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. 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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 in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy with a Major in Chemistry by 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 All Rights Reserved ACKNOWLEDGMENTS 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 deter- mined 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 homoaro- matic 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 (!B97X- 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 (!B97X- 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 (!B97X-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. :::::::::::::::::::::::::::::::::::