Unconventional Bonding in Organic Chemistry; Covalent Bonding in Transition Metal Clusters Alan Wilfred Humason Southern Methodist University, Ahumason@Smu.Edu

Southern Methodist University SMU Scholar

Chemistry Theses and Dissertations Chemistry

Spring 5-19-2018 Multi-Reference Systems in Chemistry; Unconventional Bonding in Organic Chemistry; Covalent Bonding in Transition Metal Clusters Alan Wilfred Humason Southern Methodist University, [email protected]

Follow this and additional works at: https://scholar.smu.edu/hum_sci_chemistry_etds Part of the Inorganic Chemistry Commons, Organic Chemistry Commons, and the Physical Chemistry Commons

Recommended Citation Humason, Alan Wilfred, "Multi-Reference Systems in Chemistry; Unconventional Bonding in Organic Chemistry; Covalent Bonding in Transition Metal Clusters" (2018). Chemistry Theses and Dissertations. 3. https://scholar.smu.edu/hum_sci_chemistry_etds/3

This Dissertation is brought to you for free and open access by the Chemistry at SMU Scholar. It has been accepted for inclusion in Chemistry Theses and Dissertations by an authorized administrator of SMU Scholar. For more information, please visit http://digitalrepository.smu.edu. MULTI-REFERENCE SYSTEMS IN CHEMISTRY UNCONVENTIONAL BONDING IN ORGANIC CHEMISTRY COVALENT BONDING IN TRANSITION METAL CLUSTERS

Approved by:

Dr. Elfriede Kraka Professor and Chair of Chemistry

Dr. Werner Horsthemke Professor of Chemistry

Dr. Peng Tao Assistant Professor of Chemistry

Dr. John Wise Associate Professor of Biology MULTI-REFERENCE SYSTEMS IN CHEMISTRY

UNCONVENTIONAL BONDING IN ORGANIC CHEMISTRY

COVALENT BONDING IN TRANSITION METAL CLUSTERS

A Dissertation Presented to the Graduate Faculty of the

Dedman College

Southern Methodist University

Partial Fulﬁllment of the Requirements

for the degree of

Doctor of Philosophy

with a

Major in Chemistry

Alan Humason

Bachelor of Science, Chemistry, University of Massachusetts, Amherst Master of Science, Chemistry, Southern Methodist University, Dallas, TX

May 19, 2018 Copyright (2018)

Alan Humason

It requires four scientists to do computational chemistry; the chemist, the physicist, the mathematician, and the computer scientist. Having been for many years merely a chemist, I must thank the many fellow scientists who have put their work aside for mine. I thank Dr. Thomas Sexton, for his clarity in explaining the physics that I had long forgotten, and the mathematics that I never knew. I thank Dr. Vytor Pinerio Oliveria, for many fruitful scholarly discussions, always freely granted without bravado and (I hope) to our mutual enrichment. I thank Drs. Robert John Brown Kalescky and Marek Freindorf for their expertise, their instruction, and their efforts with and against the unforgiving computer clusters. But, mostly I thank Professor Dr. Dieter Cremer, for being the true embodiment of the four scientists. He could bring the chemistry, physics, mathematics and computer sciences together, and shared that knowledge and expertise literally to the end of his days. My proudest academic accolade came at the completion of the annulene project, when he said, “I now see that you have the intelligence to make a Ph.D.” I thank and wish to praise my current research advisor, Dr. Elfi Kraka, who, after the sudden death of my advisor Dr. Cremer picked up the pieces of my academic career and carried me to this finish line. The strength, dedication, and love that that required was beyond anything that I have seen before or will probably ever see again. I wish to thank Dr. Michael Lattman, for guiding me through the intricacies of the graduate school process, and Dr. Patty Wisian-Neilson for being his right arm. Sometimes you just need friends.

iv Humason, Alan Bachelor of Science, Chemistry, University of Massachusetts, Amherst Master of Science, Chemistry, Southern Methodist University, Dallas, TX

Multi-Reference Systems in Chemistry Unconventional Bonding in Organic Chemistry Covalent Bonding in Transition Metal Clusters

Advisor: Dr. Elfriede Kraka Doctor of Philosophy degree conferred May 19, 2018 Dissertation completed April 19, 2018

The geometries, chemical properties, and reactivities of molecules are determined by their electronic structure. The field of ab initio computational chemistry works to calculate the kinetic and potential energies between the nuclei and electrons of a molecule. These calculations usually begin with the determination the electronic ground state. Molecules that cannot be adequately described with a single, ground state configuration are called multi-reference systems, which require the calculation of a linear combination of all pertinent electronic configurations, with a corresponding increase in computational cost. This is not ‘black box’ methodology, because solving these systems requires a good understanding of the chemistry being described, so that the important configurations among millions of possibilities can be selected. Their multi-reference character also makes them some of the most interesting molecules in chemistry. In this dissertation, we have studied ultra-long CC bonds in simple and unique organic molecules, biradical pancake bonded species, fluxional bridged annulenes, and covalently bonded transition metal diatoms. We find that CC ultra-long bonds and electrostatic pancake bonding interactions can be described by single-reference methods, but that fluxional bridged annulenes require multi- reference methods. Transition metal diatoms can only be described by multi-reference methods. We determined which methods, basis sets, and active spaces work best in each of the 30 cases.

v TABLE OF CONTENTS

LIST OF FIGURES ...... vii

LIST OF TABLES ...... xi

LIST OF SYMBOLS AND ACRONYMS ...... xiii

CHAPTER

1. Introduction ...... 1

1.1. Multireference Systems - What, Why and How? ...... 1

2. Characterization of Carbon-Carbon Single Bond Strength ...... 4

2.1. Single-Reference Descriptions ...... 4

2.2. Application of Vibrational Spectroscopy ...... 6

3. General Characterization of Carbon-Carbon Bond Strength ...... 13

3.1. Extension of the Single-Reference Description to Unconventional Systems . . 13

3.2. Reﬁnement of Single-Reference Descriptions...... 13

3.3. The Shortest CC Single Bonds in Chemistry ...... 20

3.4. The Longest CC Single Bonds in Chemistry...... 21

4. Characterization of Multi-reference Systems by Single-reference Density Func- tional Theory - Pancake Bonding ...... 23

4.1. Reﬁnement of Single-Reference Calculations - Broken Symmetry...... 23

4.2. Characterization of Pancake Bonding Interactions ...... 25

5. Bridged Annulenes; The Longest CC Bonds? ...... 36

5.1. The Puzzle of 11,11-Dimethyl-methano[10]annulene ...... 36

5.2. Analysis of the Annulene Systems by Multiple Levels of Theory ...... 38

5.3. Does 11,11-dimethyl-methano[10]annulene possess the longest homoaromatic CC bond of neutral hydrocarbons? ...... 57

vi 6. Multi-Reference Systems in Inorganic Chemistry ...... 65

6.1. Transition Metal Diatoms ...... 65

6.2. A Survey of All Transition Metal Diatoms ...... 65

6.3. Integration of all Findings ...... 77

7. Transition Metal Diatoms - Maximum Bond Multiplicity ...... 80

8. Conclusions ...... 82

8.1. Single-Reference Systems ...... 82

8.2. Single-Reference Methods on Multi-Reference Systems ...... 83

8.3. Multi-Reference Methods in Organic Chemistry ...... 83

8.4. Multi-Reference Methods in Inorganic Chemistry...... 84

8.5. Outlook ...... 84

9. Calculations and Methodology ...... 86

9.1. Single-Reference Computational Methods - Organic Chemistry ...... 86

9.2. Single-Reference Computational Methods Beyond Energies ...... 89

9.3. Multi-Reference Computational Methods ...... 91

APPENDIX

A. Publications, Supporting Information and Manuscripts ...... 95

BIBLIOGRAPHY ...... 205

vii LIST OF FIGURES

Figure Page

2.1 Local Mode Stretching Force Constants (ka) to Bond Strength Order (ωB97X- D/aug-cc-pVTZ), Single Bonds. This plot serves as a conversion chart between the two parameters...... 9

2.2 Organic molecules investigated in this work. The single and multiple bonds reported are in red. All molecules have singlet ground states...... 10

3.1 Organic molecules investigated in this work. The single and multiple bonds reported are in red...... 14

3.2 Local Mode Stretching Force Constants (ka) to Bond Strength Order (ωB97X- D/aug-cc-pVTZ), Single, Multiple and Aromatic Bonds. This plot serves as a conversion chart between the two parameters...... 16

3.3 Bond Length (ωB97X-D/aug-cc-pVTZ) to Bond Strength Order for CC single bonds. [139,140,239–241](R2 = 0.9955) ...... 17

4.1 Pancake bonded molecules investigated in this work. 4.1) HCNSSN dimer. 4.2) HCNSeSeN dimer. 4.3) HCNTeTeN dimer. 4.4) phenalenyl dimer. 4.5) 2,5,8-trimethylphenalenyl dimer. 4.6) 2,5,8-tri-t-butylphenalenyl dimer. Pancake Bonding Interactions are displayed in red...... 24

4.2 C2 Symmetry geometries for the HCNTeTeN dimer. a) Singlet. b) Triplet. .... 27

4.3 Triplet state geometries for the phenalenyl dimer. a) Staggered. b) Eclipsed. c) Minimum energy geometry...... 28

4.4 Dissociation Curves for sytems 1 and 2 (BS-UM06/6-311G(d,p), 3 (BS- UM06/SDD), 4 and 5. (BS-UM05-2X/6-31++G(d,p).) ...... 29

4.5 Bond Strength Orders (BSO) and Optimized Bond Lengths (in parentheses, A)˚ for the Phenalenyl, Trimethylphenalenyl and tri-tert-Butylphenalenyl Radical Monomers and Dimers (4.4 through 4.6.) The Aromaticity In- dices (AI), Bond Weakening/Strengthening parameters (WS) and Bond Alteration parameters (ALT) for the full carbon ring structures (FULL) and the outer ring structure (OUTER) are indicated in boxes...... 33

5.1 Annulene species investigated in this work...... 37

viii 5.2 Representation of the energy as a function of the 1,6-distance obtained at multiple levels of theory. a)11,11-dimethyl-1,6-methano[10]annulene b)1,6-methano[10]annulene and c) 1,3,5-cycloheptatriene...... 39

5.3 Representation of the energy and enthapy as a function of the 1,6-distance of a)11,11-dimethyl-1,6-methano[10]annulene b)1,6-methano[10]annulene and c) 1,3,5-cycloheptatriene. a) was obtained by CASPT2(14,14)/6-311G(d,p)// B3LYP/6-311G(d,p) and CCSD(T)/6-311G(d,p)// B3LYP/6/311G(d,p), b) by CASPT2(14,14)/6-311G(d,p)// B3LYP/6/311G(d,p), and c) by CASPT2(10,10)/6-311G(d,p)// B3LYP/6-311G(d,p). In all cases, the relative energy and enthalpy (∆H(298K)) are included...... 41

5.4 Dimer and tetramer configurations that were calculated for this work. The green structure shows how two unit cells fit together in the crystal structure. The numbers on this structure are taken from Bianchi’s x-ray structure. The blue structure shows the arrangement that was calculated and optimized searching for packing effects. The orange structure shows the geometry and hydrogen-to-ring distance for the two optimized structures, ωB97X-D/6-311G(d,p)...... 53

5.5 a) Dependence of calculated NMR chemical shifts [ppm] as a function of the C1,C6 interatomic distance of 11,11-dimethyl-1,6-methano[10]annulene as obtained at the B3LYP/GIAO/6-311G(d,p) level of theory. b) NMR ab inito analysis of the mean deviation between measured and calculated 13C NMR chemical shifts...... 55

5.6 Dependence of calculated NMR spin-spin coupling constants [Hz] as a function of the C1,C6 interatomic distance of 11,11-dimethyl-1,6-methano[10]annulene as obtained at the B3LYP/GIAO/6-311G(d,p) level of theory...... 56

5.7 Bond strength orders for carbon-carbon bonding interactions in 11,11-dimethyl- 1,6-methano[10]annulene system as a function of C1,C6 interatomic distance, analyzed by adiabatic mode analysis, B3LYP/6-311G(d,p)...... 58

5.8 Dependence of a) electron density distribution and b) energy density distribution on the C1,C6 interatomic distance of 11,11-dimethyl-1,6-methano[10]annulene as obtained from the AIMAll program...... 60

5.9 B3LYP geometries of 5.1 - 5.6. Bond lengths in A˚ and bond angles in degrees. 63

6.1 Calculated Bond Length by Periodic Table Row, All Diatoms...... 75

6.2 Calculated Bond Dissociation Energy by Periodic Table Row, All Diatoms. .... 76

6.3 Calculated Stretching Force Constant by Periodic Table Row, All Diatoms. .... 77

ix 6.4 Calculated Stretching Force Constant versus Bond Strength Order, All Di- atoms. This plot serves as a conversion chart between the two parameters. . 78

8.1 Local Mode Stretching Force Contants (ka) versus Number of Methyl Groups for a Series of Organic Compounds...... 85

x LIST OF TABLES

Table Page

2.1 Calculated and experimental Carbon-Carbon Bond Lengths R [A],˚ Bond Dissociation Enthalpies BDH [kcal/mol], local mode stretching con- a 1 stants k [mdyn/A],˚ local mode frequencies ωa [cm− ], Bond Strength Orders BSO, and Energy Densities [Hartree/A˚3] for all molecules, ωB97X- D/aug-cc-pVTZ ...... 8

3.1 Calculated and experimental Carbon-Carbon Bond Lengths R [A],˚ Bond Dissociation Enthalpies BDH [kcal/mol], local mode stretching con- a 1 stants k [mdyn/A],˚ local mode frequencies ωa [cm− ], Bond Strength Orders BSO, and Energy Densities [Hartree/A˚3] for all molecules, ωB97X- D/aug-cc-pVTZ...... 15

3.2 Calculated Carbon-Carbon Bond Lengths (re) for various 1,1,1-Trihaloethanes, ωB97X-D/3-21G...... 18

3.3 Calculated Carbon-Carbon Bond Lengths (re) for C-C Single Bonds hybridized by multiple or aromatic carbons, ωB97X-D/aug-cc-pVTZ ...... 21

4.1 Energy Gap results for all Species. CC Distance [A],˚ Triplet/Singlet Gap [kcal/mol] ...... 26

4.2 Calculated and experimental Carbon-Carbon interatomic distances R [A],˚ Dissociation Energies, Counterpoise Complexation Energies and Bond Dissociation Energies DEcalc, CECP and BDEexp [kcal/mol], local mode a a 1 stretching constants k [mdyn/A],˚ local mode frequencies ω [cm− ], Bond Strength Orders BSO, and Electron and Energy Densities, ρ and 3 3 Hb [electron/A˚ and Hartree/A˚ , respectively] for all molecules. Level of Theory is UM06/6-311G(d,p) for 4.1 and 4.2, UM06/SDD for 4.3, and UM05-2X/6-31++G(d,p) for 4.4, 4.5 and 4.6...... 30

4.3 Aromaticity Indices for the Phenalenyl, Trimethylphenalenyl and tri-tert- Butylphenalenyl Free Radical Dimers...... 32

5.1 Relative Energies and Tautomerization Barriers of 11,11-Dimethyl-1,6-methano[10]annulene. 42

5.2 Relative Energies and Tautomerization Barriers of 1,6-Methano[10]annulene.... 47

5.3 Relative Energies and Tautomerization Barriers of 1,3,5-Cycloheptadiene and Norcaradiene...... 48

xi 5.4 Bond Strength Orders for all pertinent C,C interactions of 11,11-Dimethyl- 1,6-methano[10]annulene at the stationary geometries (ethane = 1, ethene = 2.) ...... 58

6.1 AQCC, CASPT2, RASPT2 Calculations by aug-cc-pVQZ basis sets and RASPT2 Calculations by ANO-RCC basis set. Summary of all results...... 73

6.2 Summary of Bond Strength Orders (BSO) and the methods which produced the best results for each transition metal diatom...... 75

xii LIST OF SYMBOLS AND ACRONYMS

ke - Equilibrium Stretching Force Constant ka - Local Mode (Adiabatic) Stretching Force Constant ωa - Local Mode (Adiabatic) Vibrational Frequency rCC - Carbon-Carbon Interatomic Distance

R - rC1,C6 for Annulene Systems re - Equilibrium Bond Length re - Bond Length by electron diﬀraction rb - Bond Critical Point rr - Ring Critical Point

ρr - Electron Density

Hb - Energy Density me - millielectrons - dielectric constant µ - dipole moment ∆E - Energy Change ∆H - Enthalpy Change ∆G - Gibbs Free Energy Change

BDE - Bond Dissociation Energy BDH - Bond Dissociation Enthalpy BSO - Bond Strength Order NBO - Natural Bond Order PEC - Potential Energy Curve

xiii PHC - Potential Enthalpy Curve PGC - Potential Gibbs Free Energy Curve ZPE - Zero Point Energy TS - Transition State LCAO - Linear Combination of Atomic Orbitals HOMO - Highest Occupied Molecular Orbital LUMO - Lowest Unoccupied Molecular Orbital

HF - Hartree Fock Theory WFT - Wave Function Theory FCI - Full Conﬁguration Interaction CAS - Complete Active Space RAS - Restricted Active Space SCF - Self Consistent Field CSF - Conﬁguration State Function

DFT - Density Functional Theory

AIM - Atoms-in-Molecules (Topological Analysis) BCP - Bond Critical Point RCP - Ring Critical Point CCP - Cage Critical Point

AI - Aromaticity Index WS - Bong Weakening/Strengthening Parameter ALT - Bond Strength Alteration Parameter

xiv This is dedicated to my family, for their support, and to my students, for their patience. But mostly this is dedicated to my wife, Melissa McNamara Humason, B.M.E., M.S., for her unﬂagging belief that I would succeed. Chapter 1

Introduction

Multireference Systems in Computational Chemistry.

1.1. Multireference Systems - What, Why and How?

Systems that can be described with good precision by determining the electronic configuration in the ground state are called single reference systems. From the ground state the gap between the highest energy occupied molecular orbital (HOMO) and the lowest energy unoccupied molecular orbital (LUMO) can be determined, and if that energy is reasonably large, then a single reference description can be used. Much of computational chemistry is done by single reference calculations, working with single molecules, in vacuum and at 0K. The energy differences between a molecule at 0K in vacuum and a system of molecules at 298K at one atmosphere are significant, but when making comparisons between two systems (different constitutional or rotational isomers, molecules before and after a reaction, larger versus smaller systems), the relative energy differences are usually comparable, and this approximation is usually valid. Using a single reference description is also an approximation, and not all systems can be adequately described this way. Some systems that cannot be described by their ground electronic state are:

Molecular systems with low-lying excited states (a narrow HOMO-LUMO gap.) • Molecules with signiﬁcant biradicaloid character. • Fluxional molecules, that undergo interchange of atoms between symmetry-equivalent • positions.

Metallic systems, which participate in metallic bonding. • 1 Small metal clusters, which participate in covalent bonding, but with many low-lying • excited states.

Chemically reacting molecules, in the process of bond breaking and/or bond formation. • In these cases, the ground state configuration of the molecule does not fully or accurately describe the electronic state of the molecule, and the inclusion of additional electronic configurations, known as configuration state functions (CSF’s) is necessary. These cases are called multi-reference systems. The calculation of all likely electronic states for multi-reference systems is expensive, as each additional CSF increases the cost. The best results are obtained by including all possible electronic states, with each electron placed into every occupied orbital in turn, which is known as a ‘full configuration interaction’ (FCI) calculation. Although this method is proven to be the best possible, the number of CSF’s increases so rapidly that FCI becomes unfeasible for systems greater than 10 electrons (as in water.) Therefore, to analyze a system of larger size, additional approximations are required. The chemistry of a molecule usually depends upon the valence shell electrons. Cost can be reduced by excluding CSF’s which involve the promotion of lower energy core electrons into valence and excited state orbitals. Excitations into very high excited states will make only small contributions, and can be excluded to save cost. These are the first steps in defining an ‘active space’ to describe a molecule. When the task is to define a certain chemistry, the calculation can be reduced further by including only the electrons and basis functions that describe that chemistry. For example, the Walsh orbital description of cyclopropane puts six bonding electrons into three bonding and three antibonding molecular orbitals. [52] Therefore, the bonding in this molecule can be described by placing the six electrons into the six Walsh orbitals in every possible arrangement. In shorthand, this is known as a (6,6) active space. Selecting an active space requires a very good knowledge of the chemistry being described. In the case of cyclopropane, the six Walsh orbitals may not be the three highest energy occupied orbitals and the three lowest energy unoccupied (virtual) orbitals. Orbitals must

2 be selected to have the correct spacial arrangement and symmetry. These methods anr not ‘black box’ applications. Much research effort had been placed into designing single-reference methods that approximate the solutions to multi-reference systems, because of the cost and complexity of the multi-reference calculations. Generally, these efforts require the inclusion of semi-empirical parameters to obtain reasonable results within a given training set. This dissertation is about multi-reference systems. This work will examine first organic systems, and then inorganic, transition metal clusters. In chapters2 and3, we will study CC bonding in simple and unique organic molecules, to see how single-reference systems can be best described with single-reference methods. In chapter4, we will study multireference pancake bonded organic species using single-reference methods. In chapter5, we will study fluxional bridged annulene systems, which can only be described with multi-reference methods. Finally, in chapters6 and7, we will look at covalently bonded inorganic transition metal diatoms, and their multi-reference descriptions.

3 Chapter 2

Characterization of Carbon-Carbon Single Bond Strength

2.1. Single-Reference Descriptions

Breaking a carbon-carbon bond is likely to go by homolytic cleavage, resulting in two free radical fragments. This bond breaking would be correctly described by multi-reference calculations. The same bond stretched to its longest possible point might be expected to have biradical character, any may require multi-reference treatment. To save the cost of multi-reference calculations, a well defined single-reference method was tested. For this, we calibrated a double-hybrid density functional theory (DFT) method with a large basis set, using local mode vibrational analysis. The foundation of density functional theory is that the energetics, and all other parameters for a molecule, can be described by calculating the electron density at every point in a molecule, rather than solving for each orbital basis function. Empirical adjustments can then be made for electron correlated motion, exchange repulsion, and long-range dispersion effects. The problem with any empirical method is that it is dependent upon a ‘training set’ of molecules. The parameters are adjusted to obtain results in good agreement with experimental results, or the results of higher level methods (often multi-reference methods) for the entire training set of molecules. The method can then be expected to return accurate results for molecules that are chemically similar to the species in the training set. To obtain results which will be accurate for a wide range of systems, we need a set of parameters which includes the extreme cases. In this first study, we defined the extreme cases as those that result in the longest and shortest CC bonds in organic chemistry, and employed vibrational spectroscopy methods to see if they can be parameterized to give consistent results for this

4 entire range. There are many factors that can lead to the lengthening of a bond. (i) Exchange (steric) repulsion between bulky substitutents has long been known to lengthen interatomic distances. [65,94,128,187,206] The central bond of 2,2,3,3-tetramethylbutane (2.6, r = 1.582 A˚ by electron diffraction, Figure 2.2) is one of the first molecules thus investigated. [19] (ii) Loss of bonding electrons or electron density can lead to electron deficient bonding.

[51, 52, 59, 74, 208, 210] Here, the ethane cation (3.37, re = 1.935 A˚ by calculation, ωB97X- D/aug-cc-pVTZ, Figure 3.1) is a classic example. [91,180] (iii) By using bridging atoms which enforce a “cage”-topology, known as clamped bonds. [138,171] Light, heat and pressure sensitive bi(anthracene-9,10-dimethylene) (3.31 is a much investigated example. [196] (vi) Sterically hindered systems where decoupled spin paired electrons lead to open singlet states, or pancake bonds,[25,108,120,132,157,221] of which the 2,5,8-tri- tert-butylphenalenyl neutral free radical dimer (4.5) and the dichalchodiazolyl free radical dimers (4.1 and 4.2) are examples [204] (see Chapter4.) (v) Electrostatically hindered ionic free radical species, [35, 82, 115, 164, 165, 222] where electrostatic repulsion is overcome by bonding orbital overlap. This is a special case of pancake bonding. The tetracyanoethylene anion dimer is an example. [157] Forces which affect the length of a bond necessarily affect the strength of the bond. This leads to an empirical observation that “longer bonds are weaker, and shorter bonds are stronger.” This simple model has been refuted in the literature. [60] Some past studies of this relationship have depended on compiling the work of many researchers, using different measurement techniques, [93, 152, 154, 236] so that it is difficult to place confidence in the comparability of the data set. Bond lengths, bond dissociation energies and spectroscopic vibrational analysis are determined by several different methods, at different temperatures and different pressures. The work is necessarily conducted on a set of similar molecules (i.e.: CC single bonds), to ensure that there is any comparability at all. The result is that the

5 differences between the measured parameters is relatively small. To get a consistent set of bond length and bond strength values for a large range of molecules under identical conditions, ab initio computational chemistry is ideal. By analyzing a training set of molecules at identical levels of computational theory, under the identical conditions of 0K and vacuum, the results will be consistent, and even small variations of less than 0.01 A˚ can be considered as significant. The factors that shorten a CC bond are relatively straight forward. It is known that double bonds are shorter than single bonds, and triple bonds are shorter still. It is also known that the bonds in an aromatic system, with a bond order of 1.5, are intermediate length between single and double bonds. As our study will show, the variations between sets of CC double bonds or sets of triple bonds are quite small, compared to the variations between CC single bonds. In the intermediate case, for CC single bonds which are flanked by double or triple bonds, the bond lengths are known to be affected by what is described as increased s-character of the sp2 or sp-hybridized carbons participating in the internal single bond. Here we seek a description which will be useful in all of these situations.

2.2. Application of Vibrational Spectroscopy

Accurate determinations of bond length is complicated by the fact that atoms within molecules are in constant motion, as required by the Heisenberg uncertainty principle. Equi- librium bond lengths can only be determined computationally. In other cases, such as in small ring compounds, the bonds as defined by the maximum electron density (MED) path between atoms are bent. The MED path is longer than the interatomic distance, renewing the discussion of how the ‘bond length’ should be defined. Then, there are the limitations of experimental measurement. Methods in use include electron diffraction, x-ray diffraction, microwave spectroscopy and infrared spectroscopy methods. For this work, a careful review of the scientific literature was conducted to find all available experimental data. When multiple bond length values were available, the experi-

6 mental values varied by an average of 0.034 A.˚ Here again, which values are correct? In this work, to have consistent and comparable parameters, we will use calculated equilibrium bond lengths, determined at the same level of theory, ωB97X-D/aug-cc-pVTZ. Some cases where a smaller basis set was necessary are noted in Table 2.1. Measured bond dissociation enthalpies (BDH’s) or calculated bond dissociation energies (BDE’s) are generally accepted as methods for assessing bond strength. These methods determine the diﬀerence in energy between an intact molecule and the free radical fragments resulting from homolytic cleavage of the bond. This means separating the fragments to well beyond bonding distance, resulting in rehybridization of the atoms at the point of attachment, changes in electronic state, and relaxing of the molecular geometry, all of which obscure the intrinsic bond strength. Using ethane (2.1) as a model, the bonded molecule consists of a σ-bond between two sp3 carbons, each bonded in turn to three hydrogen atoms. This results in a neutral, singlet state molecule with D3d symmetry and a CC bond distance of 1.536 A.˚ [211] Upon homolytic cleavage of this bond, two identical free radical fragments are formed, each in the doublet

2 state, with sp hybridization and D3h symmetry. With loss of the CC bond, the CH bond energies would change, due to rehybridization and relaxation of angle strain, thereby affecting the apparent BDH of the target bond. Hence, the BDH or BDE obtained includes the energies of rehybridization and geometry relaxation, as well as the intrinsic energy of the bond. Experimentally, BDH measurements are not attainable for every bond in a molecule. Values for the BDH of energetically unfavorable bond cleavages are difficult and sometimes impossible to obtain. For example, cleavage of the CC triple bond in propyne (2.25) while leaving the CC single bond unperturbed would be difficult. As has been cited in the literature [60,122,131,144], this gives a limited and skewed, and therefore unreliable indication of the actual bond strength. To validate our procedures, we have implemented a set of thirty training molecules (Fig- ure 2.2.) These molecules were chosen based on the availability of experimental values of

7 bond length and bond dissociation energies. In some cases, experimental parameters are unavailable, as will be outlined in the text. All molecules are known to have singlet ground

a a No. Bond ID Rcalc Rexp BDHcalc BDHexp k ω BSO ρ Hb 2.1 Me-Me 1.523 1.536 89.01 89.68 4.216 1092.07 1.000 1.659 -1.431 2.2 Me-Et 1.524 1.528 87.43 87.2 4.160 1084.81 0.989 1.671 -1.443 2.3 iPr-Me 1.526 1.535 86.66 88.9 4.092 1075.90 0.976 1.675 -1.442 2.4 tBu-Me 1.530 1.539 87.45 86.0 3.992 1062.70 0.957 1.669 -1.422

2.5 (iPr)2 1.542 1.544 82.79 86.6 3.754 1030.49 0.911 1.641 -1.362

2.6 (tBu)2 1.578 1.582 80.41 76.0 3.195 955.86 0.800 1.544 -1.182

2.7 (PhCH2)2 1.542 1.55 66.88 66.6 3.675 1019.63 0.895 1.601 -1.322 a 2.8 (AdMe2C)2 1.629 1.677 53.37 43.7 2.414 826.37 0.639 1.387 -0.925

2.9 (Et2MeC)2 1.597 1.601 73.09 60.2 2.784 903.81 0.716 1.506 -1.118

2.10 (Et3C)2 1.611 1.635 61.21 51.0 2.888 872.66 0.737 1.443 -1.015 a 2.11 (PhEt2C)2 1.631 1.635 52.21 44.7 2.285 804.04 0.611 1.277 -0.934

2.12 (Ph3C)2 1.699 N/A N/A 16.6 1.518 677.89 0.439 1.188 -0.663 2.13 b hexakis 1.669 1.67 33.9 [94] N/A 1.919 736.76 0.526 1.275 -0.830 2.14 Et-Et 1.524 1.539 86.04 87.2 4.177 1087.06 0.993 1.683 -1.454

2.15 (iPrMe2C)2 1.599 1.601 70.30 62.2 2.852 898.14 0.730 1.476 -1.070

2.16 (tBuMe2C)2 1.622 1.63 50.00 44.0 2.508 842.25 0.658 1.410 -0.965

2.17 (iBuMe2C)2 1.589 1.606 72.13 57.8 3.050 928.86 0.770 1.506 -1.118

2.18 Me-CH=CH2 1.495 1.501 99.96 100.9 4.575 1137.58 1.068 1.770 -1.637

2.19 H2C=CH2 1.322 1.339 173.88 172.2 9.961 1678.62 2.000 2.449 -3.214

2.20 (CH2=CH)2 1.457 1.467 144.00 116.0 5.119 1203.32 1.169 1.920 -1.934

2.21 Et-CH=CH2 1.497 1.502 98.17 99.6 4.484 1126.24 1.051 1.776 -1.639

2.22 iPr-CH=CH2 1.501 1.5 97.32 99.7 4.382 1113.42 1.032 1.775 -1.628

2.23 tBu-CH=CH2 1.520 1.522 96.05 97.5 4.071 1087.45 0.972 1.749 -1.573 2.24 HC CH 1.194 1.208 228.13 229.9 17.777 2242.50 3.190 2.894 -4.700 ≡ 2.25 Me-C CH 1.455 1.45 124.30 123.5 5.254 1219.14 1.194 1.844 -1.895 ≡ 2.26 Me-C N 1.455 1.458 122.88 121.1 5.141 1205.90 1.173 1.827 -1.930 ≡ 2.27 CH =CH-C CH 1.425 1.431 135.25 133.6 5.778 1278.42 1.289 1.974 -2.151 2 ≡ 2.28 CH =CH-C N 1.430 1.429 131.69 132.1 5.586 1257.05 1.255 1.938 -2.141 2 ≡ 2.29 HC C-C CH 1.372 1.383 158.27 155 7.406 1447.44 1.575 2.142 -2.517 ≡ ≡ 2.30 HC C-C N 1.375 1.379 150.85 152.4 7.348 1441.71 1.565 2.122 -2.491 ≡ ≡ Table 2.1: Calculated and experimental Carbon-Carbon Bond Lengths R [A],˚ Bond Dissoci- ation Enthalpies BDH [kcal/mol], local mode stretching constants ka [mdyn/A],˚ local mode 1 3 frequencies ωa [cm− ], Bond Strength Orders BSO, and Energy Densities [Hartree/A˚ ] for all molecules, ωB97X-D/aug-cc-pVTZ aωB97X-D/cc-pVTZ. bωB97X-D/6-311++G(d,p). N/A: Not Applicable.

8 1.6 HC C C CH

CH2

HC C C

H H C C CH 1.4 H 29 H 30

H H Me H Me Me Me C Me C C C C H 1.2 Me H H Me Me 27 Me Me C C H 28 H H H 26 25 Me Me 1.0 Me C Me Me C C 22 21 18 Me Me C Me Me 0.8 Me 2014 1 C C 7 5 4 23 3 2 0.6 1517 6 BondStrength Order 9 0.4 1011 8 16 Single Bonds 1213 2 0.2 Single Bonds - sp , sp CH3- Strain 0 0 1 2 3 4 5 6 7 8 Local Mode Stretching Force Constants [mDyne/Å]

Figure 2.1: Local Mode Stretching Force Constants (ka) to Bond Strength Order (ωB97X- D/aug-cc-pVTZ), Single Bonds. This plot serves as a conversion chart between the two parameters.

states, meaning that they have no unpaired electrons. We will use local mode vibrational spectroscopy analysis, which is described in Section 9.2 and elsewhere. [139, 140, 239–241] This method determines the vibrational frequencies and local stretching force constants (ka) of individual bonds, uncoupled from the bulk of the molecule. With the local mode tools, we can investigate any or all bonds in a molecule. With local modes, we are equipped to discuss the different approaches for lengthening a CC bond, making comparisons and finding trends. Figure 2.1 gives the relationship between ka and BSO for C-C single bonds. The calculated results and experimental results obtained from the scientific literature are shown in Table 2.1.

9 Group I

H H Me H H H Me H H Me H H H H Me C C C C C C C C C C

H H Me Me Me H H H H Me H Me H Me H 2.1 2.2 2.3 2.4 2.5

Me Me Me Me C Me C C Me Me Me C C Me C Me Me C C C C C C C C C Me C Me C Me C C C Me H Me Me Me Me H Me H H Me Me 2.6 2.7 2.8 2.9 2.10

C C Me C C C C C C

Me C C

Me 2.11 2.12 2.13

H Me H H H Me Me H Me Me Me Me H C Me C C C Me C Me Me H Me H Me Me C C C C C C Group II C C Me Me Me Me H H Me C Me Me C Me Me C C H H Me Me H H Me H Me 2.14 2.15 2.16 2.17

Group III

H CH H H CH H CH Me CH 2 H H CH2 2 2 2

C C C C C C C C C C C C H C C H

H H H H Me Me H H H2C H Me H Me H Me H 2.18 2.19 2.20 2.21 2.22 2.23 2.24

H H CH2 CH2

C C CH C CN HC C C CN C HC C C CH HC C CN

H H H H H H 2.25 2.26 2.27 2.28 2.29 2.30

Figure 2.2: Organic molecules investigated in this work. The single and multiple bonds reported are in red. All molecules have singlet ground states.

10 The thirty training molecules investigated in this work are divided into three groups; CC single bonds, CC single bonds stretched by tert-butyl groups, and CC multiple bonds. We will examine each group separately, and determine what trends are deﬁnable.

Group I: (2.1 - 2.13) CC Single Bonds: The first group of molecules have central CC single bonds which are subjected to increasing steric repulsion, due to sequential addition of more and larger hydrocarbon groups (methyl, ethyl, phenyl, and adamantyl.) For all cases in Group I the CC bonds are formed by sp3-sp3 hybrid orbital overlap. The simplest case, ethane (2.1), exhibits the shortest bond, at 1.523 A.˚ Bond lengthening continues in the order 2.1 < 2.2 < 2.3 < 2.4 < 2.5, with the addition of more methyl groups. Examination of this series gives insight into the steric requirements of the four substituents. The sequence 2.5 < 2.7 < 2.6 indicates that, while a phenyl group is sterically larger than a methyl group, we discover that it also creates more steric hinderance than two methyl groups, but not as much as three. The sequence 2.9 < 2.10 < 2.11 indicates that a phenyl group is also larger than an ethyl group. This is counterintuitive, as the phenyl group is flat, or nearly flat, and is expected to have small steric hindrance. 2.8 has a significantly longer experimental C-C bond length than 2.11 due to the adamantyl groups being much larger than phenyl groups. Much of what we report here had been deduced empirically. The agreement between intuition and calculation verifies the calculations and quantifies the deductions. This analysis is useful for the development of molecular mechanical modeling methods, which we will not discuss here. Although 2.12 has not been isolated, its substituted analog, 2.13, has been synthesized and characterized. [121] The calculation of an optimized geometry and frequencies for this 212-atom molecule with the ωB97X-D functional and the aug-cc-pVTZ basis set did not converge after several months. Therefore the calculation was done using the augmented Pople 6-311++G(d,p) basis set and 1.6 TB of memory dedicated to the calculation, and has

11 the longest CC bond in this sequence. Molecule 2.12 reports a longer CC bond, but this is unreliable, because 2.12 auto-dissociates into two tri-phenylmethyl free radicals, and cannot be isolated. Any method that describes this species as a stable molecule is describing an intermediate species prior to bond ﬁssure. Therefore, this result is excluded from the data plots.

Group II: (2.14 - 2.17) tert-Butyl groups: While the addition of methyl groups adds steric strain to a molecule, the addition of tert-butyl groups will add much more. Progressing through zero, one and two methyl groups (2.1, 2.2, 2.14) results in a bond lengthening of only 0.001 A,˚ and diﬀerences in ka of only 0.056 mdyn/A.˚ Increasing steric strain by starting with four methyl and sequentially adding two isobutyl groups (2.17), two isopropyl groups (2.15), and two tert-butyl groups (2.16) increases bond lengths by 0.098 Aand˚ ka’s by 1.669 mdyn/A.˚ The aﬀect is much larger, as predicted.

Group III: (2.18 - 2.30) Multiple Bonds: Two interactions play a role in describing CC single bonds. The bonds are lengthened by the addition of bulky groups, and are shortened by changes in hybridization of the carbons of interest, with increased ‘s’ character on the bonded C’s resulting in shorter bonds. Hence, the shortest C-C bond in this study is the sp-sp single bond in acetylene (2.24.) There are also several molecules in this series where -C CH bond is replaced with the -C N bond of a cyano group. The species with the cyano ≡ ≡ triple bonds display slightly longer C-C single bonds, in agreement with experimental results. The hybridization changes have a greater aﬀect on the ﬁnal result than the steric hinderance changes.

With these results, we have a working model of the bond length/local mode stretching force constant relationship.

12 Chapter 3

General Characterization of Carbon-Carbon Bond Strength

3.1. Extension of the Single-Reference Description to Unconventional Systems

In Chapter2, we established a single-reference description using a training set of thirty relatively unperturbed, well-behaved CC single bonds. We are now interested in extending that work to systems which are not as easily investigated experimentally, and which have been outliers in other interpretation schemes.

3.2. Reﬁnement of Single-Reference Descriptions

We will examine twenty-three exceptional molecules, to determine the quality of our methodology. The new species are shown in Figure 3.1 and the associated calculated results and experimental results from the scientiﬁc literature are shown in Table 3.1. For molecules which have double and/or triple bonds, such as 2.27 and 2.29, the local mode ka values can be obtained for both the single and multiple bonds. Experimental BDH’s for the multiple bonds are not available in the scientiﬁc literature. For clamped systems, such as 3.31 and 3.32, ka’s can be determined where BDH determinations may be impossible. Figure 3.2 give the relationship of ka to BSO, and Figure 3.3 gives the relationship between the calculated bond length (rCC) and BSO. This shows how this method can be applied to a wide range of molecules.

Group IV: ( 3.31 - 3.33) Clamped bonds: Three clamped bond cases [77, 138, 171, 196] are included in this study. Very long bonds are possible for these molecules due to their arrangement of stabilizing, unstressed bonds which hold the molecule into bonding alignment. The biradicaloid structures which would be formed by homolytic bond cleavage would recombine.

13 Group IV

O N C N C C N Cl C Fe Fe C Cl N N C O N N 3.31 3.32 3.33

Group V H H C H Cl Cl Cl D3d 2h Cl Cl H H H H H C H H C C C C C C C C C CN H H Cl H Cl Cl Cl Me H H H H H Me 3.34 3.35 3.36 3.37 3.38

Group VI

3.39 3.40 3.41

3.42 3.43 3.44

Group VII

H Me Me Me H Me Me C C C C C H H H H Me H 3.45 3.46 3.47 3.48 3.49

CH2

C C CH CN

H 3.50 3.51 3.52 3.53

Figure 3.1: Organic molecules investigated in this work. The single and multiple bonds reported are in red. 14 a a No. Bond ID Rcalc Rexp BDHcalc BDHexp k ω BSO ρ Hb 3.31 bianthracene 1.642 1.64 N/A N/A 2.411 825.82 0.637 1.317 -0.857 3.32 tetra-Ph-acenaphthene 1.708 1.754 N/A N/A 1.788 711.09 0.502 1.153 -0.620 3.33 IRON 1.6507 N/A N/R N/A 1.617 676.40 0.462 1.344 -0.866

3.34 H3C-CCl3 1.512 1.555 86.94 88.3 4.154 1084.04 0.988 1.747 -1.615

3.35 (Cl3C)2 1.583 1.564 73.42 70.1 2.944 912.63 0.749 1.574 -1.181 3.36 tBu-C N 1.472 1.46 119.2 115.8 4.433 1119.76 1.041 1.787 -1.852 ≡ + 3.37 CH3-CH3 D3d 1.935 N/A 41.20 N/R 0.894 502.92 0.286 0.523 -0.194 + 3.38 CH3-CH3 C2h 1.591 N/A 42.67 N/R 0.971 524.03 0.306 1.232 -0.929 3.39 a diAd-Ad 1.614 1.66 78.63 N/R 2.787 887.94 0.717 1.422 -0.983 3.40 a diAd-diAd 1.648 1.649 71.41 71 2.400 842.03 0.636 1.326 -0.843 ≈ 3.41 a triAd-Ad 1.657 1.661 64.26 N/R 2.245 796.95 0.603 1.305 -0.812 3.42 a triAd-diAd 1.693 1.70 N/R N/R 1.874 728.08 0.521 1.218 -0.694 3.43 a triAd-triAd 1.787 N/A N/R 36.1 1.142 568.43 0.351 1.014 -0.465 ≈ 3.44 a tetraAd-diAd 1.695 1.707 N/R 70.0 1.861 725.59 0.519 1.211 -0.687 ≈ 3.45 Me-Ph 1.504 1.521 103.36 103.9 4.528 1131.75 1.059 1.745 -1.581 3.46 Et-Ph 1.506 1.524 101.75 102.3 4.446 1121.46 1.044 1.751 -1.585 3.47 iPr-Ph 1.514 1.515 124.95 102.1 4.272 1099.32 1.011 1.732 -1.540 3.48 tBu-Ph 1.530 1.524 99.40 97.4 3.966 1059.21 0.952 1.681 -1.439

3.49 Ph-cycloC3H5 1.486 1.52 138.91 111.9 4.751 1159.30 1.101 1.815 -1.708

3.50 Ph-CH=CH2 1.471 1.475 161.97 116.9 4.918 1179.45 1.132 1.867 -1.819 3.51 Ph-C CH 1.430 1.436 174.81 140.7 5.750 1275.41 1.284 1.961 -2.112 ≡ 3.52 Ph-C N 1.433 1.438 166.05 132.7 5.569 1255.09 1.252 1.929 -2.116 ≡ 3.53 Ph-Ph 1.482 1.48 267.19 118.0 4.850 1171.33 1.120 1.840 -1.752

Table 3.1: Calculated and experimental Carbon-Carbon Bond Lengths R [A],˚ Bond Dissoci- ation Enthalpies BDH [kcal/mol], local mode stretching constants ka [mdyn/A],˚ local mode 1 3 frequencies ωa [cm− ], Bond Strength Orders BSO, and Energy Densities [Hartree/A˚ ] for all molecules, ωB97X-D/aug-cc-pVTZ. aωB97X-D/cc-pVTZ N/A: Not Applicable. N/R: Not Reported.

The calculated CC bond length for 3.31 agrees well with experiment, giving conﬁdence to the result. The ka and BSO values for 3.31 ﬁt neatly with other molecules of this bond length.

For 3.32, however, the calculated re (1.708 A)˚ is much shorter than the experimental value of 1.754 A,˚ obtained by low temperature x-ray crystallography. This is evidence of multi-reference character for this molecule, which is being currently investigated by our group.

15 Triple 3.0 Bonds

2.5 Double Bonds

2.0 Aromatic Bonds 1.5 All Single Bonds

BondStrength Order Diamondoids 1.0 Clamped Bonds Multiple Bonds 0.5 Aromatic Bonds e- Deﬁcient Bonds

0 0 2 4 6 8 10 12 14 16 18 Local Mode Stretching Force Constants [mDyne/Å]

Figure 3.2: Local Mode Stretching Force Constants (ka) to Bond Strength Order (ωB97X- D/aug-cc-pVTZ), Single, Multiple and Aromatic Bonds. This plot serves as a conversion chart between the two parameters.

Species 3.33 is modified from a published structure [77] which has eight phenyl groups attached to the SP2-hybridized carbons of the outer 5-membered rings. Here those phenyl groups were replaced with methyl groups, to reduce computational cost. The resultant re (1.651 A)˚ is significantly shorter than the reported length for the octaphenylated compound. It may be that the steric hindrance and/or electronic contributions of the phenyl rings have a strong effect on the central CC bond. Our theoretical case fits the curve, showing that local mode analysis describes these three clamped bond cases well.

Group V: (3.34 - 3.38) Electron Deﬁcient Bonding: The electron density of a bond can be reduced by 1) attaching electron withdrawing groups or 2) removing electrons to form a cationic species. In this work (3.34 and 3.35), three and six electronegative Cl atoms

16 1.2

1.1 36 Single Bonds 1 Clamped Bonds 14 - 1.0 34 e Deﬁcient 2 3 CH - Strain 4 5 3 0.9 Diamondoid 7 6 + CH3-CH C2h 0.8 17 3 35 15 31 0.7 9 39 40 16 41 0.6 8 11 13 42

BondStrength Order 0.5 10 44 32 33 12 0.4 37 43 0.3 38

0.2 1.5 1.6 1.7 1.8 1.9

C-C Bond Length (rCC) [Å]

Figure 3.3: Bond Length (ωB97X-D/aug-cc-pVTZ) to Bond Strength Order for CC single bonds. [139,140,239–241]( R2 = 0.9955)

are added, respectively, to ethane as electron withdrawing groups, to determine if bond lengthening is observed. However, for 3.34, we ﬁnd a signiﬁcantly shortened bond length of 1.512 A,˚ in excellent agreement with the experimental value, and the empirical rule of Sugie, et al. [202], who found that addition of Cl atoms will shorten a CC bond. The C-Cl bonds have partial multiple bond character, resulting in an increase of s-character in the normally sp3 hybridized C’s, which would be expected to shorten the CC bond. In Table 3.2, CC bond lengths of 1,1,1-trihaloethane species for H, F, Cl, Br and I are calculated at the ωB97X-D/3-21G level of theory, showing that the CC bond for these species increase with increasing halogen size. This bond lengthening is likely attributable to steric strain, as decreased electronegatively should shorten the bond.

17 Species Bond Length [A]˚

CH3CH3 1.540

CH3CF3 1.496

CH3CCl3 1.506

CH3CBr3 1.517

CH3CI3 1.536

Table 3.2: Calculated Carbon-Carbon Bond Lengths (re) for various 1,1,1-Trihaloethanes, ωB97X-D/3-21G.

In comparison, hexachloroethane (3.35) shows a bond lengthening of 0.06 A,˚ compared to the parent compound. From what is learned from 3.34, it must be deduced that this CC bond is being lengthened by the steric bulk of the six Cl atoms, rather than by electron withdrawing effects. The cyano group, -C N, is known to be an electron withdrawing group. However, 3.36 ≡ has a short rCC of 1.472 A.˚ This is attributable to increased s-character of the CC single bond by the C N triple bond. This is in agreement with the bond shortening observed in ≡ 2.26, the methyl derivative of 3.36. The more interesting case is the ethane cation (3.37 and 3.38), [74,91,180] because this system, being a charged species, differs substantially from the original list. Experimentally, the ethane cation is found to have two geometries, differing only slightly in energy by 0.3 kcal/mol. [109,116,151] The ethane D 3d geometry (3.37) yields an ultra-long bond of 1.935

A.˚ However, the lower energy conﬁguration, symmetry C2h (3.38), has two anti H’s with

C-C-H angles of 83.1◦, indicating H-bridging bonding, and a CC bond length of 1.591 A,˚ much closer to the value for the neutral compound 2.1. To determine which of these species is appropriate for inclusion in this study, we applied the Cremer-Kraka criteria for covalent bonding, as described in section 9.2 and elsewhere [55].

Electron density (ρr) and energy density (Hb) calculations show that 3.37 and 3.38 have the necessary maximum electron density path and bond critical points, reporting ρ values of

3 3 0.523 and 1.232 e/A˚ and Hb values of -0.194 and -0.929 Hartree/A˚ , respectively. That is,

18 the energy densities are negative, and stabilizing. This makes both molecules viable additions

a to this study. For 3.37 the k versus re data point ﬁts neatly onto the curve reported here, and deﬁnes a BSO of 0.286. This extends the curve well beyond Zavitsas’ theoretical CC bond length limit of 1.75 A[˚ 236] to nearly 2.0 A.˚ The H-bridged 3.38 gives a BSO of 0.306,

a and the k versus re data point falls far from the curve defined by the neutral species (see Figure 3.3.) The much shorter bond is not significantly stronger, indicating that the bond is shortened by H-bridging, without significantly stabilizing the electron deficient C-C bond. The molecule in this symmetry was excluded from the ‘electron deficient bond’ Group III, and the ‘clamped bond’ category of Group II.

Group VI: (3.39 - 3.44) Diamondoid dimers: We established in Chapter2 that adamantyl groups signiﬁcantly lengthen a CC bond. Fokin, Schreiner and other [76] recently synthesized, characterized, and computationally investigated a series of diamondoid homo- and heterodimeric compounds connected by exceptionally long CC bonds. Along with the exceptionally long central bonds, the compounds are found to have exceptional stability, being

stable to temperatures greater than 200◦C. They note that free radical fragments resulting from homolytic cleavage are capable of very little geometry relaxation or rehybridization, losing what the authors referred to as “radical-stabilizing effects.” [229] This is an excellent test case for bond-strength determination, as observed by Shreiner, Kaupp, and others. [130] In the case of 3.44, the bond length of 1.707 A˚ and estimated BDE of 70 kcal/mol is “well off the line!” of Zavitsas’ empirical relationship. [236] They also propose a compound (3.43) which has evaded synthesis, but for which they theorize the longest possible CC bond. One can say that the BDH for these diamondoid dimers approaches the intrinsic bond dissociation energy for homolytic cleavage, as defined by Cremer and others [60] because of the lack of geometry relaxation and a lessening of rehybridization and steric strain reduction. Hence, it is correctly predicted that the near-intrinsic BDE would be much greater than what is observed with more conventional molecules, which experience steric strain reduction and rehybridization.

19 We calculated 3.39 through 3.44 by ωB97X-D/cc-pVTZ. This level of theory reproduces the experimental and computational results well for all six molecules. However, it is discov-

ered for 3.43, that the previously calculated rCC of 1.83 A˚ was reproducible, but is not a

global minimum. A second rotational isomer was discovered, with an rCC-value of 1.787 A,˚ which is -17.8 kcal/mol lower in energy.

a Once again, the calculated rCC’s and k ’s for 3.39 through 3.44 neatly ﬁt our curve. As with 2.12, species 3.43 is excluded from the curve, as this species has not been isolated. Hence, these cases which confound all past relationships work well by local modes analysis.

Group VII: (3.45 - 3.53) Aromatic Bonds: The hybridization of aromatic C-C bonds shortens the bond similarly to the trends found with the sp2 hybridized alkene derivatives. The phenyl group shortening is consistently less than the shortening for a vinyl group. This could be attributable to aromatic sp2 hybridization being different from isolated sp2 hybridization, or to the vinyl group causing less steric strain than a phenyl group. Bonding the aromatic carbon with an sp2 or sp hybridized carbon shortens the bond and, once again, substitution of -C CH with -C N results in a small lengthening of the bond. It is also ≡ ≡ notable that cyclopropylbenzene (3.49) has a significantly shorter aromatic bond (by 0.028 A)˚ than cumene (3.47), but longer than styrene (3.50), showing the partial sp2 character of the cyclopropyl system. Finally, biphenyl (3.53) exhibits a longer bond than 3.50. This could be attributable to differences in sp2 hybridization of aromatic versus isolated carbons, or to increased aromatic character in 3.50, due to the molecule being more nearly planar.

Interference between the vinylic H’s of 3.50 results in a dihedral angle of 11.4◦, versus 41.4◦ for 3.53.

3.3. The Shortest CC Single Bonds in Chemistry

Seeking the longest CC bond in chemistry obviously involves the investigation of all CC single bonds. CC double and triple bonds will be shorter than CC single bonds, and need not be considered. Compiling the calculated bond lengths for CC single bonds between C’s

20 hybridized by multiple and/or aromatic bonds (Table 3.3), we find that the shortening effect on the bonds is strongest for greater s-character, following the order: sp > sp2 > aromatic > sp3. This quantified result is in agreement with experiment and chemical deduction, and the shortest CC bonds are those between two sp hybridized carbons, 2.24 and 2.25. This is a reasonable summarization of the effects which shorten a CC single bond.

Hybridization sp3-sp2 sp3-sp sp2-sp2 sp2-sp sp-sp Ar-sp3 Ar-sp2 Ar-sp Ar-Ar Bond Length [A]˚ 1.495 1.455 1.457 1.425 1.372 1.504 1.471 1.430 1.482 1.497 1.455 1.430 1.375 1.506 1.433 1.501 1.514 1.520 1.530 Average Bond Length [A]˚ 1.503 1.455 1.457 1.428 1.374 1.514 1.471 1.432 1.482

Table 3.3: Calculated Carbon-Carbon Bond Lengths (re) for C-C Single Bonds hybridized by multiple or aromatic carbons, ωB97X-D/aug-cc-pVTZ

3.4. The Longest CC Single Bonds in Chemistry

More interesting are the effects which lengthen a CC bond. Bulky, sterically hindering groups lengthen bonds. With this study, we discover that steric size runs in the order: H < methyl < ethyl < phenyl < tert-butyl < adamantyl < di-, tri-, tetra-adamantyl Adamantyl (diamondoid) substituents create the largest steric lengthening effect, but a much smaller bond breaking effect, due to the restrictions on the geometry relaxation and rehybridization of the fragments. This results in long bonds with exceptional stability, which approach the true intrinsic bond dissociation energy. Bond lengthening by methyl or tert-butyl groups is consistently smaller in magnitude. The clamped bond systems investigated report bond lengths comparable to the longest Diamondoid dimers, but for very different reasons. The restrictions are against bond cleavage, rather than against fragment relaxation. Very long bonds are possible here, but care must be taken not to assign covalent bond character to biradicaloid species. The use of

21 the Cremer-Kraka bond criteria prevents this misrepresentation, where a spin-paired biradical species having a positive Hb, would confirm the presence of an electrostatic interaction, rather than a covalent bond. Electron deficiency results in the greatest lengthening of CC bonds, although the introduction of chlorines as electron withdrawing groups does not have this effect. In the case of the ethane cation, the D3d symmetry gives the longest CC bond observed in this study. What would create the longest bond possible? Combining the bond lengthening effects should produce longer CC bonds. An electron deficient diamondoid or clamped bond should be a longer bond, but which would be the longest? To investigate this phenomenon, cationic forms of 3.32 and 3.41 were calculated, at the ωB97X-D/cc-pVTZ level of theory. For the clamped system 3.32, which is highly aromatic and delocalized, the positive charge from the removal of one electron was shared over the entire molecule, resulting in an increase in CC bond length from 1.708 A˚ to 1.709 A.˚ A change this small could not be exploited to achieve significant bond lengthening. Upon removal of an electron, the diamondoid system (3.41) dissociated into two fragments, rather than lengthening the bond. Therefore, the effect of electron deficiency is clearly strongest on the smallest molecules, making the ethane cation the longest bond in chemistry.

22 Chapter 4

Characterization of Multi-reference Systems by Single-reference Density Functional Theory - Pancake Bonding

4.1. Reﬁnement of Single-Reference Calculations - Broken Symmetry

Having established that DFT local mode analysis works well for the characterization of all types and lengths of singlet CC bonds, as well as the ethane cation, we then applied this tool to known organic multi-reference systems. Open-shell, free radical, pancake bonded dimers are such a system. They have been extensively studied, due to their applicability to the development of conductive polymers [25, 108, 120, 133, 157, 221]. Pancake bonding involves the stacking of relatively flat free radical dimers, which can not react to form a single covalently bonded dimer (σ-dimer), due to steric hindrance. Pancake bonded systems are often compared to π-stacking interactions, [10,87,88,96,114,160,198,219–221] but differ in that the interatomic CC distances are shorter than the sum of the van der Waals radii for carbon (< 3.4 A)˚ and the molecules align in a specific, minimum energy orientation, where π-stacked species have a low rotational barrier between the monomers. In both cases, the dissociation enthalpies for the complexes are estimated to be much less than those of a normal covalent bond. Mulliken and Muller proposed the existence of these molecules in the 1950’s, [161, 162] although the term “pancake bonds” did not appear in the literature until 1969. [163] They

2 ﬁrst presented the tetracyanoethylene anionic dimer (TCNE2−) as a case of pancake bonding between carbons. Being ionic, charged counterions are necessary to stabilize this system. More pertinent to the study of long CC bonds are the neutral dimers. Here, we examine six species; ﬁve known compounds [25,81,87,88,90,96,204], and one theoretical compound.

23 H H H H H H

C C C C C C N N N N N N N N N N N N S S Se Se Te Te

S S Se Se Te Te 4.1 4.2 4.3 (theoretical)

CH3

H3C

H3C CH3

CH3

H3C 4.4 4.5 4.6

Figure 4.1: Pancake bonded molecules investigated in this work. 4.1) HCNSSN dimer. 4.2) HCNSeSeN dimer. 4.3) HCNTeTeN dimer. 4.4) phenalenyl dimer. 4.5) 2,5,8- trimethylphenalenyl dimer. 4.6) 2,5,8-tri-t-butylphenalenyl dimer. Pancake Bonding In- teractions are displayed in red.

The known species, for which experimental data is available, are the 1,2,3,5-dithiadiazolyl (4.1), 1,2,3,5-diselenadiazolyl (4.2), phenalenyl (4.4), [62] 2,5,8-trimethylphenalenyl (4.5), and 2,5,8-tri-tert-butylphenalenyl (4.6) radical dimers. X-ray crystal structures and spectroscopic data are available for these compounds. [25,81,90,204,235] The 1,2,3,5-ditelluradiazolyl free radical dimer (4.3) is not known, but is a logical extension of the dichalocodiazolyl system and is included as a theoretical case. The phenalenyl dimer (4.4) exists as a ﬂuxional compound between the covalently σ-bonded dimer and the pancake dimer. [160, 197, 219] This is a problem for experimental parameterization. The addition of alkyl groups to block σ-dimer formation, as in 4.5 and 4.6, solves this problem. The known systems were veriﬁed experimentally [81, 90, 214] to be diamagnetic, indicating a singlet electronic ground state, with all electrons spin paired. This is positive indication of the multi-reference character of these systems, making them a useful test case for single-reference methodology. Others report that the interaction between these molecules exhibit covalent bonding character, in which the spin-paired singly occupied molecular or-

24 bitals (SOMO) combine to form a ﬁlled highest occupied molecular orbital (HOMO) and a corresponding empty antibonding LUMO. [198, 214, 221] The interactions occur at rigid rotational geometries, due to SOMO-SOMO overlap, explaining the rotational stability of the dimers. The importance of dispersion or van der Waals interactions for the overall stabilization of the dimers have been suggested. [25,157,198] The three phenalenyl free radical monomers are stabilized by aromaticity, with a total of 13 delocalized electrons. Thus, the dimers will have a total of 26 electrons, which suggests a H¨uckel-allowed [111] (4n + 2) system. We will investigate these characteristics computationally.

4.2. Characterization of Pancake Bonding Interactions

For the pancake bonded dimer to form, the spin-paired singlet state must be energetically favored over the triplet state. The total energy of the triplet state can be calculated by two diﬀerent methods: 1) The dimer is optimized in the singlet state, and the energy of the singlet geometry in the triplet state can be calculated, or 2) the dimer can be re-optimized in the triplet state, to a new stable geometry. This results in two diﬀerent parameters,

ESOMO and Egap, which are deﬁned by the following equations:

E = E E (4.1) SOMO (singlet) − (triplet, singlet geometry)

E = E E (4.2) gap (singlet) − (triplet, triplet geometry)

Following Mou and Kertesz, [158] ESOMO defines the energy associated with the spin pairing and bonding overlap of the SOMO’s. The ESOMO values for these molecules show significant contributions to the stabilization of the pancake bonded systems. Egap quantifies the difference in energy between the triplet and open shell singlet states for the dimer.

Gr¨afensteinand others [92] have determined that the Egap must be small for broken symmetry

DFT to accurately describe an open shell system. The Egap is small in all cases, as reported

25 in Table 4.1. The energy diﬀerence between the electronic states is small in all cases, but for

4.3 in the C2v symmetry common to 4.1 and 4.2, the triplet state was lower energy than the singlet state, indicating an unstable arrangement. When the singlet state was allowed to

relax from C2v symmetry, a lower energy structure of C2 symmetry was found, with BCP’s between the N-N, Te-Te and N-Te atoms (Figure 4.3.)

symmetry symmetry singlet triplet OPT

dimer monomer CC Distance CC Distance ESOMO Egap

4.1 HCNSSN C2v C2v 3.036 3.452 -15.61 -2.17

4.2 HCNSeSeN C2v C2v 3.119 3.208 -13.90 -2.09

4.3 HCNTeTeN C2v C2v 3.165 3.362 -13.26 0.96

4.3 HCNTeTeN C2 C2 3.563 3.104 -8.46 -1.35

4.4 Phenalenyl Dimer D3d C3h 3.152 3.622 -12.97 -5.98

4.5 tMP Dimer D3d C3h 3.093 3.744 -19.26 -5.44

4.6 tTBP Dimer S6 C3h 3.281 3.855 -6.11 -3.13

Table 4.1: Energy Gap results for all Species. CC Distance [A],˚ Triplet/Singlet Gap [kcal/mol]

In the triplet state, the optimized geometry of 4.3 was with the monomers rotated

72◦ about the CC interdimer axis, to give a C2 alignment where N-N and N-Te bonding were prevalent, and the CC interatomic distance decreased from 3.563 to 3.104 A.˚ This indicates attractive interactions between the monomers which are not related to SOMO- SOMO overlap. This observation is consistent with the findings of Gleiter and Haberhauer in their calculations on dithiatriazines. For those six-member ring molecules which can be reoriented to optimize different interactions, SN and SC chalcogen bonding was found be stronger than SS bonding. [96] This gives evidence that chalogen bonding, electrostatic attraction between a chalcogen and a less electronegative atom, plays a significant role in the stabilization of the dichalcodiazolyl dimers.

26 When 4.5 and 4.6 were in the triplet states, the interatomic distances between the central carbon atoms once again increased from 3.093 and 3.281 A˚ to 3.744 and 3.855 A,˚ respectively. There were no changes in rotational alignments between the two species, because they are hindered by the pendent methyl or tert-butyl groups. However, for molecule 4.4, the triplet geometry exhibited three minima (Figure 4.3.) Staggered and eclipsed geometries were observed, with the staggered conﬁguration being -1.7 kcal/mol lower in energy than the eclipsed conformer. These systems have central CC interatomic distances of 3.62 and 3.89 A,˚ respectively, which is signiﬁcantly longer than the sum of the van der Waals radii. However, the most stable arrangement was found to be an intermediate structure with a rotational dihedral of 40.5◦. This geometry results in the shortest CC interatomic distance of 3.58 A,˚ and is -0.4 kcal/mol lower in energy than the staggered rotamer. Thus it is shown that the triplet phenalenyl dimer is a π-complex, because it has separation greater than the sum of the van der Waals radii for carbon, and a low rotational barrier.

H 88.5º

(a)

H 99.2º H

(b)

Figure 4.2: C2 Symmetry geometries for the HCNTeTeN dimer. a) Singlet. b) Triplet.

27 40.5°

3.62Å 3.89Å 3.58Å

(a) (b) (c)

Figure 4.3: Triplet state geometries for the phenalenyl dimer. a) Staggered. b) Eclipsed. c) Minimum energy geometry.

Dimer Dissociation Energy: The dissociation energies for all species were calculated by varying the geometry of each pancake bonded dimer from 2.5 A˚ to 8.0 A,˚ applying counterpoise corrections to the ﬁnal results, to correct for basis set superposition error, which may be expected for dimeric systems. [10, 25, 62, 198, 221] For the dichalcodiazoyl systems, the selected levels of theory yielded smooth Morse potential curves, exhibiting dissociation energies of 5.8, 4.7 and 6.0 kcal/mol, respectively, in good agreement with the available experimental bond dissociation enthalpy (BDH) of 5.32 kcal/mol for 4.1 [25] These values are more similar to the dissociation energy for an electrostatic interaction than a covalent bond (Figure 4.4). The calculated CC interatomic distances of 3.183, 3.343 and 3.165 A˚ are again in excellent agreement with experiment (see Table 4.2.) The dissociation energies of 8.9, 12.3 and 9.8 kcal/mol for 4.4, 4.5 and 4.6, respec-

tively, are in good agreement with the experimentally determined enthalpy change (∆HD) of 9.5 kcal/mol for 4.6.[198] The difference between the dissociation energies, 4.5 being 3.4 kcal/mol more stable than 4.4, gives a measure of the dispersion stabilization of 4.5 due to the methyl groups. The smaller difference between 4.6 and 4.4 indicates that there is a trade-off between the dispersion stabilization and the steric repulsion of the tert-butyl groups.

28 6

2 HCNSeSeN 0 HCNSSN -2 HCNTeTeN

-4 Phenalenyl Dimer -6

-8 tri-tert-Butylphenalenyl Dimer

RelativeEnergy[kcal/mol] -10 CH3

H3C

H3C -12 CH3 tri-Methylphenalenyl Dimer CH3 -14 H3C

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 Interatomic Distance (C-C) [Å]

Figure 4.4: Dissociation Curves for sytems 1 and 2 (BS-UM06/6-311G(d,p), 3 (BS- UM06/SDD), 4 and 5. (BS-UM05-2X/6-31++G(d,p).)

What can be deduced from these calculations is that 1) all dissociation energies are much lower than the BDE’s for a covalent bond, 2) the higher dissociation energy for 4.5 shows that the substituted species has a more stable equilibrium geometry, and 3) the highest dissociation energy for 4.6 shows the eﬀect of reduced steric repulsion. 4) The attractive dispersion interactions between the tert-butyl groups are greater than the exchange repulsion between them, and the smaller methyl groups also contribute attractive dispersion interactions. Cremer-Kraka Bonding Criteria: We applied the Cremer-Kraka covalent bonding criteria to all species (Section 9.2.) For the dichalcodiazolyl dimers, bond critical points (BCP) are found between the CC, NN [189, 190] and EE (calcogen-chalcogen) [168] pairs in all three systems. In all cases, the CC and NN Hb’s are positive. All three systems also display N-N-chalcogen-chalcogen ring critical points (RCP) and cage critical points (CCP’s) at the geometric center of the dimeric system. The RCP gives the point of lowest electron density in the center of a ring of bonded atoms, showing that bonding is continuous around the ring.

29 The CCP gives similar information at the center of a three-dimensional structure. Therefore, there are interactions between all heavy atoms.

a a No. Species rcalc rexp DEcalc DHcalc DECP CECP BDEexp k ω BSO ρ Hb 1 HCNSSN (ring) 3.071 5.8 3.9 2.3 2.4 5.3 0.657 146.5 0.214 0.0163 0.00464 C-C 3.036 3.18 0.208 242.6 0.083 0.0406 0.00701 N-N 3.034 0.128 176 0.056 0.052 0.00369 S-S 3.125 0.192 142.6 0.078 0.1036 -0.00031 2 HCNSeSeN (ring) 3.21 4.7 1.8 2.9 2.6 N/R 0.302 71.6 0.113 0.0148 0.00372 C-C 3.119 3.31 0.08 150.8 0.038 0.0343 0.00609 N-N 3.152 0.074 133.8 0.036 0.0421 0.00334 Se-Se 3.313 0.151 80 0.064 0.0983 -0.00081

3 HCNTeTeN C2v (ring) 3.514 6.0 3.4 4.3 4.2 N/A 0.049 23.4 0.021 0.013 0.00132 C-C 3.219 N/A 0.029 83.4 0.014 0.0364 0.00555 N-N 3.333 0.032 29 0.016 0.0385 0.00605 Te-Te 3.84 0.045 122.6 0.022 0.0729 0.00151

HCNTeTeN C2 (ring) 3.413 8.4 5.8 6.1 6.2 N/A 0.162 42.8 0.062 0.0176 0.00186 N-N 3.342 0.112 164.8 0.045 0.0461 0.00931 Te-Te 3.82 0.038 65 0.018 0.0864 0.00334 N-Te 3.51 0.045 77.8 0.021 0.0688 0.00684

4 phenalenyl (periphery) 3.11 N/A 11.0 9.8 8.9 9.0 N/A 0.366 122.9 0.136 0.0718 0.00537 center 3.152 N/A 0.293 287.8 0.113 0.0631 0.00607 5 tMP (periphery) 2.997 3.053 14.8 10.8 12.3 12.9 N/R 0.172 63.8 0.074 0.0903 0.00577 center 3.093 3.145 0.167 217.3 0.072 0.0703 0.00657 6 tTBP (periphery) 3.391 3.306 12.4 10.3 9.8 11.5 9.5 0.194 67.6 0.081 0.0467 0.00334 center 3.287 3.201 0.147 204 0.065 0.0501 0.00499

Table 4.2: Calculated and experimental Carbon-Carbon interatomic distances R [A],˚ Dis- sociation Energies, Counterpoise Complexation Energies and Bond Dissociation Energies a DEcalc, CECP and BDEexp [kcal/mol], local mode stretching constants k [mdyn/A],˚ local a 1 mode frequencies ω [cm− ], Bond Strength Orders BSO, and Electron and Energy Densi- 3 3 ties, ρ and Hb [electron/A˚ and Hartree/A˚ , respectively] for all molecules. Level of Theory is UM06/6-311G(d,p) for 4.1 and 4.2, UM06/SDD for 4.3, and UM05-2X/6-31++G(d,p) for 4.4, 4.5 and 4.6. N/A: Not Applicable. N/R: Not Reported.

In the case of 4.1 and 4.2, the energy density at the BCP of the intermolecular SS bonds have negative, very small values of -0.0003 and -0.0008 Hartree/A˚3, respectively. This indicates the presence of chalcogen-chalcogen bonding between the SS and SeSe species. [168] As the pancake bonded species are drawn apart, the molecules tip outward, so that the chalogens are separated at a slower rate than the carbons and nitrogens. This shows that chalogen bonding plays a stabilizing role in the dimerization of the known species, which is

30 in agreement with Gleiter and Haberhauer. [87, 88, 96] The tellurium system, 4.3, however,

exhibits a positive Hb value at all interatomic distances, so chalogen bonding is not indicated

in the theoretical case. We theorize that the C2v ditellurodiazolyl dimer does not exist, because of this lack of chalcogen-chalcogen bonding. BCP analysis for the phenalenyl free radical dimer systems, 4.4 through 4.6, found BCP’s between all overlapping CC atoms (one at the center, six on the periphery), with positive

Hb’s for all geometries. The BCP’s persist at separations up to 4 A.˚

The ρ and Hb values obtained for the substituted 4.5 and 4.6 systems, and the unsubstituted (4.4) system are nearly identical, indicating that the results for 4.4 are a good approximation for 4.5, as has been asserted by many researchers. [10,63,198,214] The phenalenyl dimers exhibit three CCP’s and fifteen RCP’s, located equidistantly between the monomers. However, none were located near the central inversion point of the complex, and therefore did not appear to enhance the overall stability of the complex. Aromaticity Index: To test how the aromaticity of the system is affected by 1) substitution and 2) dimerization, the monomers and dimers of 4.4 through 4.6 were subjected to aromaticity index (AI) analysis (Section 9.2.) [123, 191] For each structure, the AI was determined twice; first, for all CC bonds in the dimer and monomer systems, and then for all CC bonds except those to the central carbon. The results of this analysis are summarized in Table 4.3 and Figure 4.5. The figure shows the bond strength order (BSO) for each unique CC bond in the aromatic systems, and reports the AI of each monomeric and dimeric system. Additionally, the parameters WS, which gives the bond weakening/strengthening relative to the average bond strength, and ALT, bond strength alteration parameter, were reported. Both the WS and ALT parameters indicate a loss of aromaticity, due to increased irregularity of the structures. In other words, the more regular (rather than symmetrical) the aromatic perimeter, the greater the aromaticity. An example is benzene, which has six identical sides, is highly regular, and has a high AI. Looking first at substituent effects, we found that in 4.4 the six outermost CC bonds are identical, with BSO’s of 1.412, near the BSO value of 1.451 for benzene. (The BSO

31 molecule AI, all carbons AI, outer carbons Phenalenyl Dimer 0.934 0.938 Phenalenyl Monomer 0.915 0.915 tMP Dimer 0.918 0.914 tMP Monomer 0.906 0.898 tTBP Dimer 0.908 0.894 tTBP Monomer 0.901 0.885

Table 4.3: Aromaticity Indices for the Phenalenyl, Trimethylphenalenyl and tri-tert- Butylphenalenyl Free Radical Dimers

for benzene is based on comparison to the local stretching force constants for ethane and ethylene, rather than the ‘classical bond order’ of 1.5.) This arrangement is skewed for 4.5, where the lowest energy rotational isomer for the methyl groups is the orientation where one H atom is in the plane of the three rings, and the other two extend above and below the ring. This makes the environment of the outer bonds dissimilar. The bond which is coplanar with the hydrogen increases in length by only 0.002 A,˚ but exhibits a large reduction in BSO by 0.032. The outer CC bond not attached to the alkyl group has an even lower BSO, being reduced by 0.065. For 4.6, the same effect is observed, where the bulky tert-butyl groups cause a lengthening of the outer CC bonds, and reduction of the BSO by 0.037 and 0.061, respectively, for the side in which the methyl group is coplanar with the aromatic system and the side which is not. For the unsubstituted periphery CC bonds, the effect of substitution is much smaller, with bond lengths varying from 1.412 to 1.415 A,˚ and the BSO’s range from 1.283 to 1.312. The largest effect on bond weakening for the target bonds is observed in 4.6. Conversely, the three bonds which radiate from the central C in each case increase in BSO strength by 0.005 between 4.4 and 4.5, and by 0.039 between 4.5 and 4.6. This indicates that electron density lost by the deformation of the outer CC bonds redistributes to the inner bonds of this system. This results in small fluctuations in the aromaticity from 0.915 to 0.918 to 0.901 for 4.4, 4.5, and 4.6, respectively.

32 FULL FULL 1.441 1.412 (1.390) (1.390) AI 0.915 AI 0.934 WS 0.066 WS 0.043 ALT 0.018 ALT 0.024 1.312 1.292 (1.415) (1.415) OUTER OUTER 1.337 1.336 (1.425) (1.425) AI 0.915 AI 0.938 WS 0.062 WS 0.035 ALT 0.023 ALT 0.027

H H 1.385 H 1.382 H H FULL FULL 1.380 H 1.347 (1.393) (1.393) (1.392) (1.398) H H AI 0.918 H H AI 0.918 WS 0.072 H H WS 0.073 ALT 0.010 1.303 1.300 ALT 0.009 (1.414) 1.277 1.288 (1.414) (1.418) (1.414) OUTER 1.350 OUTER 1.341 H (1.421) H H (1.423) H H AI 0.911 H H AI 0.914 WS 0.077 H H WS 0.075 H H H ALT 0.012 ALT 0.011 H H H

1.390 1.336 FULL FULL 1.375 1.359 (1.393) (1.401) (1.393) (1.401) AI 0.901 AI 0.908 WS 0.089 WS 0.081 ALT 0.010 1.285 1.304 ALT 0.011 (1.412) 1.305 1.283 (1.418) (1.418) (1.415) OUTER 1.379 OUTER 1.380 (1.418) (1.418) AI 0.885 AI 0.894 WS 0.108 WS 0.096 ALT 0.008 ALT 0.010

MONOMERS DIMERS

Figure 4.5: Bond Strength Orders (BSO) and Optimized Bond Lengths (in parentheses, A)˚ for the Phenalenyl, Trimethylphenalenyl and tri-tert-Butylphenalenyl Radical Monomers and Dimers (4.4 through 4.6.) The Aromaticity Indices (AI), Bond Weakening/Strengthening parameters (WS) and Bond Alteration parameters (ALT) for the full carbon ring structures (FULL) and the outer ring structure (OUTER) are indicated in boxes.

The trend is more pronounced for the pancake bonded dimeric systems. However, the ALT parameter is less for the substituted dimers, 4.5 and 4.6, than for the unsubstituted species, 4.4. This indicates that bringing the six methyl or tert-butyl groups together, alternating between the rings, gives an overall more stable and regular arrangement. The lowest energy rotational isomer of 4.5 has a diﬀerent orientation of the methyl groups than the monomer. In the pancake bonded dimer case, six hydrogens are rotated inward, toward the center of the molecule. In this arrangement, there are three unique bond types, as in the monomer and dimer of 4.4. This results in a very small ALT parameter of 0.009

33 for the full system, compared to the large WS weakening/strengthening parameter of 0.073, and an AI much lower than that of the unsubstituted 4.4 dimer. This trend was continued in dimer 4.6, showing that adding substituents to the molecule, while essential to preventing σ-dimer formation, reduces the overall regularity and aromaticity of both the monomers and the dimers. Most importantly, in all cases, the dimeric systems display a higher AI than the monomeric systems. This indicates that dimerization enhances the aromaticity of the systems. This observation is in agreement with the nucleus-independent chemical shift (NICS) NMR analysis of Suzuki, et al, [204] and indicates that the SOMO-SOMO overlap in the dimerized system supports and stabilizes the aromaticity of the molecules, overall. Gleiter and Haberhauer propose that pancake bonded systems are stabilized by the combination of the delocalized electrons in two dimers to create a Hückel-allowed [111] (4n + 2 electron) 3-dimensional aromatic system. In the case of the dichalcodiazoyl systems, each monomer contributes 7 electrons, for the allowed total of 14 electrons. On the phenalenyl systems, each monomer contributes 13 electrons, for a total of 26. This conclusion is supported by the finding that the dimers exhibit higher aromaticity than the monomer. The structure of 4.6 is affected by the six tert-butyl groups, which lock the dimer in the staggered configuration. Steric repulsion between these groups also causes concave pyra- midalization of the central phenalenyl system, [62] such that the central CC interatomic distance is shorter than that of the outer CC interactions, unlike 4.4 and 4.5. This results in an increased deviation from the optimum geometry and bond strengths, as reflected by small increases in the bond alteration (ALT) parameters of 0.001 to 0.002 units. Ultimately we discover that the substituents which are added to the parent phenalenyl system to inhibit σ-dimerization reduce the aromaticity of the systems. We here confirm that these multi-reference systems can be well characterized by broken symmetry hybrid DFT methods and large basis sets. Analysis of the parameters of

a equilibrium geometries, rCC , local stretching force constant, k , Bond Strength Order and

electron density, ρr and energy density, Hb, are in excellent agreement with experimental

34 observations, and can fully characterize these systems. In Chapter5, we study bridged annulene systems, to determine 1) the level of theory required to reproduce experimental results, and 2) whether bridged annulene systems show signiﬁcant multi-reference character.

35 Chapter 5

Bridged Annulenes; The Longest CC Bonds?

5.1. The Puzzle of 11,11-Dimethyl-methano[10]annulene

Some organic systems display biradicaloid character at much closer CC distances than pancake bonded systems, requiring different computational approaches. In this work we focused on the interactions between two C atoms, which are separated by 1.8 A˚ and may be covalently bonded: a molecular system that has puzzled chemists for over 50 years. We used the measurable quantities of electron density distribution, vibrational frequencies, NMR chemical shifts, and indirect spin-spin coupling constants (SSCCs) to characterize the CC interactions investigated as being a covalent bond or a through-space interaction. The target system 5.1 (see Figure 5.1) belongs to the group of bridged [10]annulenes, the parent member of which, 1,6-methano[10]annulene (5.2) was first synthesized by Roth and Vogel in 1964. [227] Vogel then reported that there were two possible bond structures for this molecule which satisfy the valence requirements of all atoms (valence tautomers.) Annulene 5.2 was experimentally characterized as an aromatic 10π-system fulfilling the Hückel 4n+2 rule [111], with a slightly distorted ring perimeter and having a C1C6 distance R of 2.235 A.˚ [27] Therefore, it adopts structure 5.2a rather than that of the bisnorcaradiene (tricyclo[4,4,1,01,6]undeca-2,4,7,9-tetraene) form 5.2b. This measurement was verified in dozens of experimental investigations [14,27,28,32,37,43,66,85,119,137,148,226] as well as computational investigations. [36, 43, 83, 84, 119, 195] Therefore, it was an unexpected result when in 1973 the 11,11-dimethyl derivative 5.1, also synthesized by the Vogel group, was found to adopt a tricyclic structure with an R value close to 1.8 A˚ by X-ray diffraction [26] (1.827 and 1.771 A˚ were observed in the unit cell which contains two slightly different

36 H H H H H H H H

C C C C H H H H

5.1a 5.1b

2 N H C 1 1 6 H 3 C 5.2a 5.2b 5.4 N 5.5

H H H C 1 H C 6 H 5.3a 5.3b H 5.6 Figure 5.1: Annulene species investigated in this work.

geometries [26]) that suggests structure 5.1b rather than 5.1a. The corresponding cyano, methyl derivative had a similar R value to 5.1 [26] and finally the dicyano derivative with an R value of 1.558 A[˚ 26,228] clearly confirmed the existence of a bisnorcaradiene form. Günther and others carried out nuclear magnetic resonance (NMR) investigations on valence tautomeric systems such as 5.1 and 5.2 and showed that any shift to the bisnorcaradiene or annulene form leads to characteristic changes in the 13C chemical shifts. [8,95] These studies were latter confirmed by Frydman and co-workers [80] and Dorn and co-workers [69] who also documented a strong temperature dependence of the 13C NMR signals of 5.1. It was questioned whether bridged annulenes could be considered as fluxional systems which changed their bonding structure according to the valence tautomeric rearrangement indicated in Figure 5.1 or whether they possessed long CC bonds. Since the available experimental evidence for 5.1 favored the bisnocaradiene form, the molecule was considered as the neutral hydrocarbon with the longest covalent cyclopropane C(sp2)C(sp2) bond. Thereafter, 5.1 was computationally investigated multiple times to rationalize the bonding situation, [36, 43, 83, 84, 119, 195] but none gave results which were

37 consistent with the experimental data. The following questions will be answered in this work: i) Which electronic factors determine the shape of the potential? For example, are there specific interactions between bridge and π-perimeter, which may influence structure and dynamics of 5.1? ii) What level of theory is required to guarantee the needed accuracy of the quantum chemical description? iii) Do temperature, entropy, or environmental effects such as solvation or crystal packing influence the shape of the potential energy surface? iv) Does 5.1 contain a weak covalent C1C6 bond? Is this the longest uncharged hydrocarbon C(sp2)C(sp2) single bond ever observed?

5.2. Analysis of the Annulene Systems by Multiple Levels of Theory

In Figure 5.2, the calculated potential energy curves (PEC) for a representative number of different methods applied in this work are shown. These include wave functional theory (WFT), DFT, and complete active space self consistent field (CASSCF) methods. The final, most accurate, enthalpy curves are given in Figure 5.3. Relative energies ∆E, ∆H(298), and ∆G(298) obtained at different levels of theory are listed in Table 5.1. In figures 5.2a and 5.3a, ∆E = 0 was chosen for R = 2.1 A.˚ In Table 5.1, the reference point of all energy difference determinations is always the most stable annulene form. When one of the target geometries was located on a shoulder of the PEC (or the corresponding enthalpy curve), the R value of the inflection point or the R of the annulene minimum of a closely related method was taken, as is indicated in Table 5.1. In the following, we will first analyze the potential energy curves (PEC’s), potential enthalpy curves (PHC’s), and potential free energy curves (PGC’s) obtained for target system 5.1. They are rather inconclusive since the methods first tried in this work fail to reliably account for the experimental results. Therefore, we investigated the valence tautomeric molecules 5.2 and 5.3 to clarify which quantum chemical method can provide a reliable answer to the common problems presented by these systems. To improve the accuracy of the PECs, we will also discuss the impact of vibrational, temperature, entropy, solvent and

38 25

H H H H H H H H

C C C C 20 H H H H

15 NEVPT2(10,10) 5.1b 5.1a MP2//MP2 MP2//B3LYP 10 B3LYP BD(T) CCSD(T) 5 B2PLYPD MP4(SDTQ)

Relative[kcal/mol] Energy Δ E ωB97X-D -5 MP3 REKS/ωB97X-D CASPT2(10,10)

BD CASSCF(10,10) -10 CCSD MP4(SDQ)

1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å] (a)

NEVPT2(10,10) 25 MP2//B3LYP MP2//MP2 5.2b 5.2a 20 MP4(SDTQ)

B2PLYPD 15 B3LYP BD(T) 10 CCSD(T)

5 RelativeEnergy[kcal/mol] Δ E

0 BD MP3 wB97X-D CCSD CASPT2(10,10) CASSCF(10,10) MP4(SDQ)

1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å] (b)

16 5.3b 5.3a 14 BD 12 CCSD MP3 B3LYP B2PLYPD 10 MP4(SDQ)

8 BD(T) CCSD(T) 6

Relative[kcal/mol]Energy Δ E 2

0 CASPT2(8,8) ωB97X-D

-2 MP2//MP2 MP4(SDTQ)

1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å] (c)

Figure 5.2: Representation of the energy as a function of the 1,6-distance obtained at multiple levels of theory. a)11,11-dimethyl-1,6-methano[10]annulene b)1,6-methano[10]annulene and c) 1,3,5-cycloheptatriene.

39 crystal packing effects on the shape of the PECs. We will answer the question whether 5.1 possesses a covalent CC bond with an R value close to 1.8 A.˚ The potential energy curve of 5.1 as described by WFT and DFT: The PECs calculated for 5.1 reveal that the following must be considered as important electronic effects: i) π- electron delocalization in annulene and bisnorcaradiene ii) σ-π interactions in the distorted ring perimeter iii) homoaromatic through-bond and through-space interactions (as defined by Cremer and co-workers [52]) iv) the generation of a biracialoid and its stabilization by electron delocalization, v) strain effects in the bisnorcardiene form, and vi) bridge-ring interactions. The different methods account for these effects in different ways so that the PEC varies in form. The forms include a single-well with a shoulder at small R values (SW+1S), a single-well with a shoulder at large R values (SW+2S), a double-well with a local minimum for small R values (DW-F1M), or a double-well with a local minimum for large R values (DW-F2M.) HF and dynamical electron correlation: Hartree Fock (HF) theory makes the approximation of non-interacting electrons, which does not account for their correlated motion. Therefore, HF will return the lowest energy for the structure which has the greatest number of CC bonds, 5.1b rather than 5.1a. HF exaggerates bond alternation because the description of π-delocalization requires a dynamical electron correlation method. Accordingly, 5.1a corresponds to a shoulder of the PEC(HF,SW+2S), which is 9.3 kcal/mol above the minimum (Table 5.1). Møller Plesset Perturbation Theory, 2nd, 3rd, and 4th Order: Second order Møller Plesset Perturbation Theory (MP2) introduces pair electron correlation effects, which is a prereq- uisite for a description of π-delocalization. [50] The minimum is shifted to form 5.1a (2.154 A),˚ which is stabilized by 6.3 kcal/mol relative to the value at 1.64 A˚ occupied by form 5.1b (asymmetric SW+1S PEC, see Figure 5.2). There is hardly any difference in the shape of the PEC for MP2, or higher levels of theory, whether geometries are optimized at the HF, B3LYP, ωB97X-D, or MP2. So the following discussion is based on B3LYP geometries, because DFT has advantages when calculating vibrational frequencies (see below).

40 16

H 12 H H H H H H H C C C C H H H H 10

8 5.1b 5.1a 6 ΔE(R) CASPT2(14,14) 4 ΔH(R) CASPT2(14,14) ΔG(R) CASPT2(14,14) 2

RelativeEnergies[kcal/mol] ΔH(R) est

ΔH(R) CCSD(T) -2 ΔG(R) CCSD(T)

1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å] (a)

8 2b 2a 16 5.2b 5.2a

14 ΔE = 11.48 12 ΔG = 10.30

8 ΔH = 10.16 6

RelativeEnergies[kcal/mol] 4

-2 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å]

(b)

a 14 ΔE = 12.20 a ΔG = 12.22 3b5.3b 3a5.3a 12 ΔHa = 11.53

6 ΔG = 6.18

4 ΔH = 5.89

RelativeEnergies[kcal/mol] ΔE = 6.05 2

-2 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å]

(c)

Figure 5.3: Representation of the energy and enthapy as a function of the 1,6- distance of a)11,11-dimethyl-1,6-methano[10]annulene b)1,6-methano[10]annulene and c) 1,3,5-cycloheptatriene. a) was obtained by CASPT2(14,14)/6-311G(d,p)// B3LYP/6- 311G(d,p) and CCSD(T)/6-311G(d,p)// B3LYP/6/311G(d,p), b) by CASPT2(14,14)/6- 311G(d,p)// B3LYP/6/311G(d,p), and c) by CASPT2(10,10)/6-311G(d,p)// B3LYP/6- 311G(d,p). In all cases, the relative energy and enthalpy (∆H(298K)) are included.

41 Method Curve a R(5.1b)b R(5.1a) ∆E(5.1b)c ∆E(TS)d HF SW+2S 1.552 (2.120) -9.29 - SVWN5 SW+1S (1.640) 2.125 3.26 - BLYP SW+1S (1.640) 2.212 6.99 - B97 SW+1S (1.685) 2.134 2.84 - B3LYP SW+1S (1.640) 2.167 3.67 - ωB97 SW+2S 1.595 (2.040) -4.28 - ωB97X SW+2S 1.595 (2.040) -7.03 - ωB97X-D DW-F2M 1.638 2.039 -1.02 0.07 (1.09) REKS/ωB97X-D DW-F2M 1.637 2.039 -0.98 0.07 (1.05) B2P-LYP-D DW-F2M 1.605 2.118 -0.08 1.05 (1.13) MP2 SW+1S (1.640) 2.154 6.31 - MP3 DW-F2M 1.587 2.065 -3.10 0.04 (3.14) MP4(SDQ) SW+2S 1.581 (2.120) -5.28 - MP4(SDTQ) SW+1S (1.640) 2.150 2.92 - CCSD SW+1S 1.590 (2.120) 4.25 - BD SW+1S 1.590 (2.120) 4.21 - CCSD(T) DW-F2M 1.641 2.120 -0.42 0.62 (1.04) BD(T) DW-F2M 1.641 2.120 -0.42 0.62 (1.04) CASSCF(10,10) DW-F2M 1.529 2.148 -7.81 0.63 (8.44) CASPT2(10,10) DW-F2M 1.613 2.159 -0.97 1.07 (2.04) NEVPT2(10,10) DW-F1M 1.598 2.172 2.49 3.59 (1.10) CASPT2(14,14) DW-F1M 1.647 2.130 0.91 1.32 (0.41) Estimate DW-F2M 1.643 2.123 0.26 0.93 (0.67) ∆H(5.1b) ∆H(TS) B2P-LYP-D DW-F2M 1.694 2.110 0.61 1.14 (0.53) CCSD(T) DW-F2M 1.680 2.120 -0.68 0.03 (0.71) BD(T) DW-F2M 1.684 2.120 -0.75 0.02 (0.77) CASPT2(14,14) DW-F1M 1.640 2.120 0.66 - Estimate DW-F2M 1.662 2.125 -0.11 0.08 (0.19) ∆G(5.1b) ∆G(TS) B2P-LYP-D DW-F2M 1.680 2.114 0.16 0.83 (0.67) CCSD(T) DW-F2M 1.658 2.080 -1.09 0.20 (1.29) BD(T) DW-F2M 1.658 2.120 -1.12 0.19 (1.31) CASPT2(14,14) DW-F1M 1.665 2.120 0.22 0.73 (0.51) Estimate DW-F2M 1.662 2.100 -0.45 0.42 (0.87)

Table 5.1: Relative Energies and Tautomerization Barriers of 11,11-Dimethyl-1,6- methano[10]annulene.

42 aCurve indicates the shape of the potential energy well. (DW-F1M - Double Well with Local First Minimum, DW-F2M - Double Well with Local Second Minimum, SW+1S - Single Well with Left Shoulder, SW+2S - Single Well with Right Shoulder.) bR(5.1b) and R(5.1a) indicate the C1C6 distance for each structure in angstroms. (Values in parentheses are approximate values taken from shoulders.) c∆E(5.1b) gives the energy diﬀerence between tautomers, relative to 5.1b [kcal/mol.] d∆E(TS), ∆H(TS) and ∆G(TS) give the energy barriers for the tautomerization from 5.1a to 5.1b [kcal/mol.] (Values in parentheses are for the reverse reactions.) All calculations were completed using the 6-311G(d,p) basis set. MP3, MP4, CAS and coupled cluster calculations were computed with B3LYP/6-311G(d,p) optimized geometries.

MP2 is known to overestimate pair correlation and the stabilizing effects of π-delocalization since MP2 does not include the coupling between different pair-correlation effects. MP3 ac- counts for some of the pair-pair coupling effects and accordingly the PEC minimum is shifted back to form 5.1b which becomes 3.1 kcal/mol more stable than form 5.1a with DW-F2M PEC. MP4(SDQ) leads to a similar result, however with a somewhat larger energy difference (5.3 kcal/mol, see Table 5.1) between forms 5.1b and 5.1a than calculated with MP3. The situation changes qualitatively and quantitatively with the inclusion of triple excitation correlation effects at the MP4 level of theory. The energy minimum of the SW+1S PEC is again shifted to 5.1a, and 5.1b at 1.64 A˚ is now just 2.9 kcal/mol higher in energy. Three-electron correlation effects are not only important for a balanced description of π-delocalization, but also for those forms with a long C1C6 bond close to the breaking point where these effects are uncoupled and might be exaggerated. Coupled cluster theory provides infinite order correlation effects so that coupling of the specified 2- or 3-electron correlations is accurately described. The coupled cluster with with single and double excitations (CCSD) and coupled cluster with Brueckner orbitals and double excitations (BD) PEC’s are largely identical and appear between PEC(MP4(SDQ)) and PEC(MP3), leading to a SW+1S form. Infinite order correlation effects in the SD-space provide a correct description of orbital-relaxation and pair correlation effects, which leads to a 4.2 kcal/mol stabilization of form 5.1b relative to 5.1a. If infinite order 3-electron correlation effects are added at the CCSD(T) or BD(T) levels of theory, the MP4(SDTQ)

43 PEC is corrected in the way that the destabilization of 5.1b relative to 5.1a is reduced from 2.9 to -0.4 kcal/mol, i.e. the PEC becomes rather flat in the range from 1.6 to 2.2 A˚ with a slight preference for 5.1b at R = 1.641 A.˚ Almost the same result is obtained by BD(T) (see Figure 5.1 and Table 5.1.) DFT descriptions: In DFT, the larger the electron density or both electron density and electron density gradient are, the larger are the correlation effects. [49, 101] The analysis of the electron density distribution ρ(r) in 5.1a and 5.1b (see below) reveals that the bond density is larger in the case of the annulene over the bisnorcaradiene form because 5.1a has 5 CC double bonds rather than just 4 when adopting form 5.1b. Hence, the larger correlation energy of 5.1a leads to its stabilization relative to 5.1b where the effect for a generalized gradient approximation (GGA) functional such as BLYP (dependence on density and its gradient: SW+1S) must be larger (7.0 kcal/mol, Table 5.1) than that of a local-density approximation (LDA) functional (dependence on just the electron density value) such as SVWN5 (3.3 kcal/mol, Table 5.1). The B3LYP potential curve is close to the SVWN5 curve and somewhat above the MP4(SDTQ) curve (Figure 5.1; Table 5.1: ∆E = 3.7 compared to 2.9 kcal/mol). This indicates the dominance of the correlation energy of the BLYP functional, although by the admixture of LDA correlation and exchange as well as HF exchange (leading to some stabilization of 5.1b) the correlation energy is significantly reduced. Results obtained with an ωB97-type of functional differ significantly from those obtained with LDA or GGA, or other hybrid functionals as they predict a minimum for 5.1b being 7.0 (ωB97), 4.3 (ωB97X), or 1.0 kcal/mol (ωB97X-D) below the energy of 5.1a, the latter being located on a shoulder of the PEC close to 2.04 A.˚ B97 performs in a similar way to all other GGA functionals (PEC: SW+1S, Table 5.1). Hence, the inclusion of long-range exact HF exchange (used to reduce the self interaction error of B97 [23,57,172,173]) must be considered as the cause for this preference of 5.1b. These long range HF-exchange effects play a role for spin-pairing and the formation of the C1C6 bond. For B97, self-exchange is larger than self-electron repulsion so that in a situation of large exchange interactions the molecule is

44 artificially stabilized. The approximate exchange of B97 also overestimates interelectronic exchange, which is relevant for a bond-no bond process. For the C1C6 bonding situation (lowering exchange in the bonding region) the exchange interactions play a smaller role than in a non-bonding situation. Therefore 5.1a is artificially stabilized relative to 5.1b. This is parallel to the correlation effects discussed above: The density gradient is larger in the no bond situation and leads to a larger α- and β-electron separation via correlation, again stabilizing 5.1a. By including exact-exchange for the long-range part of ωB97, the stabilizing effect of the exchange interactions is significantly reduced, thus leading to a relative stabilization of 5.1b. If also the short-range exchange effects are improved, another stabilization of the bisnorcaradiene form (from -4.3 to -7.0 kcal/mol, Table 5.1) results. ωB97X-D reduces the energy difference between 5.1a and 5.1b to -1.0 kcal/mol indicating that dispersion forces may lead to a 5 kcal/mol stabilization of the annulene form 5.1a. This seems to indicate a large increase of bridge-ring interactions for increasing R. This can however not be justified in view of the reduction of the exact exchange of this functional from 40% in ωB97X to 20% in ωB97X-D with regard to the long and the short-range exchange. A relatively flat C1C6-potential was obtained using the double hybrid functional B2PLYPD. By mixing in both HF exact exchange, dispersion corrections, and MP2 pair correlation effects, the annulene form becomes sufficiently stabilized and a DW-F2M results (∆ E = -0.1; barrier: 1.0 kcal/mol) so that the overall result is somewhat closer to the experimental observation suggesting a rapid valence-tautomeric rearrangement with an average R-value of 1.86 A.˚ Non-dynamical electron correlation effects: We also investigated whether a multireference description with DFT leads to a significant change utilizing the REKS(2,2) method of Filatov. [49,101] However, no improvements of the PEC were obtained thus indicating that the bond- no bond process is not an isolated 2-electron problem but involves all 10 π-electrons of the annulene perimeter.

45 CASSCF includes multireference effects, but is lacking dynamic electron correlation. We first used a (10,10) active space, to describe the 10-electron aromatic system with 10 electrons in 5 bonding and 5 antibonding orbitals. CASSCF(10,10) leads to an overestimation of the stability of 5.1b by 7.8 kcal/mol similar to the HF result (9.3 kcal/mol, Table 5.1). The PEC takes a DW-2FM form, which is characterized by a flat energy region from 1.9 to 2.2 A,˚ that is, an extension of the “annulene shoulder” of the HF potential. Obviously, a full CI on a (10,10) active space including all π-electrons is not sufficient to describe π-delocalization in a balanced way, especially when σ-π interactions become important. CASSCF(10,10) corrects the description of the transition state region of the valence tautomeric rearrangement by adjusting its energy to that of the annulene form. However, it fails to adjust these energies to those of 5.1b. CASSCF with electron correlation added by MP2 theory (CASPT2) with the (10,10) active space leads to significantly improved results, with the difference between 5.1a and 5.1b reduced to 1 kcal/mol, a consequence of the improved description of π-delocalization of the annulene form. N-Electron Valence State Perturbation Theory (NEVPT2) is similar to CASPT2, but additionally takes into account the two-electron interactions of the active space electrons and excludes intruder states. Both effects are relevant for the description of the annulene form (2.5 kcal/mol more stable than 5.1b) by improving the description of 10π-delocalization along a distorted parameter and by excluding intruder states (more likely for 5.1a than 5.1b), which changes the PEC form to DW-F1M, indicating that the annulene form is more stable. This is the opposite of the PEC(CASPT2) result. Despite the testing of a large number of different WFT and DFT methods (more than 20), none of the results is in line with the experimental X-ray diffraction and NMR findings. Therefore the question remains whether other effects such as thermochemical corrections, entropy contributions, crystal packing or solvent contributions may improve the agreement between theory and experiment.

46 Method Curve a R(5.2b)b R(5.2a) ∆E(5.2b)c ∆E(TS)d HF DW-F1M 1.562 2.219 0.63 3.27 (2.64) B3LYP SW+1S (1.610) 2.280 13.60 - ωB97 DW-F2M 1.560 2.226 -1.12 1.48 (2.60) ωB97X DW-F1M 1.546 2.226 2.71 3.39 (0.68) ωB97X-D SW+1S (1.610) 2.240 7.22 - B2P-LYP-D SW+1S (1.610) 2.250 9.22 - MP2 SW+1S (1.610) 2.254 13.93 - MP3 DW-F1M 1.630 2.240 4.20 4.68 (0.48) MP4(SDQ) DW-F1M 1.610 2.214 1.88 3.00 (1.12) MP4(SDTQ) SW+1S (1.610) 2.265 10.48 - CCSD DW-F1M 1.613 2.235 3.21 4.04 (0.83) BD DW-F1M 1.612 2.234 3.25 4.06 (0.81) CCSD(T) SW+1S (1.610) 2.254 7.29 - BD(T) SW+1S (1.610) 2.256 7.32 - CASSCF(10,10) DW-F1M 1.540 2.268 4.37 7.65 (3.28) CASPT2(10,10) SW+1S (1.610) 2.254 5.32 - NEVPT2(10,10) SW+1S (1.610) 2.230 14.86 - CASPT2(14,14) SW+1S (1.700) 2.256 11.48 - ∆H(5.2b) ∆H(TS) B2P-LYP-D SW+1S (1.610) 2.267 12.59 - CCSD(T) SW+1S (1.700) 2.256 5.60 - BD(T) SW+1S (1.700) 2.258 5.55 - CASPT2(14,14) SW+1S (1.700) 2.256 10.16 - ∆G(5.2b) ∆G(TS) B2P-LYP-D SW+1S (1.610) 2.267 12.23 - CCSD(T) SW+1S (1.700) 2.256 5.77 - BD(T) SW+1S (1.700) 2.258 5.74 - CASPT2(14,14) SW+1S (1.700) 2.256 10.30 -

Table 5.2: Relative Energies and Tautomerization Barriers of 1,6-Methano[10]annulene.

a Curve indicates the shape of the potential energy well (DW-F1M - Double Well with Local First Minimum, DW-F2M - Double Well with Local Second Minimum, SW+1S - Single Well with Left Shoulder.) bR(5.2b) and R(5.2a) indicate the C1C6 distance for each structure in angstroms. (Values in parentheses are approximate values taken from shoulders.) c∆E(5.2b) gives the energy diﬀerence between tautomers, relative to 5.2b [kcal/mol.] d∆E(TS), ∆H(TS) and ∆G(TS) give the energy barriers for the tautomerization from 5.2a to 5.2b [kcal/mol.] (Values in parentheses are for the reverse reactions.) All calculations were completed using the 6-311G(d,p) basis set. MP3, MP4, CAS and coupled cluster calculations were computed with B3LYP/6-311G(d,p) optimized geometries.

47 Method Curve a R(5.3b)b R(5.3a) ∆E(5.3b)c ∆E(TS)d HF DW-F1M 1.557 2.395 7.03 12.70 (5.67) B3LYP DW-F1M 1.644 2.351 7.51 7.89 (0.38) ωB97 DW-F2M 1.576 2.366 -0.80 5.43 (6.23) ωB97X DW-F1M 1.576 2.350 2.18 6.14 (3.96) ωB97X-D DW-F1M 1.585 2.355 2.20 6.28 (4.08) B2P-LYP-D DW-F1M 1.594 2.364 7.13 8.92 (1.79) MP2 DW-F1M 1.675 2.286 3.02 3.07 (0.05) MP3 DW-F1M 1.591 2.373 4.38 8.31 (3.93) MP4(SDQ) DW-F1M 1.582 2.385 4.37 8.89 (4.52) MP4(SDTQ) DW-F1M 1.623 2.341 4.64 5.85 (1.21) CCSD DW-F1M 1.583 2.382 4.69 8.76 (4.07) BD DW-F1M 1.585 2.380 4.62 8.68 (4.06) CCSD(T) DW-F1M 1.607 2.370 4.99 7.33 (2.34) BD(T) DW-F1M 1.607 2.366 5.10 7.34 (2.24) CASPT2(6,6) DW-F1M 1.633 2.310 4.36 4.84 (0.48) CASPT2(10,10) DW-F1M 1.593 2.334 6.05 12.20 (6.15) ∆H(5.3b) ∆H(TS) B2P-LYP-D DW-F1M 1.653 2.245 6.33 6.34 (0.01) CCSD(T) DW-F1M 1.738 2.476 4.95 6.92 (1.97) BD(T) DW-F1M 1.738 2.476 4.96 6.93 (1.97) CASPT2(10,10) DW-F1M 1.641 2.334 5.89 11.53 (5.64) ∆G(5.3b) ∆G(TS) B2P-LYP-D DW-F1M 1.697 2.245 6.47 6.64 (0.17) CCSD(T) DW-F1M 1.698 2.482 5.35 7.62 (2.27) BD(T) DW-F1M 1.698 2.482 5.34 7.59 (2.25) CASPT2(10,10) DW-F1M 1.618 2.334 6.18 12.22 (6.04)

Table 5.3: Relative Energies and Tautomerization Barriers of 1,3,5-Cycloheptadiene and Norcaradiene.

a Curve indicates the shape of the potential energy well (DW-F1M - Double Well with Local First Minimum - Double Well with Local Second Minimum.) bR(5.3b) and R(5.3a) indicate the C1C6 distance for each structure in angstroms. (Values in parentheses are approximate values taken from shoulders.) c∆E(5.3b) gives the energy diﬀerence between tautomers, relative to 5.3b [kcal/mol.] d∆E(TS), ∆H(TS) and ∆G(TS) give the energy barriers for the tautomerization from 5.3a to 5.3b [kcal/mol.] (Values in parentheses are for the reverse reactions.) All calculations were completed using the 6-311G(d,p) basis set. MP3, MP4, CAS and coupled cluster calculations were computed with B3LYP/6-311G(d,p) optimized geometries.

48 Valence tautomerism of 1,6-methano[10]annulene and cycloheptatriene: Extensive spectroscopic and diffraction measurements were carried out in the case of 5.2.[27,80,85,95] The difference between 5.2a (being more stable) and 5.2b is estimated to be smaller than 10 kcal/mol, and all measured NMR, infrared, Raman or UV values exclude a second minimum for the bisnorcaradiene form 5.2b. Hence, a SW+1S form of the PEC is most likely. [27,80,85,95] In the case of the cycloheptatriene-norcaradiene system, a DW PEC has been verified by both NMR and kinetic studies. [18, 38, 186] Experiments conducted by Rubin [186] led to a free activation energy for the transition 5.3b 5.3a of ∆Ga(298) = 7.2 kcal/mol → and estimated the free energy of 5.3b to be 4 2 kcal/mol less stable than 5.3a with a ± zero-entropy change assumed [186]. The estimates were based on NMR results of Günther and co-workers, who estimated that 5.3b should have a finite concentration of 0.1% at room temperature. [89] In this work, we find that concentration of 5.3b to be just 0.003%. As in the case of 5.2, most of the methods applied failed to provide PECs and relative energies that are in line with these experimental observations (see Tables 5.2 and 5.3 as well as Figure 5.3.) The rationalization of these shortcomings in terms of dynamical and non-dynamical electron correlation effects are similar to those given for 5.1. ωB97X-D, CCSD(T), BD(T), MP4(SDTQ), and B2PLYPD lead to reasonable PECs for 5.2 suggesting that the bisnorcaradiene form 5.2b is located on a shoulder of the PEC. However, only MP4(SDTQ), and B2PLYPD provided a relative energy of 5.1b to be close to 10 kcal/mol, and unexpectedly the multi-reference CASPT2(6,6), CCSD(T), and BD(T) methods severely underestimate the destabilization of 5.3b. Particularly, the PEC of CASPT2(6,6) leads to a rearrangement barrier 5.3a 5.3b, which is 4.8 kcal/mol, more than 6 kcal/mol below → the experimentally estimated ∆Ga(298) of 11 kcal/mol. The CASPT2(6,6) active space is too small to provide a reliable description of the valence tautomeric rearrangement. Previous work by Cremer and co-workers has emphasized the homoaromatic interactions of the two π-bonds of norcaradiene with the three σ-bonds of the cyclopropyl group. [57] We found that these are essential for a correct description of the

49 process 5.3a 5.3b. Accordingly, we enlarged the (6,6) active space to (10,10) by including → six rather than two Walsh orbitals for the cyclopropyl group. With this active space, the barrier increases to 12.2 kcal/mol and the relative energy of norcaradiene 5.3b adopts a value of 6.0 kcal/mol (Table 3.2). Previous investigations of 5.3 by Jarzeki and co-workers [118] led to much different ∆E values (CASSCF: 21.6 kcal/mol; multireference perturbation corrections (MROPT2); 8.9 kcal/mol) based on the smaller (6,6) active space. Similarly all single reference calculations provided poor results. [53, 54] However, the CASPT2(10,10) results, if converted into ∆G(298) with the help of B3LYP-calculated ZPE, entropy and thermochemical corrections, lead to ∆Ga(298)5.3b 5.3a = 6.0 kcal/mol in good agreement with the corresponding ex- → perimental value of 7.2 kcal/mol (6.1 kcal/mol at 100 K.) [186] The potential curve obtained for ∆H(298) is shown in Figure 5.3 and probably presents the most accurate description of the energetics of the valence tautomeric system 5.3. Based on our experience with 5.3 we extended the (10,10) active spaces of 5.1 and 5.2 to (14,14) spaces, which include the C1C11, and C1C6 σ and σ? Walsh orbitals. For 5.2, the PEC is still obtained in a SW+1S form, where 5.2b is now 11.5 rather than 5.3 kcal/mol higher in energy than the annulene form at the potential minimum at R = 2.256 A˚ (X-ray: 2.235 A[˚ 27]). The corresponding ∆H(298) and ∆G(298) values are 10.2 and 10.3 kcal/mol, respectively, in line with experimental observations. [8, 14, 27, 28, 32, 37, 43, 66, 85, 95, 119, 137, 148, 226] Clearly, 5.2 is a [10]annulene rather than a bicyclic, homoaromatic π-system because R = 2.256 A˚ is too large to lead to sizable through-space interactions. [51] These results show that CCSD(T) and BD(T), although they may account for some non-dynamical effects beside the dynamical electron correlation effects, fail to describe the transition state region and 5.3b correctly. This can also be observed for 5.2b where too much stability is found in the norcaradiene forms. Therefore, we repeated the CASPT2 calculations for 5.1 with the larger (14,14) active space. Additional CASPT2 results and the consideration of thermochemical corrections: With the CASPT2(14,14) active space, 5.1a becomes the minimum of a relative flat potential

50 (0.91 kcal/mol below 5.1b) with activation energies of 1.32 and 0.41 kcal/mol for the valence tautomeric rearrangement (Table 5.1). Small changes in the ZPE and thermal correction values lead to a slight stabilization of 5.1b and a vanishing of the rearrangement barrier for the enthalpy curve (see Figure 5.3). For CCSD(T) and BD(T), the conversion into enthalpies has a similar effect on the potential (Table 5.1). ZPE and thermochemical corrections are based on harmonic frequencies, which may change differently with R than anharmonically corrected frequencies. We recalculated all vibrational corrections with scaled frequencies employing the scaling factors suggested by Scott and Radom [188] for DFT, resulting in no significant changes to the final result. As mentioned above, even a (14,14) active space may not be sufficient to describe all non- dynamical electron correlation effects resulting from the interactions of σ- and π-electrons, the stabilizing interactions in the intermediate biradicals and the bridge-ring interactions. Apart from this, the amount of dynamical electron correlation provided by CASPT2 is much too small and biased to prefer the annulene. Conversely, CCSD(T) or BD(T) are not suitable of correctly describing non-dynamical correlation. Since a combined method is not available, we constructed a model PEC by averaging the enthalpy curves for CASPT2(14) and CCSD(T), which gives a broad single well potential slightly preferring the bisnorcaradiene form by -0.1 kcal/mol (activation enthalpies: 0.1 and 0.2 kcal/mol.) The ∆G(R) curve increases the preference of 5.1b and introduces a somewhat stronger asymmetry of the potential (Figure 5.3). The degree of asymmetry of the potential curve increases with the admixture of additional non-dynamical electron correlation. Such a broad asymmetric SW potential explains the observed strong temperature-dependence of the 13C chemical shifts of 5.1 (they indicate a stronger population of the annulene form at higher temperature [69,80]) and the fact that 5.1 adopts two different forms in the unit cell, probably influenced by crystal packing effects (R = 1.836 and 1.780 A[˚ 27]). Therefore, we will investigate environmental influences on the PECs shown in Figure 5.2 in the following subsection. Consideration of solvent and crystal packing effects: The dipole moment (µ) of annulene 5.1a is 0.35 Debye at R = 2.039 and 0.11 Debye for R = 1.638 A(˚ ωB97X-D calculations)

51 where the orientation is along the C2 axis (bridge: positive, center of the perimeter: negative end). There is a charge transfer from the CMe2 bridge to the annulene perimeter, which changes, contrary to the changes in the dipole moment, from 13 (R = 2.039 A)˚ to 9 millielectrons (R= 1.638 A).˚ Experimental work with 5.1 was carried out in nonpolar solvents such as cyclohexane,

CS2, CCl4, or in the polar solvent methanol. [69,85,227] Therefore, we calculated the solvent influence by increasing the dielectric constant from 2 to 32.7 [100] using Tomasi’s polarizable continuum method (PCM.) [223] In all calculations, changes in the relative free energies ∆G(298) were 1 kcal/mol or smaller, always in favor of the annulene form (in line with the calculated dipole moments), which in the case of the of the estimated potential of Figure 5.3 (see also Table 5.1) would reduce the ∆G(298) difference between 5.1a and 5.1b favoring the annulene form with increasing temperature as found in the NMR experiments. [69, 80]. Hence, environmental effects cannot be ignored if free energy differences smaller than 0.6 kcal/mol are being considered. There is also the possibility that the unusual C1C6 distances observed in the crystal structure analysis [26] are the result of packing effects. Clusters of molecule 5.1 in parallel arrangements form molecular sheets, [26] where molecules which are on top of each other in different sheets could widen the C12C11C13 bridge angle via exchange repulsion, causing stronger bridge-perimeter interactions. It is shown in Figure 5.4 that the downward oriented methyl hydrogens are just 2.4 A˚ away from the center of the C3C4 and C8C9 bond, respectively (Figure 5.4). Considering that these H atoms carry a small positive charge and that the sum of the van der Waals distances for H and C is 1.2 + 1.6 = 2.8 A,˚ [100] the downward oriented methyl H atoms should be attracted by the π-density of the [10]annulene perimeter. There will be a stabilizing H-π-interaction at a distance of 2.4 A,˚ as is qualitatively confirmed by the increase in stabilization of the annulene form when comparing ωB97X-D and ωB97X results. However, the hypothesis of an increased bridge-perimeter attraction caused by bridge angle widening could not be confirmed by widening of the CCC-bridge angle, as it did not

52 have a signiﬁcant impact on the parameter R. Widening the bridge angle C12C11C13 by

10◦ leads to a increase in R of only 0.048 A.˚

2.420

2.383 2.389 2.486 1.836(7) 1.836 1.780(7)

1.836 1.836(7) 1.780(7)

1.951 2.148

5.1a (2.039 Å) 5.1b (1.636 Å)

Figure 5.4: Dimer and tetramer configurations that were calculated for this work. The green structure shows how two unit cells fit together in the crystal structure. The numbers on this structure are taken from Bianchi’s x-ray structure. The blue structure shows the arrangement that was calculated and optimized searching for packing effects. The orange structure shows the geometry and hydrogen-to-ring distance for the two optimized structures, ωB97X-D/6-311G(d,p).

Next, we calculated the geometry of the dimer and the tetramer shown in Figure 5.4 applying a constrained optimization, in which the distance(s) between the monomers and the relative orientation to each other were frozen (ωB97X-D calculations). The diﬀerences between the monomer and dimer geometries were small, with R being found to be 1.635 A˚ for the lower monomer and 1.631 A˚ for the upper monomer, which conﬁrms the direction of changes observed in the crystal (1.834 and 1.787 A,˚ Figure 5.4). Similar changes were calculated for the tetramer, which suggests that more realistic models comprising at least

53 sixteen monomers (twelve monomers surrounding a tetramer) at fixed distances and orientations may come close to what has been experimentally observed. However, this calculation (432 atoms) would be computationally prohibitive. In another set of calculations, the dimer shown on the left side of Figure 5.4 (with frozen distance and relative orientation of the monomers) was optimized for fixed R (1.6 < R < 2.2 A)˚ values of either the upper or the lower monomer, and optimizing the remaining geometrical parameters. For all these geometry optimizations, R of the second monomer changed maximally by 0.005 A˚ relative to the corresponding gas phase value where especially the positions of the methyl H atoms were sensitive. We conclude that, in view of the broad asymmetric SW potential calculated, crystal packing effects should have an impact on R and explain the existence of two molecules of 5.1 with different geometries in the unit cell. NMR investigation - An independent determination of the equilibrium geometry of 5.1: In previous work, Cremer has shown how an easily changing geometrical parameter of a flexible system can be determined in solution with the help of measured and calculated chemical shifts. [59,91] In Figure 5.5a, calculated 13C and 1H chemical shift values are given as a function of R and compared with the available 13C chemical shifts indicated as dashed horizontal lines. There are 5 unique C’s and 5 unique H’s, labeled as C1, C3, C3, C11, C12, H15, H16, H17, H19 and H20. The figure shows that the shift value of C1 is the most sensitive. This shift increases from a typical value for vinyl cyclopropane (42.5 ppm [125]) to that found for the parent annulene 5.2a (114.6 ppm [125]) and directly reflects the changes in R. At R = 1.763 A,˚ the calculated C1 value becomes equal to the measured one, suggesting that this R value is the one 5.1 adopts in solution or, alternatively, corresponds to a time-averaged value if the valence-tautomeric rearrangement of 5.1 is fast on the NMR time-scale. A similar observation can be made for the NMR chemical shift of C11, which increases from a value typical of a cyclopropane (13C shift: -2.8 ppm [125]) to the one measured for 5.2a (34.8 ppm [125]) crossing the observed C11 shift at R = 1.782 A.˚ The chemical shifts of the methyl carbon nuclei coincide at 1.865 A˚ with the corresponding measured value.

54 140 C2 8 C2 exp. C3 exp. 120 7 C3 H17

6 1 H H H H20 100 H15 Shift [ppm] H Chemical

C13 C12 C11 H H19 5 C1 exp. 80 C2 H15 C1 C3

4 60 C1 H16 H18 H17

3 40

CChemical [ppm] Shift C12 2 13 C11 exp.20 C12 exp. 1 H20 0

0 C11 H19 -20 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å] (a)

8 H H H H H H H H 7.5 C C C C H H H H 7

6.5

6 1b 1a

5.5

4.5 C Chemical Shifts [ppm]

13 4

3.5

2.5 Mean Deviation of

1.5 1.775 Å

1 1.6 1.65 1.7 1.75 1.8 1.85 R(C1,C6) Distance [Å]

(b)

Figure 5.5: a) Dependence of calculated NMR chemical shifts [ppm] as a function of the C1,C6 interatomic distance of 11,11-dimethyl-1,6-methano[10]annulene as obtained at the B3LYP/GIAO/6-311G(d,p) level of theory. b) NMR ab inito analysis of the mean deviation between measured and calculated 13C NMR chemical shifts.

55 However these 13C shifts are less sensitive, as are those of C2 (coincidence at R = 1.788 A)˚ and C3 (coincidence at R = 2.168 A,˚ Figure 5.5a.) The mean deviation between measured and calculated 13C chemical shifts for the C atoms of the perimeter adopts a minimum at R = 1.775 A˚ as is shown in Figure 5.5a. NMR chemical shift calculations are normally less accurate for conjugated systems, especially if these are nonplanar (the shifts of C2 and C3 are close to the experimental ones in the whole range 1.7 < R < 2.2 A˚ and a specific R value is difficult to determine). We note that when C11, C12, C13, C1, and C6 are used for the comparison with experiment a value of R = 1.775 A˚ results (Figure 5.5b), in good agreement with the X-ray diffraction values of R, which are close to 1.8 A.˚ [26]

80 10 C2C3 H16H17

70 J( 1

H15H16 8 H 1 60 C3C4 Constants [Hz] Coupling H) Spin-Spin

6 50 C1C2

H H H H20

40 C13 C12 C11 C11C12 H H19 4 C2 H15 C1 C3 30 C6

H16 2 20 H18 H17 C1C11 10 C12C13 0

C)Spin-Spin Coupling Constants[Hz] 0 13

C -2 13 -10 J( H17H18 C1C6 -20 -4 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å]

Figure 5.6: Dependence of calculated NMR spin-spin coupling constants [Hz] as a function of the C1,C6 interatomic distance of 11,11-dimethyl-1,6-methano[10]annulene as obtained at the B3LYP/GIAO/6-311G(d,p) level of theory.

So both the bisnorcaradiene and the annulene can be excluded as clearly dominating the valence tautomeric rearrangement of 5.1. The remaining possibility is a rapid rearrangement in solution via a small barrier of a DW PEC or a broad SW PEC with a large-amplitude

56 vibration in solution similar to the one suggested in Figure 5.3a. Accordingly, 5.1 has to be considered as a ﬂuxional molecule with rapid changes in bonding. The calculated SSCCs J(13C13C) and J(1H1H) given as a function of R are shown in Figure 5.6. When R is close to 1.5 A,˚ the values of 1J(C1C6) and 1J(C1C11) adopt the values typical of cyclopropane (12.4 Hz [125]). For increasing R the former 1J-value decreases to - 12.4 Hz at 1.8A.˚ This is comparable to the geminal 1J(CC) value in a substituted cyclobutane (-8 Hz [125]) and then increases to a zero value at large R. This indicates that through-bond or through-space coupling are small because the CCC-angle dependence of 2J implies for this situation a zero value, 5J coupling along the perimeter is too weak, and/or the C1C6 through-space overlap is too small. Hence, a temperature dependent measuring of J(C1C6) should provide an excellent possibility for an experimental determination of R. 1J(C1C11) increases from about 16 Hz at R = 1.60 A˚ to 28 Hz typical of a 1J(CC) value such as cyclobutane. [125] 1J(C11C12) changes from 45 to 39 Hz for the same R values while 3J(H15H16) increases from 5.0 to 7.2 Hz. Since the changes in the J(CC) values are larger, they should give the more reliable determination of the R value of 5.1 in solution.

5.3. Does 11,11-dimethyl-methano[10]annulene possess the longest homoaromatic CC bond of neutral hydrocarbons?

System 5.1 is unusual because of its broad SW potential, which makes a large amplitude C1C6 vibration, and a barrierless interconversion of the annulene into the bisnorcaradiene form possible. We clariﬁed the question of the nature of the C1C6 interactions by two diﬀerent model approaches utilizing the topological analysis of Bader [11], Cremer and Kraka [55, 142] and the local vibrational mode approach of Cremer, Zou, and Konkoli. [11, 139, 241] In Figure 5.7, the bond strength orders (BSO(CC)) based on the calculated local CC stretching force constants are plotted as a function of R. For each set of local vibrational modes at a given R-value the adiabatic connection scheme [241] is applied to determine whether a given local mode is still contained in a set of 3N-L modes directly related to the 3N-L normal vibrational modes. As can be seen from Figure 5.7, close to R = 1.7 A˚ the

57 C1C6 stretching mode drops out of the 3N-L set of vibrational modes, indicating that for larger R values there is no C1C6 covalent bond.

1.8

1.6 C2C3

1.4 C1C2 n(CC) C3C4 1.2

Order 1

0.8 C1C11 Strength 0.6 H H HH H H HH C C C C

Bond 0.4 C1C6 H H H H 0.2

0 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 R(C1,C6) Distance [Å]

Figure 5.7: Bond strength orders for carbon-carbon bonding interactions in 11,11-dimethyl- 1,6-methano[10]annulene system as a function of C1,C6 interatomic distance, analyzed by adiabatic mode analysis, B3LYP/6-311G(d,p).

C1C6 [A]˚ BSOC1C6 BSOC1C11 BSOC1C2 BSOC2C3 BSOC3C4 1.636 0.307 0.846 1.059 1.786 1.164 2.04 - 0.991 0.977 1.358 1.143

Table 5.4: Bond Strength Orders for all pertinent C,C interactions of 11,11-Dimethyl-1,6- methano[10]annulene at the stationary geometries (ethane = 1, ethene = 2.)

All other BSO(CC) values change smoothly from the bisnorcaradiene form to the annulene form. In the annulene case the alternation of bonds is similar to that found for naphthalene [123, 240], bonds C2C3, C4C5, etc. are the strongest, followed by bonds C3C4 and C8C9. The CC bridge bonds of 5.1b are weaker than the normal CC bonds with C1C6 being the weakest. The calculated AI (as deﬁned in section 9.2) of 5.1a is 64% of the value

58 obtained for benzene (100%), which is smaller than the value for 5.2a (73%) and signiﬁ- cantly smaller than the value for naphthalene (86%). [123] This is because 5.2a and 5.3a experience a strong perturbation of their 10π-perimeter caused by the 1,6-bridge leading to torsional angles up to 37◦.

In Figure 5.8a, the changes in the bond critical and ring critical points rb and rr of the electron density distribution ρ(r) are shown as a function of R. Some, but not all, of the changes are in agreement with those given by the BSO(CC) based on the local CC stretching force constants (Figure 5.7.). This is attributable to the fact that the electron density determined at one specific point in the bond region cannot reflect all the density changes taking place in the zero-flux surface between two bonded atoms apart from the influences of bond polarity, charge transfer, and other effects given by the changes in the virial (atomic) spaces of the molecule during change in R. The local CC stretching force constants account for these effects and therefore are more reliable as CC bond strength descriptors, as discovered in Chapter3. The Cremer-Kraka bond criteria state that covalent bonding requires the existence of a bond critical point and zero-flux surface between the atoms in question and that the energy

density at this bond critical point, H(rb) must be negative and stabilizing. [55,56,142] This criterion is fulﬁlled for all CC bonds in 5.1, except the C1C6 bond, which converts into a non-covalent interaction at R = 1.696 A˚ (Figure 5.8.) There the C1C6C11 ring critical point merges with the C1C6 bond critical point, leading to a singularity in the Hessian of ρ(r) and the C1C6 maximum electron density path connecting these atoms vanishes. We conclude that a C1C6 covalent bond with R = 1.80 A˚ does not exist, but that a homoaromatic interaction in the sense of a through-space overlap of π-orbitals exists leading to a small electron density increase between atoms C1 and C6. Impact of the bridge on the 10π-perimeter: The inﬂuence of electron-withdrawing and electron-donating substituents of a cyclopropane ring has been amply described in the literature (for a review, see citation 57). Two cyano groups at C11 lead to a shortening of the distal bond, and lengthening of the vicinal bonds (see 5.5 as compared to 5.4 in Figure 5.9.)

59 This was exploited to synthesize 11,11-dicyano-bisnorcaradiene, the dicyano analogue

rr(C1C11C6) -0.5 H3C CH3 C11 1.696 Å C2 C1 C3 ]

3 r (C1C6) -1.0 b C6 C4

rb(C1C11)

-1.5 rb(C1C2)

-2.0 rb(C3C4)

rb(C2C3) EnergyDensity [Hartrees/Å

-2.5

1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å] (a)

2.4

rb(C2C3)

2.2

] 2.0 3 rb(C3C4)

1.8 rb(C1C2)

1.6 rb(C1C11) H3C CH3 C11

Electron[e/Å Density 1.4 rb(C1C6) C2 C1 C3

C6 C4 1.2 rr(C1C11C6) 1.696 Å

1.0 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 C1,C6 Interatomic Distance [Å] (b)

Figure 5.8: Dependence of a) electron density distribution and b) energy density distribution on the C1,C6 interatomic distance of 11,11-dimethyl-1,6-methano[10]annulene as obtained from the AIMAll program.

of 5.1b.[226] The eﬀect of two methyl groups has been predicted to lead to a slight CC lengthening of the distal bond (slight shortening of the vicinal CC bonds) [57] as is conﬁrmed by the bond lengths given for 5.6 in Figure 5.9. This indicates that dimethyl-substitution at C11 in 5.1 should favor a larger rather R regardless of any other stabilizing bridge-perimeter interactions.

60 The isodesmic energies (B3LYP, in kcal/mol) for the the formal reactions:

4 + CH CH CH 6 + CH , ∆E = 3.78 3 2 3 → 4 −

2b + CH CH CH 1b + CH ∆E = 3.38 3 2 3 → 4 −

2a + CH CH CH 1a + CH ∆E = 4.92 3 2 3 → 4

(∆E values in kcal/mol) suggest a similar stabilization by the two methyl groups for cyclopropane and 5.2b, but a 5 kcal/mol destabilization for 5.2a. This is in line with a shortening of two vicinal and one distal CC bond. Molecule 5.6 has a smaller external CCC angle than the HCH angle in its parent molecule (Figure 5.9), which is the result of steric repulsion between methyl groups and the ring. For the same reason, 5.1b has an even smaller external angle (110.2◦, Figure 5.9), where the folding back of the two diene units as shown in the side view at the bottom of Figure 5.4 leads to some reduction of the steric repulsion between methyl groups and ring perimeter. In the case of 5.1a, steric attraction between methyl groups and π-perimeter and steric repulsion (for 5.1a the H-center(C3C4) distance is decreased from 2.148 to 1.951 A,˚ ωB97X-D, see Figure 5.4) must be balanced, which leads to a small C12C11C13 angle (105.3◦, Figure 5.4), methyl-methyl repulsion, and an overall destabilization as reﬂected by the energy of the isodesmic reaction given above (4.9 kcal/mol).

The destabilizing eﬀect of the CMe2 bridge leads to an increase of the relative energy of 5.1a, which in view of π-delocalization is more stable for the parent system 5.2. π- Delocalization and bridge-perimeter destabilization lead to 5.1b and 5.1a having comparable energies.

61 A basic problem of previous studies was that they were based on quantum chemical methods of low accuracy. Depending on whether HF or MP2 is used, the preference for different valence tautomeric forms is found. This also holds for the XC functionals of DFT as we have demonstrated in this work for the first time. This leads to rather limited insight into the possible cause of a quantum mechanical (electronic structure) effect. For example, Simonetta and co-workers [194] have used Hoffmann’s approach [57, 104] to rationalize the stability of substituted cyclopropanes, and explain substituent effects in bridged [10]annulenes where his arguments were based on low level calculations. As was pointed out by Cremer and co-workers, [57] the orbital model used does not even explain all substituent effects for the simpler cyclopropane calculations. Furthermore, it does not consider the impact of bridge- perimeter interactions, the stabilization of biradicaloid structures for medium-sized R values by conjugation, or the dynamic aspects of the valence tautomeric rearrangement. The topological analysis of ρ(r) by Gatti and co-workers, [83] which was interpreted as proof for a long covalent C1C6 bond, has to be criticized because they were carried out at the HF/minimal basis set level without using any quantum mechanical criterion for covalent bonding. Other investigations were based on the natural bond order (NBO) analysis or heuristic models utilizing the degree of bond length alternation in the ring perimeter. [36] Whatever property is used, it must be evaluated with regard to the corresponding value of a suitable reference system. An interesting rationalization of the carrying dynamic behavior of bridged [10]annulenes was proposed by Choi and Kertesz, [43] who model the opening of the cyclopropane ring in 5.1 or 5.2 by its conversion into a trimethylene biradical in its triplet ground state. The stabilization of the triplet trimethylene by substituents as described by DFT provides a basis to understand whether the bisnorcaradiene or annulene form is more stabilized. The radical centers are part of a conjugated system and a more realistic model would be the opening of 3-substituted 1,2-divinylcyclopropanes.

62 110.2 105.3 H C CH3 H3C CH3 3 1.533 1.516 65.2 89.4 1.514 1.518

125.8 121.8 120.0 1.452 120.6 1.425 2.120 1.636

1.423 124.6 1.437 123.3 1.371 119.4 1.342 115.1 5.1a 5.1b

110.3 116.6 H H H H 1.089 1.089 64.3 99.6 1.492 1.503

121.6 116.4 127.7 118.2 1.424 2.279 1.453 1.600 122.4 1.408 122.5 1.475 1.390 126.7 1.347 117.7 5.2a 5.2b

114.9 108.6 H H H H 1.084 1.084 1.090 1.097 66.7 102.8 1.496 1.503 1.380 121.5 123.0 1.454 119.5 1.645 125.4 2.350 123.2 1.451 113.6 1.352 1.370 1.446 121.3 5.3a 5.3b

H 1.539 N 1.512 H C C 1.508 H 1.487 1.520 H 114.2 115.8 113.3 H H C C 1.083 1.442 N 1.514 H H 5.4 5.5 5.6

Figure 5.9: B3LYP geometries of 5.1 - 5.6. Bond lengths in A˚ and bond angles in degrees.

63 Dorn and co-workers [69] used 13C CPMAS (cross-polarization magic angle spinning) spectra to refute a rapid valence-tautomeric process for 5.1. Instead, these authors suggested that an asymmetric PEC and a different population of the vibrational levels at higher temperature would lead to the observed temperature dependence of the NMR spectra. Alter- natively, temperature dependent intermolecular interactions could cause the observed temperature dependence. Our high level results are in line with the first explanation where strong intermolecular interactions cannot be confirmed. Kaupp and Boy [128] analyzed the measured temperature factors of the crystal data and concluded that a structural disorder in the solid state leads to the coexistence of bisnorcaradiene and [10]annulene, which implies that the measured R values are just averages. Our results are not in contradiction with this hypothesis and our study of packing effects is too limited to provide any arguments for or against structural disorder. With this comprehensive description of the previously controversial bridged annulene system 5.1, we demonstrate the solution of an organic multi-reference system. All manner of density functional (B3LYP, ωB97X-D, B2P-LYP-D, etc.) analysis, coupled cluster analysis (CCSD, CCSD(T), BD, BD(T)) and Møller Plesset perturbation (MP2, MP3, MP4) analysis did not provide satisfactory results. Complete active space/self consistent field calculations still failed, until a carefully selected active space of adequate size was employed. This is the cost, both in terms of computational resources and thoughtful examination of the active space, of multi-reference computational chemistry.

64 Chapter 6

Multi-Reference Systems in Inorganic Chemistry

6.1. Transition Metal Diatoms

In the ﬁeld of organic chemistry, the examples of multi-reference problems are relatively rare, and often unique and interesting. In inorganic chemistry, multi-reference systems are ubiquitous. Bulk metals participate in metallic bonding, rather than covalent bonding, described as a matrix of metallic nuclei in a sea of electrons. This is what gives metals their distinctive properties of lustre, malleability and conductivity. The primary reason for this is the wealth of s-, p- and d-orbitals in large nuclei, resulting in a ‘band’ of low-lying unoccupied orbitals and low-lying excited states. However, when considering small clusters of metal atoms, the electronic structure is that of covalent bonding, with low-lying excited states still present. For this work, we investigated the ‘d-block’ transition metals, in groups 3-12 and rows 4-6 of the periodic table. We selected the smallest possible clusters of two atoms (diatoms.) These systems have been extensively studied experimentally and computationally, but compilations of multi-reference calculations for the entire set of transition metals do not exist.

6.2. A Survey of All Transition Metal Diatoms

The results of all calculations are summarized in Table 6.1. Generally, CASSCF/MR- AQCC and CASSCF/CASPT2 calculations were run using a (2g,12) complete active space, where g is the group number, 2g the total valence electrons, and 12 the number of orbitals in the complete active space. The RASSCF/RASPT2 calculations were generally run using a (2g,18) restricted active space. The active spaces which gave the best results are summarized

65 in Table 6.2. For each diatom, the electronic state (term symbol) of the ground states was taken from the literature. Where more than one ground state was reported, the ground state which gave calculated results nearest the experimental values was used. The basis sets employed are discussed in Section 9.3.

Group 12; Zn2, Cd2, Hg2: These diatoms have ﬁlled valence shells (24 electrons), and are known to form van der Waals complexes, [24, 64, 141, 201] and are therefore of minimal interest to this study. They were run at the CASSCF-CASPT2 level of theory, with the aug-cc-pVQZ-DK (Zn2) and aug-cc-pVQZ-PP (Cd2 and Hg2) basis sets. The (24,14) active space (24 electrons in 14 orbitals) was used, rather than the (24,12) active space, due to the near degeneracy of the valence orbitals. This added the p-πu orbitals to the complete active space. Based on what was learned from the Mn2 van der Waals complex (See Group 7 below), the higher levels of theory were not used. With all orbitals ﬁlled, they exhibit the

1 + Σg ground state.

1 + Group 11; Cu2, Ag2, Au2: Spectroscopically, these species are found to be in the Σg ground state. With 22 valence electrons, these diatoms have a formal bond order of 1 in the ground state with all d-electrons existing as unshared electron pairs. For Cu2 and Ag2, selecting an active space of 14 orbitals (CASPT2(22,14)), using the (n)d, (n+1 )s and (n+1 )p orbitals to describe the d-σg, d-σu, d-πu, d-πg, d-δg, d-δu, s-σg, s-σu and p-πu molecular orbitals gave the best orbital description, giving results in close agreement with experimental values. However, the RASPT2(22,18) restricted active space results also gave reasonable results.

For Au2, a better description was obtained with 18 active orbitals, (RASPT2(22,18)), including the 5d, 6s and 6p orbitals. This was attributable to the lowering of the excited state energies from the relativistic contraction of the (n+1 )s and (n+1 )p orbitals. This brings these orbitals into alignment, by size and energy, with the (n)d orbitals. This phenomenon is less pronounced in the 3d, 4s and 4p orbitals, owing to the lack of nodal planes in the 3d

66 orbitals, and most prevalent in the 5d, 6s and 6p orbitals, since relativistic contraction is strongest for the largest nuclei.

These eﬀects are reﬂected in the equilibrium bond lengths (Re), bond dissociation energies (BDE’s) and stretching force constants (ke) for each diatom. For Au2, the greater contributions by the excited states into the 6s and 6p orbitals resulted in the highest BDE and ke of the sequence, 56.91 (53.06 [156]) kcal/mol and 2.187 (2.12 [106]) mdyn/A,˚ respectively. (Experimental values are in parentheses.) These are much higher than the values

36.05 (38.74 [6]) kcal/mol and 1.212 (1.18 [106]) mdyn/A˚ for Ag2. The BDE values for Cu2,

43.84 (47.97 [174]) kcal/mol and 1.332 (1.33 [103]) mdyn/A˚ are higher than Ag2, which is attributable to the shorter bond length, and lower than Au2, which is attributable to the lack of low-lying excited states.

Comparing our BDE results to previously reported theoretical values, our Ag2 results are in better agreement with experiment than those reported by Andrea and others (27.67 kcal/mol, MRCI(SD)/(22,12) [6]), and the results for Cu2 and Au2 by Roos and others (45.43 kcal/mol, CASPT2(22,2) [174].) Barysz and Pyykkö’sresults (52.35 kcal/mol, CASPT2(22,12)/BSSE corrected [20]) are slightly better than the numbers reported here. In a recent paper, Radenkovićand others [177] calculated these diatoms using “breathing orbital” valence bond theory, and a (2,2) active space, excluding all d-orbitals. We find that the resultant bond dissociation energies of 40.7, 28.9, and 47.4 kcal/mol for Cu2, Ag2 and

Au2, do not improve on the results obtained with the larger active spaces. Since most of the bonding is described by s-orbital overlap, these systems were relatively easy to calculate.

Unlike most other groups, the Re’s, BDE’s and ka’s for all group 11 species gave reasonable results for nearly any of the active spaces selected.

+ Group 10; Ni2, Pd2, Pt2: Spectroscopically, Ni2 was found to be in the Og ground state, 3 while Pd2 and Pt2 are in the Σg− ground state. Ni2 is best described by an active space of

12 orbitals (20,12), using the 3d and 4s orbitals to describe the d-σg, d-σu, d-πu, d-πg, d-δg, d-δu, s-σg and s-σu molecular orbitals. The aug-cc-pVQZ-DK basis set was used.

67 Pd2, and Pt2, were best described with 18 restricted active orbitals, (RASPT2(20,18)), using the 4d, 5s and 5p atomic orbitals, and 5d, 6s and 6p atomic orbitals, respectively, to generate the d-σg, d-σu, d-πu, d-πg, d-δg, d-δu, s-σg, s-σu, p-πu, p-πg, p-σg and p-σu molecular orbitals. The aug-cc-pVQZ-PP basis set was used.

Agreement between the calculated and experimental values for Re, BDE and ke are excellent; Ni2 - 2.180 (2.154 [170]) A,˚ 47.49 (47.46 [42]) kcal/mol, 1.156 (1.16 [150]) mdyn/A;˚

Pd2 - 2.411 (2.48 [110]) A,˚ 23.24 (24.05 [103]) kcal/mol, 1.489 (1.38 [106]) mdyn/A˚ and Pt2 - 2.345 (2.333 [2]) A,˚ 72.64 (72.72 [103]) kcal/mol, 2.848 (2.66 [106]) mdyn/A.˚ Once again, experimental results are in parentheses. In particular, the BDE values calculated in this work are improvements on past calculations reported in the literature: Ni2 45.083 kcal/mol [42], Pd2 22.6 kcal/mol [61], and Pt2 60.0 kcal/mol [61]. Note that the stretching force constants increase going down the group, as relativistic contraction of the outlying orbitals increases. Although all methods tried gave generally useful results, some variability was found in the ke descriptions of Pd2, and Pt2, where the values varied widely by method. The method which gave the best agreement with the experimental results for Pd2 and Pt2 is RASPT2(20,18) with the Dunning basis set. The stretching force constant (ke) is the most reliable of the three parameters that we employ, because it is a second order property, incorporating a range of geometries. Experimental values for this parameter are also relatively easy to obtain spectroscopically for diatoms, because there is no mode coupling, and the Badger rule is fully applicable in its original format. [12,13,146]

Unlike most other groups, but similar to group 11, the Re’s, BDE’s and ka’s for all group 10 species gave reasonable results for nearly any of the active spaces selected.

5 Group 9; Co2, Rh2, Ir2: These species are all found to be in the ∆g ground state. In all cases, the best descriptions were obtained with (18,18) active spaces, which include all (n)d,

(n+1 )s and (n+1 )p orbitals. The best basis sets for Co2, Rh2, and Ir2 were aug-cc-pVQZ- DK, aug-cc-pVQZ-PP and ANO-RCC, respectively.

68 Agreement between the calculated and experimental values of Re for Rh2 is good; 2.25 A˚ versus 2.28 A[˚ 15]. Experimental Re values for Co2 and Ir2 are not found in the literature.

The comparison between calculated and experimental values of ke’s are excellent for Co2 and

Ir2; 1.580 mdyn/A˚ (1.53 [68]) and 4.471 mdyn/A˚ (4.44 [150]), respectively. This parameter is reasonable for Rh2, with values of 1.981 versus 2.44 mdyn/A[˚ 150], here using the (18,12) complete active space. Once again, the BDE values in this work are signiﬁcant improvements on what was previously available in the literature. Multi-reference BDE calculations for Co2 and Ir2 have

not been reported. This work reports the following values: Co2, 32.48 versus 38.51 kcal/mol [71] (by DFT) (39.43 6.42 kcal/mol [126]), Rh , 32.65 versus 49.3 kcal/mol [15] (32.68 ± 2 kcal/mol [230]) and Ir2, 82.76 versus 75.84 kcal/mol [71] (by DFT) (79.99 kcal/mol [155], empirical estimate.)

Group 8; Fe2, Ru2, Os2: These diatomic molecules were all found in septuplet ground states

7 + 7 7 of Σg , ∆u and ∆u, respectively. The (16,18) active space worked well for all three diatoms.

Fe2 gave the best results with the ANO-RCC basis set, while Ru2 and Os2 worked best with the aug-cc-pVQZ-PP basis set.

Re values for Fe2 and Ru2 agreed well with experiment: 2.149 versus 2.02 A[˚ 175] and

2.270 versus 2.54 A[˚ 45], respectively. An experimental Re value is not available for Os2.

Stretching force constants, ke are in less good agreement with experiment for Fe2 and Ru2, 1.713 mdyn/A˚ (1.48 [106]) and 2.511 mdyn/A˚ (3.59 [150].) However, this parameter is in

excellent agreement with experiment for Os2: 6.104 mdyn/A˚ (6.26 [150].) All BDE values in this work are improvements on what was previously available in the

literature: Fe2, 26.97 versus 27.76 kcal/mol [105] (26.95 kcal/mol [105]), Ru2, 73.45 versus

58.23 kcal/mol [136], (73.56 kcal/mol [136]), and Os2, 108.42 versus 77.25 kcal/mol [135], (101.00 kcal/mol [135], empirical estimate.)

69 Group 7; Mn2, Tc2, Re2: Mn2 presents the same computational challenge as Zn2, Cd2 and

Hg2, that the diatomic molecule is found to be a van der Waals complex, resulting in a very large Re and very small BDE and ke.[34] Tc2 being a synthetic element not found in nature, experimental parameters are diﬃcult to obtain, or trust. Re2 is important to this study,

2 because the Re2Cl8− anion was the ﬁrst veriﬁed quadruple bond, and is one of the reference species used for the BSO calibration of this work.

1 + 3 Mn2 and Re2 are found to have the Σg ground state, while Tc2 has the Σg− ground state.

Mn2 was found to be reasonably described with a (14,12) active space, and the larger (14,18) active space over-bound the molecule, resulting in a description equivalent to a full covalent bond, with Re’s in the 2.1 to 2.4 A˚ range, and a ke 20 times greater than the reported experimental value. Tc2 was found to be best described with a (14,12) active space, and

Re2 required a (14,18) restricted active space. These resulted in Re and BDE values in good agreement with experiment; Mn2 - 3.220 (3.4 [150]) A,˚ 4.16 (3.22 [217]) kcal/mol; Tc2

- 2.073 A˚ (no experimental value available), 87.64 (80.48 [216]) kcal/mol; and Re2 - 2.139 (2.18 [203]) A,˚ 93.66 (92.24 [150]) kcal/mol. The BDE values were comparable to previously reported calculated values. Comparing this work to other for the Mn2 van der Waals complex, the results, 4.162 versus 3.05 [216] kcal/mol were both within 1 kcal/mol of the experimental value. For Tc2, 87.63 versus

82.2 [216] kcal/mol (empirical estimate) were comparable. For Re2 93.66 versus 84.53 [203] kcal/mol was a signiﬁcant improvement, which was to be expected, since Sun’s result is from a single-reference DFT calculation.

Calculations for ke values have proven diﬃcult for Mn2 and Tc2; 0.0671 (0.094 [106]) mdyn/A,˚ and 2.257 (4.37 [150]) mdyn/A,˚ respectively. For Mn2, where the dimer is a van der Waals complex, it is to be expected that the stretching force constant would be very low, and so the low numbers are entirely consistent. For Tc2, there are few measurements in the literature, because this synthetic and radioactive molecule is expensive and diﬃcult to obtain, leaving some question about accuracy of the available experimental values. For the critical dimer, Re2, the calculated vale of 6.377 mdyn/A˚ is in excellent agreement with the

70 experimental value of 6.26 mdyn/A[˚ 107].

1 + Group 6; Cr2, Mo2,W2: All of these diatoms exhibit Σg symmetry. Having 12 valence electrons, exceptionally short bonds and the largest stretching force constants, they are the candidates for sextuple bonding.

For Cr2, a (12,20) restricted active space proved to be necessary for best results, improving on the (12,18) restricted active space calculations with the aug-cc-pVQZ-DK basis set. For

Mo2, the (12,12) complete active space with the ANO-RCC basis set gave good results, where for W2, the (12,18) restricted active space with the aug-cc-pVQZ-PP basis set was best.

Agreement between the calculated and experimental values for Re, BDE and ke are very good; Cr2 - 1.775 (1.6788 [29]) A,˚ 33.95 (33.95, 35.97 [217]) kcal/mol, 4.060 (3.54 [217]) mdyn/A,˚ Mo2 - 1.943 (1.929 [73]) A,˚ 114.72 (103.17 [181]) kcal/mol, 6.447 (6.43 [150]) mdyn/A˚ and W - 2.110 (2.048 [7]) A,˚ 122.54 (115.48 23.48 [181]) kcal/mol, 5.919(6.14 2 ± [106]) mdyn/A.˚ These species are the most analyzed of all of the transition metal diatoms, with a host of calculated results that are in line with the ones reported here.

3 Group 5; V2, Nb2, Ta2: All of these diatoms were found in the Σg− state. They were best described with RASPT2 (10,18) active spaces. It was found that for the ANO-RCC basis set run on the Molcas software [3], the (10,18) complete active space, with up to 9,000,000 conﬁguration state functions (CSF), can be run in a reasonable timeframe.

For V2, agreement between the calculated and experimental values for Re, BDE and ke are very good; 1.820 A˚ (1.766 A[˚ 149]), 52.96 kcal/mol (58.06 kcal/mol [166]), and 3.990 mdyn/A˚ (4.33 mdyn/A[˚ 30]), respectively. We found no calculated values for these parameters in the literature. Nb2 resulted agree well with experimental values: Re, 2.101 (2.087 [117])

A,˚ BDE 138.48 (128.67 [16]) kcal/mol, ke 3.374 (4.84 [30]) mdyn/A.˚ Agreement was also very good for Ta2, between the calculated and experimental values for Re, BDE and ke ; 2.374 A˚ (2.374 A[˚ 203]), 128.82 kcal/mol (114.38 - 124.52 kcal/mol [30]), and 5.362 mdyn/A˚ (4.80 mdyn/A[˚ 30]), respectively. The BDE, calculated with a (10,18) active space, was in

71 better agreement with experiment than Borin and Gobbo’s calculation with a (10,12) active space. [30]

3 Group 4; Ti2, Zr2, Hf2: Ti2 was found to be in the ∆g state, and was best described with

1 + an (8,12) active space and the aug-cc-pVQZ-DK basis set, while Zr2 and Hf2 are in the Σg state. Zr2 and Hf2 were best described with an (8,18) active space. Here, too, it is found that the ANO-RCC basis set can be run with an (8,18) complete active space. However, in this case, only the results for Hf2 were improved over the restricted active space calculation with the aug-cc-pVQZ-PP basis set. The agreement between the calculations reported here and experimental values is good.

For Ti2, Zr2 and Hf2, the Re values of 1.909 (1.9422 A[˚ 70]), 2.265 (2.24 A[˚ 150]) and 2.315 (2.46 A[˚ 203]), the agreement between the calculations reported here and experimental values is good. The values for BDE: 38.58 ( 31.109 kcal/mol [207]), 64.89 (70.38 kcal/mol [9]) ≥ and 92.31 (78.41 kcal/mol [203], empirical estimate) are in reasonable agreement with the experimental values, as many of the experimental values report large margins of error. For ke values, the results for Ti2 and Hf2, 2.628 (2.35 mdyn/A[˚ 107]) and 1.505 (1.63 mdyn/A[˚ 107]) are good, and the results for Zr2, 3.573 (2.51 mdyn/A[˚ 107]) are the only computational results reported in the literature to date. There are relatively few calculated results reported for these compounds [17,21,207], but the results of this work are in better agreement with the experimental values than previously published work.

5 Group 3; Sc2,Y2, La2: Each of these diatoms are all found to be in the Σu− state. In all cases, an active space of (6,18) was required for a good description of the molecule. In these cases, the ANO-RCC (6,18) complete active space did not improve the results over the restricted active space results with the aug-cc-pVQZ-DK or aug-cc-pVQZ-PP basis sets.

Agreement with experimental values for Re, BDE and ke were good. Sc2: 2.653 A˚ (2.70

A[˚ 224]), 22.61 (25.9 kcal/mol [224]), and 0.853 (0.76 mdyn/A.˚ [106]) Y2: 2.841 (2.80 A[˚ 224]),

72 5 3 3 1 + 1 + 7 + 5 + 1 + 1 + Diatom Sc2 Σu− Ti2 ∆g V2 Σg− Cr2 Σg Mn2 Σg Fe2 Σg Co2 ∆g Ni2 Og Cu2 Σg Zn2 Σg Re [A]˚ AQCC 3.220 2.020 2.350 2.231 2.230 CASPT2 2.572 1.909 1.868 3.220 2.191 2.332 2.180 2.195 5.340 RASPT2 2.787 1.825 1.775 2.073 2.350 2.195 2.176 RAS-ANO 2.653 1.975 1.820 1.876 2.468 2.149 2.195 2.483 2.224 experiment 2.7 1.9422 1.766 1.6788 3.4 2.02 2.154 2.2193 4.49 BDE [kcal/mol] AQCC 26.97 34.42 46.28 42.59 CASPT2 24.16 38.58 82.19 4.16 39.44 34.40 47.49 43.84 3.20 RASPT2 84.51 52.97 21.24 32.48 46.82 92.54 RAS-ANO 22.61 74.34 44.83 14.02 26.18 26.52 57.36 experiment 25.9 5 31.109 58.06 3.76 33.95, 35.97 3.22 26.95 2.50 39.43 6.42 47.46 0.42 47.97 0.81 ± ≥ ± ± ± ± ke[mdyn/A]˚ AQCC 4.630 2.033 1.053 1.428 CASPT2 1.371 2.628 7.027 0.0671 3.224 1.156 1.522 10.107 RASPT2 0.816 12.033 4.060 0.178 0.975 1.151 1.332 RAS-ANO 0.853 1.827 3.990 2.704 1.713 1.580 0.823 1.147 experiment 0.76 2.35 4.33 3.54 0.094 1.48 1.53 1.16 1.33 0.013

5 1 + 3 1 + 3 7 5 3 1 + 1 + Diatom Y2 Σu− Zr2 Σg Nb2 Σg− Mo2 Σg Tc2 Σg− Ru2 ∆u Rh2 ∆g Pd2 Σg− Ag2 Σg Cd2 Σg Re [A]˚ AQCC 2.909 2.330 2.087 1.960 2.277 2.252 2.424 2.548 CASPT2 2.862 2.281 2.101 2.060 2.209 2.220 2.176 2.313 2.498 4.29 RASPT2 2.856 2.265 2.101 1.940 2.073 2.270 2.525 2.411 2.490 RAS-ANO 2.841 2.194 2.316 1.943 1.925 2.180 2.300 2.480 2.471 experiment 2.80 2.24 2.087 1.929 2.54 2.28 2.48 2.33 4.07 BDE [kcal/mol] AQCC 23.22 52.63 152.91 204.85 78.37 39.51 20.56 36.05 CASPT2 28.49 89.44 57.68 180.11 87.64 73.46 61.97 31.67 43.63 1.82 RASPT2 82.80 64.89 147.85 158.17 74.37 32.65 23.24 30.05 RAS-ANO 87.20 53.53 138.58 114.72 26.81 54.96 experiment 82.16 9.36 70.38 128.67 103.17 0.23 80.48 73.56 32.68 7.31 24.05 0.46 38.74 0.92 ± ± ± ± ke[mdyn/A]˚ AQCC 0.950 7.767 2.623 1.981 1.191 1.123 CASPT2 0.943 3.536 3.374 4.156 2.257 2.175 1.557 0.981 1.400 0.633 RASPT2 1.011 3.573 4.745 2.511 1.135 1.489 1.236 RAS-ANO 0.739 1.459 6.556 6.447 6.540 2.475 4.691 1.366 experiment 0.89 2.51 4.84 6.43 4.37 3.59 2.44 1.38 1.18 0.017

5 1 + 3 1 + 1 + 5 5 3 1 + 1 + Diatom La2 Σu− Hf2 Σg Ta2 Σg− W2 Σg Re2 Σg Os2 Πg Ir2 ∆g Pt2 Σg− Au2 Σg Hg2 Σg Re [A]˚ AQCC 2.009 2.550 2.316 1.986 2.009 2.167 2.359 2.313 2.498 CASPT2 3.314 2.567 2.247 2.094 2.009 2.234 3.923 2.344 2.442 3.44 RASPT2 3.175 2.315 2.110 2.073 2.254 2.327 2.345 2.454 RAS-ANO 2.898 2.603 2.374 2.021 2.139 2.219 2.176 2.298 2.475 experiment 2.8 2.46 2.23 2.048 2.18 2.333 2.4715 3.34 BDE [kcal/mol] AQCC 21.66 42.12 160.43 84.33 93.66 47.11 49.44 66.75 48.11 CASPT2 10.49 57.68 210.71 215.16 78.07 80.59 58.47 1.91 RASPT2 28.49 92.31 122.54 65.21 54.79 72.64 56.91 RAS-ANO 60.58 118.95 128.82 189.83 112.65 108.42 82.77 51.29 65.82 experiment 57.6 5 78.4 14 114.4-124.5 115.5 23.5 92.24 101 79.99 72.72 0.77 53.08 0.73 1.0 0.1 ± ± ± ± ± ± ke[mdyn/A]˚ AQCC 0.592 1.772 3.162 12.498 3.202 5.859 2.637 3.315 1.971 CASPT2 0.691 1.925 3.877 7.216 2.091 6.796 2.967 1.421 2.520 0.249 RASPT2 0.802 2.053 5.903 6.104 3.463 2.848 2.187 RAS-ANO 1.268 1.505 5.362 5.441 6.377 4.727 4.471 3.249 2.265 experiment 0.76 1.63 4.80 6.14 6.26 6.26 4.44 2.66 2.12 0.02

Table 6.1: AQCC, CASPT2, RASPT2 Calculations by aug-cc-pVQZ basis sets and RASPT2 Calculations by ANO-RCC basis set. Summary of all results.

82.80 (82.18 kcal/mol [75]), and 1.011 (0.89 mdyn/A.˚ [150]) La2: 2.898 (2.80 A[˚ 224]), 60.58 (57.6 kcal/mol [224]), and 0.802 (0.76 mdyn/A.˚ [150])

73 Computationally, Sc2 has been investigated many times [33, 127, 217], reporting results from 39.66 to 54.42 kcal/mol. The results of this work are in better agreement with the

experimental values than those previously published results. Results for Y2 improve the

value reported by Tamukong, et al [216]. No computational results are available for La2, so this work reports that, now. Bond Strength Descriptors: Having determined the best values for bond length, bond dissociation energy and stretching force constant for all of the transition metal diatoms, we now consider which parameter gives the best description of bond strength. The calculated bond lengths for all diatoms are given in Figure 6.1. Here we ﬁnd a

reasonable pattern, which is disturbed primarily by the van der Waals complexes; Mn2, Zn2,

Cd2 and Hg2. Without speculating about bond order, it can be stated that the third group represents 6 electron bonding, the forth group represents 8 electron bonding, etc, and that, through the sixth group the bonds grow shorter with increase of bonding electrons. For the later groups, additional electrons are going into antibonding orbitals, and the bonds become longer. Variability is greatest for the forth row elements, where the energy gaps between the 3d and 4s orbitals are larger than in rows 5 and 6. The calculated bond dissociation energies are given in Figure 6.2. Here it is shown once again that the 6 electron bond has a lower BDE than the 8 electron bond, and so forth, and that the rows beyond row six report lower BDE’s due to additional electrons ﬁlling antibonding orbitals. The exception to this pattern, aside from the van der Waals complexed diatoms, is that the ﬁfth group, V2, Nb2 and Ta2, have larger BDE’s than the

3 sixth. Each of the fifth group diatoms are found to be in the Σg− state, indicating an equal number of occupied orbitals for both groups, albeit there are half-filled orbitals in group 5. The results for stretching force constants, shown sorted by their groups in the periodic table in Figure 6.3, invert the bond length results. The shortest bond lengths, in group six, report the largest ke’s. The ke and BSO values for all diatoms are listed in Table 6.2. The ke’s for Re2 and Os2 are greater than that for W2. This is very significant, because W2 is considered a sextuple bonding candidate, and the other diatoms are not.

74 5.5 Zn2

5.0

4.5 Cd2

4.0 La2 Ag2 Hg2 Y2 3.5 Ta Mn Pd 2 2 Co 2 Au Sc Hf2 Ru 2 2 2 W2 2 Nb2 Pt2 BondLength [Å] 3.0 Rh Cu Zr2 Os2 2 2 Mo2 V2 Tc 2 Ni2 Ti Fe Ir2 2.5 2 2 Cr2 Re2

2.0

1.5 3 4 5 6 7 8 9 10 11 12 Periodic Table Group

Figure 6.1: Calculated Bond Length by Periodic Table Row, All Diatoms.

5 3 3 1 + 1 + 7 + 5 + 1 + 1 + Diatom Sc2 Σu− Ti2 ∆g V2 Σg− Cr2 Σg Mn2 Σg Fe2 Σg Co2 ∆g Ni2 Og Cu2 Σg Zn2 Σg Method CASPT2 CASPT2 CASPT2 RASPT2 CASPT2 CASPT2 RASPT2 CASPT2 CASPT2 CASPT2 Active (6,18) (8,12) (10,18) (12,20) (14,12) (16,18) (18,18) (20,12) (22,14) (24,14) Space complete complete complete restricted complete restricted restricted complete complete complete Basis Set ANO-RCC aVQZ-DK ANO-RCC aVQZ-DK aVQZ-DK aVQZ-DK aVQZ-DK aVQZ-DK aVQZ-DK aVQZ-DK BSO 0.688 2.141 3.263 3.320 0.053 1.390 1.281 0.935 1.079 0.085 comments vdW all work well all work well vdW

5 1 + 3 1 + 3 7 5 3 1 + 1 + Diatom Y2 Σu− Zr2 Σg Nb2 Σg− Mo2 Σg Tc2 Σg− Ru2 ∆u Rh2 ∆g Pd2 Σg− Ag2 Σg Cd2 Σg Method RASPT2 RASPT2 CASPT2 RASPT2 CASPT2 CASPT2 RASPT2 RASPT2 CASPT2 CASPT2 Active (6,18) (8,18) (10,18) (12,12) (14,12) (16,18) (18,18) (20,18) (22,14) (24,14) Space restricted restricted complete complete complete restricted restricted restricted complete complete Basis Set aVQZ-PP aVQZ-PP ANO-RCC ANO-RCC aVQZ-PP aVQZ-PP aVQZ-PP aVQZ-PP aVQZ-PP aVQZ-PP BSO 0.595 2.919 2.755 5.294 1.836 2.045 1.610 1.207 1.000 0.509 comments also ANO also ANO all work well all work well vdW

5 1 + 3 1 + 1 + 5 5 3 1 + 1 + Diatom La2 Σu− Hf2 Σg Ta2 Σg− W2 Σg Re2 Σg Os2 Πg Ir2 ∆g Pt2 Σg− Au2 Σg Hg2 Σg Method CASPT2 CASPT2 CASPT2 RASPT2 RASPT2 RASPT2 RASPT2 RASPT2 RASPT2 RASPT2 Active (6,18) (8,18) (10,18) (12,18) (14,18) (16,18) (18,18) (20,18) (22,18) (24,14) Space complete restricted complete restricted restricted restricted restricted restricted restricted complete Basis Set ANO-RCC aVQZ-PP ANO-RCC aVQZ-PP ANO-RCC aVQZ-PP ANO-RCC aVQZ-PP aVQZ-PP aVQZ-PP BSO 0.646 1.220 4.396 4.844 5.236 5.010 3.660 2.321 1.778 0.199 comments also ANO all work well all work well vdW

Table 6.2: Summary of Bond Strength Orders (BSO) and the methods which produced the best results for each transition metal diatom. aVQZ-DK = aug-cc-pVQZ-DK; aVQZ-PP = aug-cc-pVQZ-PP; vdW = van der Waals complex; also ANO = ANO-RCC also worked well

75 Nb2 140

120 Ta 2 Os2 Mo2 Re 100 Hf2 2 Y2 Ir2 Ru2 Pt 80 Tc 2 2 La 2 Au V 2 60 Ti 2 2 Ni2 Cu2 Zr2 Cr Co2 40 2 Zn2 Fe Pd Sc 2 2 2 Ag Cd2

BondDissociation Energy[kcal/mol] 2 Rh2 20 Hg Mn2 2

3 4 5 6 7 8 9 10 11 12 Periodic Table Group

Figure 6.2: Calculated Bond Dissociation Energy by Periodic Table Row, All Diatoms.

Hence, it is shown that three metrics, bond length, bond dissociation energy, and stretching force constant do not give a simple correlation, with BDE showing the greatest variability. In some sense, this is unexpected, because the homolytic cleavage of a diatom should be energetically predictable, as there are no secondary considerations of geometry relaxation. Thus, with BDE being variable and bond length being an averaged value, it is found that stretching force constant, which is a second order parameter and thus the best descriptor of a system in motion, proves also to be the best descriptor of bond strength. Finally, a plot of all stretching force constants versus bond strength order (BSO) is shown in Figure 6.4. This leads to a single curve which describes the BSO, and thus the bond strength, of all diatoms.

76 7 Mo2 Re2 Os2 6 Ta 2 W2 5 Ir2 V2 Cr2 4 Ti2

Zr2 Pt2 3 Nb2 Ru2 Au2 Rh2 2 Pd2 Tc 2 Cu2 Sc2 Fe2 1 Hf2 Co2 Cd2 Ni Ag2 StretchingForceConstant[mdyn/Å] 2 Y2 La2 0 Hg Mn2 2 Zn2 3 4 5 6 7 8 9 10 11 12 Periodic Table Group

Figure 6.3: Calculated Stretching Force Constant by Periodic Table Row, All Diatoms.

6.3. Integration of all Findings

Analyzing all of the transition metal diatoms by three methods, two basis sets, and two or more active spaces yielded a wealth of information. To apply this information generally, observations and explanations of trends are compiled here (Table 6.2.) We deﬁne ﬁve subsections that yield the best results: 1) Groups 3, 4 and 5 : Using the Molcas ANO-RCC basis set, these species can be run with (6,18), (8,18) and (10,18) complete active spaces, respectively, using the (n)d, (n+1 )s and (n+1 )p atomic orbitals (n = 3 for row 4, 4 for row 5, and 5 for row 6) to generate the d-

σg, d-σu, d-πu, d-πg, d-δg, d-δu, s-σg, s-σu, p-πu, p-πg, p-σg and p-σu molecular orbitals. This yields the largest number of successful calculations, as judged by agreement with experiment. In some cases, the (2g,12) (g = group number) active space gives reasonable results, but not typically better results.

77 6 Mo2 W2 5 Ta 2 Re2 Os2 Ir2 4 Cr2 2- Re2Cl8 3 Pt2 V2 Ru Zr2 2 Nb Au2 2 2 Rh2 Co 2 Ti2

BondStrength Order Pd 2 Tc 2 Ni2 Sc2 Fe2 1 Y2 Hf2 Hg2 Cu Zn 2 2 Ag2 La2 0 Cd2 Mn2 0 1 2 3 4 5 6 7 Stretching Force Constant [mdyn/Å]

Figure 6.4: Calculated Stretching Force Constant versus Bond Strength Order, All Diatoms. This plot serves as a conversion chart between the two parameters.

2) Group 6 : The members of group 6, Cr2, Mo2 and W2, are seen as candidates for sextuple bonding. Each of these diatoms presented a unique challenge, such that they do not ﬁt into any particular group, or even with each other. The best method for each diatom

(RASPT2(12,20)/ANO-RCC for Cr2, CASPT2(12,12)/ANO-RCC for Mo2, and CASPT2(12,12)/aug- cc-pVQZ-PP for W2) was determined by extensive trial and error. 3) Groups 7, 8 and 9 : Using the (2g,18) restricted active space yielded the best results in most cases for these nine diatoms. However, with the larger number of electrons, (14, 16 or 18), a complete active space was no longer practical for either the ANO-RCC or aug- cc-pVQZ-DK/PP basis sets. Accordingly, both basis sets were useful. In this work, the

ANO-RCC basis set yielded the best results for Re2, Fe2, Os2, Co2 and Ir2, where the aug- cc-pVQZ-PP basis set gave the best results for Tc2, Ru2, and Rh2. As noted earlier, the

Mn2 van der Waals complex was best described by CASPT2(14,12)/aug-cc-VQZ-DK.

78 4) Groups 10 and 11 : These six diatoms were well behaved by all methods. The group 11 diatoms were often described as singly bonded species, as was done in this work. It would seem a logical extrapolation that the group 10 diatoms be described as double bonds, but none of the metrics (Re, BDE, ke) support this model. As the electron count is large and the analysis straight forward, a (2g,12) active space, with any of the trial basis sets, is recommended. MR-AQCC [212] also worked well for the the diatoms in these groups. The method has the shortcoming of being limited to complete active spaces of 16 orbitals or less, so the (2g,12) active space was also used here. Restricted active space methods are not available for this method. 5) Group 12 : Where all of these species are van der Waal complexes, a (2g,12) active space is recommended. It may be that multi-reference calculations do not improve the description of these molecules, over the less computationally intensive DFT methods.

79 Chapter 7

Transition Metal Diatoms - Maximum Bond Multiplicity

Is there Sextuple Bonding? In the previous chapter, we completed a comprehensive survey of the multi-reference description of covalent bonding in transition metal diatoms. What remains is a standing controversy concerning the maximum possible bond orders in chemistry. Setting aside f-orbital bonding trans-lanthanides, because there is little experimental conﬁrmation of that form of bonding, the ﬁve d-orbitals on each of two atoms should the- oretically combine to form 5 bonding orbitals and 5 anti-bonding orbitals, or a maximum possible bond order of 5. However, it has been theorized [181] that relativistic contraction of 5s and 6s orbitals, and corresponding relativistic expansion of 4d and 5d orbitals can cause these shells to be similar in size and energy, creating the possibility of sextuple bonding. This phenomenon has not been attributed to the 3d/4s orbital mix in the forth row of the periodic table, because the lack of spherical nodes in the 3d orbitals limits their potential for relativistic expansion, as described by Kaupp [129] by the term ‘hybridization defect.’ Additionally, to create a sextuple bond, there is the need that each atom donate six valence electrons. Fewer electrons would be inadequate to produce six bonds, and additional electrons would occupy anti-bonding orbitals, lowering the bond order. By this formula, the elements that could potentially create a neutral sextuple bond are limited to molybdenum (Mo) and tungsten (W). The speculation on the existence of sextuple bonding is supported

by the fact that Cr2, Mo2 and W2 are found to have the shortest bond lengths, and among

the largest stretching force constants (ke) for all transition metal diatoms.

Maximum Bond Orders: Figure 6.4 indicates that Mo2 and W2 have BSO’s of 5.294 and

4.844, respectively, which would indicate that Mo2 exhibits a sextuple bond. However, these

2 numbers are based on Ag2 and Re2Cl8− having bond orders of 1.0 and 4.0, respectively.

80 Although a bond order of 1 for Cu2, Ag2 and Au2 is generally accepted, their properties of bond length, BDE and ke are dissimilar both experimentally and computationally. Hence,

2 whichever of the three is chosen will effect the final result. The true bond order of Re2Cl8− has been debated. Roos et al., for example, calculate an ‘effective bond order’ of 3.2 for this species. [181] Using that value lowers the BSO’s for Mo2 and W2 to 4.05 and 3.76,

2 respectively. Krapp [147] theorizes that bonding in Re2Cl8− can be described entirely by σ- and π-bonding, and has a bond order which is very near 3, and does not have a stronger bond

2 than the triple-bonded neutral Re2Cl8. Hence, without proving that the historical Re2Cl8− quadruple bond is indeed a quadruple bond, the Mo2 sextuple bond cannot be conﬁrmed.

Further, the BSO of Mo2 is not signiﬁcantly higher (and W2 is lower) than the Re2 and

Os2 diatoms, which clearly cannot exhibit sextuple bonding, due to having greater than 12 valence electrons. Hence, we do not ﬁnd evidence of sextuple bonding here.

81 Chapter 8

Conclusions

In this dissertation, we have undertaken the study of multi-reference systems in chemistry. All systems are multi-reference by their nature, but most do not require the inclusion of multiple electronic states to be described within the models of modern quantum chemistry. The computational expense of multi-reference calculations, even with the economy of using complete active space and restricted active space calculations, which reduce cost, but increase complexity, has led to much eﬀort to develop methods where multi-reference systems can be described with some degree of conﬁdence with single-reference methods. This work focuses on the systems that require descriptions beyond the electronic ground state. In this dissertation, we have looked at some of the methods, and some of the strategies for the description of multi-reference systems, hoping to establish guidelines that streamline the use of multi-reference methods, and possibly facilitate their broader use.

8.1. Single-Reference Systems

We demonstrated that single-reference systems can be well characterized by hybrid DFT

methods and large basis sets. Analysis of the parameters of equilibrium geometries, rCC,

a local stretching force constant, k , Bond Strength Order, electron density, ρr and energy

density, Hb can fully characterize these systems. We calibrated these tools against a training set of well-behaved molecules, to be equipped to investigate the chemistry of unique systems: extremely strained molecules, clamped molecules, diamondoid stabilized molecules and electron deﬁcient molecules. This was, in eﬀect, a search for systems we could not describe.

82 8.2. Single-Reference Methods on Multi-Reference Systems

Moving to adapt our methods to multi-reference systems, we considered pancake bonding. These species are found experimentally to be spin-paired open-shell dimers, and therefore have multi-reference character. Using broken symmetry DFT, we were able to reproduce the experimental observations on a series of dichalcodiazolyl and phenalenyl pancake-bonded dimers. With DFT methods, topological analysis and local mode vibrational analysis, we were also able to demonstrate that, in diﬀerent cases, chalcogen bonding, aromaticity and dispersion forces all contribute to the stabilization of these molecules. We were able to establish that pancake bonding is a non-covalent, electrostatic interaction and propose a new, ditelluradiazolyl pancake bonded dimer, with a unique symmetry. We also found evidence of 3-dimensional aromaticity in the phenalenyl systems.

8.3. Multi-Reference Methods in Organic Chemistry

We then attempted to describe the bridged annulene systems whose nature had been debated since they were first synthesized in 1964, and whose character (single or multi- reference) is in dispute. An extensive survey of single-reference methods succeeded in reproducing and extending on the work of past researchers, and being equally unsuccessful in describing and explaining the chemistry of these molecules. Many multi-reference methods produced more unsupportable results, and FCI was impossible for systems of this size. The breakthrough on this analysis was to redefine the orbital description of the molecules to include the strained chemistry of the cyclopropyl ring in the ‘norcaradiene’ valence tautomer of each system. To verify our findings, topological analysis, local mode analysis, aromaticity indices, and computational analysis of experimental NMR data and crystal packing effects resulted in a complete description of the target molecule and the answers to the questions that have stood for over half a decade.

83 8.4. Multi-Reference Methods in Inorganic Chemistry

Many have investigated the covalent bonding descriptions of small transition metal clusters, where covalent bonding, low-lying excited states and clustered σ-, π- and δ-molecular orbitals guarantee multi-reference behavior. Where hundreds of publications exist, the ones that attempt to describe every transition metal diatom have used single-reference methods, primarily DFT. In our study, we analyzed every transition metal diatom by four different multi-reference methods and three different basis sets, to establish patterns and guidelines for larger systems. We succeeded in reproducing or improving on past work, as well as filling some of the empty spaces in the literature. We have generated an extensive database of results for these methods, and developed guidelines for method, basis set, and active space selection for all species.

8.5. Outlook

Extending on the projects we present here, the following studies present themselves: Long Carbon-Carbon Bonds: The possibility exists of of creating a tool for predicting local mode stretching force constants for CC single bonds, based on substitutions. This could be central to designing molecules with longer CC bonds. The relationship would logically be quadratic, since kas are based on frequencies, and the harmonic approximation. The calculations of known systems have given enough information to run a curve on methyl groups (see Figure 8.1.) Many more simple molecules (1,2,3,4,5,6 phenyl groups, for example) would need to be analyzed to complete the other curves. However, our preliminary work shows that we need not depend on experimental observations to verify our results. Then, the extension of these algorithms to mixed substitutions could be investigated. Clamped Bonds: The calculated geometries for the clamped molecules of Suzuki’s group (such as 3.32) are not in close agreement with experimental results. These molecules can be analyzed by multi-reference methods, to determine if there is biradicaloid or ﬂuxional character in these long bonds.

84 4.3 4.2 4.1 [mdyn/Å] a 4.0 3.9 2 3.8 R = 0.998 3.7 3.6 3.5 3.4 3.3 3.2

LocalMode Stretching ForceContant k 3.1 0 1 2 3 4 5 6 Methyl Groups

Figure 8.1: Local Mode Stretching Force Contants (ka) versus Number of Methyl Groups for a Series of Organic Compounds.

The iron-bridged, clamped molecule calculated in this work (textbf3.33) was simpliﬁed from the molecule published by Moret’s group, by replacing 8 phenyl groups with methyl groups. This was done to save computational cost, but resulted in a CC distance much shorter than the experimental result. An analysis of the full molecule may give the correct geometry, or reveal multi-reference character. Bridged Annulenes: The molecule 11-cyano-11-methyl-1,6-methano[10]annulene has been synthesized, and found to have a C1C6 interatomic distance of 1.8 A,˚ similar to 11,11- dimethyl-1,6-methano[10]annulene, but in disagreement with the result for 11, 11-dicyano- 1,6-methano[10]annulene. CASPT2(14,14) and CCSD(T) calculations would be useful to discover the chemistry of this molecule.

Transition Metal Diatoms: The sextuple bond question remains for the Mo2 and W2 diatoms. Better reference molecules to deﬁne the BSO description can be sought.

85 Chapter 9

Calculations and Methodology

Multi-reference Systems in Computational Chemistry: In this dissertation, we made use of a signiﬁcant fraction of all available quantum chemistry methods, both utilizing wave function theory and density functional theory. Ultimately, true multi-reference systems can only be reliably described with multi-reference, wave function theory methods, which are unfortunately the most computationally expensive, are impracticalfor very large molecules, and requires substantial knowledge of the chemistry being described. Therefore, we weighed these many methods for their applicability to speciﬁc questions.

9.1. Single-Reference Computational Methods - Organic Chemistry

Long Carbon-Carbon Bonds: Many diﬀerent Density Functional Theory (DFT) methods are available, which range widely in parameterization, computational cost, and range of applicability. In the case of the description of long bonds, we are looking for a functional which will provide consistent results for a wide range of organic compounds, many quite large. Since we are less concerned about atoms heavier than carbon, we can use relatively expensive hybrid functionals, which combines Hartree Fock and other DFT functionals to achieve the widest applicability. The ωB97X-D functional [23] was chosen because it includes Grimme D2 dispersion correction [94] and Chai-Head-Gordon long-range corrections. [39, 40] As the CC bonds get longer, long range augmented basis sets with correction for the correlated motion of electrons are required to accurately describe the extreme cases. For this purpose, Dunning’s aug-cc-pVTZ basis set [72] was used whenever possible. For some of the largest molecules, the augmented basis set would not converge, and the cc-pVTZ basis set was used. Finally, the largest molecule in the sequence, hexakis-(3,5-di-tert-butylphenyl)ethane, required Pople’s 6-311++G(d,p) [67, 98] basis set to complete the second derivative matrix

86 and frequency calculations which are needed for the analysis of vibrational frequencies to be completed in a reasonable time frame (under 1 year of wall time.) Pancake bonding: To describe the spin-paired open shell singlet state of pancake bonded systems, we applied broken symmetry calculations. [46, 92] This was accomplished in two steps. First, a single point calculation of the initial guess equilibrium structure was completed in the triplet state. This was followed by a full optimization in the singlet state, using the triplet state orbital description. Frequency calculations were conducted on the final singlet state geometries. For the dichalodiazolyl molecules 4.1 through 4.3, the unrestricted BS-UM06 DFT methodology was used [102, 225], following the method of Kertesz and others. [25, 120] The M06 functional is well parameterized for the chalogens (sulfur, selenium and tellurium), yielding consistent results which were in good agreement with experiments. The Pople triple-ζ 6-311G(d,p) basis set was used [98] for compounds 4.1 and 4.2, again following Kertesz’ procedure on the description particularly of the selenium compound. [25] The Stuttgart/Dresden effective core potential SDD basis set was used for (4.3), as tellurium is parameterized in few other basis sets. Having established the equilibrium geometry, the dimers were then separated in 0.1 A˚ increments, spanning the equilibrium distance approximately 1 A˚ in either direction. For longer distances, 1.0 A˚ increments were used, for a total range of 2.5 to 8.0 A.˚ These values were plotted to generate potential energy curves were generated, from which dissociation energies could be deduced. (See Figure 4.4.) The phenalenyl systems (4.4) through (4.6) were analyzed using M05-2X [159] and M06- 2X DFT functionals. [225] The 6-31++G(d,p) basis set [98] with polarization and diffuse orbitals was used, to ensure the coverage of dispersion and other long range effects. For the purposes of comparability with species 4.1 through 4.3, the M06 functional was considered desirable. However, calculating the system by both M05-2X and M06-2X, M05- 2X BDH’s for these systems agreed well with experiment, where the M06-2X functional gave results that were too high by a factor of 2. This is in agreement with the findings of Kertesz,

87 et al. [159] Therefore, the M05-2X functional was used for all calculations. Counterpoise corrections were carried out on all pancake species, to remove basis set superposition error, and determine the complexation energy between the radical fragments, which gives an independent evaluation of the dissociation energy of the dimers in the absence of geometry relaxation. Annulenes: The C1C6 potential energy curves (PECs) of molecules 5.1, 5.2, and 5.3 were calculated by stepwise increasing of the distance R = R(C1,C6) from 1.4 to 2.6 A˚ in increments of 0.1A˚ and then, optimizing all other geometrical parameters of the molecule in question. These energy values were fitted to a suitable analytic function using standard fitting techniques. For the analytical PECs thus obtained, the R value(s) of the minimum or minima were determined and then utilized for accurate reoptimization. This procedure was carried out at the Hartree-Fock (HF) [188] level, density functional theory (DFT) level using various LDA, GGA, meta-GGA, hybrid, and double-hybrid functionals (see below) as well as the second, third and forth order Møller-Plesset Perturbation Theory (MP2, MP3, MP4) level of theory [47,102]. Using the geometries determined in the first step, single point calculations with a variety of electron correlation WFT (wave function theory) methods were carried out to obtain more accurate PECs. It turned out that the use of different geometries based on HF, DFT, or MP2 calculations did not change the resulting PECs significantly. However, the vibrational frequencies obtained with DFT methods such as B3LYP [22,200] or ωB97X-D [39,40] agree better with measured values than HF or MP2 frequencies, indicating that the thermochemical corrections calculated with DFT are preferable. Therefore, for reasons of consistency, we present only the PECs based on geometries obtained with the two XC (exchange and correlation corrected) functionals ω-B97X-D and B3LYP in this work. To study the influence of dynamical electron correlation on the shape of the PEC, we used nth order MP (MPn) theory and Coupled Cluster theory with HF or alternatively Brueckner (B) orbitals. [97, 178] Correlation effects were determined by considering all S (single), D (double), and T (triple) or perturbative T (denoted as (T)), and Q (quadruple)

88 excitations. In all, we used MP2, MP3, MP4(SDQ), MP4(SDTQ), [50, 102] CCSD, [176] BD, [97] CCSD(T), [179] and BD(T). [178]

9.2. Single-Reference Computational Methods Beyond Energies

Beyond the calculation of total energies for all molecules, the following parameters were determined using single-reference methodologies. Cremer-Kraka Bond Criterion: The Cremer-Kraka Bond Criteria gives a quantifiable definition of covalent bonding, and is used extensively in this work. [55] By this criterion, three conditions are required to define covalent bond:

1. There must be a maximum electron density path (MED) between the targeted atoms.

2. There must a bond critical point (BCP) of minimum electron density (ρr) located along the MED.

3. The energy density (Hb) at the BCP must be negative and stabilizing.

The determination of bond critical points (BCP’s), and electron densities (ρr) and en-

ergy densities (Hb) at the pertinent BCP’s, using Baders Atoms-In-Molecules analysis, was completed using the AIMAll software, version 12.6.03 and 17.1.25 [134] Local Mode Stretching Force Constants: Local Mode Stretching Force Constants (ka) are determined using the generalized local vibrational mode analysis as developed by Konkoli and Cremer [139,140] and its extension by Zou and Cremer. [239–241] For this work, we employ local mode analysis [140,239–241] to calculate local vibrational frequencies (ωa) and stretching force constants (ka) for the most pertinent CC single, double and triple bonds. This local CC stretching force constant ka is used as the measure of bond strength. Bond Strength Order: To translate the bond strength, as expressed by ka, into a useful format, a power relationship for the bond strength order, n(CC), was generated [78,122,124, 143] following the treatment of the generalized Badger rule of Kraka, Larsson and Cremer. [146] The relationship is deﬁned by the equation:

89 n(CC) = a(ka)b (9.1)

This deﬁnes bond strength as a bond strength order parameter (BSO) which is recog- nizable and useful to all chemists. Parameters a and b are determined in this work to be a = 0.3135 and b = 0.8062, utilizing ethane, ethene and the origin as suitable references with n(CC) = 1, 2 and 0, respectively. Aromaticity Index: Employing local mode analysis, the aromaticity index (AI) for species 4.4 through 4.6, 5.1 and 5.2 were determined by the method of Kalescky, Kraka and Cremer. [123,191] This method characterizes the degree of aromaticity of a delocalized system, based on the reference values of 1.0 for benzene, and 0.0 for “Kekule” benzene, as modeled by trans-1,3-butadiene. The AI is deﬁned as:

γ X 2 AI = 1 (nopt ni) (9.2) − NB −

where nopt is the optimum bond order for benzene, NB is the number of bonds in the aromatic

system, ni is the bond order of each of the “i” bonds in the aromatic system, and γ is a parameter to set the AI of trans-1,3-butadiene to 0.0. This equation was recast into the following form:

2 1 X 2 AI = 1 γ (nopt nav) + (nav ni) (9.3) − − NB −

= 1 (WS + ALT) (9.4) −

where nav is the average bond order, WS gives the weakening/strengthening parameter of the bonds, relative to the average bond strength (as deﬁned by the average bond order), and ALT reﬂects the degree of bond strength alteration, with the greater the bond weakening, and bond strength alteration, the weaker the aromaticity of the system, and the smaller the AI.

90 G4 Bond Dissociation Enthalpies: Bond dissociation enthalpies (BDH’s) were calculated wherever possible for the covalently bonded CC species using Gaussian G4 methodolgy. [41] These calculations were not feasible for clamped systems, because independent fragments cound not be deﬁned, aromatic systems, where the results were found in this work and by others to be unreliable, [44, 237] the largest systems, due to the tremendous computational cost of the G4 algorithms, and multiple bonds other than ethylene and acetylene. NMR analysis: To compare with available experimental NMR data for annulene system 5.1, 13C and 1H magnetic shieldings and chemical shifts (the latter with tetramethylsilanes as reference) were calculated for all systems using guage-invariant atomic orbital (GIAO) calculations at the B3LYP level of theory [234], as well as the NMR-ab intio-DFT method of Cremer and co-workers [59]. This latter method is used to determine the most stable form of a molecular system in solution, especially in the case where one geometrical parameter strongly depends on relatively small changes in environmental factors as was the case for system 5.1. Since the 13C-NMR chemical shifts of 5.1 are known [69], we determined the deviation between measured and calculated 13C chemical shifts along the PEC and determined the minimum of the mean (absolute) deviation. In addition, all J(13C13C), J(1H1H), and J(13C1H) indirect spin-spin coupling constants (SSCCs) of 5.1 were calculated using the method of Cremer and co-workers. [209] Those SSCC which show the strongest dependence on the valence-tautomeric rearrangement were analyzed as functions of R. Solvent eﬀects on the experimental NMR data were tested using the PCM (polarizing continuum model) of Tomasi and co-workers [223] where the dielectric constant was increased from 2 to the value of methanol ( = 32.7 [100]) which was used as the solvent for the NMR investigations of 5.1.[69,80] The single-reference quantum chemical calculations were performed with the program packages COLOGNE14 [145], CFOUR, [199] and Gaussian [79].

9.3. Multi-Reference Computational Methods

Annulenes: For systems 5.1 through 5.3, the inﬂuence of non-dynamical electron corre-

91 lation effects was studied utilizing CASSCF (complete active space self consistent field), [153] CASPT2 (CASSCF with second order MP perturbation theory), [4] and NEVPT2 (n-electron valence perturbation theory of second order).) [99] For these multi-reference calculations, active spaces of 5.1a and 5.2a with 10 electrons (all π) and 10 orbital (5 occupied π-orbitals and the lowest 5 virtual π-MOs were selected. In the case of 5.3a the corresponding (6,6)- active space was chosen. In the valence-tautomeric rearrangement of the annulene (triene) form to the bisnorcaradiene (norcaradiene) form π-orbitals are converted into C1C6 σ and σ? orbitals and other σ-orbitals mix with the π-orbitals, changing their character. Apart from this, one has to consider that π- and σ-orbitals may be ordered in a different way. Therefore, it was carefully monitored that when changing R the (10,10) or (6,6) active spaces were consistently maintained along the path defined by R. This procedure led to unsolvable problems in the case of system 5.3 where the non planarity of 5.3 (see Figure 5.1) leads to strong σ π mixing. We found that a consistent − description can only be obtained by a (10,10) active space for the norcaradiene form, which includes besides the π-system also the 6 electrons and 6 Walsh orbitals of the cyclopropyl ring. By converting one of the Walsh orbitals into a π-orbital for increasing R, a consistent (10,10) description could been found for system 5.3a. The following orbitals comprised the

(10,10) space of 5.3b: 10a0, 14a0, 19a0, 8a00, 12a00, 16a00 (Walsh orbital set), 15a0, 16a0, 10a00,

11a00 (π-orbital set). The multi-reference description of systems 5.1 and 5.2 is a similar way, recreating the PEC calculations with (14,14) active space including the Walsh orbitals of the cyclopropyl rings of the bisnorcaradiene forms and the σ (σ?) orbitals of the C1C11 and C6C11 bonds.

For 5.1b the following orbitals established the (14,14) space: 14a1, 16a1, 9b1, 12b1, 17b1,

15b2 (Walsh orbital set), 15a1, 17a1, 10b1, 11b1, 12b2, 13b2, 8a2, 10a2 (π-orbital set). In the case of 5.2b, the (14,14) space comprised: 10a1, 13a1, 17a1, 8b2, 11b2, 14b2 (Walsh orbital set), 12a1, 15a1, 9b1, 10b1, 9b2, 10b2, 7a2, 9a2 (π-orbital set). We also applied the smaller active spaces to multi-reference averaged quadratic coupled cluster theory (MR-AQCC.) [212] In addition, systems 1a/1b and 2a/2b were also investi-

92 gated utilizing the DIP-EOM-CCSD (equation of motion double ionization potential coupled cluster with S and D excitations) [192] method. Transition Metal Diatoms: Three multireference methods were used to generate the transition metal diatom results reported from this study:

1. Complete active space self-consistent ﬁeld multireference average quadrature coupled cluster calculations (CASSCF/MR-AQCC.) [212]

2. Complete active space self-consistent ﬁeld calculations with non-dynamical correlation by second order perturbation (CASSCF/CASPT2.) [4]

3. Restricted active space self-consistent ﬁeld calculations with non-dynamical correlation by second order perturbation (RASSCF/RASPT2.) [153]

Three relativistic basis sets were employed.

1. The augmented, correlation corrected Dunning quadruple-zeta basis set with Douglas- Kroll-Hess relativistic correction was used for forth period atoms (aug-cc-pVQZ-DK.) [233]

2. The augmented, correlation corrected Dunning quadruple-zeta basis sets with eﬀective core potential relativistic correction was used for ﬁfth and sixth period atoms (aug-cc- pVQZ-PP.) [233]

3. The Roos atomic natural orbital relativistic correlation consistent (ANO-RCC) basis set was used on all diatoms. [5,182–184]

For the systematic design of active space, each diatom was ﬁrst analyzed at the Hartree- Fock level of theory to determine the order and occupancy of the molecular orbitals. The active space for each diatom was chosen to include all electrons in the (n)d and (n+1)s valence shells are considered. Since this work was restricted to homodiatomic species, the number of valence electrons is twice the number of the column in the periodic table. Either the orbitals formed by the overlap of all (n)d and (n+1)s atomic orbitals was used, that is d-

σg/d-σu (2), d-πu/d-πg (4), d-δg/d-δu (4), and s-σg/s-σu (2) orbitals, for a total of 12 orbitals,

93 or else the sum of all of these, plus the orbitals formed by the overlap of the (n+1)p atomic

orbitals (p-σg/p-σu (2) and p-πu/p-πg (4)), for a total of 18 active space orbitals. The 18- orbital active space usually required the use of a restricted active space, to reduce the number of conﬁguration state functions (CSF’s) and to reduce computational cost. Generally, the Molpro program [232] can operate on up to 1,000,000 CSF’s. In a few cases, as noted in Section 3, other active spaces, such as (22,14) and (12,20) were analyzed, too. This is usually necessitated by having the 12th or 18th orbital being degenerate. The electronic state of each diatom was taken from the experimental literature. In cases where more than one electronic state was reported, we calculated both states, and reported the electronic conﬁguration which yielded results which agreed with the experimental parameters. For each species, bond lengths (re) are determined by geometry optimization. Bond dissociation energies (BDE’s) are determined by subtracting twice the energy of the free atoms from the total energy of the diatom, using one half as many orbitals and valence electrons as for the molecular species. Hence, Sc2, analyzed with a (6,18) active space, is compared to the Sc atom with a (3,9) active space. The multiplicity of the atomic species are taken as reported in the literature, or on the NIST periodic table. [1]

Stretching force constants (ke’s) are determined numerically by calculating the energy of the molecule at 0.005 A˚ intervals around the optimized geometry, and calculating the curvature of the resultant potential curve. To convert this parameter into a bond strength

2 order, we used Ag2, the octachlorodirhenium dianion (Re2Cl8−) and the origin as references, assigning bond orders of 1, 4, and 0, respectively. These references deﬁne the true Badger- type [12, 13] power relationship, n(MM) = a(ka)b, with variables of a = 0.8075 and b = 1.009. The Molpro program package [232] was used for all calculations involving the Dunning basis sets. The calculations using the atomic natural orbital basis sets (ANO-RCC) [183] were completed using the Molcas program package. [3] The quantum chemical calculations to analyze the Hartree-Fock molecular orbitals were performed with the Gaussian 09 program package. [79].

94 Appendix A

Publications, Supporting Information and Manuscripts

11, 11-Dimethyl-1, 6-methano[10]annulene - An Annulene with an Ultralong CC Bond or a Fluxional Molecule? (2015) The Longest Covalent CC Bonds - Characterized with Vibrational Spectroscopy (Manuscript in process) Local Mode and Aromaticity Index Analysis of Pancake Bonded Systems (Manuscript in process) A Study of Various Multi-Reference Methods for the Characterization of 30 Transition Metal Diatoms (Manuscript in process)

95 Article

pubs.acs.org/JPCA

11,11-Dimethyl-1,6-methano[10]annuleneAn Annulene with an Ultralong CC Bond or a Fluxional Molecule? Alan Humason, Wenli Zou, and Dieter Cremer* Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314, United States *S Supporting Information

ABSTRACT: Extensive quantum chemical calculations involving more than 20 different methods and including vibrational, temperature, entropic, and environmental corrections suggest that 11,11-dimethyl-1,6- methano[10]annulene (1) is characterized by a broad, asymmetric single well potential minimum in which the molecule can carry out a large- amplitude vibration. This result is obtained by using CASPT2(14,14) and CCSD(T) together with a VTZ basis set. The average R(C1C6) distance of 1 is close to 1.8 Å, in agreement with X-ray diffraction measurements. Lower level methods fail because a reliable account of the electronic structure of bridged annulenes requires a balanced description of nondynamical and dynamical electron correlation effects as well as a correct assessment of bridge−annulene interactions. An independent determination of the distance R using the mean deviation between the calculated and measured 13C NMR chemical shifts of 1 leads to a value of 1.79 Å. By using electron density, energy density, and the local C1C6 stretching mode, it is demonstrated that the covalent bond ceases to exist at 1.695 Å and that for larger R values through-space homoaromatic interactions lead to some stabilization. The peculiar potential of 1 is shown to be a result of the interaction of the methyl groups with the perimeter CC bonds bisected by the symmetry plane of the molecule. CASPT2(14,14), CASPT2(10,10), CCSD(T), and BD(T) calculations were also used to provide for the first time reliable descriptions of the valence tautomeric potentials for the parent molecule, 1,6-methano[10]annulene (2), and the system 1,3,5-cycloheptatriene− norcardiene (3). In the latter case, calculations confirm a previous kinetic measurement of the free activation energy but correct NMR-based estimates. The methodology described can be applied to other annulenes and fullerenes.

1. INTRODUCTION Typical electron pair bonds between neighboring C atoms can be lengthened as a consequence of (i) exchange (steric) For the purpose of getting a better understanding of the nature 3−8 of the chemical bond, chemists have always been interested in repulsion between bulky substituents, (ii) a loss of bonding electrons or electron density leading to electron deficient answers to questions such as “What is the strongest (weakest) 9−13 or shortest (longest) bond ever observed or may be in general bonding, (iii) the occupation of antibonding orbitals, or 1−3 (iv) decoupling of spin pairs leading to open singlet states (e.g., possible?” Since the chemical bond is a concept rather than 6,14−16 an observable quantity, which can be extensively described by pancake bonds). (v) In turn, interacting CC atoms at large distances can be clamped together by electrostatic suitable measurements, answers to these questions may have 17−21 only heuristic value if not handled within a well-defined model attraction when highly polar or ionic, by dispersion interactions,3 or by connecting bridges enforcing a “cage”- of the chemical bond. The typical superlative questions lead 22 fi topology (clamped bonds ). Packing effects in a solvent cage or only to useful answers if they are de ned as precisely as ff possible, thus clarifying definitions and evaluation methods in a crystal could also be possible. Often these e ects cannot be within given models and concepts. clearly separated because they support each other. Many In this work, we focus on (through-space or through-bond) examples have been given for such long CC bonds or CC interactions between two C atoms, which are separated by 1.8 interactions where one has to ask in each case whether a stable Å and investigate the question whether these interactions lead molecule or a labile intermediate was obtained. to a covalent bond. This implies that we contrast the interaction in question on the background of other long CC Special Issue: 25th Austin Symposium on Molecular Structure and bonds, clarify which bonding models and definitions we will Dynamics use, and why the investigation is important in connection with a Received: August 16, 2014 molecular system that has puzzled chemist for almost 50 years Revised: October 20, 2014 (see below). Published: October 21, 2014

The existence of a chemical bond can be verified using 13C NMR signals of 1. Hence, the basic question was whether experimental data. Pauling suggested that a chemical bond is bridged annulenes could be considered as fluxional systems given when two atoms or fragments are kept together by some forces which changed their bonding structure according to the valence that it seems to be justified to consider the resulting entity as an tautomeric rearrangement indicated in Figure 1 or whether they independent molecule.1 Less vague definitions of a chemical bond possessed long CC bonds. can be obtained utilizing energy, geometrical, orbital or density Since the available experimental evidence for 1 favored the characteristics. There is a myriad of bond definitions within bisnocaradiene form, the molecule was considered as the specific models. We will avoid an explicit discussion of these neutral hydrocarbon with the longest (covalent) cyclopropane definitions and models by exclusively focusing in this work on C(sp2)C(sp2)bond.Therefore,1 was computationally measurable quantities such as electron density distribution, investigated multiple times to rationalize the bonding vibrational frequencies, NMR chemical shifts, and indirect situation.32,39−43 However, this work was hampered by the spin−spin coupling constants (SSCCs). From these properties fact that the size of the molecule and the requirements for the we will determine quantities that make it possible to basis set made state-of-the-art computations that guarantee high characterize the CC interactions investigated in this work as accuracy results extremely difficult. In this work, we will close being covalent bonding or just through-space interactions. this gap in the description of 1 by carrying out coupled cluster The target system 1 investigated in this work (see Figure 1) and multireference calculations and providing a reliable belongs to the group of bridged [10]annulenes, the parent description of the electronic structure. The following questions will be answered in this work: (i) What is the exact shape of the C1C6 potential of 1 (single or double well)? (ii) Which electronic factors determine the shape of the potential? For example, are there specific interactions between bridge and π- perimeter, which may influence the structure and dynamics of 1? (iii) How does π-delocalization in 1 and 2 compare with that of benzene? (iv) What level of theory is required to guarantee a reliable description of the properties of 1 (or 2)? (v) Do temperature, entropy, or environmental effects such as solvation or crystal packing influence the shape of the potential? (vi) How does the valence tautomeric behavior of 1 relate to that of other closely related molecules such as 2 or the system cycloheptatriene-norcaradiene (3, Figure 1)? (vii) Are there other observations which may lead to a confirmation of the shape of the potential of 1? (viii) Does 1 contain a long covalent C1C6 bond, as is generally believed today, and if so, is this the longest C(sp2)C(sp2) single bond of an uncharged hydrocarbon ever observed? Figure 1. Molecules investigated in this work. We will present the results obtained in this work in the following way. In section 2, the computational means used in member of which, 1,6-methano[10]annulene (2), was first this work are described. The results and discussion are synthesized by Roth and Vogel in 1964.23 Annulene 2 was presented in section 3. The chemical relevance of this work experimentally characterized as an aromatic 10π-system ful- is outlined in section 4. Conclusions are drawn in section 5. filling the Hückel 4n + 2 rule, however with a distorted ring perimeter and a C1C6 distance R of 2.235 Å;24,25 that is, it 2. COMPUTATIONAL METHODS adopts structure 2a rather than that of the bisnorcaradiene The C1C6 potential energy curves (PECs) of molecules 1, 2, (tricyclo[4.4.1.01,6]undeca-2,4,7,9-tetraene) form 2b (see Fig- and 3 were calculated by stepwise increasing of the distance R = ure 1), as was verified in dozens of experimental inves- R(C1,C6) from 1.4 to 2.6 Å in increments of 0.1 Å, and then tigations23−37 as well as computational investigations.32,38−43 optimizing all other geometrical parameters of the molecule in Therefore, it was an unexpected result when in the early question. The energy values thus obtained were fitted to a 1970ies the 11,11-dimethyl derivative 1, also synthesized by the suitable analytic function using standard fitting techniques. For Vogel group, was found to adopt according to X-ray diffraction the analytical PECs thus obtained, the R value(s) of the studies44 a “tricyclic” structure with an R value close to 1.8 Å minimum or minima were determined and then used for an (1.827 and 1.771 due to 2 molecules in the unit cell44) that accurate reoptimization. This procedure was carried out at the speaks in favor of structure 1b rather than 1a. With the Hartree−Fock (HF) level, density functional theory (DFT) discovery that the corresponding 11-cyano-11-methyl derivative level using various LDA, GGA, hybrid, and double-hybrid had similar R values45 and the dicyano derivative had even an R functionals (see below) as well as the second order Møller− value of 1.558 Å,44,46 the existence of a bisnorcaradiene form Plesset Perturbation Theory (MP2) level of theory.51,52 was fully confirmed. Using the geometries determined in the first step, single Günther and others carried out NMR (nuclear magnetic point calculations with a variety of electron correlation WFT resonance) investigations on valence tautomeric systems such (wave function theory) methods were carried out to obtain as 1 and 2 and showed that any shift to the bisnorcaradiene or more accurate PECs. It turned out that the use of different annulene form leads to characteristic changes in the 13C geometries based on HF, DFT, or MP2 calculations did not chemical shifts.47,48 These studies were latter confirmed by change the resulting PECs significantly. The vibrational Frydman and co-workers49 as well as Dorn and co-workers,50 frequencies obtained with DFT methods such as B3LYP53,54 who all documented a strong temperature dependence of the or ωB97X-D for 2a agree better with measured values34 than 97 1667 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

HF or MP2 frequencies, thus indicating that thermochemical For the HF, DFT, and MP2 PECs, the corresponding corrections calculated with DFT are preferable. Therefore, we enthalpy and free energy curves were determined by calculating present in this work for reasons of consistency only the PECs vibrational, thermal, and entropy corrections. In this way, the based on geometries obtained with the two XC functionals enthalpy and free energy curves associated with the PEC could ωB97X-D and B3LYP. be analyzed. At the DFT level, solvation effects were tested with For the purpose of studying the influence of dynamical the PCM (polarizable continuum model) of Tomasi and co- electron correlation on the shape of the PEC, we used nth workers65 where the dielectric constant ϵ was increased from 2 66 order MP (MPn) theory and Coupled Cluster theory with HF to the value of methanol (ϵ = 32.7 ), which was used as a 49,50 or alternatively Brueckner (B) orbitals. Correlation effects were solvent for some of the NMR investigations of 1. determined by considering all S (single), D (double), and T The influence of the methyl groups on the stability of the (triple) or perturbative T (denoted as (T)) and Q (quadruple) annulene was determined by utilizing isodesmic reaction excitations. In all, we used MP2, MP3, MP4(SDQ), MP4- energies. For reasons of comparison, cyclopropane (4), 1,1- (SDTQ),51,52 CCSD,55 BD,56 CCSD(T),57 and BD(T).58 dicyanocyclopropane (5), and 1,1-dimethylcyclopropane (6) The influence of nondynamical electron correlation effects were investigated. All these calculations were carried out at the B3LYP and ωB97X-D levels of theory. Throughout this work was studied utilizing CASSCF (complete active space self- 67 consistent field),59 CASPT2 (CASSCF with second order MP Pople’s augmented VTZ basis 6-311G(d,p) was employed at ff perturbation theory),60 and NEVPT2 (n-electron valence all levels of theory. We also tested the necessity of using di use 61 functions by applying Dunning’s aug-cc-pVTZ basis set. In the perturbation theory of second order). For these multi- ff reference calculations, active spaces of 1a and 2a with 10 case of B2PLYP-D, the inclusion of di use functions only led to electrons (all π) and 10 orbitals (5 occupied π-orbitals and the small changes in the relative energies of 1. Because of lowest 5 virtual π-MOs) were selected. In the case of 3a the computational limitations in the case of the WFT methods, corresponding (6,6)-active space was chosen. In the valence- we employed the smaller VTZ basis throughout this work. tautomeric rearrangement of the annulene (triene) form to the Several molecular properties and their changes along the PEC were also calculated and analyzed. These included the bisnorcaradiene (norcaradiene) form, π-orbitals are converted 68 into C1C6 σ and σ* orbitals and other σ-orbitals mix with the NBO (natural bond order) charges, the charge transfer π π-orbitals, changing their character. Apart from this, one has to between bridge and -perimeter in the cases of 1 and 2, electron densities, energy densities, NMR (nuclear magnetic consider that π- and σ-orbitals can change their energies and resonance) properties, and local vibrational mode properties. order. Therefore, it was carefully monitored that when The last three properties will be shortly discussed in the changing R the (10,10) or (6,6) active spaces were consistently following. maintained along the path defined by R. Electron density analysis. The electron density distribu- This procedure led to unsolvable problems in the case of 69 tion ρ(r) was analyzed with the help of topological analysis to system 3 where the nonplanarity of 3 (see Figure 1) leads to determine all CC and CH bond critical points r (CC) and strong σ−π mixing. We found that a consistent description can b rb(CH) as well as the ring critical points rr of ρ(r). In this only be obtained by a (10,10) active space for the norcaradiene connection, the Cremer−Kraka definition of covalent bonding form, which includes besides the π-system also the 6 electrons fl was used: (i) A zero- ux surface and bond critical point rb has and 6 Walsh orbitals (for pictorial representations of these to exist between the atoms in question (necessary condition). orbitals, see ref 62.) of the cyclopropyl ring. By converting one (ii) The local energy density H(rb) must be negative and of the Walsh orbitals into a π-orbital for increasing R,a thereby stabilizing (sufficient condition for covalent bonding). consistent (10,10) description could be found for system 3a. ApositiveH(rb)indicatesadominanceofelectrostatic The following orbitals comprised the (10,10) space of 3b: 10a′, interactions.70,71 The Cremer−Kraka criterion reveals at 14a′, 19a′, 8a″, 12a″, 16a″ (Walsh orbital set), 15a′, 16a′, 10a″, which R value the C1C6 bond ceases to exist (or is formed). 11a″ (π-orbital set). NMR analysis. 13C and 1H magnetic shieldings and This observation encouraged us to improve the multi- chemical shifts (using tetramethylsilane as reference) were reference description of systems 1 and 2 in a similar way, calculated for all systems using the gauge-invariant atomic repeating the PEC calculations with a (14,14) active space orbital (GIAO) method72 in connection with B3LYP, which including the Walsh orbitals of the cyclopropyl rings of the leads to useful 13C values.73 For the determination of R(1) in bisnorcaradiene forms and the σ (σ*) orbitals of the C1C11 solution, the NMR-ab intio method of Cremer and co- and C6C11 bonds of the annulene. For 1b, the following workers74,75 was used. Since the 13C-NMR chemical shifts of 50 orbitals established the (14,14) space: 14a1, 16a1, 9b1, 12b1, 1 are known, the deviation between measured and calculated 13 17b1, 15b2 (Walsh orbital set); 15a1, 17a1, 10b1, 11b1, 12b2, C chemical shifts along the PEC was calculated and the 13b2, 8a2, 10a2 (π-orbital set). In the case of 2b, the (14,14) minimum of their mean (absolute) deviation was determined, space comprised the following: 10a1, 13a1, 17a1, 8b2, 11b2, 14b2 because the latter is a reliable indicator of the R value of 1 in 13 13 1 1 13 1 (Walsh orbital set); 12a1, 15a1, 9b1, 10b1, 9b2, 10b2, 7a2, 9a2 (π- solution. In addition, all J( C C), J( H H), and J( C H) orbital set). indirect spin−spin coupling constants (SSCCs) of 1 were Clearly, a (34,34) active space would have been ideal for the calculated using the method of Cremer and co-workers.76 inclusion of all σ−π interactions. However, this approach was Those SSCCs which show the strongest dependence on the outside the computational possibilities. We also used the valence-tautomeric rearrangement were analyzed as functions smaller active space for multireference averaged quadratic of R. coupled cluster theory (MR-AQCC).63 In addition, systems Local vibrational mode analysis. Generalized local 1a/1b and 2a/2b were also investigated utilizing the DIP- vibrational modes are the unique equivalents of the 3N − L EOM-CCSD (equation of motion double ionization potential (N: number of atoms; L: number of translations and rotations) coupled cluster with S and D excitations) method.64 generalized normal vibrational modes and their properties 98 1668 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

(local mode frequency ωa, mass ma, force constant ka, intensity Ia) were calculated according to the theory of Konkoli and Cremer77−79 and its extension by Zou and Cremer.80−82 The local CC stretching force constant ka is a reliable measure of the strength of the corresponding bond and can be used to calculate with the help of a power relationship the bond 2,83−85 b strength order (BSO) n: n(CC)=a(ka) . Parameters a and b were determined in this work to be a = 0.3116 and b = 0.8066, utilizing ethane and ethene as suitable references with n(CC) = 1 and 2, respectively. Additionally, n(CC) = 0 was imposed for ka = 0. The calculated BSOs provide a measure for the degree of π-delocalization in aromatic molecules, as was recently shown by Kalescky and co-workers.86 These authors derived an AI (aromaticity index) based on benzene (AI = 1.0) and “Kekule benzene” (1,3,5-cyclohexatriene: AI = 0) where in the latter case 1,3-butadiene was used to define a suitable reference geometry. A fully aromatic system is predicted to have all conjugated CC bonds equal to the benzene CC bond length, whereas deviations from this value indicate the degree of bond alternation and bond strengthening (weakening).86 AI values were calculated for the annulene forms. The AI model based on benzene and Kekule benzene cannot be applied to homoaromatic systems, i.e. systems for which the π- delocalization is interrupted by one or more C atoms with 4 formal single bonds, as is the case of 1b and 2b. Analysis of crystal packing effects. To test the possibility of the unusual R value of 1 being the result of crystal packing effects, two different situations were considered. (i) In the unit cell of 1, one molecule sits beside the other.44 We considered the interactions between molecules in different unit cells, especially that situation where one molecule sits on top of the other, slightly shifted. Steric repulsion caused by packing effects could force the widening of the external C12− C11−C13 bridge angle β, and with this widening the R value could be forced to decrease. Therefore, the changes in R were calculated for β values from 102 to 120°; that is, geometry optimizations were carried out for a series of fixed β values. (ii) Utilizing the crystal data, the dimer geometry was optimized under the constraint that the distance between the monomers and the relative orientation to each other does not change. Under the same conditions, R was fixed for one monomer and the geometry of the dimer reoptimized. (iii) A tetramer defined by the crystal structure was analyzed under the conditions described in (ii). The quantum chemical calculations were performed with the program packages MOLPRO,87 COLOGNE14,88 CFOUR,89 and Gaussian.90

3. RESULTS AND DISCUSSION In Figure 2, the calculated PECs for a representative number of the different methods applied in this work are shown. The most accurate enthalpy and free energy curves, ΔH(R) = PHC and ΔG(R) = PGC, respectively, are given in Figure 3. Relative Figure 2. Representation of the energy changes as a function of the energies ΔE, ΔH(298), and ΔG(298) obtained at different 1,6-distance R of (a) 11,11-dimethyl-1,6-methano[10]annulene (1a), levels of theory are listed in Table 1. In Figures 2 and 3, ΔE =0 (b) 1,6-methano[10]annulene (2a), and (c) 1,3,5-cycloheptatriene or ΔH(298) = 0 was arbitrarily chosen for R = 2.1 Å. In Table (3a) obtained at multiple levels of theory. For 1 and 2, R values of 2.1 1, the reference point of all energy difference determinations is and 2.25 Å have been used to determine the energy zero level, thus facilitating the comparison. always the most stable annulene form. However, when one of the target geometries was located on a shoulder of the PEC (or the corresponding PHC and PGC), the R value of the inflection point or the R of the annulene (bisnorcaradiene) minimum of a Figure 4, some representative geometries of 1 and the reference closely related method was taken, as is indicated in Table 1. In molecules investigated in this work are shown. 99 1669 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

reveal that (i) π-electron delocalization in annulene and bisnorcaradiene, (ii) σ−π interactions in the distorted ring perimeter, (iii) homoaromatic through-bond and through-space interactions (as defined by Cremer and co-workers10), (iv) the generation of a biradicaloid and its stabilization by electron delocalization, (v) strain effects in the bisnorcardiene form, and (vi) bridge−ring interactions have to be considered as important electronic effects. Different methods account for these effects in different ways so that the PEC adopts either a single well (SW) form, a SW with a shoulder at small or large R values (SW + 1S or SW + 2S), as well as a double-well (DW) with a flat minimum for small R (DW-F1M) or large R (DW- F2M). Details of the analysis of the PECs for the different WFT and DFT methods, especially their account of dynamical and nondynamical electron correlation effects, are given in the Supporting Information. Despite the testing of a large number of different WFT and DFT methods (more than 20 as shown in Table 1 and Figure 2a), none of them provides a balanced account of effects (i) to (vi), and none of the results is in line with experimental observations made for 1. Therefore, the question remains whether other effects such as thermochemical corrections, entropy contributions, crystal packing, or solvent effects may improve the agreement between theory and experiment. Rather than investigating these possibilities first, we pursue an alternative way, which leads to the description of the smaller, closely related valence tautomeric systems 2 and 3, for which all experimental information available implies the existence of a SW potential (2)25,34,47,49 or a DW potential favoring the no-bond form 3a (3),91−94 which should be much easier to describe. Valence tautomerism of 1,6-methano[10]annulene and cycloheptatriene. Extensive spectroscopic and diffraction measurements were carried out in the case of 2.25,34,47,49 The difference between 2a (being more stable) and 2b was estimated to be ≤10 kcal/mol. All measured NMR, infrared, Raman, or UV values exclude a second minimum for the bisnorcaradiene form 2b. Hence, a SW+1S form of the PEC is most likely.25,34,47,49 In the case of the cycloheptatriene−norcaradiene system 3,a DW PEC has been verified by both NMR and kinetic studies.91,93 Experiments conducted by Rubin93 led to a free activation energy for the transition 3b → 3a of ΔGa(298) = 7.2 kcal/mol. Rubin estimated ΔG(298, 3b) to be 4 ± 2 kcal/mol, which implies ΔGa(298, 3a → 3b) = 11 ± 2 kcal/mol where a zero-entropy change was assumed.93 The estimates were based on the NMR results of Gorlitz and Günther, who estimated that 3b should have a finite concentration of 0.1% at room temperature.91 In this work, we find the concentration of 3b to be just 0.003%. As in the case of 1, most of the methods applied failed to provide PECs and relative energies that are in line with these Figure 3. Representation of energy, enthapy, and free energy changes experimental observations (see Tables 2 and 3 as well as Figure as a function of the 1,6-distance R of (a) 11,11-dimethyl-1,6- 2b and 2c), where the rationalization of these shortcomings in methano[10]annulene (1a), (b) 1,6-methano[10]annulene (2a), and terms of dynamical and nondynamical electron correlation (c) 1,3,5-cycloheptatriene (3a). Potential energy curves in (a) are effects are similar to those given for 1. ωB97X-D, CCSD(T), obtained at the CASPT2(14,14) and CCSD(T) levels of theory. For estimated (est) curves, see text. Potential energy curves in (b) and (c) BD(T), MP4(SDTQ), and B2PLYPD lead to reasonable PECs are determined at CASPT2(14,14) and CASPT2(10,10) levels of for 2, suggesting that the bisnorcaradiene form 2b is located on theory. See text. a shoulder of the PEC. However, only MP4(SDTQ) and B2PLYPD provide a relative energy of 1b close to 10 kcal/mol, whereas especially CASPT2(10,10), CCSD(T), and BD(T) In the following, we will first analyze the PECs, PHCs, and severely underestimate the destabilization of 2b. Especially, the PGCs obtained for target system 1. The PECs calculated for 1 PEC of CASPT2(6,6) leads to a rearrangement barrier 3a → 100 1670 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

Table 1. Relative Energies and Rearrangement Barriers of 11,11-Dimethyl-1,6-methano[10]annulene

Method Curvea R(1b)b R(1a) ΔE(1b)c ΔE(TS)d HF SW+2S 1.552 (2.120) −9.29 SVWN5 SW+1S (1.640) 2.125 3.26 BLYP SW+1S (1.640) 2.212 6.99 B97 SW+1S (1.685) 2.134 2.84 B3LYP SW+1S (1.640) 2.167 3.67 ωB97 SW+2S 1.595 (2.040) −7.03 ωB97X SW+2S 1.595 (2.040) −4.28 ωB97X-D DW-F2M 1.638 2.039 −1.02 0.07 (1.09) REKS/ωB97X-D DW-F2M 1.637 2.039 −0.98 0.07 (1.05) B2P-LYP-D DW-F2M 1.605 2.118 −0.08 1.05 (1.13) MP2 SW+1S (1.640) 2.154 6.31 MP3 DW-F2M 1.587 2.065 −3.10 0.04 (3.14) MP4(SDQ) SW+2S 1.581 (2.120) −5.28 MP4(SDTQ) SW+1S (1.640) 2.150 2.92 CCSD SW+1S 1.590 (2.120) 4.25 BD SW+1S 1.590 (2.120) 4.21 CCSD(T) DW-F2M 1.641 2.120 −0.42 0.62 (1.04) BD(T) DW-F2M 1.641 2.120 −0.42 0.62 (1.04) CASSCF(10,10) DW-F2M 1.529 2.148 −7.81 0.63 (8.44) CASPT2(10,10) DW-F2M 1.613 2.159 −0.97 1.07 (2.04) NEVPT2(10,10) DW-F1M 1.598 2.172 2.49 3.59 (1.10) CASPT2(14,14) DW-F1M 1.647 2.130 0.91 1.32 (0.41) Estimate DW-F2M 1.643 2.123 0.26 0.93 (0.67)

ΔH(1b) ΔH(TS) B2P-LYP-D DW-F2M 1.694 2.110 0.61 1.14 (0.53) CCSD(T) DW-F2M 1.680 2.120 −0.68 0.03 (0.71) BD(T) DW-F2M 1.684 2.120 −0.75 0.02 (0.77) CASPT2(14,14) DW-F1M 1.640 2.120 0.66 Estimate DW-F2M 1.662 2.125 −0.11 0.08 (0.19)

ΔG(1b) ΔG(TS) B2P-LYP-D DW-F2M 1.680 2.114 0.16 0.83 (0.67) CCSD(T) DW-F2M 1.658 2.080 −1.09 0.20 (1.29) BD(T) DW-F2M 1.658 2.120 −1.12 0.19 (1.31) CASPT2(14,14) DW-F1M 1.665 2.120 0.22 0.73 (0.51) Estimate DW-F2M 1.662 2.100 −0.45 0.42 (0.87) aCurve indicates the shape of the rearrangement potential. DW-F1M, double well with flat first minimum; DW-F2M, double well with flat second minimum; SW+1S, single well with shoulder at small R; SW+2S, single well with shoulder at large R. bR(1b) and R(1a) indicate the C1C6 distance for each structure in Å. Values in parentheses are approximate values to determine the position of the shoulder. cΔE(1b) gives the energy difference relative to 1a in kcal/mol. For the explanation of the estimated values, see text. dΔE(TS), ΔH(TS), and ΔG(TS) give the energy barriers for valence tautomerization from 1a to 1b in kcal/mol. Values in parentheses are for the reverse reactions.

3b, which is 4.8 kcal/mol, more than 6 kcal/mol below the kcal/mol) because these authors used a (6,6) active space. estimated ΔGa(298) of 11 kcal/mol.93 Similarly, all single reference calculations provided poor The CASPT2(6,6) results reveal that the active space chosen results.38,96 The CASPT2(10,10) results of this work, if is too small to provide a reliable description of the valence converted into ΔG(298) with the help of B3LYP-calculated tautomeric rearrangement. Previous work by Cremer and co- ZPE, entropy, and thermochemical corrections, lead to workers has emphasized the homoaromatic interactions of the ΔGa(298,3b → 3a) = 6.0 kcal/mol, in good agreement with two π-bonds of norcaradiene with the 3 σ bonds of the the corresponding experimental value of 7.2 kcal/mol (6.1 cyclopropyl group.62 Obviously, these are essential for a correct kcal/mol at 110 K).93 The deviation results from an description of the process 3a → 3b. Accordingly, we enlarged exaggeration of ΔSa by the experiment: −4.5 e.u. (derived the (6,6) to a (10,10) active space by including all 6 rather than from the Arrhenius A factor) vs −1.3 e.u. calculated in this just 2 Walsh orbitals of the cyclopropyl group. The result of this work. Rubin’s other estimates are corrected by our calculated extension of the active space is stunning: The barrier increases ΔGa(298, 3a → 3b) of 12.2 kcal/mol and the relative value of to 12.2 kcal/mol, and the relative energy of norcaradiene 3b 3b: ΔGa(298, 3b) = 6.2 kcal/mol; that is, they show that just adopts a value of 6.0 kcal/mol (Table 3). 0.003% of 3b are in equilibrium with 3a at room temperature, Previous multireference investigations of 3 by Jarzeki and co- where the previous 0.1% estimate was based on NMR workers95 led to diﬀerent ΔE values (CASSCF: 21.6 kcal/mol; experiments.91 The potential curve obtained for ΔH(298) is MROPT2 (multireference with perturbation corrections): 8.9 shown in Figure 3c and probably presents the most accurate 101 1671 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

Figure 4. B3LYP geometries of 1−6. Bond lengths in Å and bond angles in degrees. description of the energetics of the valence tautomeric system 3 These results show clearly that CCSD(T) and BD(T), obtained so far. although they may account for some nondynamical effects Based on the experience earned for 3, we extended the besides the dynamical electron correlation effects, fail to (10,10) active spaces of 1 and 2 to (14,14) spaces, which describe the TS region and 3b correctly, which can also be include the C1C11 and C1C6 σ and σ*-orbitals (Walsh observed for 2b, as too much stability is assigned to the orbitals). Here we discuss first the results for 2. The PEC is still norcaradiene forms. Therefore, we repeated the CASPT2 obtained in a SW+1S form where 2b is now 11.5 rather than calculations for 1 with the larger (14,14) active space. Revised CASPT2 results and the consideration of 5.3 kcal/mol higher in energy than the annulene form at the thermochemical corrections. CASPT2(14,14) leads to a potential minimum at R = 2.256 Å (X-ray: 2.235 Å25). The PEC where the relative energies of 1a and 1b are interchanged corresponding ΔH(298) and ΔG(298) values are 10.2 and 10.3 compared to the CASPT2(10,10) PEC; that is, 1a becomes the kcal/mol, respectively, in line with experimental observa- minimum of a relatively flat potential (0.91 kcal/mol below 1b) 24−27,29−31,33−35,37,47,48 tions. Clearly, 2 has to be considered with barriers of 1.32 and 0.41 kcal/mol for the valence as [10]annulene rather than a bicyclic, homoaromatic π-system tautomeric rearrangement (Table 1). Small changes in the ZPE because R = 2.256 Å is too large to lead to sizable through- and thermal correction values lead to a slight stabilization of 1b space interactions.10 and a vanishing of the rearrangement barrier for the PHC (see 102 1672 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

Table 2. Relative Energies and Rearrangement Barriers of 1,6-Methano[10]annulene

Method Curvea R(1b)b R(1a) ΔE(1b)c ΔE(TS)d HF DW-F1M 1.562 2.219 0.63 3.27 (2.64) B3LYP SW+1S (1.610) 2.280 13.60 ωB97 DW-F2M 1.560 2.226 −1.12 1.48 (2.60) ωB97X DW-F1M 1.546 2.226 2.71 3.39 (0.68) ωB97X-D SW+1S (1.610) 2.240 7.22 B2P-LYP-D SW+1S (1.610) 2.250 9.22 MP2 SW+1S (1.610) 2.254 13.93 MP3 DW-F1M 1.630 2.240 4.20 4.68 (0.48) MP4(SDQ) DW-F1M 1.610 2.214 1.88 3.00 (1.12) MP4(SDTQ) SW+1S (1.610) 2.265 10.48 CCSD DW-F1M 1.613 2.235 3.21 4.04 (0.83) BD DW-F1M 1.612 2.234 3.25 4.06 (0.81) CCSD(T) SW+1S (1.610) 2.254 7.29 BD(T) SW+1S (1.610) 2.256 7.32 CASSCF(10,10) DW-F1M 1.540 2.268 4.37 7.65 (3.28) CASPT2(10,10) SW+1S (1.610) 2.254 5.32 NEVPT2(10,10) SW+1S (1.610) 2.230 14.86 CASPT2(14,14) SW+1S (1.700) 2.256 11.48

ΔH(1b) ΔH(TS) B2P-LYP-D SW+1S (1.610) 2.267 12.59 CCSD(T) SW+1S (1.700) 2.256 5.60 BD(T) SW+1S (1.700) 2.258 5.55 CASPT2(14,14) SW+1S (1.700) 2.256 10.16

ΔG(1b) ΔG(TS) B2P-LYP-D SW+1S (1.610) 2.267 12.23 CCSD(T) SW+1S (1.700) 2.256 5.77 BD(T) SW+1S (1.700) 2.258 5.74 CASPT2(14,14) SW+1S (1.700) 2.256 10.30 aCurve indicates the shape of the rearrangement potential. DW-F1M, double well with flat first minimum; DW-F2M, double well with flat second minimum; SW+1S, single well with shoulder at small R; SW+2S, single well with shoulder at large R. bR(2b) and R(2a) indicate the C1C6 distance for each structure in Å. Values in parentheses are approximate values to determine the position of the shoulder. cΔE(2b) gives the energy difference relative to 2a in kcal/mol. For the explanation of the estimated values, see text. dΔE(TS), ΔH(TS), and ΔG(TS) give the energy barriers for valence tautomerization from 2a to 2b in kcal/mol. Values in parentheses are for the reverse reactions.

Figure 3a). For CCSD(T) and BD(T), the conversion into preferring the bisnorcaradiene form by −0.1 kcal/mol enthalpies has a similar effect on the potential (Table 1). (activation enthalpies: 0.1 and 0.2 kcal/mol). The ΔG(R) Considering that ZPE and thermochemical corrections are curve increases the preference of 1b and introduces a somewhat based in this work on harmonic frequencies, which may change stronger asymmetry of the potential (Figure 3a). Obviously, the ff di erently with R than anharmonically corrected frequencies, degree of asymmetry of PHC and PGC increases with the we recalculated all vibrational corrections with scaled admixture of an additional nondynamical electron correlation. frequencies employing the scaling factors suggested by Scott Such a broad asymmetric SW potential would explain the 97 fi and Radom for DFT. However, no signi cant changes were observed strong T-dependence of the 13C chemical shifts of 1 obtained in this way. (they indicate a stronger population of the annulene form at As mentioned above, even a (14,14) active space may not be higher T49,50) and the fact that 1 adopts in the unit cell two sufficient to describe all nondynamical electron correlation different forms probably influenced by crystal packing effects (R effects resulting from the interactions of σ- and π-electrons, the = 1.836 and 1.780 Å44). Therefore, we will investigate stabilizing interactions in the intermediate biradicals, and the environmental influences on the PECs, PHCs, and PGCs bridge−ring interactions. Apart from this, the amount of shown in Figures 2a and 3a in the following subsection. dynamical electron correlation provided by CASPT2 is much ff too small and biased to prefer the annulene. Conversely, Consideration of solvent and crystal packing e ects. CCSD(T) or BD(T) is not capable of correctly describing the The dipole moment of annulene 1a is 0.35 D at R = 2.03 and nondynamical correlation. Since our computational possibilities 0.11 D for R = 1.638 Å (ωB97X-D calculations), where the do not provide a combination of these methods, we orientation is along the C2 axis (bridge, positively charged; constructed a model PEC, PHC, and PGC by simply averaging center of the perimeter, negatively charged). There is a charge the corresponding curves for CASPT2(14,14) and CCSD(T). transfer from the CMe2 bridge to the annulene perimeter, Although this model PHC (given in Figure 3a) may be which changes, in agreement with the changes in the dipole considered to provide only a semiquantitative insight into the moment, from 13 (R = 2.039 Å) to 9 me (millielectrons; R = problem, it suggests a broad single well potential slightly 1.638 Å). 103 1673 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

Table 3. Relative Energies and Rearrangement Barriers of 1,3,5-Cycloheptadiene and Norcaradiene

Method Curvea R(3b)b R(3a) ΔE(3b)c ΔE(TS)d HF DW-F1M 1.557 2.395 7.03 12.70 (5.67) B3LYP DW-F1M 1.644 2.351 7.51 7.89 (0.38) ωB97 DW-F2M 1.576 2.366 −0.80 5.43 (6.23) ωB97X DW-F1M 1.576 2.350 2.18 6.14 (3.96) ωB97X-D DW-F1M 1.585 2.355 2.20 6.28 (4.08) B2P-LYP-D DW-F1M 1.594 2.364 7.13 8.92 (1.79) MP2 DW-F1M 1.675 2.286 3.02 3.07 (0.05) MP3 DW-F1M 1.591 2.373 4.38 8.31 (3.93) MP4(SDQ) DW-F1M 1.582 2.385 4.37 8.89 (4.52) MP4(SDTQ) DW-F1M 1.623 2.341 4.64 5.85 (1.21) CCSD DW-F1M 1.583 2.382 4.69 8.76 (4.07) BD DW-F1M 1.585 2.380 4.62 8.68 (4.06) CCSD(T) DW-F1M 1.607 2.370 4.99 7.33 (2.34) BD(T) DW-F1M 1.607 2.366 5.10 7.34 (2.24) CASPT2(6,6) DW-F1M 1.633 2.310 4.36 4.84 (0.48) CASPT2(10,10) DW-F1M 1.593 2.334 6.05 12.20 (6.15)

ΔH(1b) ΔH(TS) B2P-LYP-D DW-F1M 1.653 2.245 6.33 6.34 (0.01) CCSD(T) DW-F1M 1.738 2.476 4.95 6.92 (1.97) BD(T) DW-F1M 1.738 2.476 4.96 6.93 (1.97) CASPT2(10,10) DW-F1M 1.641 2.334 5.89 11.53 (5.64)

ΔG(1b) ΔG(TS) B2P-LYP-D DW-F1M 1.697 2.245 6.47 6.64 (0.17) CCSD(T) DW-F1M 1.698 2.482 5.35 7.62 (2.27) BD(T) DW-F1M 1.698 2.482 5.34 7.59 (2.25) CASPT2(10,10) DW-F1M 1.618 2.334 6.18 12.22 (6.04) aCurve indicates the shape of the rearrangement potential. DW-F1M, double well with flat first minimum; DW-F2M, double well with flat second minimum; SW+1S, single well with shoulder at small R; SW+2S, single well with shoulder at large R. bR(3b) and R(3a) indicate the C1C6 distance for each structure in Å. cΔE(3b) gives the energy difference relative to 3a in kcal/mol. For the explanation of the estimated values, see text. dΔE(TS), ΔH(TS), and ΔG(TS) give the energy barriers for valence tautomerization from 3a to 3b in kcal/mol. Values in parentheses are for the reverse reactions.

Experimental work with 1 was carried out in nonpolar 2.8 Å,66 the downward oriented methyl H atoms should be 23,34,50 solvents such as cyclohexane, CS2, CCl4, or methanol. attracted by the π-density of the [10]annulene perimeter. There Therefore, we calculated the solvent influence by increasing the is a stabilizing H−π interaction at a distance of 2.4 Å, which is dielectric constant ϵ from 2 to 32.766 and using Tomasi’s PCM qualitatively confirmed by the increase in the stabilization of the method.65 In all calculations, changes in the relative free annulene form when comparing ωB97X-D and ωB97X results energies ΔG(298) were 0.1 kcal/mol or smaller, always in favor (see Supporting Information). of the annulene form (in line with the calculated dipole The hypothesis of an increased bridge−perimeter attraction moments), which in the case of the estimated potential of caused by bridge angle widening in the course of crystal state Figure 3a (see also Table 1) would decrease the ΔG(298) packing effects was confirmed as a widening of the CCC-bridge difference between 1a and 1b and lead to a larger population of angle had a significant impact on the parameter R: Widening the annulene form with increasing T, as found in the NMR the bridge angle C12C11C13 by 10° leads to an increase in R experiments.49,50 Hence, environmental effects cannot be by 0.048 Å. ignored if free energy differences smaller than RT = 0.6 kcal/ Next, we calculated the geometry of the dimer and the mol have to be discussed. tetramer shown in Figure 5 by applying a constrained There is also the possibility that the unusual C1C6 distances optimization, in which the distance(s) between the monomers observed in the crystal structure analysis44 are the result of and the relative orientation to each other were frozen (ωB97X- packing effects. In this connection, it has to be pointed out that D calculations). The differences in the monomer geometries strings of molecules 1 arranged in parallel form molecular are small for the dimer (R: 1.635 for the lower monomer; 1.631 sheets.44 Molecules which are on top of each other in different Å for the upper monomer). However, for the tetramer, R values sheets could, via exchange repulsion, widen the external of 1.636 (top, left), 1.642 (top, right), 1.637 (bottom, left), and C12C11C13 bridge angle, thus causing stronger bridge− 1.619 Å (bottom, right) are obtained, leading to a total perimeter interactions. As is shown in Figure 5, the downward variation of 0.023 Å. These changes are in line with the X-ray oriented methyl hydrogens are just 1.96−2.15 Å away from the diffraction result (ΔR in the unit cell: 0.056 AA44) where one center of the C3C4 and C8C9 bond, respectively. Considering has to consider that only the lower right monomer (the one that these H atoms carry a small positive charge and that the with the short R) has an environment close to that which it sum of the van der Waals distances for H and C is 1.2 + 1.6 = would have in the solid state. For reproducing the experimental 104 1674 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

Figure 5. Dimer and tetramer configurations that were calculated to investigate crystal packing effects. The green structures give a tetramer of 1 and show how two unit cells are arranged in the crystal.44 The blue structures on the left show the arrangement for the dimer of 1 that was calculated in the search for packing effects. The red structures give for the ωB97X-D optimized geometry of 1a and 1b the shortest hydrogen-to-ring distances. See text. situation, a more realistic model comprising at least 16 value becomes equal to the measured one, thus suggesting that monomers (12 monomers surrounding a tetramer) at fixed this R value is the one 1 adopts in solution or, alternatively, distances and orientations would be needed. Apart from this, corresponds to a time-averaged value if the valence-tautomeric one has to consider that effects would become larger if ωB97X- rearrangement of 1 is fast on the NMR time-scale. D could correctly describe the asymmetric SW potential A similar observation can be made for the NMR chemical obtained at higher levels of WFT. shift of C11, which increases from a value typical of a In another set of calculations, the dimer shown on the left cyclopropane (13C shift: −2.8 ppm98) to the one measured for side of Figure 5 (with frozen distance and relative orientation of 2a (34.8 ppm98) crossing the observed C11 shift at R = 1.782 fi the monomers) was optimized for xed R (1.6 < R < 2.2 Å) Å. The chemical shifts of the methyl carbon nuclei coincide at values of either the upper or the lower monomer, and 1.865 Å with the corresponding measured value. However, optimizing the remaining geometrical parameters. For all these 13C shifts are less sensitive, as are those of C2 these geometry optimizations, R of the second monomer (coincidence at R = 1.788 Å) and C3 (coincidence at R = changed maximally by 0.005 Å relative to the corresponding 2.168 Å, Figure 6a). The mean deviation Δ between measured monomer value where especially the positions of the methyl H and calculated 13C chemical shifts for the C atoms of the atoms were sensitive. We conclude that, in view of the broad perimeter adopts a minimum at R = 1.775 Å, as is shown in asymmetric SW potential calculated and the results obtained for Figure 6. NMR chemical shift calculations are normally less the tetramer, crystal packing effects have an impact on R and accurate for conjugated systems, especially if these are explain the existence of two molecules of 1 with different geometries in the unit cell. nonplanar (the shifts of C2 and C3 are close to the NMR investigation and an independent determina- experimental ones in the whole range 1.7 < R < 2.2 Å, and a fi ffi tion of the equilibrium geometry of 1. In previous work, speci c R value is di cult to determine). We note that when one of us has shown how an easily changing geometrical C11, C12, C13, C1, and C6 are used for the comparison with parameter of a flexible system can be determined in solution experiment, a value of R = 1.79 Å results, in good agreement 74,75 ff with the help of measured and calculated chemical shifts. In with the X-ray di raction values of R, which are close to 1.8 44 Figure 6a, calculated 13C and 1H chemical shift values are given Å. as a function of R and compared with the available 13C chemical The bisnorcaradiene and the annulene forms can both be shifts indicated as dashed horizontal lines. Examination of this excluded as clearly dominating the valence tautomeric figure reveals that the shift value of C1 is the most sensitive. rearrangement of 1 in the sense of a DW potential. The This shift increases from a typical value for vinyl cyclopropane remaining possibility is a rapid rearrangement in solution via a (42.5 ppm98) to that found for 2a (114.6 ppm98) and directly small barrier of a DW potential or, more likely in view of our reflects the changes in R. At R = 1.763 Å, the calculated C1 calculations, a broad asymmetric SW potential. This speaks for 105 1675 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

Figure 6. (a) Dependence of calculated NMR chemical shifts [ppm] of 1 on the distance R(C1C6) as calculated at the B3LYP/GIAO level of theory. (b) Mean absolute deviation [ppm] between measured and calculated 13C NMR chemical shifts of the ring carbon atoms given as a function of R. a large-amplitude vibration in solution similar to the one perimeter is too weak, and/or the C1C6 through-space overlap suggested in Figure 3a. is too small. Hence, a measuring of J(C1C6) (best in Also informative in this connection are the calculated SSCCs dependence of T) should provide an excellent possibility for J(13C13C) and J(1H1H) given as a function of R (see Figure 7). an experimental determination of R. When R is close to 1.5 Å, the values of 1J(C1C6) and Also informative should be the measurement of 1J(C1C11), 1J(C1C11) adopt the values typical of cyclopropane (12.4 1J(C11C12), and 3J(H15H16). The former J value increases Hz98). For increasing R the former 1J value decreases to −12.4 from about 16 Hz at R = 1.60 Å to 28 Hz, typical of a 1J(CC) Hz at 1.8 Å. This is comparable to the geminal 1J(CC) value in value such as that of cyclobutane.98 1J(C11C12) changes from a substituted cyclobutane (−8 Hz98) and then increases to a 45 to 39 Hz for the same R values while 3J(H15H16) increases zero value at large R, indicating that through-bond or through- from 5.0 to 7.2 Hz. Since the changes in the J(CC) values are space coupling are small because the CCC-angle dependence of larger, they should be preferably used for an independent 2J implies for this situation a zero value, 5J coupling along the determination of the R value of 1 in solution. 106 1676 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

Figure 7. Dependence of calculated NMR spin−spin coupling constants J [Hz] on R(C1,C6) of system 1.

4. DOES 11,11-DIMETHYL-METHANO[10]ANNULENE mode drops out of the 3N-L set of vibrational modes, POSSESS THE LONGEST CC BOND OF NEUTRAL indicating that for larger R values there is no C1C6 covalent CYCLOPROPYL DERIVATIVES? bond. All other BSO(CC) values change smoothly from the System 1 is unusual because of its broad SW potential, which bisnorcaradiene form to the annulene form where in the latter makes a large-amplitude C1C6 vibration possible, making a case the alternation of bonds is similar to that found for barrierless interconversion of the annulene into the bisnorcar- 81,86 fi naphthalene; that is, bonds C2C3, C4C5, etc. are the adiene form possible. In this work, we clari ed the question of strongest, followed by bonds C3C4 and C8C9, whereas the the nature of the C1C6 interaction by two different model 69 weakest conjugated CC bonds sit at the bridge. The CC bridge approaches utilizing the topological analysis of ρ(r) in the bonds of 1b are weaker than the normal CC bonds, with C1C6 way given by Cremer and Kraka70,71,99 and the local vibrational 77,80,100 being the weakest. The calculated AI of 1a is 64% of the value mode approach of Cremer, Zou, and Konkoli. In Figure obtained for benzene (100%), which is smaller than the value 8, the BSO values n(CC) based on the calculated local CC for 2a (73%) and significantly smaller than the value for stretching force constants are plotted as a function of R. For naphthalene (86%).86 This is in line with the fact that 2a and 3a each set of local vibrational modes at a given R value, the π 80 experience a strong perturbation of their 10 -perimeter caused adiabatic connection scheme is applied to determine whether by the 1,6-bridge leading to torsional angles up to 37°. a given local mode is still contained in a set of 3N-L modes In Figure 9a, the changes in the bond critical and ring critical directly related to the 3N-L normal vibrational modes. As can points rb and rr of the electron density distribution ρ(r) are be seen from Figure 8, close to R = 1.7 Å the C1C6 stretching shown as a function of R. Some of the changes are similar and some are different from those given by the n(CC) based on the local CC stretching force constants (Figure 8). This is attributable to the fact that the electron density determined at one specific point in the bond region cannot reflect all the density changes taking place in the zero-flux surface between two bonded atoms apart from the influences of bond polarity, charge transfer, and other effects given by the changes in the virial (atomic) spaces of the molecule during a change in R. The local CC stretching force constants account for these effects and therefore are more reliable CC bond strength descriptors. However, it is an accepted fact that covalent bonding requires the existence of a bond critical-point and zero-flux surface between the atoms in question and that the energy density at this bond critical point, H(rb), must be stabilizing, i.e. smaller than zero (Cremer−Kraka criteria of covalent bonding).70,71,99 This criterion is clearly fulfilled for all CC Figure 8. Bond strength orders n(CC) derived from local CC bonds and R values of 1 investigated, except the C1C6 stretching force constants given as a function of R(C1,C6) of system 1. interaction, which converts into a noncovalent interaction at R 107 1677 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article

than a smaller R, irrespective of any other stabilizing bridge− perimeter interactions. The isodesmic energies for the formal reactions

4 +CH323 CH CH→6 + CH 4 ,ΔE =− 3.78

2b1b+CH323 CH CH→+ CH 4 ,ΔE =− 3.38

2a1a+CH323 CH CH→+ CH 4 ,ΔE = 4.92 (B3LYP values in kcal/mol) suggest a similar stabilization by the two methyl groups for cyclopropane and 2b but a 5 kcal/ mol destabilization for 2a. The first two values are in line with a shortening of two vicinal and a lengthening of just one distal CC bond. Molecule 6 has a smaller external CCC angle than the HCH angle in its parent molecule (Figure 4), which is the result of steric repulsion between methyl groups and the ring. For the same reason, 1b has an even smaller external angle (110.2°, Figure 4), where the folding back of the two diene units as shown in the side view at the bottom of Figure 5 leads to some reduction of the steric repulsion between methyl groups and the 6-membered rings. In the case of 1a, steric attraction between methyl groups and the π-perimeter and steric repulsion (for 1a the H-center(C3C4) distance is decreased from 2.148 to 1.951 Å, ωB97X-D, see Figure 5) must be balanced, which leads to a small C12C11C13 angle (105.3°, Figure 4), methyl−methyl repulsion, and an overall destabilization, as reflected by the energy of the isodesmic reaction given above (4.9 kcal/mol). ff The destabilizing e ect of the CMe2 bridge leads to a raising of the relative energy of 1a. π-Delocalization and bridge− perimeter destabilization lead to the fact that 1b and 1a have comparable energies. A basic problem of previous studies was that they were based on quantum chemical methods of low accuracy. Depending on whether HF or MP2 is used, the preference for different Figure 9. (a) Electron density ρ(r) and (b) energy density H(r) at valence tautomeric forms is found, which holds also for the XC bond critical and ring critical points given as a function of R(C1,C6) of functionals of DFT, as we have demonstrated in this work for system 1. the first time. This leads to rather limited insight into the possible cause of a quantum mechanical (electronic structure) = 1.696 Å. There the C1C6C11 ring critical point merges with effect. For example, Simonetta and co-workers101 have used the C1C6 bond critical point, thus leading to a singularity in the Hoffmann’sapproach62,102 to rationalize the stability of Hessian of ρ(r) and the C1C6 maximum electron density path substituted cyclopropanes to explain substituent effects in connecting these atoms vanishes. Applying the Cremer−Kraka bridged [10]annulenes where their arguments were based on criterion, there is no longer a covalent C1C6 bond for R ≥ 1.70. low level calculations. As was pointed out by Cremer and co- This is in line with the independent observation made in workers,62 the orbital model used does not even explain all connection with the local vibrational modes. We draw the substituent effects for cyclopropanes. Furthermore, it does not conclusion that a C1C6 covalent bond with R = 1.80 Å does consider the impact of bridge−perimeter interactions, the not exist but that a homoaromatic interaction in the sense of a stabilization of biradicaloid structures for medium-sized R through-space overlap of π-orbitals exists leading to a small values by conjugation, or the dynamic aspects of the valence electron density increase between atoms C1 and C6. tautomeric rearrangement. Impact of the bridge on the 10π-perimeter. The Similarly, use of the topological analysis of ρ(r) by Gatti and electronic influence of electron-withdrawing and electron- co-workers,40 results of which were interpreted as proof for a donating substituents of a cyclopropane ring are well-known long covalent C1C6 bond, have to be criticized because they and has been amply described in the literature (for a review, see were carried out at the HF/minimal basis set level without ref 62). Two cyano groups at C11 lead to a shortening of the using any quantum mechanical criterion for covalent bonding. distal bond (lengthening of the vicinal bonds; see 5 as Other investigations were based on the NBO analysis or compared to 4 in Figure 4), which has been exploited to heuristic models utilizing the degree of bond length alternation synthesize 11,11-dicyano-bisnorcaradiene, i.e. the dicyano in the ring perimeter.42 These studies were insofar questionable analogue of 1b.35 The effect of two methyl groups has been as the properties analyzed were not referenced with regard to a predicted to lead to a slight CC lengthening of the distal bond suitable reference system. (slight shortening of the vicinal CC bonds)62 as is confirmed by An interesting rationalization of the carrying dynamic the bond lengths given for 6 in Figure 4. This indicates that behavior of bridged [10]annulenes was proposed by Choi dimethyl-substitution at C11 as in 1 should favor a larger rather and Kertesz,32 who model the opening of the cyclopropane ring 108 1678 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article in 1 or 2 by its conversion into a trimethylene biracial in its introducing steric strain via the geminal dimethyl group. This triplet ground state. The stabilization of the triplet trimethylene is a direct consequence of balancing methyl-perimeter exchange by substituents as described by DFT provides then a basis to repulsion against (electrostatic or dispersion driven) attraction. understand whether the bisnorcaradiene or annulene form is π-delocalization stabilizes the biradicaloid structure generated more stabilized. We note in this connection that the radical for medium-sized R values, which otherwise would lead to a centers are part of a conjugated system, and a more realistic relatively high barrier of valence tautomerization. Without the model would be the opening of 3-substituted 1,2-divinylcyclo- methyl-annulene interactions, π-delocalization and the resulting propanes. aromatic 10π-stabilization would shift the global minimum Dorn and co-workers50 excluded, on the basis of 13C CPMAS always to 1a. (cross-polarization magic angle spinning) spectra, a rapid (4) The analysis of the vibrational modes of 1 as well as its valence−tautomeric process for 1. Instead, these authors electron and energy density distribution reveals that covalent suggested that an asymmetric PEC and a different population C1C6 bonding ceases to exist beyond R = 1.7 Å on to larger of the vibrational levels at higher temperature would lead to the values of R.Hence,at1.8Åonecanonlyspeakof observed temperature dependence of the NMR spectra. homoaromatic through-space interactions, which will play little Alternatively, temperature dependent intermolecular interac- role for distances larger than 2 Å, i.e. for the annulenic form. tions could cause the observed temperature dependence.50 Our (5) In the course of this work, it became necessary to high level quantum chemical results are in line with the first accurately determine the PEC of the parent system 2. explanation whereas strong intermolecular interactions cannot CASPT2(14,14) calculations predict a SW potential with a be confirmed. shoulder between 1.6 and 1.9 Å. For an assumed R value of 1.70 103 Kaupp and Boy analyzed the measured temperature Å, the bis norcaradiene form has a relative enthalpy ΔH(298), factors of the crystal data and concluded that a structural which is 10.2 kcal/mol higher than that of the annulene form, disorder in the solid state leads to the coexistence of i.e. at room temperature the percentage of bisnorcaradine is bisnorcaradiene and [10]annulene, which would imply that finite but close to zero. the measured R values are just averages. Our results do not (6) Because of its close relationship to systems 1 and 2, we agree with this hypothesis, as the modeling of packing effects investigated also the valence-tautomeric system 3.The using a tetramer of 1 leads to changes in R that are in the range CASPT2(10,10)-based free activation energy ΔGa(298) of 44 of R differences measured by X-ray diffraction. cycloheptatriene rearranging to norcaradiene is 12.2 kcal/mol in forward and 6.0 kcal/mol in the reverse reaction where the 5. CONCLUSIONS latter value is identical to a kinetic value obtained at 110 K, but This investigation provides a convincing explanation for the 1.2 kcal/mol smaller than a derived value at 298 K obtained in 93 puzzling observations made in connection with molecule 1. the same study. We show that the latter deviation is caused by This explanation is based on extensive calculations with more an overly large entropy change ΔSa used in the experimental than 20 different quantum chemical methods and the analysis study. The ΔG(298) value of 3b relative to 3a is 6.2 kcal/mol. of energy, geometry, dipole moment, charge transfer, NMR The latter value replaces a previous NMR-based estimate of 4 ± 93,104 chemical shifts, indirect spin−spin coupling constants, local 2 kcal/mol. The concentration of 3b at room temperature vibrational modes, and electron and energy density changes is just 0.003% rather than the previously estimated value of given as a function of the critical distance R(C1C6). Our work 0.1%. has led to a number of methodological insights and (7) Although 1, 2, and 3 are closed shell molecules, their experimentally relevant conclusions, which are of general description requires the inclusion of both dynamical and relevance for future experimental or theoretical work on related nondynamical electron correlation to a high degree, i.e. for the molecules, especially in connection with materials science. former T excitations are absolutely necessary as is a (14,14) (1) The investigation presented here reveals that system 1 active space (because of σ − π mixing and conjugative possesses a broad, slightly asymmetric SW potential (or a very stabilization of a transient biradicaloid) provided at least second flat DW minimum) in which it carries out a large C1C6 order perturbation theory is used. Ideally, these systems would amplitude vibration. Forms 1b and 1a have almost identical be investigated with MR-AQCCSD based on a large active relative energies and enthalpies. A methodologically independ- space. A basis set of VTZ quality is absolutely needed, because ent determination of the critical distance R based on a the calculations of this work reveal that an augmentation with comparison of measured and calculated 13C NMR chemical diffuse functions is also required together with the multi- shifts leads to a value of 1.775 Å. By using only those shift reference description and the T dynamical correlation effects. values strongly dependent on R, the NMR-based determination This is currently beyond computational possibilities but will be of R can be improved to 1.79 Å in line with the X-ray diffraction a target for future studies. values of 1.780(7) and 1.836(7) Å.44 (8) This work has also shown the usefulness of long-range (2) This work suggests that the R value in solution exact exchange and the promising performance of double- corresponds to a time-averaged value whereas the R values of hybrid XC functionals. We suggest that the energetics for 1, 2, the unit cell are adopted by molecules of 1 being exposed to and 3 obtained in this work will be included in the standard different packing effects. Our investigation could confirm the reaction sets for the testing of new XC functionals. We see the existence of packing effects using small models (dimer, possibility of combining different flavors of MP2 spin scaling tetramer.) For a tetramer model, a ΔR value of 0.023 Å was and dispersion corrections in a double-hybrid functional to get calculated suggesting a structure distortion as it was found in more accurate results, as is obtained with the B2PLYPD the solid state: ΔR = 0.056 Å determined by the X-ray functional in this work. diffraction analysis.44 (9) The bridged annulenes synthesized in the Vogel group (3) The peculiar valence tautomeric potential of 1 is the have so far evaded thorough quantum chemical investigations, result of the destabilization of the annulene form by as they can only be accurately described by combining 109 1679 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 The Journal of Physical Chemistry A Article dynamical and nondynamical electron correlation in a post-HF methylacridan) Derivatives with an Acenaphthene, Pyracene, or method. This work shows that the active space has to include Dihydropyracylene Skeleton. Chem.Eur. J. 2008, 14, 5780−5793. also the σ orbitals (or Walsh-orbitals) of the annulene bridge to (7) Suzuki, T.; Takeda, T.; Kawai, H.; Fujiwara, K. Ultralong C-C describe π-delocalization reliably. A quantum chemical Bonds in Hexaphenylethane Derivatives. Pure Appl. Chem. 2008, 80, investigation of the bridged annulenes can predict those 547−553. properties that may be interesting in connection with polymer (8) Tanaka, K.; Takamoto, N.; Tezuka, Y.; Kato, M.; Toda, F. Preparation and Structural Study of Naphtho- and Anthrocyclobutene chemistry, materials chemistry, or nanochemistry. We note in Derivatives Which Have Extremely Long C-C Bonds. Tetrahedron this connection that the synthesis of bridged annulenes involves 2001, 57, 3761−3767. carbene addition, which is a technique more and more used in (9) Grafenstein, J.; Kraka, E.; D. Cremer, D. The Impact of the Self- fullerene chemistry where systems with perturbed π-delocaliza- interaction Error on the Density Functional Theory Description of tion and specific material properties are generated in this way. Dissociating Radical Cations: Ionic and Covalent Dissociation Limits. The procedures used in this work would also be useful for the J. Chem. Phys. 2004, 120, 524−539. quantum chemical investigation of these systems employing (10) Cremer, D.; Childs, R. F.; Kraka, E. In The Chemistry of fine-tuned double hybrid functionals. Functional Groups, The Chemistry of the Cyclopropyl Group; Rappoport, (10) Finally, it is noteworthy that a system such as 1 is the Z., Ed.; Wiley: Chichester, UK, 1995; Vol. 2, pp 339−410. basis for a molecular switch, which by ring substitution or (11) Childs, R. F.; Cremer, D.; Elia, G. In The Chemistry of Functional suitable interactions with the environment can be pushed into Groups, The Chemistry of the Cyclopropyl Group; Rappoport, Z., Ed.; an on- (e.g., 1b) or off-position (1a). Wiley: Chichester, UK, 1995; Vol. 2, pp 411−468. (12) Oliva, J. M.; Allan, N. L.; Schleyer, P.; Vinas, C.; Teixidor, F. Strikingly Long C··· CDistancesin1,2-Disubstitutedortho- ■ ASSOCIATED CONTENT Carboranes and Their Dianions. J. Am. Chem. Soc. 2005, 127, *S Supporting Information 13538−13547. Discussion of the calculated PECs as they reveal advantages and (13) Wannere, C. S.; Chen, Z.; Schleyer, P. Carbocation Chemistry disadvantages of a given method, and calculated geometries, Zwitterionic “Neutral” and “Anionic” Carbocation Analogs; Wiley: energies, and other properties for all molecules summarized in Hoboken, NJ, 2004. 24 tables. This material is available free of charge via the (14) Huang, J.; Sumpter, B.; Meunier, V.; Tian, Y.; Kertesz, M. Cyclo-biphenalenyl Biradicaloid Molecular Materials: Conformation, Internet at http://pubs.acs.org. Tautomerization, Magnetism, and Thermochromism. Chem. Mater. 2011, 23, 874−885. ■ AUTHOR INFORMATION (15) Jose, D.; Datta, A. Role of Multicentered Bonding in Controlling Corresponding Author Magnetic Interactions in π -Stacked Bis-Dithiazolyl Radical. Cryst. *E-mail: [email protected]. Growth Des. 2011, 11, 3137−3140. (16) Mota, F.; Miller, J.; Novoa, J. J. Comparative Analysis of the Notes Multicenter, Long Bond in [TCNE] − and Phenalenyl Radical Dimers: The authors declare no competing financial interest. A Unified Description of Multicenter, Long Bonds. J. Am. Chem. Soc. 2009, 131, 7699−7707. ■ ACKNOWLEDGMENTS (17) Capdevila-Cortada, M.; Novoa, J. J. The Nature of the [TTF] +···[TTF] + Interactions in the [TTF]2+ Dimers Embedded in Charged This work was financially supported by the National Science 2 [3]Catenanes: Room-Temperature Multicenter Long Bonds. Chem. Foundation, Grant CHE 1152357. We thank SMU for Eur. J. 2012, 18, 5335−5344. providing computational resources. An early investigation of fi (18) Novoa, J. J.; Lafuente, P.; Del Sesto, R. E.; Miller, J. S. 1 and 2 by El Kraka is acknowledged. Thanks also to Marek Exceptionally Long (>2.9 Å) C-C Bonds Between [TCNE]− Ions: Freindorf, Dani Setiawan, and Rob Kalescky for help with some 2− Two-Electron, Four-Center π*π* C-C Bonding in π−[TCNE]2 . of the calculations. Angew. Chem., Int. Ed. 2001, 40, 2540−2545. (19) Garcia-Yoldi, I.; Miller, J.; Novoa, J. 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R.; Schütz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; 112 1682 dx.doi.org/10.1021/jp5082966 | J. Phys. Chem. A 2015, 119, 1666−1682 11,11-Dimethyl-1,6-methano[10]annulene - An

annulene with a long CC bond or a ﬂuxional

molecule?

Suporting Information

Alan Humason, Wenli Zou, and Dieter Cremer⇤

Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University 3215 Daniel Ave, Dallas, Texas 75275-0314, USA

E-mail: [email protected]

⇤To whom correspondence should be addressed

113 Table 1: Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, wB97X-D/6-311G(d,p)

1.4 Å 1.5 Å 1.6 Å 1.636 Å C 0.000000 0.000000 1.2459620 C 0.000000 0.000000 1.222421 C 0.000000 0.000000 1.195511 C 0.000000 0.000000 1.185334 C -0.700000 0.000000 -0.1145630 C -0.750000 0.000000 -0.106704 C -0.800000 0.000000 -0.097416 C -0.817797 0.000000 -0.093276 C -1.401222 1.236908 -0.5768290 C -1.415470 1.240938 -0.581587 C -1.428781 1.242669 -0.586960 C -1.433327 1.242851 -0.588467 C -0.731546 2.320155 -0.9772120 C -0.729527 2.326786 -0.955280 C -0.726983 2.333094 -0.928902 C -0.725976 2.334730 -0.919836 C 0.731546 2.320155 -0.9772120 C 0.729527 2.326786 -0.955280 C 0.726983 2.333094 -0.928902 C 0.725976 2.334730 -0.919836 C 1.401222 1.236908 -0.5768290 C 1.415470 1.240938 -0.581587 C 1.428781 1.242669 -0.586960 C 1.433327 1.242851 -0.588467 C 0.700000 0.000000 -0.1145630 C 0.750000 0.000000 -0.106704 C 0.800000 0.000000 -0.097416 C 0.817797 0.000000 -0.093276 C 1.401222 -1.236908 -0.5768290 C 1.415470 -1.240938 -0.581587 C 1.428781 -1.242669 -0.586960 C 1.433327 -1.242851 -0.588467 C 0.731546 -2.320155 -0.9772120 C 0.729527 -2.326786 -0.955280 C 0.726983 -2.333094 -0.928902 C 0.725976 -2.334730 -0.919836 C -0.731546 -2.320155 -0.9772120 C -0.729527 -2.326786 -0.955280 C -0.726983 -2.333094 -0.928902 C -0.725976 -2.334730 -0.919836 C -1.401222 -1.236908 -0.5768290 C -1.415470 -1.240938 -0.581587 C -1.428781 -1.242669 -0.586960 C -1.433327 -1.242851 -0.588467 C 0.000000 1.253483 2.0896290 C 0.000000 1.249063 2.076323 C 0.000000 1.244526 2.059196 C 0.000000 1.243082 2.052512 C 0.000000 -1.253483 2.0896290 C 0.000000 -1.249063 2.076323 C 0.000000 -1.244526 2.059196 C 0.000000 -1.243082 2.052512 H -2.484854 1.201623 -0.6281960 H -2.496762 1.212471 -0.678615 H -2.504543 1.218255 -0.736931 H -2.506535 1.219837 -0.756817 H 2.484854 1.201623 -0.6281960 H 2.496762 1.212471 -0.678615 H 2.504543 1.218255 -0.736931 H 2.506535 1.219837 -0.756817 H 2.484854 -1.201623 -0.6281960 H 2.496762 -1.212471 -0.678615 H 2.504543 -1.218255 -0.736931 H 2.506535 -1.219837 -0.756817 H -2.484854 -1.201623 -0.6281960 H -2.496762 -1.212471 -0.678615 H -2.504543 -1.218255 -0.736931 H -2.506535 -1.219837 -0.756817 H -1.259541 3.198143 -1.3315080 H -1.251722 3.206040 -1.315453 H -1.243029 3.212740 -1.297278 H -1.239801 3.214679 -1.290715 H 1.259541 3.198143 -1.3315080 H 1.251722 3.206040 -1.315453 H 1.243029 3.212740 -1.297278 H 1.239801 3.214679 -1.290715 H 1.259541 -3.198143 -1.3315080 H 1.251722 -3.206040 -1.315453 H 1.243029 -3.212740 -1.297278 H 1.239801 -3.214679 -1.290715 H -1.259541 -3.198143 -1.3315080 H -1.251722 -3.206040 -1.315453 H -1.243029 -3.212740 -1.297278 H -1.239801 -3.214679 -1.290715 H 0.000000 2.172839 1.5090790 H 0.000000 2.173100 1.504011 H 0.000000 2.173921 1.496505 H 0.000000 2.173875 1.492448 H 0.884308 1.263509 2.7352720 H 0.884726 1.251290 2.720780 H 0.885116 1.239231 2.702524 H 0.885249 1.235359 2.695417 H -0.884308 1.263509 2.7352720 H -0.884726 1.251290 2.720780 H -0.885116 1.239231 2.702524 H -0.885249 1.235359 2.695417 H 0.000000 -2.172839 1.5090790 H 0.000000 -2.173100 1.504011 H 0.000000 -2.173921 1.496505 H 0.000000 -2.173875 1.492448 H 0.884308 -1.263509 2.7352720 H 0.884726 -1.251290 2.720780 H 0.885116 -1.239231 2.702524 H 0.885249 -1.235359 2.695417 H -0.884308 -1.263509 2.7352720 H -0.884726 -1.251290 2.720780 H -0.885116 -1.239231 2.702524 H -0.885249 -1.235359 2.695417 Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, wB97X-D/6-311G(d,p) (continued) 1.7 Å 1.8 Å 1.9 Å 2.0 Å C 0.000000 0.000000 1.167767 C 0.000000 0.000000 1.139077 C 0.000000 0.000000 1.110260 C 0.0000000 0.0000000 1.0821730 C -0.850000 0.000000 -0.083690 C -0.900000 0.000000 -0.067971 C -0.950000 0.000000 -0.052668 C -1.0000000 0.0000000 -0.0380860 C -1.441681 1.241613 -0.590500 C -1.455135 1.238038 -0.592364 C -1.470419 1.233371 -0.592255 C -1.4885870 1.2292030 -0.5895650 C -0.724022 2.335089 -0.906056 C -0.720726 2.333437 -0.885378 C -0.717515 2.328733 -0.867127 C -0.7147590 2.3209340 -0.8531290 C 0.724022 2.335089 -0.906056 C 0.720726 2.333437 -0.885378 C 0.717515 2.328733 -0.867127 C 0.7147590 2.3209340 -0.8531290 C 1.441681 1.241613 -0.590500 C 1.455135 1.238038 -0.592364 C 1.470419 1.233371 -0.592255 C 1.4885870 1.2292030 -0.5895650 C 0.850000 0.000000 -0.083690 C 0.900000 0.000000 -0.067971 C 0.950000 0.000000 -0.052668 C 1.0000000 0.0000000 -0.0380860 C 1.441681 -1.241613 -0.590500 C 1.455135 -1.238038 -0.592364 C 1.470419 -1.233371 -0.592255 C 1.4885870 -1.2292030 -0.5895650 C 0.724022 -2.335089 -0.906056 C 0.720726 -2.333437 -0.885378 C 0.717515 -2.328733 -0.867127 C 0.7147590 -2.3209340 -0.8531290 C -0.724022 -2.335089 -0.906056 C -0.720726 -2.333437 -0.885378 C -0.717515 -2.328733 -0.867127 C -0.7147590 -2.3209340 -0.8531290 C -1.441681 -1.241613 -0.590500 C -1.455135 -1.238038 -0.592364 C -1.470419 -1.233371 -0.592255 C -1.4885870 -1.2292030 -0.5895650 C 0.000000 1.239899 2.042936 C 0.000000 1.234756 2.027154 C 0.000000 1.229575 2.011512 C 0.0000000 1.2246520 1.9964510 C 0.000000 -1.239899 2.042936 C 0.000000 -1.234756 2.027154 C 0.000000 -1.229575 2.011512 C 0.0000000 -1.2246520 1.9964510 H -2.508812 1.220233 -0.794998 H -2.510088 1.219532 -0.853496 H -2.511012 1.220420 -0.906496 H -2.5151170 1.2256470 -0.9477930 H 2.508812 1.220233 -0.794998 H 2.510088 1.219532 -0.853496 H 2.511012 1.220420 -0.906496 H 2.5151170 1.2256470 -0.9477930 H 2.508812 -1.220233 -0.794998 H 2.510088 -1.219532 -0.853496 H 2.511012 -1.220420 -0.906496 H 2.5151170 -1.2256470 -0.9477930 H -2.508812 -1.220233 -0.794998 H -2.510088 -1.219532 -0.853496 H -2.511012 -1.220420 -0.906496 H -2.5151170 -1.2256470 -0.9477930 H -1.233684 3.214163 -1.284934 H -1.223388 3.210944 -1.277510 H -1.212318 3.205057 -1.272283 H -1.2007500 3.1971300 -1.2697700 H 1.233684 3.214163 -1.284934 H 1.223388 3.210944 -1.277510 H 1.212318 3.205057 -1.272283 H 1.2007500 3.1971300 -1.2697700 H 1.233684 -3.214163 -1.284934 H 1.223388 -3.210944 -1.277510 H 1.212318 -3.205057 -1.272283 H 1.2007500 -3.1971300 -1.2697700 H -1.233684 -3.214163 -1.284934 H -1.223388 -3.210944 -1.277510 H -1.212318 -3.205057 -1.272283 H -1.2007500 -3.1971300 -1.2697700 H 0.000000 2.174339 1.489618 H 0.000000 2.175634 1.485818 H 0.000000 2.176670 1.482064 H 0.0000000 2.1770440 1.4774520 H 0.885437 1.226683 2.685069 H 0.885534 1.213095 2.668381 H 0.885459 1.200013 2.652119 H 0.8852650 1.1880700 2.6366470 H -0.885437 1.226683 2.685069 H -0.885534 1.213095 2.668381 H -0.885459 1.200013 2.652119 H -0.8852650 1.1880700 2.6366470 H 0.000000 -2.174339 1.489618 H 0.000000 -2.175634 1.485818 H 0.000000 -2.176670 1.482064 H 0.0000000 -2.1770440 1.4774520 H 0.885437 -1.226683 2.685069 H 0.885534 -1.213095 2.668381 H 0.885459 -1.200013 2.652119 H 0.8852650 -1.1880700 2.6366470 H -0.885437 -1.226683 2.685069 H -0.885534 -1.213095 2.668381 H -0.885459 -1.200013 2.652119 H -0.8852650 -1.1880700 2.6366470 Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, wB97X-D/6-311G(d,p) (continued) 115

2.4 Å 2.5 Å 2.6 Å C 0.000000 0.000000 0.986326 C 0.000000 0.000000 0.968550 C 0.000000 0.000000 0.953760 C -1.200000 0.000000 0.014655 C -1.250000 0.000000 0.025785 C -1.300000 0.000000 0.035920 C -1.582909 1.227102 -0.563661 C -1.608410 1.229722 -0.556220 C -1.633470 1.233020 -0.549390 C -0.710436 2.267625 -0.834638 C -0.710659 2.251214 -0.834882 C -0.711210 2.234470 -0.835790 C 0.710436 2.267625 -0.834638 C 0.710659 2.251214 -0.834882 C 0.711210 2.234470 -0.835790 C 1.582909 1.227102 -0.563661 C 1.608410 1.229722 -0.556220 C 1.633470 1.233020 -0.549390 C 1.200000 0.000000 0.014655 C 1.250000 0.000000 0.025785 C 1.300000 0.000000 0.035920 C 1.582909 -1.227102 -0.563661 C 1.608410 -1.229722 -0.556220 C 1.633470 -1.233020 -0.549390 C 0.710436 -2.267625 -0.834638 C 0.710659 -2.251214 -0.834882 C 0.711210 -2.234470 -0.835790 C -0.710436 -2.267625 -0.834638 C -0.710659 -2.251214 -0.834882 C -0.711210 -2.234470 -0.835790 C -1.582909 -1.227102 -0.563661 C -1.608410 -1.229722 -0.556220 C -1.633470 -1.233020 -0.549390 C 0.000000 1.207759 1.945027 C 0.000000 1.204793 1.934585 C 0.000000 1.202420 1.925360 C 0.000000 -1.207759 1.945027 C 0.000000 -1.204793 1.934585 C 0.000000 -1.202420 1.925360 H -2.579747 1.296764 -0.993266 H -2.602120 1.322539 -0.988916 H -2.624310 1.349580 -0.983180 H 2.579747 1.296764 -0.993266 H 2.602120 1.322539 -0.988916 H 2.624310 1.349580 -0.983180 H 2.579747 -1.296764 -0.993266 H 2.602120 -1.322539 -0.988916 H 2.624310 -1.349580 -0.983180 H -2.579747 -1.296764 -0.993266 H -2.602120 -1.322539 -0.988916 H -2.624310 -1.349580 -0.983180 H -1.156715 3.145760 -1.292433 H -1.146502 3.129322 -1.303234 H -1.136670 3.112480 -1.314290 H 1.156715 3.145760 -1.292433 H 1.146502 3.129322 -1.303234 H 1.136670 3.112480 -1.314290 H 1.156715 -3.145760 -1.292433 H 1.146502 -3.129322 -1.303234 H 1.136670 -3.112480 -1.314290 H -1.156715 -3.145760 -1.292433 H -1.146502 -3.129322 -1.303234 H -1.136670 -3.112480 -1.314290 H 0.000000 2.178767 1.463138 H 0.000000 2.178895 1.459090 H 0.000000 2.179010 1.455150 H 0.883886 1.151135 2.585388 H 0.883535 1.145481 2.575280 H 0.883180 1.141210 2.566510 H -0.883886 1.151135 2.585388 H -0.883535 1.145481 2.575280 H -0.883180 1.141210 2.566510 H 0.000000 -2.178767 1.463138 H 0.000000 -2.178895 1.459090 H 0.000000 -2.179010 1.455150 H 0.883886 -1.151135 2.585388 H 0.883535 -1.145481 2.575280 H 0.883180 -1.141210 2.566510 H -0.883886 -1.151135 2.585388 H -0.883535 -1.145481 2.575280 H -0.883180 -1.141210 2.566510 Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, wB97X-D/6-311G(d,p) (continued) Table 2: Cartesian Coordinates [Å] for 1,6-Methano[10]annulene, wB97X-D/6-311G(d,p)

1.4 Å 1.5 Å 1.6 Å 1.7 Å C 0.000000 0.000000 1.607795 C 0.000000 0.000000 1.572595 C 0.000000 0.000000 1.533335 C 0.000000 0.000000 1.491360 C 0.000000 0.700000 0.266330 C 0.000000 0.750000 0.266051 C 0.000000 0.800000 0.266623 C 0.000000 0.850000 0.268452 C 1.253077 1.402312 -0.137917 C 1.257741 1.416932 -0.147709 C 1.260112 1.430505 -0.158452 C 1.259902 1.443510 -0.169389 C 2.371019 0.731334 -0.424736 C 2.377768 0.729226 -0.398107 C 2.383016 0.726676 -0.368647 C 2.385905 0.723644 -0.337312 C 2.371019 -0.731334 -0.424736 C 2.377768 -0.729226 -0.398107 C 2.383016 -0.726676 -0.368647 C 2.385905 -0.723644 -0.337312 C 1.253077 -1.402312 -0.137917 C 1.257741 -1.416932 -0.147709 C 1.260112 -1.430505 -0.158452 C 1.259902 -1.443510 -0.169389 C 0.000000 -0.700000 0.266330 C 0.000000 -0.750000 0.266051 C 0.000000 -0.800000 0.266623 C 0.000000 -0.850000 0.268452 C -1.253077 -1.402312 -0.137917 C -1.257741 -1.416932 -0.147709 C -1.260112 -1.430505 -0.158452 C -1.259902 -1.443510 -0.169389 C -2.371019 -0.731334 -0.424736 C -2.377768 -0.729226 -0.398107 C -2.383016 -0.726676 -0.368647 C -2.385905 -0.723644 -0.337312 C -2.371019 0.731334 -0.424736 C -2.377768 0.729226 -0.398107 C -2.383016 0.726676 -0.368647 C -2.385905 0.723644 -0.337312 C -1.253077 1.402312 -0.137917 C -1.257741 1.416932 -0.147709 C -1.260112 1.430505 -0.158452 C -1.259902 1.443510 -0.169389 H 0.929345 0.000000 2.159810 H 0.925597 0.000000 2.132887 H 0.922062 0.000000 2.101329 H 0.918905 0.000000 2.066344 H -0.929345 0.000000 2.159810 H -0.925597 0.000000 2.132887 H -0.922062 0.000000 2.101329 H -0.918905 0.000000 2.066344 H 1.214341 2.484630 -0.207528 H 1.229588 2.495872 -0.266151 H 1.241120 2.502321 -0.333160 H 1.249703 2.503720 -0.406117 H 1.214341 -2.484630 -0.207528 H 1.229588 -2.495872 -0.266151 H 1.241120 -2.502321 -0.333160 H 1.249703 -2.503720 -0.406117 H -1.214341 -2.484630 -0.207528 H -1.229588 -2.495872 -0.266151 H -1.241120 -2.502321 -0.333160 H -1.249703 -2.503720 -0.406117 H -1.214341 2.484630 -0.207528 H -1.229588 2.495872 -0.266151 H -1.241120 2.502321 -0.333160 H -1.249703 2.503720 -0.406117 H 3.275267 1.258130 -0.707143 H 3.285494 1.249324 -0.682444 H 3.294293 1.239835 -0.654782 H 3.299868 1.229101 -0.629244 H 3.275267 -1.258130 -0.707143 H 3.285494 -1.249324 -0.682444 H 3.294293 -1.239835 -0.654782 H 3.299868 -1.229101 -0.629244 H -3.275267 -1.258130 -0.707143 H -3.285494 -1.249324 -0.682444 H -3.294293 -1.239835 -0.654782 H -3.299868 -1.229101 -0.629244 H -3.275267 1.258130 -0.707143 H -3.285494 1.249324 -0.682444 H -3.294293 1.239835 -0.654782 H -3.299868 1.229101 -0.629244 Cartesian Coordinates [Å] for 1,6-Methano[10]annulene, wB97X-D/6-311G(d,p) 116 1.8 Å 1.9 Å 2.0 Å 2.1 Å C 0.000000 0.000000 1.447604 C 0.000000 0.000000 1.404689 C 0.000000 0.000000 1.364287 C 0.000000 0.000000 1.323619 C 0.000000 0.900000 0.271788 C 0.000000 0.950000 0.276756 C 0.000000 1.000000 0.281719 C 0.000000 1.050000 0.286221 C 1.257128 1.457325 -0.178664 C 1.253719 1.473504 -0.183981 C 1.251355 1.492887 -0.185928 C 1.250800 1.515031 -0.185228 C 2.384888 0.720313 -0.308176 C 2.380321 0.717101 -0.284957 C 2.373393 0.714489 -0.268302 C 2.365037 0.712583 -0.255936 C 2.384888 -0.720313 -0.308176 C 2.380321 -0.717101 -0.284957 C 2.373393 -0.714489 -0.268302 C 2.365037 -0.712583 -0.255936 C 1.257128 -1.457325 -0.178664 C 1.253719 -1.473504 -0.183981 C 1.251355 -1.492887 -0.185928 C 1.250800 -1.515031 -0.185228 C 0.000000 -0.900000 0.271788 C 0.000000 -0.950000 0.276756 C 0.000000 -1.000000 0.281719 C 0.000000 -1.050000 0.286221 C -1.257128 -1.457325 -0.178664 C -1.253719 -1.473504 -0.183981 C -1.251355 -1.492887 -0.185928 C -1.250800 -1.515031 -0.185228 C -2.384888 -0.720313 -0.308176 C -2.380321 -0.717101 -0.284957 C -2.373393 -0.714489 -0.268302 C -2.365037 -0.712583 -0.255936 C -2.384888 0.720313 -0.308176 C -2.380321 0.717101 -0.284957 C -2.373393 0.714489 -0.268302 C -2.365037 0.712583 -0.255936 C -1.257128 1.457325 -0.178664 C -1.253719 1.473504 -0.183981 C -1.251355 1.492887 -0.185928 C -1.250800 1.515031 -0.185228 H 0.915936 0.000000 2.029174 H 0.911665 0.000000 1.994994 H 0.907099 0.000000 1.963261 H 0.903041 0.000000 1.930552 H -0.915936 0.000000 2.029174 H -0.911665 0.000000 1.994994 H -0.907099 0.000000 1.963261 H -0.903041 0.000000 1.930552 H 1.257208 2.501825 -0.477468 H 1.267135 2.500901 -0.537188 H 1.282536 2.505622 -0.578463 H 1.302983 2.516643 -0.603487 H 1.257208 -2.501825 -0.477468 H 1.267135 -2.500901 -0.537188 H 1.282536 -2.505622 -0.578463 H 1.302983 -2.516643 -0.603487 H -1.257208 -2.501825 -0.477468 H -1.267135 -2.500901 -0.537188 H -1.282536 -2.505622 -0.578463 H -1.302983 -2.516643 -0.603487 H -1.257208 2.501825 -0.477468 H -1.267135 2.500901 -0.537188 H -1.282536 2.505622 -0.578463 H -1.302983 2.516643 -0.603487 H 3.302906 1.217261 -0.602848 H 3.302126 1.205017 -0.583978 H 3.299867 1.192944 -0.569372 H 3.296339 1.181146 -0.558890 H 3.302906 -1.217261 -0.602848 H 3.302126 -1.205017 -0.583978 H 3.299867 -1.192944 -0.569372 H 3.296339 -1.181146 -0.558890 H -3.302906 -1.217261 -0.602848 H -3.302126 -1.205017 -0.583978 H -3.299867 -1.192944 -0.569372 H -3.296339 -1.181146 -0.558890 H -3.302906 1.217261 -0.602848 H -3.302126 1.205017 -0.583978 H -3.299867 1.192944 -0.569372 H -3.296339 1.181146 -0.558890 Cartesian Coordinates [Å] for 1,6-methano[10]annulene, wB97X-D/6-311G(d,p) (continued) 2.2 Å 2.23 2.3 Å 2.4 Å C 0.000000 0.000000 1.284079 C 0.000000 0.000000 1.272580 C 0.000000 0.000000 1.248679 C 0.000000 0.000000 1.216502 C 0.000000 1.100000 0.290099 C 0.000000 1.115156 0.291771 C 0.000000 1.150000 0.296431 C 0.000000 1.200000 0.302656 C 1.252434 1.539887 -0.181824 C 1.253200 1.547737 -0.180288 C 1.255333 1.565770 -0.176086 C 1.259348 1.592625 -0.168890 C 2.355236 0.711421 -0.248509 C 2.351976 0.711195 -0.247258 C 2.344078 0.710873 -0.246230 C 2.331536 0.710836 -0.246767 C 2.355236 -0.711421 -0.248509 C 2.351976 -0.711195 -0.247258 C 2.344078 -0.710873 -0.246230 C 2.331536 -0.710836 -0.246767 C 1.252434 -1.539887 -0.181824 C 1.253200 -1.547737 -0.180288 C 1.255333 -1.565770 -0.176086 C 1.259348 -1.592625 -0.168890 C 0.000000 -1.100000 0.290099 C 0.000000 -1.115156 0.291771 C 0.000000 -1.150000 0.296431 C 0.000000 -1.200000 0.302656 C -1.252434 -1.539887 -0.181824 C -1.253200 -1.547737 -0.180288 C -1.255333 -1.565770 -0.176086 C -1.259348 -1.592625 -0.168890 C -2.355236 -0.711421 -0.248509 C -2.351976 -0.711195 -0.247258 C -2.344078 -0.710873 -0.246230 C -2.331536 -0.710836 -0.246767 C -2.355236 0.711421 -0.248509 C -2.351976 0.711195 -0.247258 C -2.344078 0.710873 -0.246230 C -2.331536 0.710836 -0.246767 C -1.252434 1.539887 -0.181824 C -1.253200 1.547737 -0.180288 C -1.255333 1.565770 -0.176086 C -1.259348 1.592625 -0.168890 H 0.899101 0.000000 1.898524 H 0.897372 0.000000 1.890050 H 0.893764 0.000000 1.872258 H 0.889973 0.000000 1.846426 H -0.899101 0.000000 1.898524 H -0.897372 0.000000 1.890050 H -0.893764 0.000000 1.872258 H -0.889973 0.000000 1.846426 H 1.328972 2.534781 -0.612390 H 1.337292 2.541307 -0.612694 H 1.356754 2.556719 -0.610790 H 1.385956 2.581316 -0.602306 H 1.328972 -2.534781 -0.612390 H 1.337292 -2.541307 -0.612694 H 1.356754 -2.556719 -0.610790 H 1.385956 -2.581316 -0.602306 H -1.328972 -2.534781 -0.612390 H -1.337292 -2.541307 -0.612694 H -1.356754 -2.556719 -0.610790 H -1.385956 -2.581316 -0.602306 H -1.328972 2.534781 -0.612390 H -1.337292 2.541307 -0.612694 H -1.356754 2.556719 -0.610790 H -1.385956 2.581316 -0.602306 H 3.291949 1.169954 -0.551293 H 3.289956 1.166594 -0.551237 H 3.284529 1.159209 -0.553750 H 3.275454 1.148739 -0.559686 H 3.291949 -1.169954 -0.551293 H 3.289956 -1.166594 -0.551237 H 3.284529 -1.159209 -0.553750 H 3.275454 -1.148739 -0.559686 H -3.291949 -1.169954 -0.551293 H -3.289956 -1.166594 -0.551237 H -3.284529 -1.159209 -0.553750 H -3.275454 -1.148739 -0.559686 H -3.291949 1.169954 -0.551293 H -3.289956 1.166594 -0.551237 H -3.284529 1.159209 -0.553750 H -3.275454 1.148739 -0.559686 Cartesian Coordinates [Å] for 1,6-Methano[10]annulene, wB97X-D/6-311G(d,p) (continued)

2.5 Å 2.6 Å

117 C 0.000000 0.000000 1.186304 C 0.000000 0.000000 1.160751 C 0.000000 1.250000 0.308440 C 0.000000 1.300000 0.315145 C 1.264380 1.619372 -0.161322 C 1.269723 1.645695 -0.153278 C 2.318628 0.711172 -0.248212 C 2.304887 0.711801 -0.251912 C 2.318628 -0.711172 -0.248212 C 2.304887 -0.711801 -0.251912 C 1.264380 -1.619372 -0.161322 C 1.269723 -1.645695 -0.153278 C 0.000000 -1.250000 0.308440 C 0.000000 -1.300000 0.315145 C -1.264380 -1.619372 -0.161322 C -1.269723 -1.645695 -0.153278 C -2.318628 -0.711172 -0.248212 C -2.304887 -0.711801 -0.251912 C -2.318628 0.711172 -0.248212 C -2.304887 0.711801 -0.251912 C -1.264380 1.619372 -0.161322 C -1.269723 1.645695 -0.153278 H 0.886667 0.000000 1.821816 H 0.884053 0.000000 1.800348 H -0.886667 0.000000 1.821816 H -0.884053 0.000000 1.800348 H 1.417060 2.606551 -0.589934 H 1.448515 2.631486 -0.575125 H 1.417060 -2.606551 -0.589934 H 1.448515 -2.631486 -0.575125 H -1.417060 -2.606551 -0.589934 H -1.448515 -2.631486 -0.575125 H -1.417060 2.606551 -0.589934 H -1.448515 2.631486 -0.575125 H 3.265255 1.138426 -0.568546 H 3.253566 1.128815 -0.580469 H 3.265255 -1.138426 -0.568546 H 3.253566 -1.128815 -0.580469 H -3.265255 -1.138426 -0.568546 H -3.253566 -1.128815 -0.580469 H -3.265255 1.138426 -0.568546 H -3.253566 1.128815 -0.580469 Cartesian Coordinates [Å] for 1,6-Methano[10]annulene, wB97X-D/6-311G(d,p) (continued) Table 3: Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, wB97X-D/6-311G(d,p)

1.4 Å 1.5 Å 1.585 Å 1.6 Å C 0.363047 1.429246 0.737113 C 0.372355 1.420481 0.734272 C 0.379414 1.413032 0.731033 C 0.38086 1.41169 0.73040 C 0.363047 1.429246 -0.737113 C 0.372355 1.420481 -0.734272 C 0.379414 1.413032 -0.731033 C 0.38086 1.41169 -0.73040 C 0.363047 0.236974 1.374873 C 0.372355 0.231939 1.385222 C 0.379414 0.226752 1.393544 C 0.38086 0.22569 1.39480 C 0.363047 0.236974 -1.374873 C 0.372355 0.231939 -1.385222 C 0.379414 0.226752 -1.393544 C 0.38086 0.22569 -1.39480 C -0.042269 -1.013792 -0.700000 C -0.066268 -1.015474 -0.750000 C -0.087580 -1.014570 -0.792496 C -0.09161 -1.01445 -0.80000 C -0.042269 -1.013792 0.700000 C -0.066268 -1.015474 0.750000 C -0.087580 -1.014570 0.792496 C -0.09161 -1.01445 0.80000 C -1.366345 -1.092368 0.000000 C -1.361552 -1.065733 0.000000 C -1.354936 -1.045459 0.000000 C -1.35371 -1.04171 0.00000 H 0.982840 2.168207 1.241228 H 0.996358 2.162134 1.229207 H 1.006587 2.157034 1.218368 H 1.00851 2.15609 1.21655 H 0.982840 2.168207 -1.241228 H 0.996358 2.162134 -1.229207 H 1.006587 2.157034 -1.218368 H 1.00851 2.15609 -1.21655 H 0.673934 0.236974 2.415023 H 0.71911 0.231939 2.414152 H 0.761199 0.226752 2.410080 H 0.76772 0.22569 2.40945 H 0.673934 0.236974 -2.415023 H 0.71911 0.231939 -2.414152 H 0.761199 0.226752 -2.410080 H 0.76772 0.22569 -2.40945 H 0.267776 -1.918514 -1.216539 H 0.231268 -1.932122 -1.249891 H 0.202113 -1.940024 -1.279014 H 0.19629 -1.94074 -1.28570 H 0.267776 -1.918514 1.216539 H 0.231268 -1.932122 1.249891 H 0.202113 -1.940024 1.279014 H 0.19629 -1.94074 1.28570 H -1.981319 -0.201513 0.000000 H -1.967058 -0.166713 0.000000 H -1.954802 -0.141301 0.000000 H -1.95209 -0.13639 0.00000 H -1.875625 -2.046751 0.000000 H -1.898418 -2.006144 0.000000 H -1.910353 -1.976025 0.000000 H -1.91197 -1.97067 0.00000 Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, wB97X-D/6-311G(d,p)

1.7 Å 1.8 Å 1.9 Å 2.0 Å C 0.388778 1.402973 0.725277 C 0.395853 1.394739 0.718239 C 0.402297 1.388171 0.709453 C -0.407334 -1.385331 0.700136 C 0.388778 1.402973 -0.725277 C 0.395853 1.394739 -0.718239 C 0.402297 1.388171 -0.709453 C -0.407334 -1.385331 -0.700136 C 0.388778 0.217222 1.403501 C 0.395853 0.205754 1.411293 C 0.402297 0.191226 1.418776 C -0.407334 -0.176692 1.427545 C 0.388778 0.217222 -1.403501 C 0.395853 0.205754 -1.411293 C 0.402297 0.191226 -1.418776 C -0.407334 -0.176692 -1.427545

118 C -0.118324 -1.010516 -0.850000 C -0.14601 -1.003558 -0.900000 C -0.174054 -0.993952 -0.950000 C 0.199546 0.983707 -1.000000 C -0.118324 -1.010516 0.850000 C -0.14601 -1.003558 0.900000 C -0.174054 -0.993952 0.950000 C 0.199546 0.983707 1.000000 C -1.34276 -1.01911 0.000000 C -1.328044 -0.997975 0.000000 C -1.309852 -0.979574 0.000000 C 1.287587 0.969007 0.000000 H 1.019039 2.150305 1.203515 H 1.027006 2.145171 1.190561 H 1.032009 2.141902 1.178724 H -1.033342 -2.141949 1.170171 H 1.019039 2.150305 -1.203515 H 1.027006 2.145171 -1.190561 H 1.032009 2.141902 -1.178724 H -1.033342 -2.141949 -1.170171 H 0.820344 0.217222 2.399958 H 0.877666 0.205754 2.384414 H 0.937683 0.191226 2.363494 H -0.99101 -0.176692 2.343297 H 0.820344 0.217222 -2.399958 H 0.877666 0.205754 -2.384414 H 0.937683 0.191226 -2.363494 H -0.99101 -0.176692 -2.343297 H 0.161693 -1.945424 -1.322926 H 0.125486 -1.945049 -1.365183 H 0.08567 -1.938756 -1.416694 H -0.041818 1.926915 -1.481455 H 0.161693 -1.945424 1.322926 H 0.125486 -1.945049 1.365183 H 0.08567 -1.938756 1.416694 H -0.041818 1.926915 1.481455 H -1.935718 -0.108545 0.000000 H -1.915661 -0.082176 0.000000 H -1.894903 -0.060213 0.000000 H 1.876208 0.050006 0.000000 H -1.920659 -1.937143 0.000000 H -1.924734 -1.904945 0.000000 H -1.923191 -1.876445 0.000000 H 1.912071 1.859196 0.000000 Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, wB97X-D/6-311G(d,p) (continued)

2.1 Å 2.2 Å 2.3 Å 2.4 Å C 0.312659 -1.411315 0.692709 C 0.338585 -1.406316 0.687900 C 0.356963 -1.401872 0.684990 C 0.371394 -1.398461 0.682941 C 0.312659 -1.411315 -0.692709 C 0.338585 -1.406316 -0.687900 C 0.356963 -1.401872 -0.684990 C 0.371394 -1.398461 -0.682941 C -0.279135 -0.345143 1.438196 C -0.27835 -0.348007 1.451900 C -0.275105 -0.353123 1.469085 C -0.270332 -0.359339 1.487964 C -0.279135 -0.345143 -1.438196 C -0.27835 -0.348007 -1.451900 C -0.275105 -0.353123 -1.469085 C -0.270332 -0.359339 -1.487964 C -0.279135 0.959917 -1.050000 C -0.27835 0.956893 -1.100000 C -0.275105 0.954279 -1.150000 C -0.270332 0.951323 -1.200000 C -0.279135 0.959917 1.050000 C -0.27835 0.956893 1.100000 C -0.275105 0.954279 1.150000 C -0.270332 0.951323 1.200000 C 0.633637 1.460048 0.000000 C 0.577498 1.464777 0.000000 C 0.525437 1.470361 0.000000 C 0.476014 1.477602 0.000000 H 0.136886 -2.376507 1.165162 H 0.18537 -2.375222 1.161065 H 0.217489 -2.374515 1.155306 H 0.241025 -2.373914 1.150422 H 0.136886 -2.376507 -1.165162 H 0.18537 -2.375222 -1.161065 H 0.217489 -2.374515 -1.155306 H 0.241025 -2.373914 -1.150422 H -0.816373 -0.643345 2.333793 H -0.81926 -0.663328 2.339737 H -0.811812 -0.67659 2.356691 H -0.80099 -0.687056 2.378006 H -0.816373 -0.643345 -2.333793 H -0.81926 -0.663328 -2.339737 H -0.811812 -0.67659 -2.356691 H -0.80099 -0.687056 -2.378006 H -0.92575 1.671488 -1.556543 H -0.911947 1.658633 -1.636362 H -0.890502 1.648129 -1.716701 H -0.865055 1.639623 -1.794266 H -0.92575 1.671488 1.556543 H -0.911947 1.658633 1.636362 H -0.890502 1.648129 1.716701 H -0.865055 1.639623 1.794266 H 1.601988 0.953164 0.000000 H 1.564496 0.991046 0.000000 H 1.531556 1.034589 0.000000 H 1.501752 1.087129 0.000000 H 0.754003 2.541764 0.000000 H 0.679577 2.549284 0.000000 H 0.604439 2.557791 0.000000 H 0.523439 2.567677 0.000000 Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene,w B97X-D/6-311G(d,p) (continued) 2.5 Å 2.6 Å C 0.383461 -1.392048 0.681897 C 0.422169 1.375432 0.681500 C 0.383461 -1.392048 -0.681897 C 0.422169 1.375432 -0.681500 C -0.26548 -0.365887 1.509583 C 0.422169 0.170732 1.532800 C -0.26548 -0.365887 -1.509583 C 0.422169 0.170732 -1.532800 C -0.26548 0.948242 -1.250000 C -0.295334 -0.93497 -1.300000 C -0.26548 0.948242 1.250000 C -0.295334 -0.93497 1.300000 C 0.430877 1.480556 0.000000 C -1.134402 -1.029712 0.000000 H 0.260321 -2.371377 1.143614 H 1.055168 2.138006 1.135255 H 0.260321 -2.371377 -1.143614 H 1.055168 2.138006 -1.135255 H -0.788794 -0.696829 2.403052 H 1.039881 0.170732 2.427714 H -0.788794 -0.696829 -2.403052 H 1.039881 0.170732 -2.427714 H -0.840822 1.633539 -1.865589 H -0.200123 -1.813846 -1.929938 H -0.840822 1.633539 1.865589 H -0.200123 -1.813846 1.929938 H 1.472081 1.130127 0.000000 H -1.84936 -0.195197 0.000000 H 0.451234 2.572184 0.000000 H -1.722138 -1.950648 0.000000 Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, wB97X-D/6-311G(d,p) (continued) 119 Table 4: Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, B3LYP/6-311G(d,p)

1.4 Å 1.5 Å 1.6 Å 1.636 Å C 0.000000 0.000000 1.245990 C 0.000000 0.000000 0.000000 C 0.000000 0.000000 1.195560 C 0.000000 0.000000 1.185290 C -0.700000 0.000000 -0.114530 C 0.000000 -0.750000 1.324084 C -0.800000 0.000000 -0.097360 C -0.817920 0.000000 -0.092970 C -1.401210 1.236900 -0.576840 C 1.242756 -1.416117 1.799466 C -1.428820 1.242680 -0.586820 C -1.433400 1.242730 -0.588450 C -0.731550 2.320160 -0.977200 C 2.328069 -0.731436 2.173033 C -0.726990 2.332890 -0.929320 C -0.726000 2.334490 -0.920020 C 0.731550 2.320160 -0.977200 C 2.328069 0.731436 2.173033 C 0.726990 2.332890 -0.929320 C 0.726000 2.334490 -0.920020 C 1.401210 1.236900 -0.576840 C 1.242756 1.416117 1.799466 C 1.428820 1.242680 -0.586820 C 1.433400 1.242730 -0.588450 C 0.700000 0.000000 -0.114530 C 0.000000 0.750000 1.324084 C 0.800000 0.000000 -0.097360 C 0.817920 0.000000 -0.092970 C 1.401210 -1.236900 -0.576840 C -1.242756 1.416117 1.799466 C 1.428820 -1.242680 -0.586820 C 1.433400 -1.242730 -0.588450 C 0.731550 -2.320160 -0.977200 C -2.328069 0.731436 2.173033 C 0.726990 -2.332890 -0.929320 C 0.726000 -2.334490 -0.920020 C -0.731550 -2.320160 -0.977200 C -2.328069 -0.731436 2.173033 C -0.726990 -2.332890 -0.929320 C -0.726000 -2.334490 -0.920020 C -1.401210 -1.236900 -0.576840 C -1.242756 -1.416117 1.799466 C -1.428820 -1.242680 -0.586820 C -1.433400 -1.242730 -0.588450 C 0.000000 1.253490 2.089650 C 1.248521 0.000000 -0.855584 C 0.000000 1.244520 2.059310 C 0.000000 1.243070 2.052680 C 0.000000 -1.253490 2.089650 C -1.248521 0.000000 -0.855584 C 0.000000 -1.244520 2.059310 C 0.000000 -1.243070 2.052680 H -2.484840 1.201580 -0.628290 H 1.214922 -2.499060 1.894566 H -2.504670 1.218370 -0.736160 H -2.506560 1.219670 -0.757010 H 2.484840 1.201580 -0.628290 H 1.214922 2.499060 1.894566 H 2.504670 1.218370 -0.736160 H 2.506560 1.219670 -0.757010 H 2.484840 -1.201580 -0.628290 H -1.214922 2.499060 1.894566 H 2.504670 -1.218370 -0.736160 H 2.506560 -1.219670 -0.757010 H -2.484840 -1.201580 -0.628290 H -1.214922 -2.499060 1.894566 H -2.504670 -1.218370 -0.736160 H -2.506560 -1.219670 -0.757010 H -1.259540 3.198100 -1.331620 H 3.208029 -1.254607 2.533966 H -1.242990 3.212840 -1.297030 H -1.239680 3.214420 -1.291150 H 1.259540 3.198100 -1.331620 H 3.208029 1.254607 2.533966 H 1.242990 3.212840 -1.297030 H 1.239680 3.214420 -1.291150 H 1.259540 -3.198100 -1.331620 H -3.208029 1.254607 2.533966 H 1.242990 -3.212840 -1.297030 H 1.239680 -3.214420 -1.291150 H -1.259540 -3.198100 -1.331620 H -3.208029 -1.254607 2.533966 H -1.242990 -3.212840 -1.297030 H -1.239680 -3.214420 -1.291150 H 0.000000 2.172810 1.509040 H 2.173185 0.000000 -0.283185 H 0.000000 2.173810 1.496400 H 0.000000 2.173950 1.492760 H 0.884310 1.263530 2.735290 H 1.250768 0.884539 -1.501492 H 0.885130 1.239240 2.702610 H 0.885250 1.235200 2.695560 H -0.884310 1.263530 2.735290 H 1.250768 -0.884539 -1.501492 H -0.885130 1.239240 2.702610 H -0.885250 1.235200 2.695560 H 0.000000 -2.172810 1.509040 H -2.173185 0.000000 -0.283185 H 0.000000 -2.173810 1.496400 H 0.000000 -2.173950 1.492760 H 0.884310 -1.263530 2.735290 H -1.250768 0.884539 -1.501492 H 0.885130 -1.239240 2.702610 H 0.885250 -1.235200 2.695560 H -0.884310 -1.263530 2.735290 H -1.250768 -0.884539 -1.501492 H -0.885130 -1.239240 2.702610 H -0.885250 -1.235200 2.695560 120 Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, B3LYP/6-311G(d,p)

1.7 Å 1.8 Å 1.9 Å 2.0 Å C 0.000000 0.000000 0.000000 C 0.000000 0.000000 1.139080 C 0.000000 0.000000 0.000000 C 0.000000 0.000000 1.082170 C 0.000000 -0.850000 1.250571 C -0.900000 0.000000 -0.067970 C 0.000000 -0.950000 1.164391 C -1.000000 0.000000 -0.038090 C 1.244273 -1.442764 1.757133 C -1.455140 1.238040 -0.592360 C 1.235826 -1.471113 1.703951 C -1.488590 1.229200 -0.589570 C 2.336238 -0.726053 2.073581 C -0.720730 2.333440 -0.885380 C 2.330122 -0.719209 1.978146 C -0.714760 2.320930 -0.853130 C 2.336238 0.726053 2.073581 C 0.720730 2.333440 -0.885380 C 2.330122 0.719209 1.978146 C 0.714760 2.320930 -0.853130 C 1.244273 1.442764 1.757133 C 1.455140 1.238040 -0.592360 C 1.235826 1.471113 1.703951 C 1.488590 1.229200 -0.589570 C 0.000000 0.850000 1.250571 C 0.900000 0.000000 -0.067970 C 0.000000 0.950000 1.164391 C 1.000000 0.000000 -0.038090 C -1.244273 1.442764 1.757133 C 1.455140 -1.238040 -0.592360 C -1.235826 1.471113 1.703951 C 1.488590 -1.229200 -0.589570 C -2.336238 0.726053 2.073581 C 0.720730 -2.333440 -0.885380 C -2.330122 0.719209 1.978146 C 0.714760 -2.320930 -0.853130 C -2.336238 -0.726053 2.073581 C -0.720730 -2.333440 -0.885380 C -2.330122 -0.719209 1.978146 C -0.714760 -2.320930 -0.853130 C -1.244273 -1.442764 1.757133 C -1.455140 -1.238040 -0.592360 C -1.235826 -1.471113 1.703951 C -1.488590 -1.229200 -0.589570 C 1.239439 0.000000 -0.875693 C 0.000000 1.234760 2.027150 C 1.228866 0.000000 -0.900927 C 0.000000 1.224650 1.996450 C -1.239439 0.000000 -0.875693 C 0.000000 -1.234760 2.027150 C -1.228866 0.000000 -0.900927 C 0.000000 -1.224650 1.996450 H 1.224680 -2.512281 1.956631 H -2.510090 1.219530 -0.853500 H 1.224161 -2.514410 2.013695 H -2.515120 1.225650 -0.947790 H 1.224680 2.512281 1.956631 H 2.510090 1.219530 -0.853500 H 1.224161 2.514410 2.013695 H 2.515120 1.225650 -0.947790 H -1.224680 2.512281 1.956631 H 2.510090 -1.219530 -0.853500 H -1.224161 2.514410 2.013695 H 2.515120 -1.225650 -0.947790 H -1.224680 -2.512281 1.956631 H -2.510090 -1.219530 -0.853500 H -1.224161 -2.514410 2.013695 H -2.515120 -1.225650 -0.947790 H 3.216203 -1.236293 2.453322 H -1.223390 3.210940 -1.277510 H 3.206963 -1.214337 2.385188 H -1.200750 3.197130 -1.269770 H 3.216203 1.236293 2.453322 H 1.223390 3.210940 -1.277510 H 3.206963 1.214337 2.385188 H 1.200750 3.197130 -1.269770 H -3.216203 1.236293 2.453322 H 1.223390 -3.210940 -1.277510 H -3.206963 1.214337 2.385188 H 1.200750 -3.197130 -1.269770 H -3.216203 -1.236293 2.453322 H -1.223390 -3.210940 -1.277510 H -3.206963 -1.214337 2.385188 H -1.200750 -3.197130 -1.269770 H 2.174247 0.000000 -0.321788 H 0.000000 2.175630 1.485820 H 2.176871 0.000000 -0.371875 H 0.000000 2.177050 1.477450 H 1.226515 0.885289 -1.519359 H 0.885530 1.213100 2.668380 H 1.199229 0.885349 -1.543087 H 0.885270 1.188070 2.636650 H 1.226515 -0.885289 -1.519359 H -0.885530 1.213100 2.668380 H 1.199229 -0.885349 -1.543087 H -0.885270 1.188070 2.636650 H -2.174247 0.000000 -0.321788 H 0.000000 -2.175630 1.485820 H -2.176871 0.000000 -0.371875 H 0.000000 -2.177050 1.477450 H -1.226515 0.885289 -1.519359 H 0.885530 -1.213100 2.668380 H -1.199229 0.885349 -1.543087 H 0.885270 -1.188070 2.636650 H -1.226515 -0.885289 -1.519359 H -0.885530 -1.213100 2.668380 H -1.199229 -0.885349 -1.543087 H -0.885270 -1.188070 2.636650 Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, B3LYP/6-311G(d,p) (continued) 2.1 Å 2.12 Å 2.2 Å 2.3 Å C 0.000000 0.000000 0.000000 C 0.000000 0.000000 1.050027 C 0.000000 0.000000 1.029580 C 0.000000 0.000000 0.000000 C 0.000000 -1.050000 1.079272 C -1.060000 0.000000 -0.020866 C -1.100000 0.000000 -0.010350 C 0.000000 -1.150000 1.003730 C 1.227726 -1.509954 1.640519 C -1.514338 1.225886 -0.583236 C -1.533030 1.225120 -0.578190 C 1.226307 -1.557674 1.577960 C 2.311289 -0.713754 1.898642 C -0.712364 2.307546 -0.843071 C -0.711340 2.297420 -0.838630 C 2.284255 -0.711319 1.840521 C 2.311289 0.713754 1.898642 C 0.712364 2.307546 -0.843071 C 0.711340 2.297420 -0.838630 C 2.284255 0.711319 1.840521 C 1.227726 1.509954 1.640519 C 1.514338 1.225886 -0.583236 C 1.533030 1.225120 -0.578190 C 1.226307 1.557674 1.577960 C 0.000000 1.050000 1.079272 C 1.060000 0.000000 -0.020866 C 1.100000 0.000000 -0.010350 C 0.000000 1.150000 1.003730 C -1.227726 1.509954 1.640519 C 1.514338 -1.225886 -0.583236 C 1.533030 -1.225120 -0.578190 C -1.226307 1.557674 1.577960 C -2.311289 0.713754 1.898642 C 0.712364 -2.307546 -0.843071 C 0.711340 -2.297420 -0.838630 C -2.284255 0.711319 1.840521 C -2.311289 -0.713754 1.898642 C -0.712364 -2.307546 -0.843071 C -0.711340 -2.297420 -0.838630 C -2.284255 -0.711319 1.840521 C -1.227726 -1.509954 1.640519 C -1.514338 -1.225886 -0.583236 C -1.533030 -1.225120 -0.578190 C -1.226307 -1.557674 1.577960 C 1.218266 0.000000 -0.927617 C 0.000000 1.218674 1.979899 C 0.000000 1.215000 1.969270 C 1.209285 0.000000 -0.950756 C -1.218266 0.000000 -0.927617 C 0.000000 -1.218674 1.979899 C 0.000000 -1.215000 1.969270 C -1.209285 0.000000 -0.950756 H 1.238293 -2.526937 2.028685 H -2.527512 1.239520 -0.977869 H -2.539760 1.253020 -0.988510 H 1.273551 -2.559565 2.001577 H 1.238293 2.526937 2.028685 H 2.527512 1.239520 -0.977869 H 2.539760 1.253020 -0.988510 H 1.273551 2.559565 2.001577 H -1.238293 2.526937 2.028685 H 2.527512 -1.239520 -0.977869 H 2.539760 -1.253020 -0.988510 H -1.273551 2.559565 2.001577 H -1.238293 -2.526937 2.028685 H -2.527512 -1.239520 -0.977869 H -2.539760 -1.253020 -0.988510 H -1.273551 -2.559565 2.001577 H 3.187649 -1.190452 2.329424 H -1.186981 3.183911 -1.273147 H -1.178150 3.174310 -1.276670 H 3.161873 -1.167800 2.291475 H 3.187649 1.190452 2.329424 H 1.186981 3.183911 -1.273147 H 1.178150 3.174310 -1.276670 H 3.161873 1.167800 2.291475 H -3.187649 1.190452 2.329424 H 1.186981 -3.183911 -1.273147 H 1.178150 -3.174310 -1.276670 H -3.161873 1.167800 2.291475 H -3.187649 -1.190452 2.329424 H -1.186981 -3.183911 -1.273147 H -1.178150 -3.174310 -1.276670 H -3.161873 -1.167800 2.291475 H 2.177893 0.000000 -0.421612 H 0.000000 2.177528 1.473711 H 0.000000 2.178170 1.471580 H 2.179132 0.000000 -0.465329 H 1.174079 0.884822 -1.569143 H 0.884912 1.174428 2.619861 H 0.884630 1.166160 2.609210 H 1.154196 0.884056 -1.592352 H 1.174079 -0.884822 -1.569143 H -0.884912 1.174428 2.619861 H -0.884630 1.166160 2.609210 H 1.154196 -0.884056 -1.592352 H -2.177893 0.000000 -0.421612 H 0.000000 -2.177528 1.473711 H 0.000000 -2.178170 1.471580 H -2.179132 0.000000 -0.465329 H -1.174079 0.884822 -1.569143 H 0.884912 -1.174428 2.619861 H 0.884630 -1.166160 2.609210 H -1.154196 0.884056 -1.592352 H -1.174079 -0.884822 -1.569143 H -0.884912 -1.174428 2.619861 H -0.884630 -1.166160 2.609210 H -1.154196 -0.884056 -1.592352 Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, B3LYP/6-311G(d,p) (continued) 121

2.4 Å 2.5 Å 2.6 Å C 0.000000 0.000000 0.986330 C 0.000000 0.000000 0.000000 C 0.000000 0.000000 0.953760 C -1.200000 0.000000 0.014660 C 0.000000 -1.250000 0.941273 C -1.300000 0.000000 0.035920 C -1.582910 1.227100 -0.563660 C 1.230387 -1.608786 1.523842 C -1.633470 1.233020 -0.549390 C -0.710440 2.267630 -0.834640 C 2.251957 -0.711215 1.801603 C -0.711210 2.234470 -0.835790 C 0.710440 2.267630 -0.834640 C 2.251957 0.711215 1.801603 C 0.711210 2.234470 -0.835790 C 1.582910 1.227100 -0.563660 C 1.230387 1.608786 1.523842 C 1.633470 1.233020 -0.549390 C 1.200000 0.000000 0.014660 C 0.000000 1.250000 0.941273 C 1.300000 0.000000 0.035920 C 1.582910 -1.227100 -0.563660 C -1.230387 1.608786 1.523842 C 1.633470 -1.233020 -0.549390 C 0.710440 -2.267630 -0.834640 C -2.251957 0.711215 1.801603 C 0.711210 -2.234470 -0.835790 C -0.710440 -2.267630 -0.834640 C -2.251957 -0.711215 1.801603 C -0.711210 -2.234470 -0.835790 C -1.582910 -1.227100 -0.563660 C -1.230387 -1.608786 1.523842 C -1.633470 -1.233020 -0.549390 C 0.000000 1.207760 1.945030 C 1.202646 0.000000 -0.967413 C 0.000000 1.202420 1.925360 C 0.000000 -1.207760 1.945030 C -1.202646 0.000000 -0.967413 C 0.000000 -1.202420 1.925360 H -2.579750 1.296760 -0.993270 H 1.322564 -2.603265 1.957817 H -2.624310 1.349580 -0.983180 H 2.579750 1.296760 -0.993270 H 1.322564 2.603265 1.957817 H 2.624310 1.349580 -0.983180 H 2.579750 -1.296760 -0.993270 H -1.322564 2.603265 1.957817 H 2.624310 -1.349580 -0.983180 H -2.579750 -1.296760 -0.993270 H -1.322564 -2.603265 1.957817 H -2.624310 -1.349580 -0.983180 H -1.156720 3.145760 -1.292430 H 3.129368 -1.146667 2.274326 H -1.136670 3.112480 -1.314290 H 1.156720 3.145760 -1.292430 H 3.129368 1.146667 2.274326 H 1.136670 3.112480 -1.314290 H 1.156720 -3.145760 -1.292430 H -3.129368 1.146667 2.274326 H 1.136670 -3.112480 -1.314290 H -1.156720 -3.145760 -1.292430 H -3.129368 -1.146667 2.274326 H -1.136670 -3.112480 -1.314290 H 0.000000 2.178770 1.463140 H 2.179646 0.000000 -0.496713 H 0.000000 2.179010 1.455150 H 0.883890 1.151140 2.585390 H 1.140888 0.883348 -1.609470 H 0.883180 1.141210 2.566510 H -0.883890 1.151140 2.585390 H 1.140888 -0.883348 -1.609470 H -0.883180 1.141210 2.566510 H 0.000000 -2.178770 1.463140 H -2.179646 0.000000 -0.496713 H 0.000000 -2.179010 1.455150 H 0.883890 -1.151140 2.585390 H -1.140888 0.883348 -1.609470 H 0.883180 -1.141210 2.566510 H -0.883890 -1.151140 2.585390 H -1.140888 -0.883348 -1.609470 H -0.883180 -1.141210 2.566510 Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, B3LYP/6-311G(d,p) (continued) Table 5: Cartesian Coordinates [Å] for 1,6-Methano[10]annulene, B3LYP/6-311G(d,p)

1.4 Å 1.5 Å 1.6 Å 1.7 Å C 0.000000 0.000000 1.618885 C 0.000000 0.000000 1.580977 C 0.000000 0.000000 1.540013 C 0.000000 0.000000 1.496086 C 0.000000 0.700000 0.269526 C 0.000000 0.750000 0.268050 C 0.000000 0.800000 0.268085 C 0.000000 0.850000 0.269854 C 1.256086 1.405415 -0.136729 C 1.260510 1.419733 -0.146658 C 1.262351 1.432909 -0.157995 C 1.261575 1.445631 -0.168865 C 2.375866 0.731191 -0.430476 C 2.383385 0.728901 -0.402194 C 2.389225 0.726274 -0.370755 C 2.392172 0.723256 -0.338750 C 2.375866 -0.731191 -0.430476 C 2.383385 -0.728901 -0.402194 C 2.389225 -0.726274 -0.370755 C 2.392172 -0.723256 -0.338750 C 1.256086 -1.405415 -0.136729 C 1.260510 -1.419733 -0.146658 C 1.262351 -1.432909 -0.157995 C 1.261575 -1.445631 -0.168865 C 0.000000 -0.700000 0.269526 C 0.000000 -0.750000 0.268050 C 0.000000 -0.800000 0.268085 C 0.000000 -0.850000 0.269854 C -1.256086 -1.405415 -0.136729 C -1.260510 -1.419733 -0.146658 C -1.262351 -1.432909 -0.157995 C -1.261575 -1.445631 -0.168865 C -2.375866 -0.731191 -0.430476 C -2.383385 -0.728901 -0.402194 C -2.389225 -0.726274 -0.370755 C -2.392172 -0.723256 -0.338750 C -2.375866 0.731191 -0.430476 C -2.383385 0.728901 -0.402194 C -2.389225 0.726274 -0.370755 C -2.392172 0.723256 -0.338750 C -1.256086 1.405415 -0.136729 C -1.260510 1.419733 -0.146658 C -1.262351 1.432909 -0.157995 C -1.261575 1.445631 -0.168865 H 0.927835 0.000000 2.172397 H 0.923836 0.000000 2.143259 H 0.920972 0.000000 2.108851 H 0.917758 0.000000 2.072096 H -0.927835 0.000000 2.172397 H -0.923836 0.000000 2.143259 H -0.920972 0.000000 2.108851 H -0.917758 0.000000 2.072096 H 1.217005 2.487699 -0.204562 H 1.231148 2.498337 -0.267091 H 1.241053 2.503731 -0.338177 H 1.248087 2.503859 -0.413983 H 1.217005 -2.487699 -0.204562 H 1.231148 -2.498337 -0.267091 H 1.241053 -2.503731 -0.338177 H 1.248087 -2.503859 -0.413983 H -1.217005 -2.487699 -0.204562 H -1.231148 -2.498337 -0.267091 H -1.241053 -2.503731 -0.338177 H -1.248087 -2.503859 -0.413983 H -1.217005 2.487699 -0.204562 H -1.231148 2.498337 -0.267091 H -1.241053 2.503731 -0.338177 H -1.248087 2.503859 -0.413983 H 3.280007 1.257546 -0.715311 H 3.291398 1.248833 -0.687045 H 3.300456 1.239458 -0.658024 H 3.306440 1.229039 -0.630066 H 3.280007 -1.257546 -0.715311 H 3.291398 -1.248833 -0.687045 H 3.300456 -1.239458 -0.658024 H 3.306440 -1.229039 -0.630066 H -3.280007 -1.257546 -0.715311 H -3.291398 -1.248833 -0.687045 H -3.300456 -1.239458 -0.658024 H -3.306440 -1.229039 -0.630066 H -3.280007 1.257546 -0.715311 H -3.291398 1.248833 -0.687045 H -3.300456 1.239458 -0.658024 H -3.306440 1.229039 -0.630066 Cartesian Coordinates [Å] for 1,6-Methano[10]annulene, B3LYP/6-311G(d,p) 122 1.8 Å 1.9 Å 2.0 Å 2.1 Å C 0.000000 0.000000 1.449543 C 0.000000 0.000000 1.404155 C 0.000000 0.000000 1.361026 C 0.000000 0.000000 1.320972 C 0.000000 0.900000 0.271738 C 0.000000 0.950000 0.275038 C 0.000000 1.000000 0.278423 C 0.000000 1.050000 0.283033 C 1.258895 1.459498 -0.178247 C 1.255900 1.475866 -0.183762 C 1.254202 1.495112 -0.186153 C 1.254174 1.517396 -0.185213 C 2.391803 0.720089 -0.308383 C 2.387925 0.717147 -0.284170 C 2.382051 0.714900 -0.266207 C 2.373882 0.713273 -0.254753 C 2.391803 -0.720089 -0.308383 C 2.387925 -0.717147 -0.284170 C 2.382051 -0.714900 -0.266207 C 2.373882 -0.713273 -0.254753 C 1.258895 -1.459498 -0.178247 C 1.255900 -1.475866 -0.183762 C 1.254202 -1.495112 -0.186153 C 1.254174 -1.517396 -0.185213 C 0.000000 -0.900000 0.271738 C 0.000000 -0.950000 0.275038 C 0.000000 -1.000000 0.278423 C 0.000000 -1.050000 0.283033 C -1.258895 -1.459498 -0.178247 C -1.255900 -1.475866 -0.183762 C -1.254202 -1.495112 -0.186153 C -1.254174 -1.517396 -0.185213 C -2.391803 -0.720089 -0.308383 C -2.387925 -0.717147 -0.284170 C -2.382051 -0.714900 -0.266207 C -2.373882 -0.713273 -0.254753 C -2.391803 0.720089 -0.308383 C -2.387925 0.717147 -0.284170 C -2.382051 0.714900 -0.266207 C -2.373882 0.713273 -0.254753 C -1.258895 1.459498 -0.178247 C -1.255900 1.475866 -0.183762 C -1.254202 1.495112 -0.186153 C -1.254174 1.517396 -0.185213 H 0.914398 0.000000 2.032778 H 0.910391 0.000000 1.995835 H 0.906244 0.000000 1.960871 H 0.901960 0.000000 1.929150 H -0.914398 0.000000 2.032778 H -0.910391 0.000000 1.995835 H -0.906244 0.000000 1.960871 H -0.901960 0.000000 1.929150 H 1.256363 2.501504 -0.485895 H 1.267917 2.501080 -0.543451 H 1.284410 2.506494 -0.582485 H 1.305947 2.518634 -0.604940 H 1.256363 -2.501504 -0.485895 H 1.267917 -2.501080 -0.543451 H 1.284410 -2.506494 -0.582485 H 1.305947 -2.518634 -0.604940 H -1.256363 -2.501504 -0.485895 H -1.267917 -2.501080 -0.543451 H -1.284410 -2.506494 -0.582485 H -1.305947 -2.518634 -0.604940 H -1.256363 2.501504 -0.485895 H -1.267917 2.501080 -0.543451 H -1.284410 2.506494 -0.582485 H -1.305947 2.518634 -0.604940 H 3.310621 1.217710 -0.600241 H 3.310996 1.206136 -0.578218 H 3.310296 1.194427 -0.560601 H 3.306977 1.183255 -0.550398 H 3.310621 -1.217710 -0.600241 H 3.310996 -1.206136 -0.578218 H 3.310296 -1.194427 -0.560601 H 3.306977 -1.183255 -0.550398 H -3.310621 -1.217710 -0.600241 H -3.310996 -1.206136 -0.578218 H -3.310296 -1.194427 -0.560601 H -3.306977 -1.183255 -0.550398 H -3.310621 1.217710 -0.600241 H -3.310996 1.206136 -0.578218 H -3.310296 1.194427 -0.560601 H -3.306977 1.183255 -0.550398 Cartesian Coordinates [Å] for 11,11-Dimethyl-1,6-methano[10]annulene, B3LYP/6-311G(d,p) (continued) 2.2 Å 2.279 Å 2.3 Å 2.4 Å C 0.000000 0.000000 1.282929 C 0.000000 0.000000 1.254190 C 0.000000 0.000000 1.248343 C 0.000000 0.000000 1.214866 C 0.000000 1.100000 0.287619 C 0.000000 1.139419 0.291432 C 0.000000 1.150000 0.293137 C 0.000000 1.200000 0.298820 C 1.256160 1.542239 -0.181279 C 1.258635 1.562522 -0.177451 C 1.259310 1.568001 -0.175988 C 1.263635 1.594683 -0.169180 C 2.364211 0.712321 -0.248853 C 2.355983 0.711955 -0.245438 C 2.353477 0.711931 -0.245809 C 2.341719 0.712009 -0.245448 C 2.364211 -0.712321 -0.248853 C 2.355983 -0.711955 -0.245438 C 2.353477 -0.711931 -0.245809 C 2.341719 -0.712009 -0.245448 C 1.256160 -1.542239 -0.181279 C 1.258635 -1.562522 -0.177451 C 1.259310 -1.568001 -0.175988 C 1.263635 -1.594683 -0.169180 C 0.000000 -1.100000 0.287619 C 0.000000 -1.139419 0.291432 C 0.000000 -1.150000 0.293137 C 0.000000 -1.200000 0.298820 C -1.256160 -1.542239 -0.181279 C -1.258635 -1.562522 -0.177451 C -1.259310 -1.568001 -0.175988 C -1.263635 -1.594683 -0.169180 C -2.364211 -0.712321 -0.248853 C -2.355983 -0.711955 -0.245438 C -2.353477 -0.711931 -0.245809 C -2.341719 -0.712009 -0.245448 C -2.364211 0.712321 -0.248853 C -2.355983 0.711955 -0.245438 C -2.353477 0.711931 -0.245809 C -2.341719 0.712009 -0.245448 C -1.256160 1.542239 -0.181279 C -1.258635 1.562522 -0.177451 C -1.259310 1.568001 -0.175988 C -1.263635 1.594683 -0.169180 H 0.897629 0.000000 1.898998 H 0.894179 0.000000 1.876304 H 0.893637 0.000000 1.871351 H 0.889214 0.000000 1.845232 H -0.897629 0.000000 1.898998 H -0.894179 0.000000 1.876304 H -0.893637 0.000000 1.871351 H -0.889214 0.000000 1.845232 H 1.332231 2.537620 -0.611442 H 1.354465 2.554430 -0.611930 H 1.360218 2.559289 -0.610717 H 1.390650 2.583952 -0.601913 H 1.332231 -2.537620 -0.611442 H 1.354465 -2.554430 -0.611930 H 1.360218 -2.559289 -0.610717 H 1.390650 -2.583952 -0.601913 H -1.332231 -2.537620 -0.611442 H -1.354465 -2.554430 -0.611930 H -1.360218 -2.559289 -0.610717 H -1.390650 -2.583952 -0.601913 H -1.332231 2.537620 -0.611442 H -1.354465 2.554430 -0.611930 H -1.360218 2.559289 -0.610717 H -1.390650 2.583952 -0.601913 H 3.302490 1.172539 -0.544514 H 3.297643 1.163577 -0.544471 H 3.295632 1.161767 -0.546103 H 3.287186 1.151381 -0.551693 H 3.302490 -1.172539 -0.544514 H 3.297643 -1.163577 -0.544471 H 3.295632 -1.161767 -0.546103 H 3.287186 -1.151381 -0.551693 H -3.302490 -1.172539 -0.544514 H -3.297643 -1.163577 -0.544471 H -3.295632 -1.161767 -0.546103 H -3.287186 -1.151381 -0.551693 H -3.302490 1.172539 -0.544514 H -3.297643 1.163577 -0.544471 H -3.295632 1.161767 -0.546103 H -3.287186 1.151381 -0.551693 Cartesian Coordinates [Å] for 1,6-Methano[10]annulene, B3LYP/6-311G(d,p) (continued)

2.5 Å 2.6 Å

123 C 0.000000 0.000000 1.184879 C 0.000000 0.000000 1.159101 C 0.000000 1.250000 0.304056 C 0.000000 1.300000 0.309953 C 1.268908 1.621298 -0.161913 C 1.274557 1.647579 -0.154103 C 2.329613 0.712445 -0.246721 C 2.316560 0.713165 -0.250037 C 2.329613 -0.712445 -0.246721 C 2.316560 -0.713165 -0.250037 C 1.268908 -1.621298 -0.161913 C 1.274557 -1.647579 -0.154103 C 0.000000 -1.250000 0.304056 C 0.000000 -1.300000 0.309953 C -1.268908 -1.621298 -0.161913 C -1.274557 -1.647579 -0.154103 C -2.329613 -0.712445 -0.246721 C -2.316560 -0.713165 -0.250037 C -2.329613 0.712445 -0.246721 C -2.316560 0.713165 -0.250037 C -1.268908 1.621298 -0.161913 C -1.274557 1.647579 -0.154103 H 0.886102 0.000000 1.820078 H 0.883298 0.000000 1.798342 H -0.886102 0.000000 1.820078 H -0.883298 0.000000 1.798342 H 1.422709 2.609166 -0.589259 H 1.454970 2.634536 -0.573362 H 1.422709 -2.609166 -0.589259 H 1.454970 -2.634536 -0.573362 H -1.422709 -2.609166 -0.589259 H -1.454970 -2.634536 -0.573362 H -1.422709 2.609166 -0.589259 H -1.454970 2.634536 -0.573362 H 3.278295 1.141482 -0.558459 H 3.267495 1.132001 -0.569478 H 3.278295 -1.141482 -0.558459 H 3.267495 -1.132001 -0.569478 H -3.278295 -1.141482 -0.558459 H -3.267495 -1.132001 -0.569478 H -3.278295 1.141482 -0.558459 H -3.267495 1.132001 -0.569478 Cartesian Coordinates [Å] for 1,6-Methano[10]annulene, B3LYP/6-311G(d,p) (continued) Table 6: Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, B3LYP/6-311G(d,p)

1.4 Å 1.5 Å 1.6 Å 1.645 Å C 0.358373 1.440754 0.735826 C 0.368403 1.431294 0.732839 C 0.376994 1.422571 0.728908 C 0.380218 1.418468 0.726767 C 0.358373 1.440754 -0.735826 C 0.368403 1.431294 -0.732839 C 0.376994 1.422571 -0.728908 C 0.380218 1.418468 -0.726767 C 0.358373 0.242427 1.377811 C 0.368403 0.236188 1.387717 C 0.376994 0.229124 1.396728 C 0.380218 0.225469 1.400740 C 0.358373 0.242427 -1.377811 C 0.368403 0.236188 -1.387717 C 0.376994 0.229124 -1.396728 C 0.380218 0.225469 -1.400740 C -0.033783 -1.011663 -0.700000 C -0.059358 -1.013336 -0.750000 C -0.085733 -1.012365 -0.800000 C -0.097834 -1.010978 -0.822721 C -0.033783 -1.011663 0.700000 C -0.059358 -1.013336 0.750000 C -0.085733 -1.012365 0.800000 C -0.097834 -1.010978 0.822721 C -1.366913 -1.123433 0.000000 C -1.362100 -1.093298 0.000000 C -1.353085 -1.067814 0.000000 C -1.347046 -1.056799 0.000000 H 0.976044 2.180925 1.239096 H 0.990023 2.174196 1.227145 H 1.001721 2.168150 1.215151 H 1.006236 2.165306 1.209385 H 0.976044 2.180925 -1.239096 H 0.990023 2.174196 -1.227145 H 1.001721 2.168150 -1.215151 H 1.006236 2.165306 -1.209385 H 0.664823 0.242427 2.418027 H 0.713248 0.236188 2.416077 H 0.764375 0.229124 2.410008 H 0.789419 0.225469 2.405421 H 0.664823 0.242427 -2.418027 H 0.713248 0.236188 -2.416077 H 0.764375 0.229124 -2.410008 H 0.789419 0.225469 -2.405421 H 0.290292 -1.909821 -1.219722 H 0.251081 -1.924034 -1.252509 H 0.215516 -1.933384 -1.286760 H 0.200052 -1.936655 -1.301979 H 0.290292 -1.909821 1.219722 H 0.251081 -1.924034 1.252509 H 0.215516 -1.933384 1.286760 H 0.200052 -1.936655 1.301979 H -2.008115 -0.253294 0.000000 H -1.993889 -0.214569 0.000000 H -1.977484 -0.182044 0.000000 H -1.969387 -0.168676 0.000000 H -1.848283 -2.091381 0.000000 H -1.871601 -2.048109 0.000000 H -1.886289 -2.010820 0.000000 H -1.890989 -1.994277 0.000000 Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, B3LYP/6-311G(d,p)

1.7 Å 1.8 Å 1.9 Å 2.0 Å C 0.384324 1.414264 0.723843 C 0.391302 1.406511 0.717663 C 0.397378 1.400373 0.710698 C 0.402877 1.396110 0.703868 C 0.384324 1.414264 -0.723843 C 0.391302 1.406511 -0.717663 C 0.397378 1.400373 -0.710698 C 0.402877 1.396110 -0.703868 C 0.384324 0.220631 1.404844 C 0.391302 0.209600 1.412578 C 0.397378 0.197308 1.420545 C 0.402877 0.185621 1.429886 C 0.384324 0.220631 -1.404844 C 0.391302 0.209600 -1.412578 C 0.397378 0.197308 -1.420545 C 0.402877 0.185621 -1.429886

124 C -0.112795 -1.008540 -0.850000 C -0.140802 -1.002426 -0.900000 C -0.167963 -0.994680 -0.950000 C -0.193165 -0.986272 -1.000000 C -0.112795 -1.008540 0.850000 C -0.140802 -1.002426 0.900000 C -0.167963 -0.994680 0.950000 C -0.193165 -0.986272 1.000000 C -1.340098 -1.045610 0.000000 C -1.324396 -1.024464 0.000000 C -1.305286 -1.007331 0.000000 C -1.283599 -0.995950 0.000000 H 1.011143 2.162455 1.203232 H 1.018730 2.157486 1.191905 H 1.023862 2.154074 1.182042 H 1.027419 2.152111 1.174465 H 1.011143 2.162455 -1.203232 H 1.018730 2.157486 -1.191905 H 1.023862 2.154074 -1.182042 H 1.027419 2.152111 -1.174465 H 0.818583 0.220631 2.399009 H 0.875996 0.209600 2.383227 H 0.930897 0.197308 2.365348 H 0.976319 0.185621 2.351200 H 0.818583 0.220631 -2.399009 H 0.875996 0.209600 -2.383227 H 0.930897 0.197308 -2.365348 H 0.976319 0.185621 -2.351200 H 0.182358 -1.938147 -1.322889 H 0.146439 -1.938298 -1.365449 H 0.107630 -1.933297 -1.418041 H 0.065198 -1.924015 -1.480828 H 0.182358 -1.938147 1.322889 H 0.146439 -1.938298 1.365449 H 0.107630 -1.933297 1.418041 H 0.065198 -1.924015 1.480828 H -1.959827 -0.154665 0.000000 H -1.940149 -0.128799 0.000000 H -1.919553 -0.108521 0.000000 H -1.900487 -0.096629 0.000000 H -1.893996 -1.977803 0.000000 H -1.897433 -1.946205 0.000000 H -1.895037 -1.919670 0.000000 H -1.886850 -1.900622 0.000000 Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, B3LYP/6-311G(d,p) (continued)

2.1 Å 2.2 Å 2.3 Å 2.4 Å C -0.300490 1.421542 0.698285 C -0.325592 1.416225 0.693878 C -0.344327 1.410838 0.691049 C -0.360303 1.405323 0.689071 C -0.300490 1.421542 -0.698285 C -0.325592 1.416225 -0.693878 C -0.344327 1.410838 -0.691049 C -0.360303 1.405323 -0.689071 C 0.273828 0.349347 1.441251 C 0.272434 0.352844 1.454640 C 0.269374 0.357822 1.471551 C 0.265468 0.363898 1.490213 C 0.273828 0.349347 -1.441251 C 0.272434 0.352844 -1.454640 C 0.269374 0.357822 -1.471551 C 0.265468 0.363898 -1.490213 C 0.273828 -0.963718 -1.050000 C 0.272434 -0.960491 -1.100000 C 0.269374 -0.957632 -1.150000 C 0.265468 -0.954565 -1.200000 C 0.273828 -0.963718 1.050000 C 0.272434 -0.960491 1.100000 C 0.269374 -0.957632 1.150000 C 0.265468 -0.954565 1.200000 C -0.638432 -1.472319 0.000000 C -0.583195 -1.477850 0.000000 C -0.532533 -1.482373 0.000000 C -0.483139 -1.487240 0.000000 H -0.109084 2.383826 1.168465 H -0.155369 2.382822 1.163798 H -0.188239 2.381591 1.158008 H -0.215409 2.379978 1.151894 H -0.109084 2.383826 -1.168465 H -0.155369 2.382822 -1.163798 H -0.188239 2.381591 -1.158008 H -0.215409 2.379978 -1.151894 H 0.799559 0.630953 2.348250 H 0.803280 0.651382 2.353419 H 0.798665 0.666295 2.368376 H 0.789101 0.678538 2.388434 H 0.799559 0.630953 -2.348250 H 0.803280 0.651382 -2.353419 H 0.798665 0.666295 -2.368376 H 0.789101 0.678538 -2.388434 H 0.922768 -1.672527 -1.554701 H 0.910790 -1.659182 -1.632171 H 0.891410 -1.649221 -1.709824 H 0.868263 -1.641087 -1.785940 H 0.922768 -1.672527 1.554701 H 0.910790 -1.659182 1.632171 H 0.891410 -1.649221 1.709824 H 0.868263 -1.641087 1.785940 H -1.614245 -0.981503 0.000000 H -1.578218 -1.022409 0.000000 H -1.545728 -1.064882 0.000000 H -1.513378 -1.109959 0.000000 H -0.747637 -2.555143 0.000000 H -0.671329 -2.563465 0.000000 H -0.595804 -2.570547 0.000000 H -0.519293 -2.577319 0.000000 Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, B3LYP/6-311G(d,p) (continued) 2.5 Å 2.6 Å C -0.373444 1.398721 0.687934 C 0.417990 1.381568 0.687381 C -0.373444 1.398721 -0.687934 C 0.417990 1.381568 -0.687381 C 0.260943 0.370613 1.511167 C 0.417990 0.182671 1.533596 C 0.260943 0.370613 -1.511167 C 0.417990 0.182671 -1.533596 C 0.260943 -0.951311 -1.250000 C -0.289624 -0.938191 -1.300000 C 0.260943 -0.951311 1.250000 C -0.289624 -0.938191 1.300000 C -0.438044 -1.490966 0.000000 C -1.133680 -1.050715 0.000000 H -0.236909 2.377620 1.144759 H 1.053340 2.143285 1.137018 H -0.236909 2.377620 -1.144759 H 1.053340 2.143285 -1.137018 H 0.778749 0.690121 2.411355 H 1.025243 0.182671 2.435067 H 0.778749 0.690121 -2.411355 H 1.025243 0.182671 -2.435067 H 0.845725 -1.634452 -1.856927 H -0.172543 -1.818400 -1.922382 H 0.845725 -1.634452 1.856927 H -0.172543 -1.818400 1.922382 H -1.483310 -1.154836 0.000000 H -1.870825 -0.236627 0.000000 H -0.444844 -2.582219 0.000000 H -1.695455 -1.986766 0.000000 Cartesian Coordinates [Å] for 1,3,5-Cycloheptatriene/Norcaradiene, B3LYP/6-311G(d,p) (continued) 125 Table 7: Relative energies [kcal/mol] for 11,11-Dimethyl-1,6-methano[10]annulene at all Geometries and all Levels of Theory

C1,C6 HF SVWN5 BLYP B97 B3LYP wB97 wB97X wB97X-D REKS/ B2P-LYP-D MP2 MP3 MP4(SDQ) MP4(SDTQ) CCSD BD CCSD(T) BD(T) CASSCF CASPT2 NEVPT2 CASPT2 Å wB97X-D (10,10) (10,10) (10,10) (14,14) 1.4 -1.75 - 18.76 - 14.34 8.96 9.09 8.72 8.72 9.13 19.03 6.14 3.99 14.61 4.97 5.01 10.16 10.17 0.63 9.72 6.39 11.22 1.5 -8.44 - 10.28 - 6.44 0.00 0.00 1.16 1.16 1.73 10.28 -1.52 -3.53 6.19 -2.68 -2.64 2.05 2.06 -7.25 1.44 -1.60 3.16 1.6 -8.84 7.53 - 3.36 3.76 0.03 0.00 -0.99 -0.99 -0.11 6.65 -3.20 -5.06 3.28 -4.36 -4.32 -0.31 -0.31 -8.56 -1.44 -4.12 0.98 1.636 -8.19 3.78 6.24 2.93 3.40 - - -1.10 ------4.19 -4.15 -0.43 -0.44 -8.14 -1.83 -4.36 0.87 1.7 -6.57 3.22 - 2.77 3.16 - - -0.88 -0.88 0.29 4.96 -2.27 -3.92 2.62 -3.40 -3.36 -0.21 -0.22 -6.79 0.47 -0.18 1.01 1.8 -3.88 2.49 4.56 2.45 2.84 3.76 2.46 -0.28 -0.28 0.92 3.62 -0.95 -2.30 2.31 -1.86 -1.83 0.40 0.39 -4.17 0.75 -1.72 1.28 1.9 -1.91 1.59 3.17 1.75 2.08 - - -0.01 -0.01 0.95 2.20 -0.21 -1.20 1.67 -0.75 -0.75 0.59 0.59 -2.02 0.90 -3.08 1.07 2.0 -0.80 - - 0.78 0.95 7.03 4.28 -0.06 -0.06 0.44 0.91 -0.12 -0.68 0.79 -0.28 -0.28 0.32 0.32 -0.74 0.41 -4.78 0.48 2.1 0.00 0.00 0.00 0.00 -0.11 - - 0.00 0.00 0.00 0.10 -0.13 -0.29 0.11 0.00 0.00 0.00 0.00 0.00 0.00 -5.39 0.00 2.2 1.30 0.25 -0.72 0.10 -0.16 9.26 5.86 0.71 0.71 0.33 0.18 0.41 0.59 0.12 0.73 0.74 0.24 0.24 0.96 - -5.01 0.19 2.3 3.79 1.76 -0.23 - 0.94 - - 2.53 2.53 1.99 1.51 2.07 2.50 1.27 2.50 2.52 1.56 1.56 2.83 1.63 -3.36 1.56 2.4 7.92 4.80 - - 3.62 15.08 11.51 5.85 5.85 5.33 4.37 5.24 5.83 3.86 5.71 5.75 4.32 4.32 6.09 4.51 -0.20 4.42 2.5 13.93 9.50 5.42 - 8.03 - - 10.85 10.85 10.53 8.88 10.14 10.80 8.06 10.58 10.64 8.73 8.73 11.06 9.07 4.62 8.97 2.6 21.89 15.92 10.73 - 14.21 27.37 23.74 17.61 17.61 17.60 15.11 16.84 17.50 13.94 17.20 17.29 14.84 14.85 17.85 15.37 11.14 15.25

Table 8: Thermodynamic Parameters [kcal/mol] for 11,11-Dimethyl-1,6-methano[10]annulene at all Geometries and Higher 126 Levels of Theory

C1,C6 CCSD(T) CASPT2(14,14) estimate B2P-LYP-D CCSD(T) BD(T) CASPT2(14,14) estimate B2P-LYP-D CCSD(T) BD(T) CASPT2(14,14) estimate Å D E D E D E D H D H D H D H D H D G D G D G D G D G 1.4 10.16 11.22 10.69 16.14 10.45 10.47 11.50 10.97 15.40 9.77 9.79 10.86 10.33 1.5 2.05 3.16 2.61 7.68 2.10 2.10 3.19 2.64 7.17 1.64 1.64 2.77 2.22 1.6 -0.31 0.98 0.34 4.47 -0.48 -0.48 0.80 0.16 4.04 -0.87 -0.87 0.45 -0.20 1.636 -0.43 0.87 0.22 - -0.67 -0.68 0.62 -0.03 - -1.10 -1.11 0.23 -0.42 1.7 -0.21 1.01 0.40 3.42 - - - - 2.64 - - - - 1.8 0.40 1.28 0.84 2.26 -0.45 -0.45 0.43 -0.01 2.44 -0.25 -0.25 0.66 0.22 1.9 0.59 1.07 0.83 1.38 -0.15 -0.15 0.32 0.08 1.68 0.15 0.15 0.65 0.41 2.0 0.32 0.48 0.40 0.86 - - - - 0.49 - - - - 2.1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.2 0.24 0.19 0.22 -0.09 0.25 0.25 0.20 0.22 0.05 0.35 0.35 0.33 0.36 2.3 1.56 1.56 1.56 1.04 1.50 1.50 1.49 1.49 1.24 1.66 1.66 1.68 1.68 2.4 4.32 4.42 4.37 3.70 4.13 4.13 4.22 4.17 3.93 4.31 4.30 4.43 4.38 2.5 8.73 8.97 8.85 8.06 8.35 8.35 8.58 8.46 8.27 8.52 8.52 8.78 8.66 2.6 14.84 15.25 15.05 14.12 14.23 14.23 14.62 14.42 14.31 14.36 14.36 14.79 14.59 Table 9: Relative energies [kcal/mol] for 1,6-Methano[10]annulene at all Geometries and all Levels of Theory

C1,C6 HF B3LYP wB97 wB97X wB97X-D B2P-LYP-D MP2 MP3 MP4(SDQ) MP4(SDTQ) CCSD BD CCSD(T) BD(T) CASSCF CASPT2 NEVPT2 CASPT2 Å (10,10) (10,10) (10,10) (14,14) 1.4 7.70 24.99 12.35 8.49 17.39 18.96 27.11 14.07 11.29 22.33 12.65 12.68 18.04 18.09 10.19 17.16 28.84 22.69 1.5 1.00 16.91 - - 9.73 11.48 18.34 6.27 3.63 13.88 5.02 5.05 9.97 10.01 3.76 8.93 20.32 14.75 1.6 0.17 13.68 2.83 -0.76 7.13 9.17 14.37 4.13 1.65 10.63 3.06 3.10 7.34 7.37 4.66 5.68 15.25 11.94 1.7 1.62 12.14 - - 6.42 8.68 11.95 4.27 2.03 9.29 3.39 3.42 6.82 6.84 6.36 4.34 11.69 11.48 1.8 2.97 10.46 3.35 1.17 5.75 7.97 9.45 4.56 2.68 8.00 3.88 3.89 6.40 6.41 7.99 3.16 8.62 10.80 1.9 3.03 8.01 - - 4.41 6.28 6.62 4.02 2.58 6.14 3.52 3.51 5.23 5.24 6.29 4.89 5.79 9.47 2.0 1.93 5.07 1.85 1.20 2.65 3.90 3.80 2.61 1.64 3.86 2.28 2.27 3.38 3.39 4.14 2.92 3.11 7.16 2.1 0.50 2.33 - - 1.00 1.59 1.49 1.01 0.46 1.71 0.83 0.81 1.47 1.47 1.87 1.07 0.96 2.09 2.2 -0.30 0.49 0.01 0.00 0.00 0.17 0.14 -0.02 -0.22 0.29 -0.08 -0.09 0.19 0.19 0.30 -0.01 -0.14 0.19 2.279 0.00 0.00 0.00 0.00 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 2.3 0.26 0.04 - - 0.36 0.20 0.13 0.17 0.21 0.08 0.18 0.18 0.10 0.10 0.10 0.17 0.22 0.17 2.4 2.61 1.29 2.73 2.92 2.30 2.05 1.76 1.98 2.18 1.43 2.01 2.03 1.59 1.59 1.68 1.95 2.31 1.80 2.5 7.04 4.45 - - 6.09 5.92 5.17 5.63 5.92 4.51 5.64 5.68 4.83 4.83 5.32 5.51 6.24 5.21 2.6 13.61 9.56 12.66 12.90 11.81 11.86 10.43 11.22 11.53 9.41 11.16 11.23 9.92 9.93 11.11 10.92 12.03 10.51

Table 10: Thermodynamic Parameters [kcal/mol] for 1,6-Methano[10]annulene at all Geometries and Higher Levels of Theory 127 C1,C6 B2P-LYP-D CCSD(T) BD(T) CASPT2(14,14) B2P-LYP-D CCSD(T) BD(T) CASPT2(14,14) Å D H D H D H D H D G D G D G D G 1.4 24.94 17.87 17.92 22.51 24.52 17.52 17.56 22.16 1.5 16.44 9.56 9.60 14.34 16.12 9.30 9.33 14.08 1.6 12.83 6.73 6.76 11.33 12.45 6.40 6.42 10.99 1.7 10.43 5.53 5.55 10.19 10.55 5.67 5.69 10.33 1.8 8.75 5.25 5.26 9.65 8.91 5.42 5.44 9.83 1.9 6.44 4.25 4.27 8.49 6.68 4.51 4.52 8.75 2.0 4.35 3.16 3.17 6.94 3.90 2.64 2.65 6.42 2.1 1.93 1.40 1.41 2.03 1.81 1.28 1.28 1.90 2.2 0.34 0.19 0.19 0.19 0.31 0.15 0.16 0.15 2.279 0.00 0.00 0.00 - 0.00 0.00 0.00 - 2.3 0.09 0.09 0.09 0.16 0.09 0.10 0.10 0.16 2.4 1.49 1.51 1.51 1.72 1.51 1.54 1.54 1.75 2.5 4.72 4.62 4.62 5.01 4.72 4.64 4.64 5.03 2.6 9.80 9.50 9.51 10.09 9.78 9.92 9.50 10.09 Table 11: Relative energies [kcal/mol] for Cycloheptatriene/Norcaradiene at all Geometries and all Levels of Theory

C1,C6 HF B3LYP wB97 wB97X wB97X-D REKS/ B2P-LYP-D MP2 MP3 MP4(SDQ) MP4(SDTQ) CCSD BD CCSD(T) BD(T) CASPT2 NEVPT2 CASPT2 Å w B97X-D (6,6) (6,6) (10,10) 1.4 14.78 17.26 8.15 10.49 10.49 - 15.59 13.08 13.40 13.09 14.61 13.41 13.34 14.60 14.60 11.72 - 15.35 1.5 8.05 9.74 - - 3.38 - 8.43 5.03 5.87 5.73 6.68 6.05 5.98 6.90 6.90 4.27 - 7.72 1.585 7.23 - -0.25 2.03 2.03 - - 2.66 4.33 4.35 4.60 4.65 4.58 5.11 5.10 - - 6.05 1.6 7.36 7.49 -0.15 2.06 - 0.00 6.81 2.49 4.33 4.38 4.50 4.68 4.61 5.06 5.05 3.10 2.77 6.04 1.61 ------1.645 - 7.34 - - 2.06 - 7.01 ------1.7 9.39 7.46 - - 3.37 - 7.52 2.21 5.55 5.80 4.80 6.02 5.96 5.81 5.79 2.89 - 7.02 1.8 11.78 7.70 4.22 5.18 5.18 0.35 8.47 2.20 7.36 7.82 5.53 7.89 7.82 7.02 7.00 3.68 2.56 8.23 1.9 12.67 7.16 - - 6.09 - 8.36 1.68 8.26 8.85 5.52 8.72 8.63 7.36 7.34 3.33 - 12.19 2.0 10.95 5.57 5.74 5.45 5.45 0.35 6.77 0.96 7.32 7.87 4.54 7.66 7.59 6.28 6.26 1.98 0.00 11.31 2.1 7.30 3.35 - - 3.54 - 4.21 0.24 4.88 5.27 2.89 5.15 5.10 4.15 4.13 0.35 - 5.98 2.2 3.53 1.27 1.73 1.44 1.44 - 1.66 -0.53 2.22 2.46 1.12 2.41 2.39 1.87 1.85 -1.10 - 1.54 2.3 0.90 0.00 - - 0.06 - 0.00 -0.82 0.40 0.51 -0.05 0.50 0.49 0.28 0.27 -1.83 - 0.00 2.4 0.00 0.00 0.00 0.00 0.00 - -0.21 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 0.26 2.5 1.20 1.58 - - 1.61 - 1.35 2.24 1.34 1.25 1.57 1.24 1.25 1.33 1.34 2.17 - 2.02 2.6 4.59 4.87 4.85 5.08 5.08 - 4.82 6.07 4.53 4.34 4.80 4.32 4.35 4.37 4.39 5.74 - 5.45 128 Table 12: Thermodynamic Parameters [kcal/mol] for Cycloheptatriene/Norcaradiene at all Geometries and Higher Levels of Theory

C1,C6 B2P-LYP-D CCSD(T) BD(T) CASPT2(10,10) B2P-LYP-D CCSD(T) BD(T) CASPT2(10,10) Å D H D H D H D H D G D G D G D G 1.4 17.11 14.85 14.86 15.77 17.23 15.03 15.04 15.92 1.5 9.13 6.86 6.86 7.85 - 9.43 7.21 7.21 8.16 1.585 - - - 6.04 - - - 6.34 1.6 6.52 4.78 4.79 5.89 6.80 5.10 5.11 6.18 1.61 ------1.645 6.24 - - - 6.41 - - - 1.7 6.24 4.52 4.52 6.78 5.99 4.25 4.25 6.47 1.8 5.93 4.70 4.70 7.30 6.48 5.28 5.28 7.84 1.9 5.54 6.00 5.99 11.35 6.09 6.58 6.57 11.89 2.0 4.19 6.42 6.42 10.56 4.72 6.98 6.97 11.08 2.1 2.86 6.03 6.02 5.91 2.25 5.46 5.45 5.30 2.2 1.09 4.00 3.99 1.56 1.05 4.00 3.99 1.53 2.3 0.00 1.69 1.68 0.00 0.00 1.73 1.72 0.00 2.4 0.09 0.00 0.00 0.15 0.06 0.00 0.00 0.11 2.5 1.66 -0.47 -0.46 1.72 1.57 -0.53 -0.52 1.62 2.6 4.89 0.62 0.64 4.92 4.72 0.48 0.51 4.75 Table 13: Electron Density, r(r) for 11,11-Dimethyl-1,6-methano[10]annulene [e/Å3]

C1,C6 [Å] C2C7 C1C2 C2C3 C3C4 C4C5 C1C2C7 1.4 2.005 1.511 1.739 2.304 1.835 1.348 1.5 1.628 1.531 1.769 2.291 1.848 1.288 1.6 1.325 1.560 1.800 2.275 1.863 1.214 1.636 1.234 1.573 1.812 2.268 1.869 1.182 1.67 1.159 1.585 1.824 2.260 1.875 1.145 1.675 1.145 1.587 1.826 2.259 1.876 1.139 1.68 1.139 1.589 1.828 2.258 1.877 1.133 1.69 1.120 1.593 1.831 2.256 1.878 1.120 1.7 - 1.579 1.824 2.237 1.883 - 1.8 - 1.636 1.872 2.228 1.900 - 2.0 - 1.681 1.947 2.171 1.937 - 2.030 - 1.683 1.958 2.161 1.942 - 2.2 - 1.668 1.999 2.121 1.957 - 2.4 - 1.589 2.028 2.084 1.960 - 2.6 - 1.460 2.042 2.057 1.950 -

Table 14: Energy Density for 11,11-Dimethyl-1,6-methano[10]annulene [Hartree/Å3]

C1,C6 [Å] C2C7 C1C2 C2C3 C3C4 C4C5 C1C2C7 1.4 -2.062 -1.179 -1.473 -2.630 -1.655 -0.818 1.5 -1.364 -1.208 -1.523 -2.601 -1.678 -0.727 1.6 -0.900 -1.250 -1.579 -2.564 -1.706 -0.644 1.636 -0.776 -1.270 -1.600 -2.549 -1.717 -0.617 1.67 -0.672 -1.288 -1.622 -2.533 -1.729 -0.594 1.675 -0.657 -1.291 -1.625 -2.530 -1.730 -0.591 1.68 -0.642 -1.294 -1.628 -2.528 -1.732 -0.588 1.69 -0.611 -1.300 -1.635 -2.523 -1.736 -0.587 1.7 - -1.270 -1.613 -2.467 -1.734 - 1.8 - -1.364 -1.712 -2.463 -1.777 - 2.0 - -1.424 -1.857 -2.340 -1.848 - 2.030 - -1.423 -1.880 -2.319 -1.859 - 2.2 - -1.383 -1.963 -2.233 -1.889 - 2.4 - -1.242 -2.024 -2.155 -1.894 - 2.6 - -1.042 -2.053 -2.099 -1.875 -

Table 15: Electron Density, r(r) for 1,6-Methano[10]annulene [e/Å3]

C1,C6 [Å] C2C7 C1C2 C2C3 C3C4 C4C5 C1C2C7 1.2 3.027 1.513 1.691 2.326 1.816 1.476 1.4 1.994 1.552 1.754 2.303 1.836 1.399 1.5 1.616 1.582 1.785 2.289 1.848 1.339 1.6 1.318 1.621 1.819 2.271 1.863 1.256 1.8 - 1.713 1.902 2.220 1.899 - 1.9 - 1.752 1.945 2.190 1.918 - 2.0 - 1.771 1.982 2.160 1.934 - 2.2 - 1.766 2.035 2.109 1.953 - 2.230 - 1.760 2.040 2.103 1.954 - 2.4 - 1.693 2.061 2.072 1.953 - 2.6 - 1.565 2.072 2.044 1.942 - 2.8 - 1.404 2.071 2.021 1.924 -

129 Table 16: Energy Density for 1,6-Methano[10]annulene [Hartree/Å3]

C1,C6 [Å] C2C7 C1C2 C2C3 C3C4 C4C5 C1C2C7 1.2 -4.584 -1.215 -1.392 -2.679 -1.622 -1.115 1.4 -2.047 -1.254 -1.495 -2.629 -1.657 -0.883 1.5 -1.351 -1.299 -1.549 -2.597 -1.680 -0.786 1.6 -0.888 -1.358 -1.612 -2.557 -1.707 -0.697 1.8 - -1.501 -1.767 -2.444 -1.778 - 1.9 - -1.559 -1.851 -2.377 -1.815 - 2.0 - -1.583 -1.925 -2.312 -1.847 - 2.2 - -1.555 -2.033 -2.202 -1.882 - 2.230 - -1.542 -2.044 -2.188 -1.884 - 2.4 - -1.415 -2.089 -2.124 -1.884 - 2.6 - -1.203 -2.113 -2.065 -1.862 - 2.8 - -0.968 -2.117 -2.017 -1.828 -

Table 17: Electron Density, r(r) for Cycloheptatriene/Norcaradiene [e/Å3]

C1,C6 [Å] C2C7 C1C2 C2C3 C3C4 C4C5 C1C2C7 1.2 2.996 1.557 1.727 2.258 1.767 1.522 1.4 1.969 1.586 1.796 2.236 1.786 1.428 1.6 1.303 1.631 1.876 2.198 1.827 1.248 1.8 - 1.697 1.991 2.126 1.905 - 1.9 - 1.728 2.063 2.070 1.962 - 2.0 - 1.750 2.134 2.008 2.024 - 2.2 - 1.752 2.230 1.903 2.117 - 2.4 - 1.683 2.274 1.841 2.161 - 2.435 - 1.702 2.277 1.884 2.216 - 2.6 - 1.555 2.292 1.800 2.173 - 2.8 - 1.388 2.301 1.769 2.168 -

Table 18: Energy Density for Cycloheptatriene/Norcaradiene [Hartree/Å3]

C1,C6 [Å] C2C7 C1C2 C2C3 C3C4 C4C5 C1C2C7 1.2 -4.530 -1.280 -1.458 -2.523 -1.546 -1.169 1.4 -2.013 -1.302 -1.574 -2.475 -1.581 -0.909 1.6 -0.871 -1.368 -1.721 -2.395 -1.655 -0.693 1.8 - -1.468 -1.948 -2.239 -1.803 - 1.9 - -1.514 -2.097 -2.123 -1.913 - 2.0 - -1.544 -2.247 -1.994 -2.034 - 2.2 - -1.531 -2.457 -1.787 -2.223 - 2.4 - -1.400 -2.554 -1.669 -2.313 - 2.435 - -1.430 -2.565 -1.744 -2.433 - 2.6 - -1.188 -2.595 -1.593 -2.338 - 2.8 - -0.947 -2.613 -1.539 -2.329

130 Table 19: Dependence of NMR Chemical Shifts [ppm] on C1,C6 Distance in 11,11-Dimethyl- 1,6-methano[10]annulene

C1,C6 [Å] C11 C1 C2 C3 C12 H14 H18 H22 H23 1.4 -14.98 47.12 138.70 127.50 17.11 5.63 5.83 1.26 1.03 1.5 -3.64 51.18 137.69 127.06 17.82 5.84 5.92 1.11 0.94 1.6 5.55 59.85 136.34 126.12 17.88 6.03 5.99 0.86 0.78 1.636 8.64 63.67 135.75 125.82 18.00 6.10 6.04 0.77 0.72 1.7 13.74 70.99 134.65 125.46 18.46 6.26 6.14 0.63 0.63 1.8 20.13 85.61 133.14 124.96 18.68 6.48 6.28 0.33 0.41 1.9 25.30 99.45 132.29 125.36 19.32 6.74 6.47 0.14 0.24 2.0 29.33 112.56 132.28 126.12 19.83 6.97 6.63 -0.06 0.02 2.030 30.68 116.40 132.46 126.47 20.09 7.06 6.68 -0.10 -0.03 2.1 32.92 122.13 133.07 127.24 20.79 7.22 6.77 -0.14 -0.09 2.2 36.29 129.34 134.11 128.05 21.53 7.42 6.86 -0.22 -0.24 2.3 39.70 134.36 135.52 128.98 22.60 7.62 6.94 -0.24 -0.30 2.4 43.49 138.02 136.65 129.37 23.30 7.77 6.96 -0.30 -0.39 2.5 47.53 140.95 138.09 130.03 24.39 7.92 7.00 -0.33 -0.41 2.6 52.58 143.59 139.00 130.22 24.93 8.02 6.99 -0.38 -0.46

Table 20: Dependence of NMR Spin-Spin Coupling Constants [Hz] on C1,C6 Distance in 11,11-Dimethyl-1,6-methano[10]annulene

C1,C6 [Å] H14H18 H18H19 H14H17 C1C6 C1C11 C11C12 C11C1C2 C12C11C13 1.4 8.09 4.67 0.22 27.01 8.96 47.53 -1.68 3.44 1.5 8.32 4.71 0.14 10.93 12.80 46.10 -1.27 3.17 1.6 8.43 5.04 0.01 -1.32 16.33 45.24 -0.68 2.99 1.636 8.47 5.14 -0.05 -4.76 17.70 44.86 -0.44 2.93 1.7 8.58 5.22 -0.17 -9.23 20.10 44.20 -0.35 2.80 1.8 8.60 5.69 -0.42 -12.41 23.26 43.21 0.69 2.66 1.9 8.71 6.02 -0.69 -12.12 25.64 42.31 1.22 2.50 2.0 8.71 6.57 -1.00 -10.02 27.38 40.92 1.60 2.33 2.030 8.73 6.74 -1.11 -9.06 27.81 40.50 1.70 2.27 2.1 8.83 6.98 -1.29 -7.46 28.41 39.89 1.84 2.15 2.2 8.88 7.47 -1.56 -5.32 28.64 38.62 1.97 1.93 2.3 9.03 7.87 -1.78 -3.91 28.15 37.81 2.04 1.72 2.4 9.14 8.27 -1.97 -2.80 26.80 36.83 2.07 1.47 2.5 9.28 8.61 -2.11 -1.79 24.86 36.23 2.07 1.25 2.6 9.40 8.94 -2.28 -0.35 22.25 35.69 1.93 1.05

Table 21: Dependence of NMR Chemical Shifts [ppm] on C1,C6 Distance in 1,6- Methano[10]annulene

C1,C6 [Å] C1 C2 C3 C4 H14 H18 H12 1.2 -27.64 39.72 141.84 125.16 5.91 5.81 -0.99 1.4 -3.82 37.33 140.77 125.87 6.21 5.90 -0.21 1.5 7.65 40.55 139.88 125.63 6.39 5.98 0.12 1.6 17.87 47.64 138.55 125.29 6.59 6.11 0.34 1.8 31.37 72.75 135.29 125.81 7.01 6.55 0.26 1.9 34.03 87.24 134.30 127.06 7.22 6.82 0.01 2.0 35.24 99.84 134.12 128.65 7.42 7.06 -0.27 2.2 36.80 116.55 135.28 131.64 7.79 7.43 -0.81 2.23 37.05 118.13 135.56 132.02 7.84 7.47 -0.88 2.4 39.26 124.07 137.03 133.72 8.09 7.64 -1.27 2.6 44.01 127.88 138.51 135.34 8.32 7.77 -1.70 2.8 51.60 131.18 139.73 136.83 8.49 7.84 -2.02

131 Table 22: Dependence of NMR Spin-Spin Coupling Constants [Hz] on C1,C6 Distance in 1,6-Methano[10]annulene

C1,C6 [Å] H14H18 H18H19 H14H17 C1C6 1.2 7.53 4.53 0.26 70.00 1.4 8.02 4.68 0.18 27.50 1.5 8.19 4.88 0.09 11.65 1.6 8.29 5.15 -0.05 -0.96 1.8 8.28 5.96 -0.51 -12.61 1.9 8.21 6.46 -0.81 -12.67 2.0 8.16 6.96 -1.11 -10.80 2.2 8.14 7.93 -1.59 -6.16 2.23 8.16 8.06 -1.64 -5.69 2.4 8.24 8.72 -1.83 -3.75 2.6 8.34 9.39 -1.91 -2.01 2.8 8.42 9.85 -1.97 0.94

Table 23: Dependence of NMR Chemical Shifts [ppm] on C2,C7 Distance in Cyclohepta- triene/Norcaradiene

C2,C7 [Å] C1 C3 C6 C7 H8 H10 H13 H14 H15 1.2 57.33 36.93 160.37 205.38 26.03 25.26 29.45 33.42 32.14 1.4 57.02 69.47 162.07 184.50 25.79 25.15 29.98 33.04 30.95 1.6 56.19 67.01 154.30 168.62 25.40 25.04 29.67 32.93 29.85 1.8 53.36 47.67 135.03 160.19 24.83 24.95 28.69 33.08 29.03 1.9 51.10 49.27 121.45 158.50 24.57 24.93 28.09 33.07 28.78 2.0 48.86 50.33 107.12 157.82 24.41 24.95 27.56 32.83 28.67 2.2 46.35 50.79 83.97 157.34 24.48 25.09 26.93 31.79 28.72 2.4 45.61 49.83 70.12 156.36 24.72 25.17 26.71 30.75 28.89 2.435 51.78 56.50 63.88 158.44 25.06 25.49 26.51 30.38 29.14 2.6 45.34 48.49 61.04 153.84 24.96 25.16 26.56 30.02 29.07 2.8 45.18 47.11 53.74 149.07 25.14 25.08 26.40 29.54 29.18

Table 24: Dependence of NMR Spin-Spin Coupling Constants [Hz] on C2,C7 Distance in Cycloheptatriene/Norcaradiene

C2,C7 [Å] H8H9 H8H10 H10H13 H13H14 H13H15 C2C7 1.2 3.84 8.87 5.84 2.43 7.18 65.47 1.4 4.08 8.83 5.33 3.29 7.41 24.50 1.6 4.60 8.45 4.98 3.96 7.32 -1.36 1.8 5.49 7.62 5.24 4.65 7.22 -12.46 1.9 6.07 7.02 5.70 4.99 7.19 -13.47 2.0 6.67 6.39 6.30 5.24 7.18 -12.63 2.2 7.61 5.54 7.23 5.25 7.03 -8.26 2.4 8.33 5.20 7.61 4.58 6.48 -5.28 2.435 9.80 5.20 8.29 4.14 6.96 -5.07 2.6 9.05 5.05 7.44 3.59 5.47 -4.16 2.8 9.78 4.99 7.05 2.60 4.17 -3.69

132 Supporting Information The Longest Covalent CC Bonds - Characterized with Vibrational Spectroscopy

Alan Humason, Dieter Cremer, and Elﬁ Kraka∗

Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University 3215 Daniel Ave, Dallas, Texas 75275-0314, USA

E-mail: [email protected]

133 Supporting Information

The compilation of experimental bond lengths summarized in Table 4, is from an extensive literature search of the target compounds.1–42 This data includes electron diffraction, x-ray diffraction, microwave spectroscopy and infrared spectroscopy methods. The parameters reported in the literature are obtained by different techniques, at different temperatures and in different matrices, all of which effects the actual values. Note that when multiple values are available, the experimental values vary by an average of 0.034 A.˚ To simplify the on-going analysis, the most accurate bond lengths are selected from among the literature values by the following criteria:

Gas phase electron diffraction experiments, yielding r values, are considered most ac- • a curate, because they are taken in the gas phase, making them more comparable to the theoretical results. These results are also more accurate than x-ray diffraction experiments, because the wavelengths of accelerated electrons are shorter than the wavelengths of x-rays, further increasing the accuracy.43 In some experiments, the electron diffraction results are combined with microwave spectroscopy rotational constants, to

obtain rg values of improved accuracy.

X-ray diffraction experiments generally have the limitations that 1) structures are de- • termined on solid crystals, and therefore are subject to packing effects, and 2) hydrogen atoms, which have no core electrons, cannot be accurately located. For this study of C-C bond lengths, the approximate hydrogen locations are not a concern, but the other considerations make these values less reliable than electron diffraction.

Microwave and infrared spectroscopy experiments, yielding r , r and r data, depend • m o s upon comparison of rotational constants for multiple isotopomers. These methods have the limitations that 1) they are dependent upon the availability of the isotopomers, and 2) the calculations are based on initial assumed geometries. These results are considered least accurate, and are used when results from the other techniques are

134 unavailable.

Although bond dissociation energies (BDE’s) are often sited as bond strength descriptors, molecular energies at 0K cannot be measured. Experimentally, only bond dissociation enthalpies (BDH’s) are accessible. Therefore, calculated (G4) values of BDH at 298K are used for comparison with reported experimental values. Several compilations of bond dissociation enthalpies are available,44–49 and are compiled in Table 5. Here again, the available data are from various methods, and are not comparable. Where multiple values are available, the BDH’s vary by an average of 4 kcal/mol. We make no diﬀerentiation of data quality here. IUPAC names for all of the target compounds are included in Table 3, to remove any ambiguity concerning structure.

Acknowledgments

This work was ﬁnancially supported by the National Science Foundation, Grant CHE 1152357. We thank SMU for providing computational resources.

References

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(2) Hilderbrandt, R.; Wieser, J. The Zero Point Average Structure of Isobutane as Deter- mined by Electron Diﬀraction and Microwave Spectroscopy. J. Mol. Struct. 1973, 15, 27–36.

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141 Electron X-Ray Microwave Infrared d No. Bond ID Diﬀraction Diﬀraction Spectroscopy Spectroscopy ∆Rexp 1 Me-Me 1.536 43 1.536 32 1.534 43 0.002 2 Me-Et 1.528 38 3 iPr-Me 1.535 (1) 2 1.525 (1) 3 0.01 4 tBu-Me 1.539 43 1.546(2) 11 0.007 39 5 (iPr)2 1.544 39 6 (tBu)2 1.582 25 25 7 (PhCH2)2 1.55 (26) 1.529 (3) 1.58 48 0.051 40 26 8 (AdMe2C)2 1.677 (30) 1.639 0.038 48a 9 (Et2MeC)2 1.601 48a 10 (Et3C)2 1.635 27 11 (PhEt2C)2 1.635 c 12 (Ph3C)2 – 13 hexakis 1.67 (3) 42 14 bianthracene 1.64 (1) 28 1.653 29 1.648 (3) 29 1.77 30 0.13 15 4-Ph-acenaphthene 1.754 (2) 31 12 16 H3C-CCl3 1.516 (4) 13 17 (Cl3C)2 1.564 (14) + c 18 CH3-CH3 D3d – + c 19 CH3-CH3 C2h – 20 Et-Et 1.539 (3) 43 21 tBu-C N 1.46 (2) 14 ≡ 48a 22 (iPrMe2C)2 1.601 40 23 (tBuMe2C)2 1.63 48a 24 (iBuMe2C)2 1.606 25 diAd-Ad 1.66 41 26 diAd-diAd 1.647 40 27 triAd-Ad 1.659 40 28 triAd-diAd 1.704 40 29 triAd-triAd –c 30 tetraAd-diAd 1.707 40 38 31 Me-CH=CH2 1.501 32 32 H2C=CH2 1.339 5 33 (CH2=CH)2 1.467 1.486 43 1.485 43 0.018 4 34 Et-CH=CH2 1.502 10 35 iPr-CH=CH2 1.500 b 48 36 tBu-CH=CH2 1.522 37 HC CH 1.208 32 38 Me-C≡ CH 1.45 43 1.458 38 1.459 43 0.009 ≡ 1.4589 1 1.4577 1 39 Me-C N 1.458 38 ≡ 1.45836 1 1.4582 1 0.004 43 43 40 CH2=CH-C CH 1.4314 1.426 0.005 ≡ 6 41 CH2=CH-C N 1.429 (5) ≡ 1.4430 (2) 6 1.430 7 1.458 38 1.429 7 0.029 42 HC C-C CH 1.383 43 1.3741 9 0.011 43 HC≡C-C≡N 1.3796 8 ≡ ≡ 1.3793 9 1.206 38 1.3775 1

142 1.382 1 0.176 44 Me-Ph 1.5214 (65) 15 1.512 (1) 33 1.523 15 1.51 (2) 16 0.013 45 Et-Ph 1.524 (9) 17 46 iPr-Ph 1.50 (5) 21 47 tBu-Ph 1.5237 23 22 48 Ph-cycloC3H5 1.520 (25) 18 49 Ph-CH=CH2 1.475 (23) 50 Ph-C CH 1.436 (4) 19 1.4447 (7) 19 0.009 51 Ph-C≡N 1.438 (5) 19 1.444 19 0.006 ≡ 1.434 (3) 19 1.4509 (6) 19 1.388 38 1.4509 (6) 20 0.063 52 Ph-Ph 1.48 24 Table 1: Experimental Carbon-Carbon Bond Lengths R [A].˚ a) MM2 force ﬁeld calculation. No experimental value available. b) Average crystallographic value for the speciﬁc type of bond. c) No experimental result for this compound. d) ∆Rexp: The range of experimental R values. The most accurate values are in bold type.

143 Table 2: Experimental Bond Dissociation Enthalpies [kcal/mol].

46 44 49 a No. Bond ID NIST Luo Griller Other Refs ∆BDHexp 1 Me-Me 89.68 90.2 0.2 88.8 88 2 43 2.2 2 Me-Et 87.2 88.5 ± 0.5 87.4± 1.3 3 iPr-Me 88.9 88.2 ± 0.9 85.7 87 2 43 3.2 4 tBu-Me 86 86.9 ± 0.7 84 82±43 4.9 5 (iPr)2 86.6 84.5 ± 1.1 81 5.6 6 (Me3C)2 (tBu)2 76 68.3 ± 1.5 72.2 4.9 7 (PhCH2)2 66.6 62.6 ± 2.2 4 8 (AdMe2C)2 ± 43.7 26 9 (Et2MeC)2 60.2 37 10 (Et3C)2 51.0 37 11 (PhEt2C)2 44.7 27 16 H3C-CCl3 88.3 87.6 2.0 87.6 2.0 36 0.7 17 (Cl3C)2 70.1 68.3 ± 1.5 70.1 ± 3.5 36 1.8 20 Et-Et 87.2 86.8 ± 0.6 86± 1.2 21 tBu-C N 115.8 117.7± 1.3 109.2 8.5 22 (iPrMe2C)2≡ ± 62.2 37 23 (tBuMe2C)2 44.0 37 24 (iBuMe2C)2 57.8 37 31 Me-CH=CH2 100.9 93 7.9 32 H2C=CH2 172.2 174.1 1.5 2.1 33 (CH2=CH)2 116 116.9 ± 1.5 0.9 34 Et-CH=CH2 99.6 100.0 ± 1.0 91.4 8.6 35 iPr-CH=CH2 99.7 99.2 ±1.5 89.2 10.5 36 tBu-CH=CH2 97.5 97.7 ± 1.3 87.3 10.4 37 HC CH 229.9 229.5± 1.0 0.4 38 Me-C≡ CH 123.5 126.0 ± 1.0 122.2 3.8 39 Me-C≡N 121.1 124.7± 118.2 122.8 34 6.4 40 CH2=CH-C≡ CH 133.6 41 CH2=CH-C≡N 132.1 133.9 1.8 1.8 42 HC C-C CH≡ 155 ± 43 HC≡C-C≡N 152.4 143.9 8.5 44 Me-Ph≡ ≡ 103.9 102.0 1.0 101 2.9 45 Et-Ph 102.3 100.2 ± 1.0 99.5 2.8 46 iPr-Ph 102.1 98.9 ±1.2 96.8 5.3 47 tBu-Ph 97.4± 93.4 4 48 Ph-cycloC3H5 109.8 1.2 111.9 47 2.1 49 Ph-CH=CH2 116.9 115.2 ± 1.3 1.7 50 Ph-C CH 140.7± 141.2 1.4 35 0.5 51 Ph-C≡N 132.7 132.8 2.0± 0.1 52 Ph-Ph≡ 118 114.4 ± 1.5 3.6 ± a) ∆BDHexp: The range of experimental BDH values.

144 Table 3: IUPAC nomenclature for all target analytes.

No. Bond ID IUPAC Name 1 Me-Me ethane 2 Me-Et propane 3 iPr-Me 2-methylpropane 4 tBu-Me 2,2-dimethylpropane 5 (iPr)2 2,3-dimethylbutane 6 (tBu)2 2,2,3,3-tetramethylbutane 7 (PhCH2)2 1,2-diphenylethane 8 (AdMe2C)2 2,3-diadamantyl-2,3-dimethylbutane 9 (Et2MeC)2 3,4-ethyl-3,4-methylhexane 10 (Et3C)2 3,3,4,4-tetraethylhexane 11 (PhEt2C)2 3,4-ethyl-3,4-phenylhexane 12 (Ph3C)2 hexaphenylethane 13 hexakis hexakis-(3,5-di-tert-butylphenyl)ethane 14 bianthracene bi(anthracene-9,10-dimethylene) 15 4-Ph-acenaphthene acenaphthene-5,6-diyl bis(diphenylmethylium) 16 H3C-CCl3 1,1,1-trichloroethane 17 (Cl3C)2 hexachloroethane + 18 CH3CH3 D3d ethane cation, D3d + 19 CH3CH3 C2h ethane cation, C2h 20 Et-Et butane 21 tBu-C N 2-cyano-2-methylpropane ≡ 22 (iPrMe2C)2 2,3,3,4,4,5-hexamethylhexane 23 (tBuMe2C)2 2,2,3,3,4,4,5,5-octamethylhexane 24 (iBuMe2C)2 2,4,4,5,5,7-hexamethyloctane 25 diAd-Ad 1-(1-adamantyl)diamantane 26 diAd-diAd 1-(1-diamantyl)diamantane 27 triAd-Ad 2-(1-adamantyl)triamantane 28 triAd-diAd 2-(1-diamantyl)triamantane 29 triAd-triAd 2-(2-triamantyl)triamantane 30 tetraAd-diAd 2-(1-diamantyl)[121]tetramantane 31 Me-CH=CH2 propene 32 H2C=CH2 ethene 33 (CH2=CH)2 1,3-butadiene 34 Et-CH=CH2 1-butene 35 iPr-CH=CH2 3-methyl-1-butene 36 tBu-CH=CH2 3,3-dimethyl-1-butene 37 HC CH ethyne 38 Me-C≡ CH propyne 39 Me-C≡N acetonitrile 40 CH =CH-C≡ CH buta-1-en-3-yne 2 ≡ 41 CH2=CH-C N cyanoethene 42 HC C-C CH≡ 1,3-butadiyne 43 HC≡C-C≡N cyanoethyne 44 Me-Ph≡ ≡ toluene 45 Et-Ph ethylbenzene 46 iPr-Ph cumene 47 tBu-Ph (1,1-dimethylethyl)benzene 48 Ph-cycloC3H5 cyclopropylbenzene 49 Ph-CH=CH2 styrene 50 Ph-C CH phenylacetylene 51 Ph-C≡N cyanobenzene 52 Ph-Ph≡ biphenyl 53 iron clamp bis(1,4,5-trimethylimidazolyl)ketone iron complex 145 1 2 C 0.000000 0.000000 0.761558 C -1.267554 -0.259242 0.000000 C 0.000000 0.000000 -0.761558 C 0.000000 0.586273 0.000000 H 0.000000 1.016010 1.157084 C 1.267554 -0.259242 0.000000 H 0.000000 -1.016010 -1.157084 H -2.163951 0.361268 0.000000 H 0.879891 -0.508005 1.157084 H -1.306571 -0.903329 0.880539 H -0.879891 -0.508005 1.157084 H -1.306571 -0.903329 -0.880539 H 0.879891 0.508005 -1.157084 H 0.000000 1.242024 0.873618 H -0.879891 0.508005 -1.157084 H 0.000000 1.242024 -0.873618 H 2.163951 0.361268 0.000000 H 1.306571 -0.903329 -0.880539 H 1.306571 -0.903329 0.880539

3 4 H 0.000000 0.000000 1.468784 C 0.000000 0.000000 1.530136 C 0.000000 0.000000 0.374644 C 0.000000 0.000000 -0.000040 C 0.000000 1.451506 -0.095632 C 0.000000 1.442664 -0.510044 C 1.257041 -0.725753 -0.095632 C 1.249384 -0.721332 -0.510044 C -1.257041 -0.725753 -0.095632 C -1.249384 -0.721332 -0.510044 H 0.000000 1.500064 -1.187506 H 0.000000 1.471374 -1.601414 H -0.882755 1.984065 0.261208 H -0.882820 1.981006 -0.159722 H 0.882755 1.984065 0.261208 H 0.882820 1.981006 -0.159722 H 1.299093 -0.750032 -1.187506 H 1.274247 -0.735687 -1.601414 H 2.159628 -0.227544 0.261208 H 2.157011 -0.225958 -0.159722 H 1.276873 -1.756521 0.261208 H 1.274191 -1.755048 -0.159722 H -1.299093 -0.750032 -1.187506 H -1.274247 -0.735687 -1.601414 H -1.276873 -1.756521 0.261208 H -1.274191 -1.755048 -0.159722 H -2.159628 -0.227544 0.261208 H -2.157011 -0.225958 -0.159722 H -0.882831 0.509703 1.920930 H 0.882831 0.509703 1.920930 H 0.000000 -1.019405 1.920930

5 6 C -0.228808 0.736301 0.000000 C 0.000000 0.000000 0.788266 C 0.228808 -0.736301 0.000000 C 0.000000 0.000000 -0.788266 H 1.325676 -0.729525 0.000000 C -0.566769 -1.313869 -1.344712 C -0.228808 -1.492129 1.247046 C -0.854459 1.147771 -1.344712 C -0.228808 -1.492129 -1.247046 C 1.421228 0.166098 -1.344712 H 0.112686 -2.527357 1.211402 H -0.680579 -1.235767 -2.427192 H 0.172816 -1.045270 2.157391 H 0.094524 -2.156817 -1.145816 H -1.316233 -1.507996 1.330515 H -1.547730 -1.547515 -0.929630 H 0.112686 -2.527357 -1.211402 H -0.729916 1.207282 -2.427192 H -1.316233 -1.507996 -1.330515 H -1.915120 0.996548 -1.145816 H 0.172816 -1.045270 -2.157391 H -0.566323 2.114131 -0.929630 H -1.325676 0.729525 0.000000 H 1.410495 0.028485 -2.427192 C 0.228808 1.492129 1.247046 H 1.820596 1.160269 -1.145816 C 0.228808 1.492129 -1.247046 H 2.114052 -0.566615 -0.929630 H -0.112686 2.527357 1.211402 C 0.854459 1.147771 1.344712 H -0.172816 1.045270 2.157391 C -1.421228 0.166098 1.344712 H 1.316233 1.507996 1.330515 C 0.566769 -1.313869 1.344712 H -0.112686 2.527357 -1.211402 H 0.729916 1.207282 2.427192 H 1.316233 1.507996 -1.330515 H 1.915120 0.996548 1.145816 H -0.172816 1.045270 -2.157391 H 0.566323 2.114131 0.929630 H -1.410495 0.028485 2.427192 H -1.820596 1.160269 1.145816 H -2.114052 -0.566615 0.929630 H 0.680579 -1.235767 2.427192

146 H -0.094524 -2.156817 1.145816 H 1.547730 -1.547515 0.929630

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150 C 0.254065 -3.235698 2.971539 C 1.506534 -3.704990 2.607580 H 2.405092 -1.312067 0.406669 H -1.174986 -1.682330 2.687360 C 3.700016 -3.548998 1.342982 C -0.655553 -3.949628 3.979108 H 1.889866 -4.616602 3.051791 C 0.052369 5.168710 0.372367 C 0.904022 5.748244 2.639945 C 2.488470 5.574577 0.697117 H -0.089696 6.235127 0.166481 H 0.222896 4.663322 -0.582368 H -0.883221 4.784366 0.789704 H 0.700746 6.800992 2.413741 H 0.021703 5.329402 3.134765 H 1.734888 5.715048 3.351073 H 2.344373 6.642215 0.495417 H 3.365152 5.468700 1.343790 H 2.709918 5.076268 -0.251275 C 4.507348 2.602318 4.569864 C 3.087799 0.631043 5.135570 C 4.763270 0.493266 3.264588 H 5.260065 2.244933 5.280126 H 5.029659 3.173746 3.795035 H 3.837633 3.281041 5.108822 H 3.843631 0.332606 5.870807 H 2.341821 1.252117 5.642448 H 2.587352 -0.276589 4.785054 H 5.520566 0.134044 3.970824 H 4.272962 -0.379195 2.821745 H 5.274597 1.034794 2.461618 C -4.507348 -2.602318 -4.569864 C -4.763270 -0.493266 -3.264588 C -3.087799 -0.631043 -5.135570 H -5.260065 -2.244933 -5.280126 H -3.837633 -3.281041 -5.108822 H -5.029659 -3.173746 -3.795035 H -5.520566 -0.134044 -3.970824 H -5.274597 -1.034794 -2.461618 H -4.272962 0.379195 -2.821745 H -3.843631 -0.332606 -5.870807 H -2.587352 0.276589 -4.785054 H -2.341821 -1.252117 -5.642448 C -0.052369 -5.168710 -0.372367 C -2.488470 -5.574577 -0.697117 C -0.904022 -5.748244 -2.639945 H 0.089696 -6.235127 -0.166481 H 0.883221 -4.784366 -0.789704 H -0.222896 -4.663322 0.582368 H -2.344373 -6.642215 -0.495417 H -2.709918 -5.076268 0.251275 H -3.365152 -5.468700 -1.343790 H -0.700746 -6.800992 -2.413741 H -1.734888 -5.715048 -3.351073 H -0.021703 -5.329402 -3.134765 C 0.000000 5.204637 -4.569864 C 1.954454 4.371746 -3.264588 C 0.997400 2.989634 -5.135570 H 0.685864 5.677816 -5.280126

151 H -0.922648 4.964008 -5.108822 H -0.233715 5.942686 -3.795035 H 2.644197 4.847972 -3.970824 H 1.741141 5.085332 -2.461618 H 2.464874 3.510896 -2.821745 H 1.633770 3.494985 -5.870807 H 1.533209 2.102418 -4.785054 H 0.086546 2.654135 -5.642448 C -4.450050 2.629708 -0.372367 C -3.583491 4.942367 -0.697117 C -4.526114 3.657028 -2.639945 H -5.444626 3.039885 -0.166481 H -4.584993 1.627291 -0.789704 H -3.927108 2.524695 0.582368 H -4.580141 5.351395 -0.495417 H -3.041218 4.884992 0.251275 H -3.053457 5.648657 -1.343790 H -5.539459 4.007360 -2.413741 H -4.081933 4.359982 -3.351073 H -4.604546 2.683496 -3.134765 C 4.507348 -2.602318 -4.569864 C 2.808816 -3.878480 -3.264588 C 2.090399 -2.358591 -5.135570 H 4.574201 -3.432883 -5.280126 H 4.760281 -1.682968 -5.108822 H 5.263374 -2.768940 -3.795035 H 2.876369 -4.713928 -3.970824 H 3.533456 -4.050538 -2.461618 H 1.808088 -3.890091 -2.821745 H 2.209861 -3.162379 -5.870807 H 1.054143 -2.379007 -4.785054 H 2.255276 -1.402018 -5.642448 C 4.502419 2.539002 -0.372367 C 6.071960 0.632211 -0.697117 C 5.430136 2.091216 -2.639945 H 5.354931 3.195243 -0.166481 H 3.701772 3.157075 -0.789704 H 4.150004 2.138628 0.582368 H 6.924514 1.290821 -0.495417 H 5.751136 0.191276 0.251275 H 6.418609 -0.179957 -1.343790 H 6.240205 2.793632 -2.413741 H 5.816821 1.355067 -3.351073 H 4.626249 2.645905 -3.134765 C -4.502419 -2.539002 0.372367 C -5.430136 -2.091216 2.639945 C -6.071960 -0.632211 0.697117 H -5.354931 -3.195243 0.166481 H -4.150004 -2.138628 -0.582368 H -3.701772 -3.157075 0.789704 H -6.240205 -2.793632 2.413741 H -4.626249 -2.645905 3.134765 H -5.816821 -1.355067 3.351073 H -6.924514 -1.290821 0.495417 H -6.418609 0.179957 1.343790 H -5.751136 -0.191276 -0.251275 C -4.507348 2.602318 4.569864 C -2.090399 2.358591 5.135570 C -2.808816 3.878480 3.264588

152 H -4.574201 3.432883 5.280126 H -5.263374 2.768940 3.795035 H -4.760281 1.682968 5.108822 H -2.209861 3.162379 5.870807 H -2.255276 1.402018 5.642448 H -1.054143 2.379007 4.785054 H -2.876369 4.713928 3.970824 H -1.808088 3.890091 2.821745 H -3.533456 4.050538 2.461618 C 4.450050 -2.629708 0.372367 C 4.526114 -3.657028 2.639945 C 3.583491 -4.942367 0.697117 H 5.444626 -3.039885 0.166481 H 3.927108 -2.524695 -0.582368 H 4.584993 -1.627291 0.789704 H 5.539459 -4.007360 2.413741 H 4.604546 -2.683496 3.134765 H 4.081933 -4.359982 3.351073 H 4.580141 -5.351395 0.495417 H 3.053457 -5.648657 1.343790 H 3.041218 -4.884992 -0.251275 C 0.000000 -5.204637 4.569864 C -0.997400 -2.989634 5.135570 C -1.954454 -4.371746 3.264588 H -0.685864 -5.677816 5.280126 H 0.233715 -5.942686 3.795035 H 0.922648 -4.964008 5.108822 H -1.633770 -3.494985 5.870807 H -0.086546 -2.654135 5.642448 H -1.533209 -2.102418 4.785054 H -2.644197 -4.847972 3.970824 H -2.464874 -3.510896 2.821745 H -1.741141 -5.085332 2.461618 Table 4: Cartesian Coordinates for Group I - Single Bonds, in angstroms. [A]˚

153 14 15 C 0.000000 0.821141 1.377215 C 3.295040 -0.000264 0.000168 C 0.000000 0.821141 -1.377215 C 1.921454 -0.000309 0.000084 C 0.000000 -0.821141 1.377215 C 4.033429 -0.151976 -1.181278 C 0.000000 -0.821141 -1.377215 C 1.190137 -0.120985 -1.182059 C 0.000000 0.766573 2.918096 C 3.330471 -0.310246 -2.356994 C 0.000000 0.766573 -2.918096 C 1.892471 -0.297963 -2.354967 C 0.000000 -0.766573 2.918096 C 1.189989 0.120632 1.182114 C 0.000000 -0.766573 -2.918096 C 4.033274 0.151833 1.181670 C 1.220925 1.408207 -0.700695 C 1.892164 0.297829 2.355078 C 1.220925 1.408207 0.700695 C 3.330174 0.310287 2.357267 C 2.317704 1.912519 -1.377477 C 5.514850 -0.103734 -0.790264 C 2.317704 1.912519 1.377477 C 5.514729 0.104053 0.790802 C 3.411838 2.419089 -0.689724 C -0.307263 -0.034958 -0.853298 C 3.411838 2.419089 0.689724 C -0.307346 0.034783 0.853169 H 2.342165 1.919101 -2.456601 H 3.842141 -0.446083 -3.302592 H 2.342165 1.919101 2.456601 H 1.366609 -0.430781 -3.293128 H 4.258273 2.809072 -1.238362 H 1.366170 0.430878 3.293133 H 4.258273 2.809072 1.238362 H 3.841718 0.446462 3.302884 C -1.220925 1.408207 0.700695 H 6.027013 0.725568 -1.286599 C -1.220925 1.408207 -0.700695 H 6.022580 -1.035647 -1.055022 C -2.317704 1.912519 1.377477 H 6.027120 -0.725085 1.287188 C -2.317704 1.912519 -1.377477 H 6.022146 1.036118 1.055633 C -3.411838 2.419089 0.689724 C -0.955238 -1.314626 -1.406483 C -3.411838 2.419089 -0.689724 C -0.375491 -2.547643 -1.079270 H -2.342165 1.919101 2.456601 C -2.076735 -1.309259 -2.233235 H -2.342165 1.919101 -2.456601 C -0.939055 -3.738425 -1.509194 H -4.258273 2.809072 1.238362 C -2.640625 -2.506692 -2.675925 H -4.258273 2.809072 -1.238362 C -2.085262 -3.723913 -2.304403 C 1.220925 -1.408207 0.700695 H 0.514596 -2.568268 -0.464765 C 1.220925 -1.408207 -0.700695 H -2.516250 -0.369964 -2.538507 C 2.317704 -1.912519 1.377477 H -0.486806 -4.679712 -1.221925 C 2.317704 -1.912519 -1.377477 H -3.515006 -2.479167 -3.315487 C 3.411838 -2.419089 0.689724 H -2.529314 -4.653659 -2.639300 C 3.411838 -2.419089 -0.689724 C -0.940638 1.234465 -1.427309 H 2.342165 -1.919101 2.456601 C -2.272192 1.548694 -1.125642 H 2.342165 -1.919101 -2.456601 C -0.214590 2.137358 -2.202235 H 4.258273 -2.809072 1.238362 C -2.854968 2.723434 -1.577155 H 4.258273 -2.809072 -1.238362 C -0.795785 3.319915 -2.659026 C -1.220925 -1.408207 -0.700695 C -2.115505 3.619710 -2.347305 C -1.220925 -1.408207 0.700695 H -2.850634 0.887393 -0.495862 C -2.317704 -1.912519 -1.377477 H 0.821056 1.929355 -2.432778 C -2.317704 -1.912519 1.377477 H -3.880275 2.949510 -1.311213 C -3.411838 -2.419089 -0.689724 H -0.206703 4.008229 -3.253484 C -3.411838 -2.419089 0.689724 H -2.564771 4.542789 -2.693065 H -2.342165 -1.919101 -2.456601 C -0.955404 1.314465 1.406231 H -2.342165 -1.919101 2.456601 C -0.375342 2.547447 1.079417 H -4.258273 -2.809072 -1.238362 C -2.077481 1.309170 2.232176 H -4.258273 -2.809072 1.238362 C -0.939207 3.738262 1.508830 H 0.871297 1.208983 3.388218 C -2.641642 2.506645 2.674421 H -0.871297 1.208983 3.388218 C -2.086005 3.723826 2.303202 H -0.871297 1.208983 -3.388218 H 0.515209 2.568001 0.465586 H 0.871297 1.208983 -3.388218 H -2.517293 0.369914 2.537141 H -0.871297 -1.208983 3.388218 H -0.486753 4.679523 1.221801 H 0.871297 -1.208983 3.388218 H -3.516474 2.479167 3.313368 H 0.871297 -1.208983 -3.388218 H -2.530307 4.653607 2.637668 H -0.871297 -1.208983 -3.388218 C -0.940880 -1.234503 1.427296

154 C -2.272315 -1.548906 1.125302 C -0.215093 -2.136977 2.202962 C -2.855266 -2.723372 1.577319 C -0.796457 -3.319264 2.660230 C -2.116092 -3.619197 2.348268 H -2.850510 -0.888007 0.494876 H 0.820469 -1.928830 2.433765 H -3.880491 -2.949583 1.311170 H -0.207582 -4.007251 3.255269 H -2.565511 -4.542040 2.694459

53 C 0.818421 -0.106748 0.000000 C -0.818421 0.106748 0.000000 O 1.510057 1.053663 0.000000 O -1.510057 -1.053663 0.000000 N 0.533094 -2.154488 1.376183 N 1.696430 -0.602872 2.374717 C 1.067649 -0.956140 1.235676 C 0.821575 -2.606466 2.640719 C 1.542504 -1.641053 3.276807 C 0.367982 -3.938630 3.121420 C 2.121359 -1.593078 4.644869 C 2.380306 0.638483 2.698024 N 1.696430 -0.602872 -2.374717 N 0.533094 -2.154488 -1.376183 C 1.067649 -0.956140 -1.235676 C 1.542504 -1.641053 -3.276807 C 0.821575 -2.606466 -2.640719 C 2.121359 -1.593078 -4.644869 C 0.367982 -3.938630 -3.121420 C 2.380306 0.638483 -2.698024 N -0.533094 2.154488 1.376183 N -1.696430 0.602872 2.374717 C -1.067649 0.956140 1.235676 C -0.821575 2.606466 2.640719 C -1.542504 1.641053 3.276807 C -0.367982 3.938630 3.121420 C -2.121359 1.593078 4.644869 C -2.380306 -0.638483 2.698024 N -1.696430 0.602872 -2.374717 N -0.533094 2.154488 -1.376183 C -1.067649 0.956140 -1.235676 C -1.542504 1.641053 -3.276807 C -0.821575 2.606466 -2.640719 C -2.121359 1.593078 -4.644869 C -0.367982 3.938630 -3.121420 C -2.380306 -0.638483 -2.698024 Fe 0.663452 2.792005 0.000000 Cl 1.110878 4.959611 0.000000 Fe -0.663452 -2.792005 0.000000 Cl -1.110878 -4.959611 0.000000 H 0.726292 -4.131955 4.130658 H -0.720665 -4.007826 3.121895 H 0.726572 -4.728684 2.462794 H 1.779903 -0.716346 5.198043 H 1.821756 -2.476850 5.202750 H 3.212759 -1.567804 4.626089 H 2.634834 1.144473 1.776971

155 H 1.727734 1.278379 3.293051 H 3.278345 0.411531 3.268018 H 1.779903 -0.716346 -5.198043 H 3.212759 -1.567804 -4.626089 H 1.821756 -2.476850 -5.202750 H 0.726292 -4.131955 -4.130658 H 0.726572 -4.728684 -2.462794 H -0.720665 -4.007826 -3.121895 H 2.634834 1.144473 -1.776971 H 3.278345 0.411531 -3.268018 H 1.727734 1.278379 -3.293051 H -0.726292 4.131955 4.130658 H 0.720665 4.007826 3.121895 H -0.726572 4.728684 2.462794 H -1.779903 0.716346 5.198043 H -1.821756 2.476850 5.202750 H -3.212759 1.567804 4.626089 H -2.634834 -1.144473 1.776971 H -1.727734 -1.278379 3.293051 H -3.278345 -0.411531 3.268018 H -1.779903 0.716346 -5.198043 H -3.212759 1.567804 -4.626089 H -1.821756 2.476850 -5.202750 H -0.726292 4.131955 -4.130658 H -0.726572 4.728684 -2.462794 H 0.720665 4.007826 -3.121895 H -2.634834 -1.144473 -1.776971 H -3.278345 -0.411531 -3.268018 H -1.727734 -1.278379 -3.293051 Table 5: Cartesian Coordinates for Group II - Clamped Bonds, in angstroms. [A]˚

156 16 17 C 0.000000 0.000000 1.766085 C 0.000000 0.000000 0.791295 C 0.000000 0.000000 0.254521 C 0.000000 0.000000 -0.791295 H 0.000000 -1.026117 2.127011 Cl 0.000000 1.667869 1.395438 Cl 0.000000 1.676473 -0.362837 Cl 0.000000 -1.667869 -1.395438 H -0.888643 0.513058 2.127011 Cl 1.444417 -0.833935 1.395438 H 0.888643 0.513058 2.127011 Cl -1.444417 -0.833935 1.395438 Cl -1.451868 -0.838237 -0.362837 Cl 1.444417 0.833935 -1.395438 Cl 1.451868 -0.838237 -0.362837 Cl -1.444417 0.833935 -1.395438

18 19 C 0.000000 0.000000 0.967574 C 0.00000 0.79554 0.00000 C 0.000000 0.000000 -0.967574 C 0.00000 -0.79554 0.00000 H 0.000000 1.074029 1.119202 H 1.12789 0.65953 0.00000 H 0.000000 -1.074029 -1.119202 H -1.12789 -0.65953 0.00000 H 0.930136 -0.537014 1.119202 H -0.34461 1.256125 0.918191 H -0.930136 -0.537014 1.119202 H -0.34461 1.256125 -0.918191 H 0.930136 0.537014 -1.119202 H 0.34461 -1.256125 0.918191 H -0.930136 0.537014 -1.119202 H 0.34461 -1.256125 -0.918191 Table 6: Cartesian Coordinates for Group III - Electron Deﬁcient Bonds, in angstroms. [A]˚

20 21 C 0.701445 1.820985 0.000000 C 0.000000 0.000000 1.193767 C 0.701445 0.298133 0.000000 C 0.000000 0.000000 -0.278206 C -0.701445 -0.298133 0.000000 C 0.000000 1.454791 -0.767329 H 1.715277 2.221508 0.000000 C 1.259886 -0.727395 -0.767329 H 0.188195 2.211540 0.880625 C -1.259886 -0.727395 -0.767329 H 0.188195 2.211540 -0.880625 H 0.000000 1.466003 -1.857705 H 1.246330 -0.069155 0.874251 H -0.883621 1.985943 -0.416077 H 1.246330 -0.069155 -0.874251 H 0.883621 1.985943 -0.416077 C -0.701445 -1.820985 0.000000 H 1.269596 -0.733002 -1.857705 H -1.715277 -2.221508 0.000000 H 2.161688 -0.227734 -0.416077 H -1.246330 0.069155 0.874251 H 1.278067 -1.758210 -0.416077 H -1.246330 0.069155 -0.874251 H -1.269596 -0.733002 -1.857705 H -0.188195 -2.211540 0.880625 H -1.278067 -1.758210 -0.416077 H -0.188195 -2.211540 -0.880625 H -2.161688 -0.227734 -0.416077 N 0.000000 0.000000 2.341161

22 23 C -0.605097 0.522636 -0.169778 C 0.394622 0.725817 0.000000 C 0.605097 -0.522636 -0.169778 C -0.394622 -0.725817 0.000000 C 0.091157 -2.006547 -0.023895 C 0.426289 -2.151307 0.000000 C 1.374714 -0.375183 -1.496892 C -1.321125 -0.812119 1.227795 C 1.629209 -0.254159 0.941239 C -1.321125 -0.812119 -1.227795 H 2.315134 -0.922716 -1.456602 H -1.849374 -1.760456 1.245445 H 0.813973 -0.748062 -2.351688 H -0.775358 -0.746711 2.162126 H 1.622059 0.666882 -1.695586 H -2.079581 -0.037613 1.227793 H 2.387723 -1.039102 0.936789 H -1.849374 -1.760456 -1.245445 H 2.149045 0.689992 0.784981 H -2.079581 -0.037613 -1.227793 H 1.184410 -0.239173 1.934262 H -0.775358 -0.746711 -2.162126 C -0.091157 2.006547 -0.023895 C -0.426289 2.151307 0.000000 C -1.374714 0.375183 -1.496892 C 1.321125 0.812119 1.227795

157 C -1.629209 0.254159 0.941239 C 1.321125 0.812119 -1.227795 H -2.315134 0.922716 -1.456602 H 1.849374 1.760456 1.245445 H -0.813973 0.748062 -2.351688 H 0.775358 0.746711 2.162126 H -1.622059 -0.666882 -1.695586 H 2.079581 0.037613 1.227793 H -2.387723 1.039102 0.936789 H 1.849374 1.760456 -1.245445 H -2.149045 -0.689992 0.784981 H 2.079581 0.037613 -1.227793 H -1.184410 0.239173 1.934262 H 0.775358 0.746711 -2.162126 C 0.976419 -3.042868 -0.725947 C -0.484721 -3.397597 0.000000 C -0.091157 -2.492839 1.420876 C 1.321125 -2.357646 -1.240916 H -0.885301 -2.062998 -0.507479 C 1.321125 -2.357646 1.240916 H 0.587979 -4.043400 -0.531894 H 0.149364 -4.283638 0.000000 H 1.014308 -2.910437 -1.804829 H -1.117290 -3.467843 0.882099 H 2.000135 -3.015708 -0.345691 H -1.117290 -3.467843 -0.882099 H -0.628987 -3.441932 1.417803 H 1.818887 -3.324649 -1.146384 H 0.874514 -2.672371 1.895896 H 0.764117 -2.385123 -2.171600 H -0.646059 -1.804849 2.050416 H 2.104843 -1.613026 -1.333176 C -0.976419 3.042868 -0.725947 H 1.818887 -3.324649 1.146384 C 0.091157 2.492839 1.420876 H 2.104843 -1.613026 1.333176 H 0.885301 2.062998 -0.507479 H 0.764117 -2.385123 2.171600 H -0.587979 4.043400 -0.531894 C 0.484721 3.397597 0.000000 H -1.014308 2.910437 -1.804829 C -1.321125 2.357646 -1.240916 H -2.000135 3.015708 -0.345691 C -1.321125 2.357646 1.240916 H 0.628987 3.441932 1.417803 H -0.149364 4.283638 0.000000 H -0.874514 2.672371 1.895896 H 1.117290 3.467843 0.882099 H 0.646059 1.804849 2.050416 H 1.117290 3.467843 -0.882099 H -1.818887 3.324649 -1.146384 H -0.764117 2.385123 -2.171600 H -2.104843 1.613026 -1.333176 H -1.818887 3.324649 1.146384 H -2.104843 1.613026 1.333176 H -0.764117 2.385123 2.171600

24 C 0.447290 -0.656641 0.057537 C -0.447290 0.656641 0.057537 C 0.447290 1.905259 0.263056 C -1.230424 0.768433 -1.257805 C -1.469584 0.626782 1.204974 H -1.945090 1.590027 -1.209056 H -0.578105 0.948941 -2.110314 H -1.800564 -0.138125 -1.460997 H -1.968955 1.592102 1.290604 H -2.244993 -0.119845 1.039854 H -0.998737 0.419470 2.166497 C -0.447290 -1.905259 0.263056 C 1.230424 -0.768433 -1.257805 C 1.469584 -0.626782 1.204974 H 1.945090 -1.590027 -1.209056 H 0.578105 -0.948941 -2.110314 H 1.800564 0.138125 -1.460997 H 1.968955 -1.592102 1.290604 H 2.244993 0.119845 1.039854 H 0.998737 -0.419470 2.166497 C -0.191847 3.291594 0.041745 H 1.330194 1.841168 -0.377633 H 0.820251 1.867967 1.287523 C 0.310482 4.279553 1.092920 C 0.080910 3.841349 -1.357654 H -1.274857 3.213648 0.163883

158 H 0.049173 3.950013 2.099558 H 1.398401 4.371851 1.044257 H -0.114738 5.272711 0.939717 H -0.402899 4.809278 -1.498196 H 1.154436 3.982312 -1.505765 H -0.277131 3.172808 -2.138570 C 0.191847 -3.291594 0.041745 H -1.330194 -1.841168 -0.377633 H -0.820251 -1.867967 1.287523 C -0.310482 -4.279553 1.092920 C -0.080910 -3.841349 -1.357654 H 1.274857 -3.213648 0.163883 H -0.049173 -3.950013 2.099558 H -1.398401 -4.371851 1.044257 H 0.114738 -5.272711 0.939717 H 0.402899 -4.809278 -1.498196 H -1.154436 -3.982312 -1.505765 H 0.277131 -3.172808 -2.138570 Table 7: Cartesian Coordinates for Group IV - Methyl-Strained Bonds, in angstroms. [A]˚

159 25 26 H -2.238592 -3.382904 0.005979 C -1.477783 0.633679 1.006774 H 3.547617 -0.308562 2.476974 C -0.809000 0.155777 -0.328060 C -2.172254 -2.292861 0.006700 C 0.808991 -0.156339 -0.327734 C 3.219315 -0.187211 1.442663 C 2.490209 -1.630890 -1.622766 C -1.167703 1.766391 1.237361 C 1.033342 -1.251084 -1.401976 C -1.281547 1.794631 -1.279134 C 1.477803 -0.631713 1.007970 C -3.361069 1.874293 0.056738 C 1.686647 1.080018 -0.742711 H -0.709645 -0.150753 2.115726 C 2.945454 -1.068344 0.749632 H 1.614940 -2.223187 -0.556042 C 3.154997 0.664521 -0.999496 H -0.767409 -0.102182 -2.188884 C 3.047783 -2.162493 -0.306095 H 1.202342 2.039191 -0.056989 C 3.261659 -0.400529 -2.081362 H -4.433767 0.007722 0.041957 C 3.774790 0.145769 0.301901 H 4.907142 0.357149 -1.361382 H 2.537766 -2.408992 -2.387555 C -1.183103 0.233000 1.211630 H 3.343469 -1.442047 1.697612 C 1.850269 -1.222449 -0.908853 H 3.694867 1.561628 -1.317963 C -1.227218 0.255202 -1.261982 H 0.501019 -2.157902 -1.123433 C 1.644473 1.203915 -0.593587 H 0.611076 -0.912641 -2.351152 C -3.394997 0.350943 0.026727 C 1.543318 0.453108 2.099777 C 3.817797 0.270523 -1.390827 H 0.950828 -1.505577 1.391444 C -2.797512 -1.731802 1.276544 H 1.324507 1.489039 -1.682702 C 3.851118 -1.274090 0.571547 C 1.694949 2.182919 0.323478 C -2.856862 -1.729673 -1.234987 H 4.090361 -2.470200 -0.422258 C 3.641448 1.189633 0.926804 H 2.483098 -3.045387 0.006168 C -0.707598 -1.888972 -0.052745 H 2.846661 -0.030352 -3.022888 C 1.690968 -0.291714 1.397372 H 4.311670 -0.644519 -2.263451 C -2.709453 -0.212859 -1.232759 H 4.801521 -0.178663 0.107891 C 3.169959 1.343186 -0.519395 C 3.774703 1.245999 1.354947 C -2.662989 -0.216116 1.251020 C -2.945423 1.069774 0.747653 C 3.377550 -1.095532 -0.872984 C -1.686626 -1.081419 -0.740653 C -0.462392 -0.357232 -0.042802 C -1.033444 1.248405 -1.404461 C 1.138346 -0.149818 -0.039154 C -3.155002 -0.666454 -0.998164 H -2.291898 -2.143586 2.154381 C -2.490313 1.627767 -1.625873 H 3.565578 -2.263107 0.939674 C -3.774786 -0.145193 0.302245 H -2.402188 -2.155140 -2.133644 C -3.047769 2.161894 -0.310167 H 3.203041 1.973254 1.550670 C -3.261748 0.396499 -2.082077 H -3.851656 -2.012678 1.347937 H -3.343429 1.445299 1.694918 H 4.941241 -1.212416 0.623205 H -3.694860 -1.564186 -1.314887 H -3.916626 -1.997905 -1.250867 H -2.537894 2.404415 -2.392141 H 4.727356 1.300854 0.983711 C -1.543223 -0.449082 2.100621 H -0.298480 -2.313167 -0.967445 H -0.950770 1.508242 1.388611 H 1.279316 0.491734 2.035329 H -1.324496 -1.492247 -1.679861 H -0.171688 -2.348077 0.781746 C -1.694905 -2.182311 0.327553 H 1.380034 -1.247051 1.827166 H -0.501168 2.155822 -1.127807 H -3.201608 0.198435 -2.118652 H -0.611277 0.908108 -2.353022 H 3.441257 2.333814 -0.890325 H -4.801524 0.178856 0.107594 H -3.110621 0.203653 2.156931 C -3.774696 -1.243388 1.357418 H 3.803633 -1.883407 -1.497655 H -2.483033 3.045353 0.000409 H -1.669643 2.108662 2.146888 H -4.090334 2.469423 -0.426872 H -0.151197 2.151707 1.288653 H -4.311777 0.640101 -2.264542 H -0.313374 2.246295 -1.445282 H -2.846815 0.024514 -3.022924 H -1.905204 2.100766 -2.124133 C 2.332342 1.666679 1.615145 H -3.906690 2.283674 -0.797432 H 2.030669 0.024300 2.980369 H -3.853288 2.239437 0.962268 H 0.562976 0.778424 2.422684 C -1.903878 2.327115 0.014045 H 0.686063 2.541124 0.529109 H -1.851890 3.417478 0.023260 H 2.260519 3.039701 -0.053453 H 1.494370 -1.152574 -1.941248 H 4.368017 2.095811 1.006538

160 H 1.351619 1.295214 -1.639987 H 4.232951 0.887214 2.280414 H 3.509978 0.396655 -2.432129 H 2.303096 2.448069 2.376945 C -2.332259 -1.663587 1.618350 H -2.030487 -0.018640 2.980452 H -0.562877 -0.773866 2.424036 H -0.686063 -2.540275 0.533840 H -2.260603 -3.039688 -0.047799 H -4.368032 -2.093844 1.010626 H -4.232936 -0.882790 2.282176 H -2.302804 -2.443495 2.381644

27 28 C -1.903276 0.685390 -1.146067 C -1.892961 -1.025299 0.724949 C -1.345416 -0.035100 0.109477 C -1.031742 0.187095 0.177780 C 0.303743 -0.030214 0.266012 C 0.619810 -0.029300 -0.122157 C 2.206295 1.274902 1.443089 C 2.437756 0.579029 -1.861177 C 0.721821 1.263210 1.051916 C 1.016589 0.868556 -1.347039 C 1.207078 -0.003756 -1.035806 C 0.962321 -1.533591 -0.412536 C 0.780709 -1.309584 1.051313 C 1.693257 0.380422 0.999037 C 2.721037 0.047656 -0.615601 C 2.385594 -1.728629 -0.965535 C 2.266113 -1.198304 1.460618 C 3.147448 0.123576 0.441616 C 3.052852 1.313415 0.170183 C 2.597790 -0.890612 -2.216465 C 2.537745 0.051775 2.281269 C 3.448762 0.980386 -0.786131 C 3.130215 -1.179634 0.188710 C 3.396648 -1.341224 0.116135 H 2.388554 2.181104 2.028619 H 2.595989 1.190376 -2.754694 H 3.291974 0.054242 -1.551088 H 2.500550 -2.788226 -1.212082 H 2.513775 -2.082337 2.054511 H 3.827051 0.415577 1.249796 C 0.456002 2.538314 0.238620 H 0.353687 0.660061 -2.182193 H 0.172140 1.307691 1.988639 C 0.953315 2.370834 -1.021822 C 1.026338 -1.291883 -1.848849 C 0.864690 -2.440245 0.828735 C 1.019410 1.264369 -1.884894 H 0.292707 -1.898523 -1.184915 H 0.185155 -1.397982 1.965141 C 1.740047 1.881351 1.347945 C 0.702347 -2.634328 0.259444 C 1.556158 -0.505794 2.244289 H 4.113954 1.292542 0.436441 H 3.592315 -1.073023 -2.632481 C 2.756854 2.556827 -0.658738 H 1.870489 -1.172935 -2.983256 H 1.927654 0.044911 3.188938 C 3.351580 2.462382 -0.451211 H 3.584715 0.076310 2.595674 H 4.459838 0.748184 -1.134160 H 4.181077 -1.079741 0.476833 H 4.411235 -1.450003 -0.279094 C 2.954220 -2.416212 -0.681942 C 3.248289 -2.166962 1.386093 C -3.437233 0.730633 -1.178930 C -3.344274 -0.570715 1.064551 C -1.989477 0.629808 1.358413 C -1.821488 0.588978 -1.121032 C -1.986293 -1.448236 0.048940 C -1.202960 1.317111 1.220651 C -3.520744 0.652843 1.308617 C -3.260389 1.054426 -0.787238 C -3.519503 -1.438898 -0.004459 C -2.636623 1.739328 1.508281 C -3.967500 1.433369 0.071206 C -4.061596 -0.118970 -0.215719 C -3.993788 -0.688083 -1.244600 C -3.386773 0.552021 2.087752 C -4.071971 -0.767986 1.249228 C -3.272369 2.209788 0.205059 H -3.739187 1.287946 -2.068206 H -3.857866 -1.446624 1.470864 H -3.883855 1.153842 2.208484 H -3.720254 1.377411 -1.726275 H -3.857904 -2.476429 -0.047972 H -2.614866 2.559792 2.228973 H -1.546245 1.706434 -1.216741 C -2.084903 -2.205105 -0.248073 H -1.562106 0.165461 -2.042060 H -1.463717 -1.371875 1.664366 H -1.665105 0.099397 2.258272 H -1.344768 1.434999 -1.606504 H -1.666571 1.661770 1.464055 C -1.928346 -0.564124 -2.130426 H -1.631427 -1.979127 -0.832519 H -0.746480 1.005867 2.158746 H -1.702065 -2.022263 0.928400 H -0.681355 2.203837 0.892357 H -5.058123 1.496339 0.035061 H -5.067845 0.223951 0.043108 H -3.586402 2.457275 0.117135 C -4.150986 -1.248045 -1.233441 H -3.638375 -1.189437 -2.148745 H -2.916635 0.235139 3.022707

161 H -5.085883 -0.672785 -1.289466 H -4.423921 0.811191 2.316970 H -5.164826 -0.756067 1.228229 H -4.299013 2.546104 0.372206 H -3.770148 -1.325734 2.139678 H -2.714511 3.061465 -0.194552 C 1.478899 -2.525996 -1.051245 C 1.830750 -1.978456 1.913570 H 1.618458 -1.218347 -2.766676 H 1.119041 -3.460039 0.524532 H -0.013501 -1.405349 -2.160275 H -0.131808 -2.490549 1.239067 H -0.301693 -2.973945 0.069677 H 0.560348 -0.411980 2.680404 H 1.162156 -3.411533 0.876758 H 2.264050 -0.161087 3.004793 H 3.270917 -3.317119 -0.150518 H 3.987476 -1.842420 2.123567 H 3.580668 -2.326780 -1.573748 H 3.431970 -3.225609 1.185007 H 1.310129 -3.421992 -1.651812 H 1.684976 -2.580830 2.812471 C 1.281916 2.529321 -1.053183 C -2.736625 -1.725100 -1.545786 H 0.753940 3.401562 0.840793 H -2.740447 -2.935835 0.234235 H -0.599684 2.675024 0.027777 H -1.169213 -2.734312 -0.469869 H 0.048281 1.303798 -2.360569 H -0.943841 -0.910855 -2.441001 H 1.747280 1.228308 -2.701967 H -2.423231 -0.195078 -3.033346 H 3.390411 2.570617 -1.549408 H -4.648774 -0.895679 -2.141026 H 2.982258 3.459469 -0.084543 H -4.747272 -2.072571 -0.834099 H 1.039240 3.411209 -1.649253 H -2.769675 -2.546917 -2.263537 C 1.949084 2.733629 0.086042 H -0.050987 2.692027 -0.765406 H 1.219227 2.926872 -1.925651 H 2.599368 2.032398 2.008903 H 0.883719 2.214254 1.917579 H 3.545823 3.067354 -1.340924 H 4.105443 2.727410 0.294526 H 1.844040 3.790276 0.339702

29 30 C -1.902500 0.282325 -1.028258 C -1.884639 -1.367359 0.239972 C -0.900219 -0.091707 0.160172 C -1.394572 0.135032 0.349462 C 0.900246 -0.091712 -0.160396 C 0.300359 0.474734 0.226220 C 2.777589 0.749042 -1.765065 C 2.609043 -0.371327 1.087441 C 1.307122 0.914231 -1.304854 C 1.114662 -0.727515 0.825310 C 1.402404 -1.543362 -0.559881 C 0.595286 1.775889 1.074015 C 1.902346 0.282424 1.028170 C 1.012188 0.788810 -1.159266 C 2.868370 -1.595385 -1.044084 C 2.088770 2.050676 1.286988 C 3.404133 0.173467 0.534606 C 2.533369 1.107572 -0.910184 C 3.080997 -0.663291 -2.218872 C 2.733107 0.860318 1.969435 C 3.711327 1.133845 -0.608106 C 3.262729 -0.065276 -0.274131 C 3.794626 -1.231440 0.118811 C 2.739870 2.351135 -0.057810 H 2.928779 1.438204 -2.599998 C 3.335308 -1.553589 1.735267 H 3.059547 -2.624153 -1.360938 H 2.166671 2.928606 1.935892 H 4.009120 0.456631 1.403029 H 2.961977 1.286888 -1.902715 H 0.681118 0.731181 -2.177781 H 0.673208 -1.005714 1.788615 C 1.234011 2.401355 -0.925045 C 1.124538 -1.973524 -0.086701 C 1.381039 -2.599824 0.571616 C -0.011354 3.034558 0.443883 H 0.822802 -1.872226 -1.415121 H 0.217151 1.651666 2.079353 C 1.818675 1.743342 1.486023 C 1.054190 -0.425307 -2.093840 C 1.773199 -0.714952 2.187680 C 0.451644 2.057501 -1.825170 H 4.107634 -0.734236 -2.588467 H 3.790213 1.058946 2.171560 H 2.419470 -0.945388 -3.043019 H 2.251307 0.675174 2.935088 C 3.533088 2.567275 -0.132769 C 3.237219 -1.291990 -1.180184 H 4.747688 0.980085 -0.923176 H 4.305363 0.224440 -0.096714 H 4.831710 -1.225024 -0.229651 H 3.813229 2.516115 0.075887 C 3.663570 -2.150640 1.323374 C 2.108669 3.568137 -0.720623 C -3.404152 0.173049 -0.534484 C -3.348863 -1.527659 0.748522 C -1.307127 0.914228 1.304749 C -2.396624 0.866690 -0.619846 C -1.402114 -1.543315 0.559791 C -1.732897 0.579671 1.803756

162 C -2.777357 0.748857 1.765146 C -3.859362 0.736589 -0.097149 C -2.868058 -1.595640 1.044147 C -3.171237 0.394129 2.254204 C -3.711463 1.133363 0.608363 C -4.303868 -0.731998 -0.152813 C -3.794375 -1.231941 -0.118717 C -3.530015 -1.078468 2.186576 C -3.080594 -0.663515 2.218970 C -4.042387 1.237363 1.329446 H -4.009359 0.456144 -1.402778 H -3.589985 -2.591625 0.669807 H -2.928617 1.438054 2.600057 H -4.489245 1.325286 -0.770565 H -3.058964 -2.624417 1.361114 H -3.257471 0.758457 3.280273 C -1.819488 1.743339 -1.486084 C -1.917334 -1.952984 -1.185343 C -1.773233 -0.714973 -2.187790 H -1.274286 -1.992100 0.891789 H -0.680856 0.731269 2.177476 H -2.173864 1.928761 -0.665627 C -1.234310 2.401368 0.924734 C -2.415321 0.314728 -2.055374 C -1.380476 -2.599803 -0.571667 H -1.071658 0.056296 2.498316 H -0.822439 -1.871921 1.415056 H -1.545162 1.640038 1.914795 H -4.747669 0.979177 0.923673 H -5.317989 -0.809490 0.250202 C -3.533706 2.566820 0.132936 C -4.278326 -1.262875 -1.576780 C -3.663156 -2.151097 -1.323312 H -2.878674 -1.650198 2.853368 H -4.831475 -1.225744 0.229708 H -4.560091 -1.254053 2.507781 H -4.107168 -0.734519 2.588726 H -5.096536 1.169450 1.610496 H -2.418928 -0.945644 3.042988 H -3.753689 2.288976 1.409892 C 2.205991 -2.128214 1.764906 C 0.622958 3.287563 -0.925570 H 1.831406 -3.512417 0.171010 H 0.193702 3.886442 1.098763 H 0.403144 -2.893852 0.901949 H -1.092238 2.971007 0.363218 H 0.749133 -0.737299 2.563687 H -0.592848 1.953049 -2.088783 H 2.401960 -0.378150 3.018024 H 0.990091 2.220235 -2.764491 H 4.328197 -1.803803 2.119485 H 2.595168 3.764206 -1.679839 H 3.958518 -3.172942 1.074077 H 2.246443 4.456260 -0.098027 H 2.058573 -2.811895 2.603249 H 0.144564 4.146557 -1.400231 C -2.084518 2.711533 -0.313770 C -2.850283 -1.147999 -2.087504 H -2.599402 1.900901 -2.237559 H -2.266883 -2.987458 -1.120705 H -0.889179 1.956659 -1.994562 H -0.940587 -1.997705 -1.645847 H -0.231769 2.758674 0.815211 H -1.450142 0.409625 -2.535905 H -1.641352 2.971447 1.764715 H -3.111214 0.918566 -2.645215 H -3.757418 3.276255 0.933408 H -4.960057 -0.687733 -2.209081 H -4.225813 2.770354 -0.688411 H -4.611427 -2.303929 -1.598807 H -1.890137 3.735184 -0.642045 H -2.782895 -1.526367 -3.109496 C 2.083681 2.711683 0.313925 C 1.763929 -1.618396 -1.436366 H 0.231398 2.758483 -0.816208 H 0.122071 -2.309359 -0.263416 H 1.641416 2.971601 -1.764700 C 1.852296 -3.144074 0.575233 H 2.598323 1.901295 2.237706 H 1.598762 -0.143191 -3.000788 H 0.888105 1.956312 1.994180 H 0.062890 -0.711622 -2.422626 H 3.756566 3.276649 -0.933319 C 3.969713 -2.455222 -0.512900 H 4.225007 2.770997 0.688690 H 3.726429 -1.044438 -2.126984 H 1.889262 3.735311 0.642125 H 1.691828 -2.485721 -2.100183 C -2.205555 -2.128365 -1.764931 C 3.308278 -2.780888 0.828591 H -0.749212 -0.737026 -2.563935 H 2.871287 -1.786784 2.698814 H -2.402257 -0.378497 -3.018067 H 4.368511 -1.257988 1.942538 H -1.830619 -3.512532 -0.171125 H 1.784976 -4.023225 -0.071747 H -0.402468 -2.893630 -0.901936 H 1.354092 -3.399284 1.515088 H -4.327892 -1.804337 -2.119366 H 5.019510 -2.189261 -0.361740 H -3.957908 -3.173462 -1.074054 H 3.950438 -3.335287 -1.161427 H -2.058040 -2.811960 -2.603324 H 3.830809 -3.610405 1.308826 Table 8: Cartesian Coordinates for Group V - Diamondoids, in angstroms. [A]˚

163 31 32 C 1.284057 0.150620 0.000000 C 0.000000 0.000000 0.660897 C 0.000000 0.472385 0.000000 C 0.000000 0.000000 -0.660897 H 1.607135 -0.883964 0.000000 H 0.000000 0.921828 1.228238 H -0.275567 1.522643 0.000000 H 0.000000 -0.921828 -1.228238 H 2.056628 0.907581 0.000000 H 0.000000 -0.921828 1.228238 C -1.131482 -0.504301 0.000000 H 0.000000 0.921828 -1.228238 H -0.770111 -1.532283 0.000000 H -1.766767 -0.363100 0.876728 H -1.766767 -0.363100 -0.876728

33 34 C 0.603789 1.736136 0.000000 C -1.715666 -0.248327 -0.291114 C 0.603789 0.407323 0.000000 C -0.537413 0.523081 0.303126 H -0.322167 2.298560 0.000000 C 0.717240 -0.292743 0.338173 H 1.547774 -0.128675 0.000000 H -2.624610 0.352907 -0.276372 H 1.524635 2.302211 0.000000 H -1.909234 -1.161876 0.273271 C -0.603789 -0.407323 0.000000 H -1.510833 -0.532277 -1.323572 C -0.603789 -1.736136 0.000000 H -0.791740 0.829373 1.321809 H 0.322167 -2.298560 0.000000 H -0.362887 1.437512 -0.267000 H -1.547774 0.128675 0.000000 C 1.848116 0.016165 -0.276766 H -1.524635 -2.302211 0.000000 H 2.718495 -0.623351 -0.217836 H 0.664684 -1.215796 0.909921 H 1.942466 0.924449 -0.860737

35 36 C 1.168988 1.259050 0.029288 C -0.351356 0.001495 0.000000 C 0.369509 0.000011 -0.312058 C 1.003747 -0.662920 0.000000 C -0.945791 -0.000016 0.410022 C 2.191389 -0.078180 0.000000 C -2.138305 -0.000026 -0.163958 C -1.112004 -0.463213 -1.250470 C 1.169023 -1.259015 0.029257 C -1.112003 -0.463213 1.250470 H 0.620002 2.160119 -0.243315 C -0.256031 1.525285 0.000000 H 1.378085 1.303045 1.100622 H -2.121147 -0.047091 -1.259580 H 2.124373 1.265301 -0.497268 H -0.600148 -0.142017 -2.158354 H 1.378121 -1.303031 1.10059 H -1.196274 -1.551079 -1.276381 H 0.620061 -2.160093 -0.243368 H -2.121146 -0.047091 1.259580 H 2.124408 -1.265227 -0.497299 H -1.196274 -1.551078 1.276381 H -3.048925 -0.000045 0.419806 H -0.600147 -0.142016 2.158354 H -0.880528 -0.000029 1.496262 H -1.255834 1.961773 0.000000 H -2.244601 -0.000014 -1.242685 H 0.268602 1.890565 0.883985 H 0.166257 0.000021 -1.386288 H 0.268602 1.890564 -0.883986 H 3.099499 -0.665766 0.000000 H 0.963919 -1.750045 0.000000 H 2.307895 0.997757 0.000000

37 38 C 0.000000 0.000000 0.596938 C 0.000000 0.000000 1.415247 C 0.000000 0.000000 -0.596938 C 0.000000 0.000000 0.218935 H 0.000000 0.000000 1.659443 H 0.000000 0.000000 2.477031 H 0.000000 0.000000 -1.659443 C 0.000000 0.000000 -1.236320 H -0.112686 H 0.000000 1.019386 -1.621399 H 1.316233 H 0.882814 -0.509693 -1.621399 H -0.172816 H -0.882814 -0.509693 -1.621399

39 40 C 0.000000 0.000000 -1.173554 C 0.790342 -1.487847 0.000000 C 0.000000 0.000000 0.280952 C -0.313675 -0.748588 0.000000

164 H 0.000000 1.022902 -1.544894 H 1.772628 -1.035934 0.000000 H 0.885859 -0.511451 -1.544894 H -1.286377 -1.226417 0.000000 H -0.885859 -0.511451 -1.544894 H 0.731517 -2.566972 0.000000 N 0.000000 0.000000 1.427185 C -0.313675 0.676608 0.000000 C -0.313675 1.875179 0.000000 H -0.313675 2.937215 0.000000

41 42 C 0.801389 -1.420218 0.000000 C 0.000000 0.000000 1.885014 C -0.318682 -0.709166 0.000000 C 0.000000 0.000000 0.686011 H 1.773288 -0.946925 0.000000 H 0.000000 0.000000 2.947280 H -1.290383 -1.184525 0.000000 C 0.000000 0.000000 -0.686011 H 0.763716 -2.500087 0.000000 C 0.000000 0.000000 -1.885014 C -0.318682 0.720494 0.000000 H 0.000000 0.000000 -2.947280 N -0.318682 1.869269 0.000000

43 C 0.00000 0.00000 -1.830293 C 0.00000 0.00000 -0.634306 H 0.00000 0.00000 -2.893626 C 0.00000 0.00000 0.740968 N 0.00000 0.00000 1.890774 Table 9: Cartesian Coordinates for Group IV - Multiple Bonds, in angstroms. [A]˚

165 44 45 C 0.005895 0.907219 0.000000 C -0.433050 -0.000051 -0.333270 C 0.005895 0.193312 1.194198 C 0.265053 -1.194491 -0.187670 C 0.005895 0.193312 -1.194198 C 0.264977 1.194444 -0.187736 C 0.005895 -1.192938 1.197170 C 1.622092 -1.197680 0.095279 C 0.005895 -1.192938 -1.197170 C 1.622014 1.197736 0.095213 C 0.005895 -1.892108 0.000000 C 2.305724 0.000054 0.238412 C -0.024215 2.410576 0.000000 C -1.916552 -0.000099 -0.591332 H 0.010429 0.730728 2.134555 H -0.261692 -2.134406 -0.301145 H 0.010429 0.730728 -2.134555 H -0.261829 2.134319 -0.301263 H 0.009263 -1.728247 2.137229 H 2.147601 -2.137332 0.200965 H 0.009263 -1.728247 -2.137229 H 2.147463 2.137428 0.200847 H 0.008999 -2.973461 0.000000 H 3.364918 0.000094 0.456405 H -1.052882 2.776593 0.000000 H -2.182549 0.875704 -1.185877 H 0.468779 2.816647 0.882559 H -2.182533 -0.876070 -1.185637 H 0.468779 2.816647 -0.882559 C -2.727405 0.000073 0.705411 H -2.495349 0.880566 1.305455 H -3.797813 0.000036 0.498713 H -2.495334 -0.880250 1.305698

46 47 C -0.294704 -1.663183 0.000000 C -0.516640 1.358042 0.000000 H -1.359414 -1.908943 0.000000 C -0.002336 2.081754 1.253974 C 0.321996 -2.271653 -1.260938 C -0.002336 2.081754 -1.253974 C 0.321996 -2.271653 1.260938 C -2.044967 1.431245 0.000000 H 0.181978 -3.353450 -1.272806 H 1.086618 2.108823 1.286170 H -0.132166 -1.856193 -2.160363 H -0.362975 3.111916 1.269064 H 1.394511 -2.074293 -1.305759 H -0.352505 1.583321 2.158712 H 0.181978 -3.353450 1.272806 H -0.352505 1.583321 -2.158712 H 1.394511 -2.074293 1.305759 H -0.362975 3.111916 -1.269064 H -0.132166 -1.856193 2.160363 H 1.086618 2.108823 -1.286170 C -0.187633 -0.153035 0.000000 H -2.472492 0.958016 0.884913 C -1.328729 0.640301 0.000000 H -2.358560 2.475823 0.000000 C 1.052790 0.480920 0.000000 H -2.472492 0.958016 -0.884913 C -1.240078 2.025137 0.000000 C -0.002336 -0.082962 0.000000 C 1.148103 1.862400 0.000000 C -0.847634 -1.187374 0.000000 C 0.000000 2.641645 0.000000 C 1.372296 -0.326587 0.000000 H -2.303243 0.167337 0.000000 C -0.344057 -2.482044 0.000000 H 1.959245 -0.111534 0.000000 C 1.880065 -1.613317 0.000000 H -2.142650 2.621492 0.000000 C 1.021081 -2.702842 0.000000 H 2.121894 2.333701 0.000000 H -1.919326 -1.053871 0.000000 H 0.073532 3.720547 0.000000 H 2.065731 0.504170 0.000000 H -1.029055 -3.319459 0.000000 H 2.951006 -1.766578 0.000000 H 1.414105 -3.710257 0.000000

48 49 C 1.576778 0.622655 -0.000014 C 0.509246 -0.219839 -0.042511 C 2.583326 -0.213419 -0.747042 C -0.401788 -1.273536 0.00193 C 2.583314 -0.213364 0.747092 C 0.009189 1.083007 -0.059739 H 1.767918 1.687407 -0.000052 C -1.767094 -1.039557 0.043295 H 3.381415 0.301746 -1.261449 C -1.352708 1.319416 -0.019247 H 2.212072 -1.091532 -1.256739 C -2.247887 0.259324 0.034876 H 3.381395 0.301839 1.261473 C 1.948577 -0.522904 -0.070612 H 2.212051 -1.091438 1.256848 H -0.032112 -2.291368 0.00859 C 0.132306 0.2759 -0.000011 H 0.689469 1.921834 -0.117028 C -0.318536 -1.043056 0.000027 H -2.454913 -1.873343 0.08063

166 C -0.818043 1.292696 -0.000045 H -1.720435 2.336505 -0.035769 C -1.672514 -1.332737 0.00003 H -3.31237 0.447212 0.064385 C -2.174495 1.006156 -0.000042 C 2.94854 0.334154 0.094592 C -2.608825 -0.309279 -0.000004 H 2.19025 -1.568535 -0.232406 H 0.392327 -1.860054 0.000054 H 2.788323 1.388191 0.280757 H -0.489528 2.324557 -0.000075 H 3.975333 -0.000887 0.055333 H -1.998542 -2.364263 0.00006 H -2.893018 1.814838 -0.000069 H -3.665954 -0.536406 -0.000001

50 51 C 0.00000 0.00000 0.585379 C 0.602454 0.000002 0.000000 C 0.00000 1.20427 -0.119284 C -0.090406 -1.208569 0.000000 C 0.00000 -1.20427 -0.119284 C -0.090406 1.208573 0.000000 C 0.00000 1.20047 -1.503159 C -1.473873 -1.202675 0.000000 C 0.00000 -1.20047 -1.503159 C -1.473873 1.202678 0.000000 C 0.00000 0.00000 -2.198026 C -2.165126 0.000002 0.000000 C 0.00000 0.00000 2.015714 C 2.035894 -0.000001 0.000000 H 0.00000 2.13685 0.427055 H 0.457971 -2.139570 0.000000 H 0.00000 -2.13685 0.427055 H 0.457971 2.139574 0.000000 H 0.00000 2.13829 -2.041352 H -2.013710 -2.138998 0.000000 H 0.00000 -2.13829 -2.041352 H -2.013710 2.139002 0.000000 H 0.00000 0.00000 -3.279335 H -3.246338 0.000002 0.000000 C 0.00000 0.00000 3.213828 N 3.184262 -0.000010 0.000000 H 0.00000 0.00000 4.275863

52 C 0.000000 0.000000 0.740768 C -0.423302 1.119580 1.454445 C 0.423302 -1.119580 1.454445 C -0.423517 1.120306 2.839632 C 0.423517 -1.120306 2.839632 C 0.000000 0.000000 3.537953 H -0.775830 1.990725 0.918094 H 0.775830 -1.990725 0.918094 H -0.763059 1.996515 3.375233 H 0.763059 -1.996515 3.375233 H 0.000000 0.000000 4.619288 C 0.000000 0.000000 -0.740768 C -0.423302 -1.119580 -1.454445 C 0.423302 1.119580 -1.454445 C -0.423517 -1.120306 -2.839632 C 0.423517 1.120306 -2.839632 C 0.000000 0.000000 -3.537953 H -0.775830 -1.990725 -0.918094 H 0.775830 1.990725 -0.918094 H -0.763059 -1.996515 -3.375233 H 0.763059 1.996515 -3.375233 H 0.000000 0.000000 -4.619288 Table 10: Cartesian Coordinates for Group VII - Aromatic Bonds, in angstroms. [A]˚

167 5 20 3 16 90 Single Bonds e- Deﬁcient CH - Strain 3 4 2 1 80 Diamondoid 26 17

70 7 6

22 24 9 50 23 11 8 10

BondDissociation Enthalpy (experimental) [kcal/mol] 40 50 55 60 65 70 75 80 85 90 Bond Dissociation Enthalpy (G4) [kcal/mol]

Figure 1: Correlation of Experimental Bond Dissociation Enthalpy to Bond Dissociations calculated by Method G4, kcal/mol.

168 1.8 15 [Å] 10 25 8 2613 1.7 CC,exp 6 24 2830 1.6 23 11 14 27 17 9 22 1.5 Single Bonds Clamped Bonds - 42 e Deﬁcient CH3- Strain 1.4 32

ExperimentalBond Length r Diamondoid Multiple Bonds 43 Aromatic Bonds 1.3 1.3 1.4 1.5 1.6 1.7

Calculated Bond Length rCC,calc [Å]

Figure 2: Correlation of Experimental Bond Length to Bond Length calculated by Method ωB97X-D, A.˚

169 Pancake Bonds - Supporting Information

Alan Humason, Dieter Cremer, and Elﬁ Kraka⇤

Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University 3215 Daniel Ave, Dallas, Texas 75275-0314, USA

E-mail: [email protected]

170 Key words: long CC bonds, pancake bonds, Cremer-Kraka bond criteria, atoms-in-molecules, bond critical point analysis, local mode analysis, bond strength order, aromaticity index,

1. Introduction

This work continues our quest for the longest covalent CC bonds.1 This document includes graphic representations of the bond critical point (BCP), electron

2 density (⇢r), and energy density (Hb)calculationsonallsystems. Also included are cartesian coordinates (A)˚ of the optimized geometries for all species.

References

(1) Humason, A.; Zou, W.; Cremer, D. 11,11-Dimethyl-1,6-methano[10]annulene - An An- nulene with an Ultralong CC Bond or a Fluxional Molecule? J. Phys. Chem A 2015, 119,1666–1682.

(2) Keith, T. A. AIMAll (Version 17.01.25);TKGristmillSoftware,OverlandPark,KS, USA, 2017.

171 Table 1: Cartesian Coordinates for the 1,2,3,5-Dichalcodiazolyl Radical Dimers 1 through 3, in angstroms. [A]˚

HCNSSN HCNSeSeN C 1.517826 -0.000008 1.495361 C -1.559826 0.000003 1.866395 N 1.516829 -1.173422 0.884924 N -1.575798 1.196906 1.306577 N 1.516766 1.173421 0.884951 N -1.576149 -1.196863 1.306507 S 1.562648 -1.078491 -0.748250 Se -1.656089 1.180793 -0.477202 S 1.562590 1.078532 -0.748225 Se -1.656435 -1.180622 -0.477271 H 1.495604 -0.000021 2.582706 H -1.514877 -0.000036 2.958512 C -1.517833 0.000002 1.495339 C 1.559602 -0.000026 1.866440 N -1.516850 1.173433 0.884885 N 1.575760 -1.196940 1.306648 N -1.516839 -1.173439 0.884905 N 1.575828 1.196863 1.306596 S -1.562601 1.078597 -0.748248 Se 1.656303 -1.180591 -0.477125 S -1.562591 -1.078631 -0.748230 Se 1.656371 1.180433 -0.477176 H -1.495622 0.000011 2.582680 H 1.513631 -0.000001 2.958502

HCNTeTeN C -1.609662 0.000029 2.150596 N -1.666551 1.228122 1.597394 N -1.666754 -1.228053 1.597392 Te -1.919837 1.428563 -0.370206 Te -1.920074 -1.428448 -0.370208 H -1.492464 0.000019 3.233692 C 1.609594 -0.000055 2.150529 N 1.666567 -1.228176 1.597402 N 1.666626 1.228068 1.597411 Te 1.919933 -1.428507 -0.370195 Te 1.920002 1.428402 -0.370185 H 1.492357 -0.000056 3.233629

172 Phenalenyl (4)tTMP(5) C -0.00293 -0.001428 1.54638 C 0 0 3.999945 C -1.382192 -0.365856 1.543435 C 1.232695 0.711697 4.00309 C 0.371079 1.375269 1.546578 C -1.232695 0.711697 4.00309 C 1.002304 -1.013694 1.545574 C 0.000000 -1.423394 4.00309 C -2.359919 0.658317 1.543119 C -1.202815 2.12692 4.007075 C -1.988548 1.997991 1.565692 C 0.000000 2.833064 4.004495 C -0.646245 2.360107 1.546197 C 1.202815 2.12692 4.007075 C 1.74691 1.709918 1.548338 C -1.240559 -2.105129 4.007075 C 2.721402 0.718428 1.569917 C -2.453505 -1.416532 4.004495 C 2.363869 -0.625078 1.547363 C -2.443375 -0.021791 4.007075 C 0.604211 -2.372516 1.544202 C 2.443375 -0.021791 4.007075 C -0.741715 -2.720735 1.563709 C 2.453505 -1.416532 4.004495 C -1.726422 -1.739313 1.542117 C 1.240559 -2.105129 4.007075 H -3.410147 0.379243 1.540869 H -2.145474 2.669815 4.012381 H -0.359855 3.408366 1.546354 H 2.145474 2.669815 4.012381 H 2.030341 2.758981 1.548482 H -1.239391 -3.192942 4.012381 H 3.128495 -1.397225 1.546751 H -3.384864 0.523127 4.012381 H 1.371013 -3.142503 1.543584 H 3.384864 0.523127 4.012381 H -2.777432 -2.015422 1.539879 H 1.239391 -3.192942 4.012381 H -2.753712 2.768629 1.572239 C 0.000000 4.341439 3.970459 H 3.771366 0.995753 1.578092 C -3.759797 -2.17072 3.970459 H -1.026542 -3.768705 1.569491 C 3.759797 -2.17072 3.970459 C 0.002924 0.001418 -1.547408 H 0.000000 4.704936 2.937377 C -1.002325 1.013699 -1.548662 H -0.885696 4.747523 4.465769 C 1.382206 0.36585 -1.544747 H 0.885696 4.747523 4.465769 C -0.371109 -1.375293 -1.549667 H -4.074594 -2.352468 2.937377 C -0.604157 2.372563 -1.546652 H -3.668627 -3.140797 4.465769 C 0.741763 2.720794 -1.557505 H -4.554324 -1.606726 4.465769 C 1.726392 1.73938 -1.542825 H 4.074594 -2.352468 2.937377 C 2.359932 -0.658409 -1.543834 H 4.554324 -1.606726 4.465769 C 1.988579 -1.998085 -1.559489 H 3.668627 -3.140797 4.465769 C 0.646309 -2.360134 -1.548641 C 0.000000 0.000000 -3.999945 C -1.747003 -1.709899 -1.552572 C -1.232695 -0.711697 -4.00309 C -2.721491 -0.718414 -1.567222 C 0.000000 1.423394 -4.00309 C -2.363929 0.625009 -1.55159 C 1.232695 -0.711697 -4.00309 H -1.370907 3.142592 -1.547595 C -1.240559 2.105129 -4.007075 H 2.77738 2.015551 -1.540814 C -2.453505 1.416532 -4.004495 H 3.41017 -0.379398 -1.541791 C -2.443375 0.021791 -4.007075 H 0.359988 -3.408402 -1.55038 C 2.443375 0.021791 -4.007075 H -2.030489 -2.758937 -1.554275 C 2.453505 1.416532 -4.004495 H -3.128594 1.397109 -1.552557 C 1.240559 2.105129 -4.007075 H 1.026997 3.768618 -1.547995 C -1.202815 -2.12692 -4.007075 H 2.754143 -2.768285 -1.539714 C 0.000000 -2.383064 -4.004495 H -3.771578 -0.995302 -1.561458 C 1.202815 -2.12692 -4.007075 H -1.239391 3.192942 -4.012381 H -3.384864 -0.523127 -4.012381 H 3.384864 -0.523127 -4.012381 H 1.239391 3.192942 -4.012381 H -2.145474 -2.669815 -4.012381 H 2.145474 -2.669815 -4.012381 C -3.759797 2.17072 -3.970459 C 3.759797 2.17072 -3.970459 C 0.000000 -4.431439 -3.97459 H -4.074594 2.352468 -2.937377 H -3.668627 3.140797 -4.465769 H -4.554324 1.606726 -4.465769

173 H 4.074594 2.352468 -2.937377 H 4.554324 1.606726 -4.465769 H 3.668627 3.140797 -4.465769 H 0.000000 -4.74936 -2.937377 H -0.885696 -4.747523 -4.465769 H 0.885696 -4.747523 -4.465769

tTBP (6) C 0.000000 0.000000 1.557471 C -1.229488 -0.709845 1.561773 C 1.229488 -0.709845 1.561773 C 0.000000 1.419691 1.561773 C 1.199055 -2.125381 1.588032 C 0.000000 -2.840430 1.649575 C -1.199055 -2.125381 1.588032 C 1.241106 2.101102 1.588032 C 2.459885 1.420215 1.649575 C 2.440161 0.024278 1.588032 C -2.440161 0.024279 1.588032 C -2.459884 1.420215 1.649575 C -1.241106 2.101103 1.588032 H 2.150814 -2.648135 1.619508 H -2.150815 -2.648135 1.619508 H 1.217945 3.186727 1.619508 H 3.368759 -0.538593 1.619508 H -3.368759 -0.538592 1.619508 H -1.217944 3.186728 1.619508 C 0.000000 -4.364675 1.829448 C 3.779919 2.182337 1.829448 C -3.779919 2.182337 1.829448 C 1.410201 -4.954305 1.927031 C -0.748990 -4.707841 3.130854 C -0.720372 -5.032970 0.648146 C 3.585453 3.698423 1.927031 C 4.451605 1.705276 3.130854 C 4.718866 1.892624 0.648146 C -4.995655 1.255882 1.927031 C -3.702615 3.002565 3.130854 C -3.998494 3.140346 0.648146 H 1.338424 -6.037889 2.064873 H 1.990422 -4.771944 1.017465 H 1.963280 -4.545068 2.778621 H -0.751031 -5.791753 3.291976 H -0.266413 -4.230989 3.989997 H -1.788693 -4.369343 3.097789 H -0.757614 -6.119013 0.788933 H -1.747398 -4.668420 0.554151 H -0.198048 -4.827160 -0.292658 H 4.559753 4.178053 2.064873 H 3.137414 4.109728 1.017465 H 2.954504 3.972785 2.778621 H 5.391321 2.245465 3.291976 H 3.797351 1.884774 3.989997 H 4.678308 0.635618 3.097789 H 5.678028 2.403394 0.788933 H 4.916669 0.820919 0.554151 H 4.279467 2.242065 -0.292658 H -5.898177 1.859835 2.064873 H -5.127836 0.662216 1.017465

174 H -4.917785 0.572283 2.778621 H -4.640290 3.546289 3.291976 H -3.530938 2.346215 3.989997 H -2.889615 3.733725 3.097789 H -4.920414 3.715619 0.788933 H -3.169271 3.847501 0.554151 H -4.081419 2.585095 -0.292658 C 0.000000 0.000000 -1.557471 C 1.229488 0.709845 -1.561773 C 0.000000 -1.419691 -1.561773 C -1.229488 0.709845 -1.561773 C 2.440161 -0.024278 -1.588032 C 2.459885 -1.420215 -1.649575 C 1.241106 -2.101102 -1.588032 C -1.241106 -2.101103 -1.588032 C -2.459884 -1.420215 -1.649575 C -2.440161 -0.024279 -1.588032 C -1.199055 2.125381 -1.588032 C 0.000000 2.840430 -1.649575 C 1.199055 2.125381 -1.588032 H 3.368759 0.538593 -1.619508 H 1.217945 -3.186727 -1.619508 H -1.217944 -3.186728 -1.619508 H -3.368759 0.538592 -1.619508 H -2.150815 2.648135 -1.619508 H 2.150814 2.648135 -1.619508 C 3.779919 -2.182337 -1.829448 C -3.779919 -2.182337 -1.829448 C 0.000000 4.364675 -1.829448 C 4.995655 -1.255883 -1.927031 C 3.702615 -3.002565 -3.130854 C 3.998493 -3.140346 -0.648146 C -3.585454 -3.698423 -1.927031 C -4.451605 -1.705276 -3.130854 C -4.718866 -1.892624 -0.648146 C -1.410201 4.954306 -1.927031 C 0.748990 4.707841 -3.130854 C 0.720373 5.032969 -0.648146 H 5.898177 -1.859837 -2.064873 H 4.917786 -0.572284 -2.778621 H 5.127837 -0.662217 -1.017465 H 4.640289 -3.546289 -3.291976 H 2.889614 -3.733724 -3.097789 H 3.530938 -2.346215 -3.989997 H 4.920413 -3.715620 -0.788933 H 4.081419 -2.585095 0.292658 H 3.169270 -3.847501 -0.554151 H -4.559754 -4.178053 -2.064873 H -2.954505 -3.972785 -2.778621 H -3.137415 -4.109728 -1.017465 H -5.391321 -2.245463 -3.291976 H -4.678307 -0.635617 -3.097789 H -3.797350 -1.884774 -3.989997 H -5.678028 -2.403393 -0.788933 H -4.279467 -2.242065 0.292658 H -4.916668 -0.820918 -0.554151 H -1.338423 6.037890 -2.064873 H -1.963280 4.545069 -2.778621 H -1.990422 4.771946 -1.017465

175 H 0.751032 5.791753 -3.291976 H 1.788693 4.369342 -3.097789 H 0.266413 4.230989 -3.989997 H 0.757615 6.119013 -0.788933 H 0.198048 4.827160 0.292658 H 1.747398 4.668419 -0.554151 Table 2: Cartesian Coordinates for the Phenalenyl, tri-Methylphenalenyl, and, tri-tert-Butylphenalenyl Radical Dimers (4, 5 and 6), in angstroms. [A]˚

176 0.110

0.100 ] 3 0.090 S-S BCP

0.080 N-N RCP S-S BCP 0.070

0.060

0.050 C-C BCP 0.040 NCNNCN RCP 0.030 NSSN RCP

Electron Density, Inter-Ring[e/Å ElectronDensity, 0.020

0.010 10-atom CCP 0.000 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 C,C Interatomic Distance [Å] (a)

0.011 0.01 ] 3 0.009 C-C BCP 0.008

0.007 NSSN RCP S-S BCP 0.006 NCNNCN RCP 0.005 0.004 10-atom CCP 0.003 0.002 S-S BCP 0.001 N-N BCP Energy Density, Inter-Ring [Hartrees/Å EnergyDensity, 0 -0.001 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 C,C Interatomic Distance [Å] (b)

Figure 1: Critical Point Analysis for the 1,2,3,5-Dithiadiazolyl Radical Dimer (1)(BS- UM06/6-311G(d,p).) a) Electron Density. b) Energy Density. (BCP = bond critical point, RCP = ring critcal point, CCP = cage critical point.)

177 0.110

0.100 ]

3 0.090 Se-Se BCP 0.080

0.070 N-N RCP

0.060

0.050 C-C BCP

0.040 NCNNCN RCP 0.030 NSeSeN RCP

Electron Density, Inter-Ring[e/Å ElectronDensity, 0.020

0.010 10-atom CCP 0.000 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 C,C Interatomic Distance [Å] (a)

0.011

0.010 N-N BCP ] 3 0.009

0.008 C-C BCP 0.007 0.006 NCNNCN RCP 0.005 NSeSeN RCP 0.004 0.003 10-atom CCP 0.002 0.001 Se-Se BCP 0.000 Energy Density, Inter-Ring [Hartrees/Å EnergyDensity, -0.001 -0.002 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 C,C Interatomic Distance [Å] (b)

Figure 2: Critical Point Analysis for the 1,2,3,5-Diselenadiazolyl Radical Dimer (2)(BS- UM06/6-311G(d,p).) a) Electron Density. b) Energy Density. (BCP = bond critical point, RCP = ring critcal point, CCP = cage critical point.)

178 0.100

0.090 ] 3 0.080 C-C BCP

0.070

0.060 Te-Te BCP

0.050 N-N BCP 0.040

0.030 NCNNCN RCP 0.020 NTeTeN RCP Electron Density, Inter-Ring[e/Å ElectronDensity,

0.010 10-atom CCP 0.000 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 C,C Interatomic Distance (a)

0.013 0.012 ] 3 0.011 N-N BCP 0.010 0.009 0.008 0.007 C-C BCP 0.006 0.005 NCNNCN RCP 0.004 0.003 Te-Te BCP NTeTeN RCP 0.002 Energy Density, Inter-Ring [Hartrees/Å EnergyDensity, 0.001 10-atom CCP 0.000 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 C,C Interatomic Distance [Å] (b)

Figure 3: Critical Point Analysis for the 1,2,3,5-Ditelluradiazolyl Radical Dimer (3)(BS- UM06/SDD.) a) Electron Density. b) Energy Density. (BCP = bond critical point, RCP = ring critcal point, CCP = cage critical point.)

179 0.22

0.20 CH3 ]

3 0.18 H3C H3C 0.16 CH3

0.14 CH3 H3C 0.12

0.10

0.08

0.06

Electron Density, Inter-Ring[e/Å ElectronDensity, 0.04

0.02

0 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 C,C Interatomic Distance [Å] (a)

0.012 0.011 ] 3 0.010 0.009 0.008 0.007 0.006 0.005

0.004 CH3

0.003 H3C H3C CH3 0.002

Energy Density, Inter-Ring [Hartrees/Å EnergyDensity, CH3

0.001 H3C 0.000 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 C,C Interatomic Distance [Å] (b)

Figure 4: Critical Point Analysis for the Phenalenyl, tri-Methylphenalenyl and tri-tert- Butylphenalenyl Radical Dimers (4 and 5.) Values at the bond critical point (BCP) between the central carbon atoms (BS-UM06-2X/6-31++G(d,p).). a) Electron Density. b) Energy Density.

180 Supplemental Information - A Study of Various Multi-Reference Methods for the Characterization of 30 Transistion Metal Diatoms

Alan Humason, Dieter Cremer, and Elﬁ Kraka⇤

Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University 3215 Daniel Ave, Dallas, Texas 75275-0314, USA

E-mail: [email protected]

181 Literature Search

Tables 1 through 10 list the reported experimental results and multireference calculations published for the 30 species in the transition metal portion of the periodic table. The results from this work are also reported.

Computational Methods

The 18 valence orbitals for the 30 species in the transition metal diatom portion of the periodic table were calculated at the HF/aug-cc-pVQZ level of theory. All are depicted in Figures 1 through 10. The multireference method calculations reported here are complete active space self- consistent ﬁeld calculations with non-dynamical correlation by second order perturbation (CASPT2),1–8 restricted active space PT2 (RASPT2),9 N-Electron Valence PT2 (NEVPT2),10,11 multireference Equation-of-Motion Coupled Cluster (MR-EOM-CC), 12 Generalized Van Vleck PT2 (GVVPT2)13,14 and multireference conﬁguration interaction (MRCI) 8,12,15–19 Bench-

20–22 mark Full Configuration Interaction (FCI) calculations were conducted for C2 and N2. Results reported from this study are complete active space self-consistent field multireference methods. These include average quadrature coupled cluster calculations (CASSCF/MR- AQCC), 23 complete active space self-consistent field calculations with non-dynamical correlation by second order perturbation (CASSCF/CASPT2),1–8,24–26 and restricted active space self-consistent field calculations with non-dynamical correlation by second order perturbation (CASSCF/RASPT2).9 The basis sets used are augmented, correlation corrected Dunning quadruple-zeta basis sets. Douglas-Kroll-Hess relativistic correction (aug-cc-pVQZ-DK) is used for the lighter forth period atoms, and e↵ective core potential relativistic correction (aug-cc-pVQZ-PP) for the heavier atoms.19 Additionally, the restricted active space self- consistent field calculations with non-dynamical correlation by second order perturbation method was employed using the atom natural orbital - relativistic correlation correction

182 basis set (CASSCF/RAS-ANO) of Roos et at.24–31 was employed.

Acknowledgments

This work was ﬁnancially supported by the National Science Foundation, Grant CHE 1152357. We thank SMU for providing computational resources.

183 Table 1: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 3.

Group 3 Dimer Scandium Publication Year 2014 12 2010 11 2010 11 2010 11 2012 13 This Work This Work This Work 5 5 5 5 5 5 5 5 State ⌃u ⌃u ⌃u ⌃u ⌃u ⌃u ⌃u ⌃u Method MRCISD(+Q) NEVPT2 NEVPT2 NEVPT2 GVVPT2 CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set CBS 21s15p10d6f4g2h/ 21s15p10d6f4g2h/ 21s15p10d6f4g2h/ aug-cc-pVTZ aug-cc-pVQZ-DK aug-cc-pVQZ-DK ANO-RCC - 10s9p8d5f4g2h 10s9p8d5f4g2h 10s9p8d5f4g2h - - - - Active Space (6,18) (6,18) (6,14) (6,12) (6,10) (6,12) (6,18) (6,18) 2 2 2 4 2 4 2 4 2 4 2 4 2 4 Term Symb ol D+ D Dg + Fg Dg + Fg Dg + Fg - Dg + Fg Dg + Fg Dg + Fg FrozenOrbitalsnone none none none none none none none ------Active Orbitals 3dg/u, 3d⇡u/g 3dg/u, 3d⇡u/g 3dg/u, 3d⇡u/g 3dg/u, 3d⇡u/g 3dg/u, 3d⇡u/g 3dg/u, 3d⇡u/g 3dg/u, 3d⇡u/g 3dg/u, 3d⇡u/g 3dg/u, 4sg/u 3dg/u, 4sg/u 3dg/u, 4sg/u 3dg/u, 4sg/u 3dg/u 3dg/u, 4sg/u 3dg/u, 4sg/u 3dg/u, 4sg/u 4pg/u, 4p⇡u/g 4pg/u, 4p⇡u/g 4pg/u --4pg/u 4pg/u, 4p⇡u/g 4pg/u, 4p⇡u/g De (calc) 50.37 41.05 39.66 40.12 54.42 24.16 84.51 22.61 32 32 32 De (exp) - - - 38.0 2.3 25.9 5 25.9 5 25.9 5 33± ± ± ± ke (mdyn/A)˚ - - - - 0.76 1.371 0.816 0.853

Dimer Yttrium Publication Year 2014 14 This Work This Work This Work This Work 5 5 5 5 5 State ⌃u ⌃u ⌃u ⌃u ⌃u Method CASSCF/GVVPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set aug-cc-pVTZ-DK aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (6,12) (6,12) (6,12) (6,18) (6,18) 2 4 2 4 2 4 2 4 Term Symb ol - D3/2 + F3/2 D3/2 + F3/2 D3/2 + F3/2 D3/2 + F3/2 184 Frozen Orbitals - 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, -3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d ----- Active Orbitals 4dg/u, 4d⇡u/g , 4dg/u, 4d⇡u/g , 4dg/u, 4d⇡u/g , 4dg/u, 4d⇡u/g , 4dg/u, 4d⇡u/g , 4dg/u, 5sg/u 4dg/u, 5sg/u 4dg/u, 5sg/u 4dg/u, 5sg/u 4dg/u, 5sg/u ---5pg/u, 5p⇡u/g 5pg/u, 5p⇡u/g De (calc) 71.95 23.22 28.49 82.80 87.20 34 34 34 34 De (exp) 80.7 9.2 82.16 9.36 82.16 9.36 82.16 9.36 82.16 9.36 33± ± ± ± ± ke (mdyn/A)˚ 0.89 0.950 0.943 1.011 0.739

Dimer Lanthanium Publication Year This Work This Work This Work This Work 2002 33 5 5 5 5 State ⌃u ⌃u ⌃u ⌃u Method CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO experiment Basis Set aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (6,12) (6,12) (6,18) (6,18) 2 2 2 4 2 2 2 2 Term Symb ol D3/2 + D3/2 D3/2 + F3/2 D3/2 + D3/2 D3/2 + D3/2 Frozen Orbitals - 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, -3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, -4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d ---- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u, 5d⇡u/g , 5dg/u, 5d⇡u/g , 5dg/u, 5d⇡u/g , 5dg/u, 6sg/u 5dg/u, 6sg/u 5dg/u, 6sg/u, 5dg/u, 6sg/u, --6pg/u, 6p⇡u/g 6pg/u, 6p⇡u/g De (calc) 21.66 10.49 28.49 60.58 D (exp) 57.6 5 32 57.6 5 32 57.6 5 32 57.6 5 32 e ± ± ± ± ke (mdyn/A)˚ 0.592 0.691 0.802 1.268 0.76 Table 2: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 4.

Group 4 Dimer Titanium Publication Year 1999 35 1991 36 This Work 3 3 3 State g g g Method CASSCF/MRSDCI+Q CASSCF/MRCI+Q/ACPF CASSCF/CASPT2 Basis Set 8s5p3d2f 14s11p6d3f/8s7p4d1f aug-cc-pVQZ-DK Active Space (8,12) (8,15) (8,12) Term Symb ol 3F+3F 3F+3F 3F+3F FrozenOrbitals none none none -- - Active Orbitals 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 4sg/u 4sg/u, 4pg , 4p⇡u 4sg/u De (calc) 22.14 21.68 38.58 De (exp) - 28.93, 33.32 31.109 37 ke (mdyn/A)˚ 2.35 -2.628

Dimer Zirconium Publication Year 1991 36 1989 38 This Work This Work This Work This Work 1 + 1 + 1 + 1 + 1 + 1 + State ⌃g ⌃g ⌃g ⌃g ⌃g ⌃g Method CASSCF/MRCI/ACPF CASSCF/MRSDCI/RCI CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set 6s5p5d3f/5s4p4d1f 5s5p4d1f aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (8,15) (8,12) (8,12) (8,12) (8,18) (8,18) Term Symb ol 3F+3F 3F+3F 3F+3F 3F+3F 3F+3F 3F+3F Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 185 ------Active Orbitals 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 5sg/u, 5pg , 5p⇡u 5sg/u 5sg/u 5sg/u 5sg/u, 5pg/u, 5p⇡u/g 5sg/u, 5pg/u, 5p⇡u/g De (calc) 50.96 56.5 52.63 89.44 64.89 53.53 39 39 39 39 De (exp) - 62.26 - 69.18 70.38 70.38 70.38 70.38 37 ke (mdyn/A)˚ 2.51 --3.5363.5731.459

Dimer Hafnium Publication Year This Work This Work This Work This Work 1993 37 1 + 1 + 1 + 1 + State ⌃g ⌃g ⌃g ⌃g Method CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO experiment Basis Set aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (8,12) (8,12) (8,12) (8,12) 3 3 3 3 3 3 3 3 Term Symb ol F2 + F2 F2 + F2 F2 + F2 F2 + F2 Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d -- -- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 6sg/u 6sg/u 6sg/u, 6pg/u, 6p⇡u/g 6sg/u, 6pg/u, 6p⇡u/g De (calc) 42.12 57.68 92.31 118.95 De (exp) 78.41 pm 14 78.41 pm 14 78.41 pm 14 78.41 pm 14 ke (mdyn/A)˚ 1.772 1.925 2.053 1.505 1.63 Table 3: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 5.

Group 5 Dimer Vanadium Publication Year 2000 40 This Work This Work 3 3 3 State ⌃g ⌃g ⌃g Method CASSCF/MRCI CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set INDO/S aug-cc-pVQZ-DK ANO-RCC Active Space (10,16) (10,18) (10,18) 4 4 4 4 Term Symb ol - F3/2 + F3/2 F3/2 + F3/2 FrozenOrbitals - none none --- Active Orbitals 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 4sg/u, 4pg , 4p⇡u 4sg/u, 4pg/u, 4p⇡u/g 4sg/u, 4pg/u, 4p⇡u/g De (calc) - 52.97 74.34 40 40 De (exp) 58.06 3.76 58.06 3.76 58.06 3.76 41± ± ± ke (mdyn/A)˚ 4.33 12.033 3.990

Dimer Niobium Publication Year 2001 42 2000 40 This Work This Work This Work This Work 3 3 3 3 3 3 State ⌃g ⌃g ⌃g ⌃g ⌃g ⌃g Method CASSCF/MRSDCI+Q CASSCF/MRCI CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set 5s5p4d4f INDO/S aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC (10,12) (10,18) (10,12) (10,12) (10,18) (10,18) 6 6 6 6 6 6 6 6 Active Space - - D1/2 + D1/2 D1/2 + D1/2 D1/2 + D1/2 D1/2 + D1/2 Term Symb ol 1sg/u, 2sg/u, 2pg/u, 1sg/u, 2sg/u, 2pg/u, 1sg/u, 2sg/u, 2pg/u, 1sg/u, 2sg/u, 2pg/u, 1sg/u, 2sg/u, 2pg/u, 1sg/u, 2sg/u, 2pg/u,

186 Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d ------Active Orbitals 5sg/u 5sg/u, 5pg , 5p⇡u 5sg/u 5sg/u 5sg/u, 5pg/u, 5p⇡u/g 5sg/u, 5pg/u, 5p⇡u/g De (calc) 98.7 - 152.91 57.68 147.85 138.58 42 42 42 42 De (exp) 93.40 - 98.70 - 128.67 128.67 128.67 128.67 41 ke (mdyn/A)˚ 4.84 --3.374-6.556

Dimer Tantalum Publication Year 2009 41 This Work This Work This Work 3 3 3 3 State ⌃g ⌃g ⌃g ⌃g Method CASSCF/CASPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RAS-ANO Basis Set 24s21p15d11f4g2h/ aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC 9s8p6d4f3g2h (VQZ) - - - Active Space (10,12) (10,12) (10,12) (10,18) Term Symb ol 4F+4F 4F+4F 4F+4F 4F+4F Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d ---- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 6sg/u 6sg/u 6sg/u 6sg/u, 6pg/u, 6p⇡u/g De (calc) 107.23 160.43 210.71 128.82 41 41 41 De (exp) 49.12 114.38 - 124.52 114.38 - 124.52 114.38 - 124.52 41 ke (mdyn/A)˚ 4.80 3.162 3.877 5.362 Table 4: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 6.

Group 6 Dimer Chromium Publication Year 2012 13 2003 27 1995 25 This Work This Work This Work 1 + 1 + 1 + 1 + 1 + 1 + State ⌃g ⌃g ⌃g ⌃g ⌃g ⌃g Method CASSCF/GVVPT2 CASSCF/CASPT2 CASSCF/LS-CASPT2 CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set cc-pVTZ, cc-VQZ 21s15p10d6f4g 8s7p6d4f aug-cc-pVQZ-DK aug-cc-pVQZ-DK ANO-RCC Active Space (12,12) (12,16) (12,12) (12,12) (12,18) (12,18) Term Symb ol - 7S+7S 7S+7S 7S+7S 7S+7S 7S+7S FrozenOrbitals none none none none none none ------Active Orbitals 3dg/u, 3d⇡u/g , 3dg/u 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u 3dg/u, 3d⇡u/g , 3dg/u 3dg/u, 3d⇡u/g , 3dg/u 3dg/u, 3d⇡u/g , 3dg/u 4sg/u 4sg/u, 4p⇡u, 4pg , 5sg 4sg/u 4sg/u 4sg/u, 4pg/u, 4p⇡u/g 4sg/u, 4pg/u, 4p⇡u/g De (calc) 36.9 - 35.51 82.19 21.24 44.37 D (exp) 33.95, 35.97, 33.44 - 33.90 2.07 33.95, 35.97 13 33.95, 35.97 13 33.95, 35.97 13 e ± ke (mdyn/A)˚ 3.54 - - 7.027 4.060 2.704

Dimer Molybdenum Publication Year 2007 26 This Work This Work This Work This Work 1 + 1 + 1 + 1 + 1 + State ⌃g (and others) ⌃g ⌃g ⌃g ⌃g Method CASSCF/CASPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set - aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (12,12) (12,12) (12,12) (12,18) (12,18) Term Symb ol - 7S+7S 7S+7S 7S+7S 7S+7S Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 187 -- --- Active Orbitals 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 5sg/u 5sg/u 5sg/u 5sg/u, 5pg/u, 5p⇡u/g 5sg/u, 5pg/u, 5p⇡u/g De (calc) 101.7 204.85 180.11 158.17 114.72 43 26 26 26 26 De (exp) 103.17 0.23 103.17 0.23 103.17 0.23 103.17 0.23 103.17 0.23 44 ± ± ± ± ± ke (mdyn/A)˚ 6.43 7.767 4.156 4.745 6.447

Dimer Tungsten Publication Year 2007 26 This Work This Work This Work This Work 1 + 1 + 1 + 1 + 1 + State ⌃g (and others) ⌃g ⌃g ⌃g ⌃g Method CASSCF/CASPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set - aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (12,12) (12,12) (12,12) (12,12) (12,12) Term Symb ol - 7S+7S 7S+7S 7S+7S 7S+7S Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d -- --- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 6sg/u 6sg/u 6sg/u 6sg/u, 6pg/u, 6p⇡u/g 6sg/u, 6pg/u, 6p⇡u/g De (calc) 123.84 84.33 - 122.54 189.83 26 26 26 26 De (exp) 115.48 23.48 115.48 23.48 115.48 23.48 115.48 23.48 115.48 23.48 37 ± ± ± ± ± ke (mdyn/A)˚ 6.14 12.498 7.216 5.903 5.441 Table 5: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 7.

Group 7 Dimer Manganese Publication Year 2012 13 2010 7 2010 7 2008 18 This Work 1993 37 1 + 1 + 1 + 1 + 1 + State ⌃g ⌃g ⌃g ⌃g ⌃g Method CASSCF/GVVPT2 CASSCF/CASPT2 CASSCF/CASPT2 CASSCF/MCQDPT CASSCF/CASPT2 experiment Basis Set cc-pVQZ aug-cc-pVQZ aug-cc-pVQZ 18s,15p,8d4f2g/ aug-cc-pVQZ-DK ---7s6p4d4f2g- Active Space (14,14) (14,12) (14,18) (14,12) (14,12) 6 6 Term Symb ol - - - - S5/2 + S5/2 FrozenOrbitals none none none none none ----- Active Orbitals 3pg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3d⇡u/g , 3dg/u 3pg/u, 3p⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u 3dg/u, 3d⇡u/g , 3dg/u 3dg/u, 4sg/u 4sg/u 3d⇡u/g , 3dg/u, 4sg/u 4sg/u 4sg/u De (calc) 1.15 3.62 3.3 2.075 - 2.537 4.16 D (exp) 3.22 - - 3.10 3.10 3.22 13 e ± ke (mdyn/A)˚ 0.09 - - - 0.0671 0.094

Dimer Technetium Publication Year 2014 14 This Work This Work 2002 33 3 3 3 State ⌃g ⌃g ⌃g Method CASSCF/GVVPT2 CASSCF/CASPT2 CASSCF/RAS-ANO experiment Basis Set aug-cc-pVTZ-DK aug-cc-pVQZ-PP ANO-RCC Active Space (14,12) (14,12) (14,12) 6 6 6 6 Term Symb ol - S5/2 + S5/2 S5/2 + S5/2

188 Frozen Orbitals - 1s, 2s, 2p, 1s, 2s, 2p, -3s, 3p, 3d 3s, 3p, 3d --- Active Orbitals 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 5sg/u 5sg/u 5sg/u, 5pg/u, 5p⇡u/g De (calc) 80.71 87.64 - 14 14 De (exp) 80.48 80.48 80.48 ke (mdyn/A)˚ - 2.257 6.540 4.37

Dimer Rhenium Publication Year This Work This Work This Work 1994 44 1 + 1 + 1 + State ⌃g ⌃g ⌃g Method CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RAS-ANO experiment Basis Set aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (14,12) (14,12) (14,18) 6 6 6 6 6 6 Term Symb ol S5/2 + S5/2 S5/2 + S5/2 S5/2 + S5/2 Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d --- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 6sg/u 6sg/u 6sg/u, 6pg/u, 6p⇡u/g De (calc) 93.66 215.16 112.65 33 33 33 De (exp) 92.24 92.24 92.24 ke (mdyn/A)˚ 3.202 2.091 6.377 6.26 Table 6: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 8.

Group 8 Dimer Iron Publication Year 2014 9 This Work This Work This Work 9 9 9 9 State ⌃g ⌃g ⌃g ⌃g Method CASSCF/RASPT2 RASSCF/MR-AQCC RASSCF/CASPT2 CASSCF/RAS-ANO Basis Set ANO-RCC-VQZP (DK) aug-cc-pVQZ-DK aug-cc-pVQZ-DK ANO-RCC Active Space (16,16) (16,12) (16,12) (16,18) 5 5 5 5 5 5 5 5 Term Symb ol D+ F D4 + F5 D4 + F5 D4 + F5 FrozenOrbitals none none none none ---- Active Orbitals 3du/g , 3d⇡u/g , 3dg/u, 3du/g , 3d⇡u/g , 3dg/u, 3du/g , 3d⇡u/g , 3dg/u, 3du/g , 3d⇡u/g , 3dg/u, 4sg/u, 4pg , 4p⇡u 4sg/u 4sg/u 4sg/u, 4pg , 4p⇡u De (calc) 17.76 26.97 39.44 14.02 9 9 9 De (exp) 26.95 2.50 26.95 2.50 26.95 2.50 26.95 2.50 37± ± ± ± ke (mdyn/A)˚ 1.48 4.630 3.224 1.713

Dimer Ruthenium Publication Year 2014 45 1991 16 This Work This Work This Work This Work 5 + 7 5 + 5 + 5 + 5 + State ⌃g u ⌃g ⌃g ⌃g ⌃g Method CASSCF/CASPT2/MRCI CAS/MCSCF+Q CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set aug-cc-pVQZ-pp 5s5p4d/3s3p3d aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (16,12) (16,12) (16,12) (16,12) (16,18) (16,18) Term Symb ol - 5F+5F 5F+5F 5F+5F 5F+5F 5F+5F Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 189 ------Active Orbitals 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u 5sg/u 5sg/u 5sg/u 5sg/u 5sg/u, 5pg/u, 5p⇡u/g 5sg/u, 5pg/u, 5p⇡u/g De (calc) 57.19 46.12 78.37 73.46 74.37 - 46 46 46 46 De (exp) 78.18 - 73.56 73.56 73.56 73.56 33 ke (mdyn/A)˚ 3.59 2.623 2.175 2.511 2.475

Dimer Osmium Publication Year 2014 8 2014 8 This Work This Work This Work 5 5 5 5 5 State ⇧u ⇧u ⇧u ⇧u ⇧u Method CASSCF/CASPT2 CASSCF/MRCI+Q CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 Basis Set def2-QZVPP dhf-QZVPP aug-cc-pVQZ-DK aug-cc-pVQZ-DK aug-cc-pVQZ-PP Active Space (16,12) (16,12) (16,12) (16,12) (16,18) 5 5 5 5 5 5 Term Symb ol - - D4 + D4 D4 + D4 D4 + D4 Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d ----- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 6sg/u 6sg/u 6sg/u 6sg/u 6sg/u, 6pg/u, 6p⇡u/g De (calc) 105.85 75.87 47.11 - 65.21 8 8 8 De (exp) 101 101 101.00 101.00 101.00 33 ke (mdyn/A)˚ 6.26 -5.8596.7966.104 Table 7: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 9.

Group 9 Dimer Cobalt Publication Year 2009 6 This Work This Work This Work This Work 1994 47 5 5 5 5 5 State g g g g g Method CASSCF/CASPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO experiment Basis Set aug-cc-pVTZ-NR aug-cc-pVQZ-DK aug-cc-pVQZ-DK aug-cc-pVQZ-DK ANO-RCC Active Space (18,12) (18,12) (18,12) (18,16) (18,16) 4 4 4 4 4 4 4 4 Term Symb ol - F9/2 + F9/2 F9/2 + F9/2 F9/2 + F9/2 F9/2 + F9/2 FrozenOrbitals none none none none none ----- Active Orbitals 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3du/g , 3d⇡u/g , 3dg/u, 3du/g , 3d⇡u/g , 3dg/u, 4sg/u 4sg/u 4sg/u 4sg/u, 4pg , 4p⇡u 4sg/u, 4pg , 4p⇡u De (calc) - 34.42 34.40 32.48 26.18 48 48 48 48 48 De (exp) 39.43 6.42 39.43 6.42 39.43 6.42 39.43 6.42 39.43 6.42 37± ± ± ± ± ke (mdyn/A)˚ 1.51 2.033 - 0.975 1.580 1.53

Dimer Rhodium Publication Year 2015 49 This Work This Work This Work 5 5 5 5 State g g g g Method CASSCF/MRCI CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 Basis Set 3s3p4d/3s2p3d aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP Active Space (18,12) (18,12) (18,12) (18,18) 4 4 4 4 4 4 4 4 Term Symb ol F9/2 + F9/2 F9/2 + F9/2 F9/2 + F9/2 F9/2 + F9/2 Frozen Orbitals - 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, -3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 190 ---- Active Orbitals 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u 5sg/u 5sg/u 5sg/u 5sg/u, 5pg/u, 5p⇡u/g De (calc) 48.42 39.51 61.97 32.65 50 50 50 50 De (exp) 32.68 7.31 32.68 7.31 32.68 7.31 32.68 7.31 33± ± ± ± ke (mdyn/A)˚ 2.44 1.981 1.557 1.135

Dimer Iridium Publication Year This Work This Work This Work This Work 2002 33 5 5 5 5 State g g g g Method CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO experiment Basis Set aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC Active Space (18,12) (18,12) (18,18) (18,18) 4 4 4 4 4 4 4 4 Term Symb ol F9/2 + F9/2 F9/2 + F9/2 F9/2 + F9/2 F9/2 + F9/2 Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d ---- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u, 5dg/u, 5d⇡u/g , 5dg/u, 5dg/u, 5d⇡u/g , 5dg/u, 5dg/u, 5d⇡u/g , 5dg/u, 6sg/u 6sg/u 6sg/u, 6pg/u, 6p⇡u/g 6sg/u, 6pg/u, 6p⇡u/g De (calc) 49.45 78.07 54.79 82.77 51 51 51 51 De (exp) 79.99 79.99 79.99 79.99 ke (mdyn/A)˚ 2.637 2.967 3.468 4.471 4.44 Table 8: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 10.

Group 10 Dimer Nickel Publication Year 2012 10 1994 24 This Work This Work This Work This Work + + + + + + State Og Og Og Og Og Og Method CASSCF/NEVPT2 CASSCF/CASPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set cc-pVQZ (DK) 21s15p10d6f4g/ aug-cc-pVQZ-DK aug-cc-pVQZ-DK aug-cc-pVQZ-DK ANO-RCC -6s5p4d3f2g---- Active Space (20,12) (20,12) (20,12) (20,12) (20,18) (20,18) 3 3 3 3 3 3 3 3 3 3 3 3 Term Symb ol D+ F D+ D F4 + F4 F4 + F4 F4 + F4 F4 + F4 FrozenOrbitals none none none none none none ------Active Orbitals 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3du/g , 3d⇡u/g , 3dg/u, 3du/g , 3d⇡u/g , 3dg/u, 4sg/u 4sg/u 4sg/u 4sg/u 4sg/u, 4pg , 4p⇡u 4sg/u, 4pg , 4p⇡u De (calc) 45.083 48.43 46.28 47.49 46.82 26.52 10 10 10 10 De (exp) 47.46 0.42 - 47.46 0.42 47.46 0.42 47.46 0.42 47.46 0.42 52± 33 ± ± ± ± ke (mdyn/A)˚ 1.36 1.16 1.053 1.156 1.151 0.823

Dimer Paladium Publication Year 1998 2 This Work This Work This Work 3 3 3 3 State ⌃g ⌃g ⌃g ⌃g Method CASSCF/CASPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 Basis Set ECP-TZ-PP aug-cc-pVQZ-DK aug-cc-pVQZ-DK aug-cc-pVQZ-DK Active Space (20,12) (20,12) (20,12) (20,18) 1 3 1 3 1 3 Term Symb ol S0 + D3 S0 + D3 S0 + D3 Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 191 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d ---- Active Orbitals 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u 5sg/u 5sg/u 5sg/u 5sg/u, 5pg/u, 5p⇡u/g De (calc) 22.6 20.56 31.67 23.24 52 52 52 52 De (exp) 24.05 0.46 24.05 0.46 24.05 0.46 24.05 0.46 37± ± ± ± ke (mdyn/A)˚ 1.38 1.191 0.981 1.489

Dimer Platinum Publication Year 1998 2 This Work This Work This Work This Work 3 3 3 3 3 State ⌃g ⌃g ⌃g ⌃g ⌃g Method CASSCF/CASPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set pVTZ-PP aug-cc-pVQZ-DK aug-cc-pVQZ-DK aug-cc-pVQZ-DK ANO-RCC Active Space (20,12) (20,12) (20,12) (20,12) (20,12) Term Symb ol 3D+3D 3D+3D 3D+3D 3D+3D 3D+3D Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d ----- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u, 5dg/u, 5d⇡u/g , 5dg/u, 5dg/u, 5d⇡u/g , 5dg/u, 5dg/u, 5d⇡u/g , 5dg/u, 5dg/u, 5d⇡u/g , 5dg/u, 6sg/u 6sg/u 6sg/u 6sg/u, 6pg/u, 6p⇡u/g 6sg/u, 6pg/u, 6p⇡u/g De (calc) 60 66.75 80.59 72.64 51.29 52 52 52 52 52 De (exp) 72.72 0.77 72.72 0.77 72.72 0.77 72.72 0.77 72.72 0.77 37± ± ± ± ± ke (mdyn/A)˚ 2.66 3.215 1.421 2.848 3.249 Table 9: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 11.

Group 11 Dimer Copper Publication Year 2017 53 1994 24 This Work This Work This Work This Work 1 + 1 + 1 + 1 + 1 + 1 + State ⌃g ⌃g ⌃g ⌃g ⌃g ⌃g Method SD-BOVB CASSCF/CASPT2 CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set LanL2TZ(f) 21s15p10d6f4g/ aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC -6s5p4d3f2g- - - - Active Space (2,2) (22,12) (22,12) (22,12) (22,18) (22,18) 2 2 2 2 2 2 2 2 2 2 2 2 Term Symb ol S+ S S+ S S1/2 + S1/2 S1/2 + S1/2 S1/2 + S1/2 S1/2 + S1/2 FrozenOrbitals- - none none none none ------Active Orbitals 4sg/u 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, 3dg/u, 3d⇡u/g , 3dg/u, -4sg/u, 4sg/u 4sg/u, 4sg/u 4sg/u, 4sg/u 4sg/u, 4sg/u, 4sg/u, 4sg/u, -- - - 4pg , 4p⇡u 4pg , 4p⇡u De (calc) 40.7 45.43 42.59 43.84 92.54 57.36 24 24 24 24 De (exp) 47.7 47.97 47.97 47.97 47.97 47.97 52 ke (mdyn/A)˚ 1.33 1.428 1.522 1.332 1.147

Dimer Silver Publication Year 2017 53 1991 54 This Work This Work This Work This Work 1 + 1 + 1 + 1 + 1 + 1 + State ⌃g ⌃g ⌃g ⌃g ⌃g ⌃g Method SD-BOVB CASSCF/MRCI(SD) CASSCF/MR-AQCC CASSCF/CASPT2 CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set LanL2TZ(f) 8s7p6d2f/ aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC -6s5p4d2f- - - - Active Space (2,2) (22,12) (22,12) (22,12) (22,18) (22,18) 192 2 2 2 2 2 2 2 2 Term Symb ol - - S1/2 + S1/2 S1/2 + S1/2 S1/2 + S1/2 S1/2 + S1/2 Frozen Orbitals - 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, -3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d 3s, 3p, 3d ------Active Orbitals 5sg/u 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u, 4dg/u, 4d⇡u/g , 4dg/u 4dg/u, 4d⇡u/g , 4dg/u -5sg/u 5sg/u 5sg/u 5sg/u, 5pg/u, 5p⇡u/g 5sg/u, 5pg/u, 5p⇡u/g De (calc) 28.9 27.67 36.05 43.63 30.05 54.96 54 54 54 54 De (exp) 38.3 38.74 38.74 38.74 38.74 38.74 37 ke (mdyn/A)˚ - 1.18 1.123 1.400 1.236 1.366

Dimer Gold Publication Year 2017 53 2000 4 1991 54 This Work This Work This Work This Work 1 + 1 + 1 + 1 + 1 + 1 + 1 + State ⌃g ⌃g ⌃g ⌃g ⌃g ⌃g ⌃g Method SD-BOVB CASSCF/CASPT2 CASSCF/MRCI(SD) CASSCF/MR-AQCC CASSCF/MR-AQCC CASSCF/RASPT2 CASSCF/RAS-ANO Basis Set LanL2TZ(f) 21s17p11d9f/ 8s7p6d2f/ aug-cc-pVQZ-PP aug-cc-pVQZ-PP aug-cc-pVQZ-PP ANO-RCC -13s11p7d4f6s5p3d2f- - - - Active Space (2,2) (22,12) (22,12) (22,12) (22,12) (22,18) (22,18) 2 2 2 2 2 2 2 2 Term Symb ol - - - S1/2 + S1/2 S1/2 + S1/2 S1/2 + S1/2 S1/2 + S1/2 Frozen Orbitals - 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, 1s, 2s, 2p, -3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, 3s, 3p, 3d, -4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d 4s, 4p, 4d ------Active Orbitals 6sg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u 5dg/u, 5d⇡u/g , 5dg/u -6sg/u 6sg/u 6sg/u 6sg/u 6sg/u, 6pg/u, 6p⇡u/g 6sg/u, 6pg/u, 6p⇡u/g De (calc) 47.4 52.35 De =38.51 48.1 58.46 56.91 65.82 55 55 55 55 55 De (exp) 52.8 53.08 0.73 -53.080.73 53.08 0.73 53.08 0.73 53.08 0.73 37± ± ± ± ± ke (mdyn/A)˚ - 2.12 -1.9712.5202.1872.265 Table 10: Experimental and Computational Bond Dissociation Energies [kcal/mol] and Stretching Force Con- stants [mdyn/A],˚ Group 12.

Group 12 Dimer Zinc Publication Year 2005 5 This Work 1 + 1 + State ⌃g ⌃g Method CASSCF/CASPT2 CASSCF/CASPT2 Basis Set 17s12p9d4f/ aug-cc-pVQZ-PP 8s8p8d4f - Active Space (4,10) (24,12) Term Symb ol 1S+1S 1S+1S Frozen Orbitals - none -- Active Orbitals 3dg/u, 3d⇡u/g , 3dg/u, 3d⇡u/g , 3dg/u, 4sg/u 3dg/u, 4sg/u De (calc) 0.78 3.2 De (exp) 0.81 0.798 37 ke (mdyn/A)˚ 0.013 0.107

Dimer Cadmium Publication Year 2000 17 This Work 1 + 1 + State ⌃g ⌃g Method CASSCF/MRDCI CASSCF/CASPT2 Basis Set DZ/3P aug-cc-pVQZ-PP Active Space - (24,14) Term Symb ol 1S+1S 1S+1S Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 193 3s, 3p, 3d 3s, 3p, 3d -- Active Orbitals 4dg/u, 4d⇡u/g , 4dg/u, 5sg/u 4dg/u, 4d⇡u/g , 4dg/u, 5sg/u De (calc) 1.38 1.82 De (exp) 0.92 0.945 37 ke (mdyn/A)˚ 0.017 0.633

Dimer Mercury Publication Year 1997 15 This Work +1+ State Og ⌃g Method CASSCF/MRCI CASSCF/CASPT2 BasisSet PP9s8p6d/ aug-cc-pVQZ-PP 8s6p3d - Active Space (20,12) (24,12) Term Symb ol 1S+1S 1S+1S Frozen Orbitals 1s, 2s, 2p, 1s, 2s, 2p, 3s, 3p, 3d, 3s, 3p, 3d, 4s, 4p, 4d 4s, 4p, 4d 4p⇡u/g , 4dg/u, 4d⇡u/g , 4dg/u 4p⇡u/g , 4dg/u, 4d⇡u/g , 4dg/u -- Active Orbitals 5dg/u, 5d⇡u/g , 5dg/u, 5d⇡u/g , 5dg/u, 6sg/u 5dg/u, 6sg/u De (calc) 0.85 1.91 De (exp) 1.00 0.06 1.086 ±37 ke (mdyn/A)˚ 0.020 0.249 References

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199 5 - 5 - 5 - Sc2 X Σu Y2 X Σu La2 X Σu σ- g - σg

- σu δu - σu πg δu πg δ πg σ+ g σ+ u u δg + π σ δu g u + σ+ πg + σg g σ πu πu + π g + σ u + πg σ u σu u δg

+ + σg σg + πu πu σu πu + σg + σg

Figure 1: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 3.

3 1 + 1 + Ti2 X Δg Zr2 X Σg Hf2 X Σg

+ - σu σu

- δu πg σg + πg πg σu δu + - δg, δu σ δg σ σ+ πu u g u πu + δg σu πu + πg σu πu πu

+ σg

πg πg + σg + σu + + σg σ + g + σg σg + σu + πu σg

Figure 2: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 4.

200 3 - 3 - 3 - V2 X Σg Nb2 X Σg Ta 2 X Σg

+ - σu σu

πg + - δu π σ δu σg + g u πg σu + δg, δu πu + - σu σu δg σg + σu δg πu + πu σg πu πu

+ σg

πg πg + σg + σu σ+ + g σg σ+ πg g + σu + σg πu

Figure 3: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 5.

1 + 1 + 1 + Cr2 X Σg Mo2 X Σg W2 X Σg π πg g πg - δ δu δu σu u + + π σ πg + πg σu g u σu + + πu + πu σg, σu + + σg πu σg, σu + + σu + σu σu

δ + σ+ g σg g δ g + δg σg

+ πu σg πu + σg + σg πu

Figure 4: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 6.

201 1 + 3 - 1 + Mn2 X Σg Tc 2 X Σg Re2 X Σg

+ πg σu + πg + πg + σu π σu π σu πg + +g g + σ , σ + + σ πu g u σg, σu g + π + σ u + πu σu u σu

+ + σg σg + σg δu

πu δu δg σ+ πu g σ+ δg g + πu σg

δu δg

Figure 5: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 7.

7 + 7 5 Fe2 X Σg Ru2 X Δu Os2 X Πg - σu πg πu πg + + πg + σ πg σu σu πg +u + πg + σ , σ + + σ πu g u σ , σ g + πu g u + σu σu + σu

+ + σg σg + σg

δu πu πu δu δg

+ σ + g δg δu σg πu δ + g σg

Figure 6: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 8 .

202 5 5 5 Co2 X Δg Rh2 X Δg Ir2 X Δg + + σu σu + + σg π + σu g σ πg + πg πu, πg u σ + + + πu g σg + πu σu, σu + σg + σu + σg σu

+ σg πg

δg + σg σ+ g δu σ+ u δu, πu δu δg δg πu πg

πu + σg

Figure 7: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 9.

1 + 3 - 3 - Ni2 X Og Pd2 X Σg Pt2 X Σg + σu

- + πg σu + σu + σ + σg g πg σ πg πu + g + σ πu + u σu πu σu + + σg + σg σu

+ πg σu + + + δu σu σg σg δg πg πu δu δg πg + πu δu σg + δg σg

πu

Figure 8: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 10.

203 1 + 1 + 1 + Cu2 X Σg Ag2 X Σg Au2 X Σg - - σg, σu

+ πg σu + πg πu σu πg + + + σg, σu σg πu + + πu σu σu

+ σg + σg

+ σ+ σg u πg π δu g + π σ+ δu σu g δg u δ δu g δ πu πu g + + πu σg + σg σg

Figure 9: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 11.

1 + 1 + 1 + Zn2 X Σg Cd2 X Σg Hg2 X Σg δu

δu δu

δg

+ + σu + δg σ πg σ u δg σ+ u + g πu + π σg πg + σg g σ + + πu u πg σ πu σu + u + πg σg π + πg σg u σg π πu u

+ + + σu σu σu + + + σg σg σg

Figure 10: Orbital Diagrams: HF/cc-pVQZ-DK and HF/cc-pVQZ-PP. Group 12.

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