Computational Studies of Actinide Complexes with Expanded Porphyrins Poppy Di Pietro UCL PhD in Chemistry 1 I, Poppy Di Pietro, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. 2 Abstract Covalency in complexes of the actinides has been identified as the potential driving force behind selective behaviour exhibited by separation ligands of use to the nuclear industry. In this thesis, complexes of actinyls with hexadentate macrocyclic expanded porphyrin ligands are investigated at the density functional level of theory and their electron densities analysed in detail. Initially, strong correlations are established between the vibrational frequencies of the distinctive uranyl stretching modes and covalency in the equatorial bonds of several simple uranyl complexes with monodentate first row ligands, with redshift of the uranyl stretching modes indicating a weakening of the U-Oyl interaction as a result of competing interactions in the equatorial plane. Subsequently, strong similarities are established in the U-N and U-Oyl bonding character of two multidentate uranyl complexes: 2+ UO2-isoamethyrin(1.0.1.0.0.0) and [UO2(bis-triazinyl-pyridine)2] , where isoamethyrin(1.0.1.0.0.0) is a hexadentate macrocyclic expanded porphyrin ligand and bis-trizinyl-pyridine (BTP) is a tridentate ligand which has shown selectivity for An(III) over Ln(III). A series of uranyl hexaphyrin complexes is then investigated, finding moderate correlations between stability, equatorial covalency and the frequencies of the uranyl stretching modes, which crucially only hold when there is a degree of relative planarity in the ligand. It is found that smaller ligands have greater stability and equatorial covalency. Broadening the study to include neptunyl and plutonyl complexes finds that the isoamethyrin complex shows some evidence for selectivity for uranyl over later actinides in the same oxidation state, but significant spin contamination throws the appropriateness of these methodologies for dealing with open-shell actinide systems into question. Preliminary calculations performed using spin constrained DFT were found to be helpful here, but a full geometry reoptimisation will ultimately be necessary to fully appreciate the effects of spin contamination on the geometry and electronic structure of the neptunyl and plutonyl complexes. 3 Publications Work completed during this PhD project has been published in: First Author: Ligand size dependence of U-N and U-O bond character in a series of uranyl hexaphyrin complexes: quantum chemical simulation and density based analysis, Poppy Di Pietro & Andrew Kerridge, PCCP, March 2017 Assessing covalency in equatorial U-N bonds: density based measures of bonding in BTP and isoamethyrin complexes of uranyl, Poppy Di Pietro & Andrew Kerridge, PCCP, June 2016 U-Oyl stretching vibrations as a quantitative measure of equatorial bond covalency in uranyl complexes: a quantum chemical investigation, Poppy Di Pietro & Andrew Kerridge, Inorganic Chemistry, January 2016 The above publications form a major part of Chapters 3, 4 and 5 of this thesis. Additionally: Contributing Author: Neptunyl(VI) centred visible LMCT emission directly observable in the presence of uranyl(VI), Sean D. Woodall, Adam N. Swinburne, Nidhu lal Banik, Andrew Kerridge, Poppy Di Pietro, Christian Adam, Peter Kaden and Louise S. Natrajan, Chemical Communications, December 2014 Acknowledgements My first and greatest thanks must go to my supervisor, Andy Kerridge, without whose help, support, and many good ideas this work would not have been possible. Also, Nik Kaltsoyannis for taking over as ‘on paper’ supervisor upon Andy’s departure and Rob Bell for taking over as ‘on paper’ supervisor upon Nik’s departure. It looks like I’ve been scaring them away… I would like to give my thanks to everyone who worked in G19 alongside me, in particular, but not limited to: Joe, Eszter, Abi, Nick, Qian-Rui, Reece, Kieran and Bengt for somehow turning a hot, windowless box into a friendly and supportive working environment. Thanks for lots of interesting conversations (sometimes even about science…!), lots of biscuits and many, many cups of tea. The support services at legion@ucl and grace@ucl, as well as at the NSCCS for answering my (occasionally silly) questions. Last but not least, thanks to Rob, whose love and support has been vital. 4 Contents Abstract 3 Publications 4 Acknowledgements 4 Contents 5 Table of Figures 9 Table of Tables 14 1. Introduction and Literature Review 19 1.1. Context: Spent Nuclear Fuel 19 1.2. Context: Computational Motivation 20 1.3. Actinyl Complexes 21 1.3.1. Introduction to Actinide and Actinyl Complexes 21 1.3.2. Relevant Literature Focussing on Actinyl Complexation 22 1.4. Expanded Porphyrins 27 1.4.1. Introduction to Expanded Porphyrins 27 1.4.2. Literature Relating to Synthesised Expanded Porphyrins 31 1.4.2.1. Systems with Five Pyrrole Units 31 1.4.2.2. Systems with Six Pyrrole Units 33 1.4.2.3. Larger Macrocycles and Hybrid Macrocycles 36 1.4.3. Computational Modelling of Expanded Porphyrins and their F-element Complexes 41 1.5. Summary 50 2. Methodology 51 2.1. Bra-Ket Notation 51 2.2. Introduction to Quantum Chemistry 51 2.3. Basis Sets 52 2.4. Introduction to Electronic Structure Calculations 55 2.5. The Hartree-Fock Method 56 2.6. Multiconfigurational (Post-HF) Methods 59 2.6.1. Introduction to Multiconfigurational Calculations 59 2.6.2. The Complete/Restricted Active Space, Self-Consistent Field Method 62 2.6.3. Many-Body Perturbation Theory and CASPT2 64 5 2.7. Relativistic Effects 66 2.7.1. Effects of Relativity in Atoms 66 2.7.2. Relativistic Hamiltonians 67 2.7.3. Relativistic Pseudopotentials 69 2.8. Density Functional Theory 69 2.8.1. The Thomas-Fermi-Dirac Model: Orbital Free DFT 70 2.8.2. The Hohenberg-Kohn Theorems 70 2.8.3. Kohn-Sham DFT 71 2.8.4. Pure Exchange-Correlation Functionals 72 2.8.5. Hybrid Exchange-Correlation Functionals 74 2.8.6. Time-Dependent DFT 75 2.8.7. Performing DFT calculations 75 2.8.8. Problems with DFT 76 2.9. Analysis Methods 77 2.9.1. The Quantum Theory of Atoms in Molecules (QTAIM) 77 2.9.2. The Electron Localisation Function 80 2.9.3. The Reduced Density Gradient 81 2.9.4. Electron Density Difference Distributions 82 2.10. Quantum Chemistry Software Packages 83 3. Results: U-Oyl Stretching Vibrations as a Quantitative Measure of Equatorial Bond Covalency in Uranyl Complexes 84 3.1. Introduction 84 3.2. Computational Details 87 3.3. Results and Discussion 88 3.3.1. Binding Energies as a Function of Coordination Number 88 3.3.2. Structural and Vibrational Characterisation 89 3.3.3. Density-Based Analyses of Electronic Structure 93 3.3.3.1. Electron Density Difference Distributions 93 3.3.3.2. Analysis with the Quantum Theory of Atoms in Molecules 97 3.3.3.3. Analysis of the Electron Localisation Function (ELF) 109 3.3.3.4. Analysis of the Reduced Density Gradient 112 3.4. Summary and Conclusions 116 3.5. Publication Notes 117 6 4. Results: Density Based Measures of Bonding in Multidentate Complexes of Uranyl: Assessing Covalency in U-N Bonds. 118 4.1. Introduction 118 4.2. Computational Details 120 4.3. Results and Discussion 121 4.3.1. Structural Characterisation 121 4.3.2. Analysis with the Quantum Theory of Atoms in Molecules 125 4.3.3. Analysis of the Electron Localisation Function 131 4.3.4. Analysis of the Reduced Density Gradient 133 4.3.5. Electron Density Difference Distributions 136 4.4. Summary and Conclusions 137 4.5. Publication Notes 139 5. Results: The Ligand Size Dependence of Equatorial Covalency and Stability, and Corresponding Effects on U-O Character, in a Series of Uranyl Hexaphyrins 140 5.1. Introduction 140 5.2. Computational Details 144 5.3. Results and Discussion 146 5.3.1. Structural Characterisation 146 5.3.2. Binding and Deformation Energies 151 5.3.3. U-O Stretching Frequencies 151 5.3.4. Topological Analysis of the Electron Density 157 5.3.5. Analysis of the Reduced Density Gradient 161 5.3.6. Integrated Properties of the Electron Density 163 5.3.7. Electron Density Difference Distributions 166 5.4. Summary and Conclusions 168 5.5. Publication Notes 171 2+ 6. Results: AnO2 (An = U, Np, Pu) Complexes With Hexaphyrin Ligands Investigated Using DFT 172 6.1. Introduction 172 6.2. Computational Details 173 6.3. Results and Discussion 175 7 2+ 6.3.1. Isolated AnO2 ; An = U, Np, Pu 175 6.3.1.1. Structural and Vibrational Characterisation 175 6.3.1.2. QTAIM - Topological and Integrated Properties 176 6.3.2. Spin Contamination Analysis for Spin Unconstrained Systems 178 6.3.3. AnO2-isoamethyrin(1.0.1.0.0.0)′; An = U, Np, Pu 180 6.3.3.1. Structural and Energetic Data 180 6.3.3.2. Vibrational Data 183 6.3.3.3. QTAIM - Topological and Integrated Properties 184 6.3.3.4. Electron Density Difference Distributions 189 6.3.3.5. Spin Density and Spin Population Analysis for AnO2- isoamethyrin(1.0.1.0.0.0)′, An = Np and Pu 191 6.3.3.6. AnO2-isoamethyrin(1.0.1.0.0.0)′ Conclusions 192 6.3.4. Density-based Analysis of AnO2-cyclo[6]pyrrole; An = U, Np, Pu: the Spin Unrestricted Approach vs. the Spin Constrained Approach. 193 6.3.4.1. Structural data 193 6.3.4.2. QTAIM - Topological and Integrated Properties 195 6.3.4.3. Electron Density Difference Distributions 201 6.3.4.4. Spin Density and Spin Population Analysis for AnO2- cyclo[6]pyrrole, An = Np and Pu 203 6.3.4.5.