.150184 -2.612935 H -5.450243 -4.129080 0.745477 C 5.736830 -0.863882 2.004787 C 4.178474 -1.166201 -1.363234 C -1.254782 -5.037737 0.728532 C 3.463617 -1.514695 -2.430680 C -2.723974 2.726591 2.433902 H -1.724951 -4.723037 1.673779 C 5.075369 -2.572059 -0.973724 C -3.139894 -2.457109 -2.323134 H -1.198679 -6.139754 0.740604 C 5.351853 2.064529 0.565646 C 5.664347 -1.110277 1.909653 H -1.927543 -4.731346 -0.086856 C 5.859313 1.023876 -1.554808 H 6.437456 -0.700010 1.256041 C -4.296301 -3.686008 -1.115982 H 2.390147 -1.453004 2.190056 C -5.104721 -2.683596 1.545533 H -4.626265 -4.456778 -1.809823 C 3.834476 -1.963639 3.725557 H -5.612018 -2.686158 2.510296 C -3.178158 4.519690 0.945024 H 6.487369 -0.426964 1.342735 C -2.846050 -2.225382 2.701490 H -3.245532 5.389117 1.596364 C 6.128865 -1.392349 3.235760 C -5.247767 -2.788998 -0.875161 C -1.491517 -3.435914 -2.847071 H 2.721549 -0.730186 -2.603603 H -5.864469 -2.873034 -1.770044 H -0.990405 -3.325247 -3.824543 C 3.704852 -2.482204 -3.406202 C -2.921862 2.480231 -2.573059 H -1.894270 -4.457662 -2.786510 H 5.610660 -2.619993 -0.023054 C 3.820470 -1.669377 -3.713578 H -0.742912 -3.313886 -2.050676 C 5.304617 -3.549420 -1.944951 H 3.298026 -1.466737 -4.651590 C -3.608343 -2.622814 -3.885110 H 4.774639 2.094537 1.493540 C 2.683423 -4.719475 0.793251 H -4.487537 -1.966185 -3.814644 C 6.322824 3.034698 0.324759 H 3.544766 -4.107302 0.485626 H -3.966030 -3.662895 -3.914379 H 5.693416 0.235967 -2.292197 H 2.950213 -5.783105 0.669333 H -3.086443 -2.413944 -4.833291 C 6.823147 2.005946 -1.800117 H 2.497535 -4.533154 1.862313 C -3.578442 4.446425 -0.399881 C 5.179060 -1.941701 4.099614 C -2.142829 -3.611187 -2.513270 H -4.008624 5.248817 -0.995082 H 3.086517 -2.396234 4.394654 H -1.650403 -3.534132 -3.495969 C -5.175343 1.975835 -2.021956 H 7.183524 -1.372034 3.521291 H -2.667730 -4.578042 -2.466721 H -5.515604 1.506739 -2.961155 H 3.162744 -2.445260 -4.354285 H -1.361451 -3.602065 -1.741188 H -5.843991 2.819996 -1.798459 C 4.625276 -3.504205 -3.163699 C 5.094299 1.223934 -0.065512 H -5.278088 1.246029 -1.204313 H 6.018835 -4.352100 -1.745482 C 6.035547 -1.767756 3.082842 C -5.604603 -0.850608 1.914724 C 7.061665 3.009893 -0.861615 H 7.094617 -1.885803 3.324942 H -5.528421 -0.109225 1.104401 H 6.499556 3.818998 1.064884 C -1.619442 3.800642 2.478191 H -5.839631 -0.324992 2.856455 H 7.394511 1.978673 -2.731203 H -1.029164 3.706013 3.404067 H -6.446331 -1.515783 1.673641 H 5.487458 -2.350389 5.064878 H -2.073320 4.803817 2.463569 C -4.546030 -2.733977 3.160320 H 4.806320 -4.270496 -3.921091 H -0.931304 3.714094 1.624640 H -5.434321 -3.343581 2.937592 H 7.819225 3.773304 -1.052887 C 1.557863 -4.665199 -2.069157 H -4.715378 -2.224052 4.122556 H 0.690416 -4.490813 -2.723756 H -3.691216 -3.416780 3.270473 Am7b SCF energy = -4121.395441 H 1.871549 -5.715914 -2.191646 C -0.822591 3.579204 2.928798 H 2.380661 -4.016813 -2.408450 H -0.439033 3.348311 3.937852 Am -1.490083 0.060926 0.001953 C -4.113366 -2.457598 -3.519150 H -0.987777 4.665252 2.871551 Ni 1.592917 0.466281 -0.004704 H -4.844942 -1.641766 -3.431972 H -0.062756 3.310661 2.180910 P 3.754830 -0.054648 0.056137 H -4.645405 -3.419947 -3.596514 C -3.152980 3.274529 3.767489 Si 1.154984 -4.324768 -0.251431 H -3.545220 -2.308230 -4.450343 H -4.148044 2.831854 3.616018 Si 2.018475 4.309096 -0.227961 C -4.935451 3.253700 1.199938 H -3.269563 4.368282 3.769800 N -2.961883 0.241216 2.282002 H -5.452904 3.409996 2.146972 H -2.777040 2.966737 4.756997 N -3.169755 0.032551 -2.149539 C -1.791112 -3.334345 2.859521 C -3.694055 3.540910 -3.279966 C 0.248526 1.815787 -0.150934 H -1.091485 -3.356166 2.011965 H -2.705072 4.011329 -3.378862 C -2.973034 2.716974 -0.069254 H -2.283145 -4.316635 2.931877 H -4.428883 4.337714 -3.090333 H -1.875323 2.573367 -0.105231 H -1.205611 -3.175002 3.779334 H -3.952679 3.061259 -4.237575 C 0.967488 -1.284253 -0.003260 C -5.644786 3.373164 0.004154 C 1.418290 -4.639039 2.173221 C -3.124544 -2.490443 0.203698 H -6.705802 3.634947 0.033221 H 2.464951 -4.304289 2.105755 H -2.021708 -2.480092 0.137418 C -5.029953 3.139989 -1.226753 H 1.414578 -5.717149 2.408122 C -1.091647 -0.794682 -2.679312 H -5.620122 3.208582 -2.141110 H 0.941662 -4.110240 3.015049 H -0.272880 -1.486821 -2.857423 C 5.312722 2.066028 1.037182 C 1.409519 -5.212970 -0.848508 C -1.030718 0.614412 -2.750502 H 4.713936 1.938460 1.942946 321

Appendix

C 5.136181 -2.186547 -1.304331 H 5.652827 -2.401267 -0.366618 C 3.392144 4.381603 -1.519565 H 4.209084 3.681192 -1.293182 H 3.813689 5.399902 -1.564906 H 2.992388 4.134381 -2.516462 C -5.852517 -2.846586 0.379919 H -6.933411 -2.993623 0.450204 C 5.058299 -2.262428 3.949902 H 5.350900 -2.768614 4.872999 C 3.708571 -2.098177 3.636931 H 2.938654 -2.475112 4.314857 C -3.556045 2.829827 3.728148 H -4.361221 2.081032 3.738644 H -3.992452 3.836040 3.838168 H -2.906002 2.645465 4.597503 C -3.852175 2.467048 -3.802725 H -3.272864 2.191229 -4.697540 H -4.290595 3.463371 -3.976469 H -4.659646 1.731158 -3.677982 C 4.781997 -2.680385 -3.649182 H 5.017087 -3.271427 -4.537479 C 0.707783 5.600486 -0.684845 H 0.353936 5.466675 -1.718794 H 1.144061 6.610824 -0.603370 H -0.165097 5.550796 -0.015041 C -0.227512 -5.492656 0.308884 H -0.322692 -5.505318 1.405271 H 0.032798 -6.514805 -0.015310 H -1.211489 -5.245627 -0.116683 C -1.816539 3.526281 -2.808064 H -1.065991 3.512383 -2.005253 H -2.257813 4.533914 -2.857148 H -1.301260 3.331089 -3.762549 C -3.670325 -2.150212 4.002633 H -3.000151 -1.917174 4.844448 H -4.162826 -3.113102 4.216181 H -4.430225 -1.357836 3.943575 C 5.431362 -2.942412 -2.441324 H 6.174756 -3.741088 -2.381023 C 7.075071 3.219048 -0.154019 H 7.846118 3.992134 -0.187553 C 5.876039 1.400739 -1.215422 H 5.725216 0.756824 -2.083911 C 6.297245 3.051452 0.995131 H 6.457033 3.693747 1.864630 C 2.672812 4.728884 1.497370 H 1.847064 4.740030 2.227121 H 3.141934 5.727183 1.495650 H 3.421655 3.998158 1.835758 C 6.859035 2.393497 -1.257314 H 7.460972 2.516686 -2.160972

322