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Electronic Structure of Three Center Two Electron Bonds in Boron

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Electronic Structure of Three Center Two Electron Bonds in Boron ELECTRONIC STRUCTURE OF THREE CENTER TWO ELECTRON BONDS IN BORON RICH MATERIALS: A STUDY OF MOLECULES, CRYSTALS, AND AMORPHOUS SOLIDS USING THE AB INITIO ORTHOGONALIZED LINEAR COMBINATION OF ATOMIC ORBITALS METHOD A THESIS IN Physics Presented to the Faculty of the University of Missouri-Kansas City in partial fulfilment of the requirements for the degree MASTER OF SCIENCE by JOSHUA RAY SEXTON B. S., University of Missouri-Kansas City, 2017 Kansas City, Missouri 2020 © 2020 JOSHUA RAY SEXTON ALL RIGHTS RESERVED ELECTRONIC STRUCTURE OF THREE CENTER TWO ELECTRON BONDS IN BORON RICH MATERIALS: A STUDY OF MOLECULES, CRYSTALS, AND AMORPHOUS SOLIDS USING THE AB INITIO ORTHOGONALIZED LINEAR COMBINATION OF ATOMIC ORBITALS METHOD Joshua Ray Sexton, Candidate for the Master of Science Degree University of Missouri-Kansas City, 2020 ABSTRACT It has been shown that isomers of carborane, α and β rhombohedral boron, α and β tetragonal boron, γ boron, and boron carbide tend to form icosahedral structures. If the icosahedra were formed with pure boron, it has been demonstrated that there is an insufficient number of electrons to populate all the molecular orbitals that would nominally be required for molecular cohesion. To overcome that electron deficiency, the icosahedral boron units tend to form interesting bonding structures with their neighbors in solids, and/or for molecular boron the icosahedra tends to incorporate substitutional carbon atoms. The resultant bonding structures are often of a 3 center 2 electron nature. The visualization of these 3 center 2 electron bonds varies in the literature and this exposes a discontinuity with how multi-center bonds should be perceived. Here, I have attempted to reconcile these delocalized bonds with the common “ball-and-stick” molecular model using an extension to Mulliken Population Analysis within the Orthogonalized Linear Combination of Atomic Orbitals method. iii iv APPROVAL PAGE The Faculty listed below, appointed by the Dean of the College of Arts and Sciences, have examined a thesis titled “Electronic Structure of Three Center Two Electron Bonds in Boron Rich Materials: A Study of Molecules, Crystals, and Amorphous Solids using the ab initio Orthogonalized Linear Combination of Atomic Orbitals Method”, presented by Joshua Ray Sexton, candidate for the Master of Science degree, and certify that in their opinion, it is worthy of acceptance. Supervisory Committee Paul Rulis, Ph.D., Committee Chair Department of Physics and Astronomy Wai-Yim Ching, Ph.D. Department of Physics and Astronomy Michelle Paquette, Ph.D. Department of Physics and Astronomy v Table of Contents ABSTRACT................................................................................................................................................ iii LIST OF TABLES ...................................................................................................................................... x ACKNOWLEDGEMENTS ..................................................................................................................... xi 1. INTRODUCTION .................................................................................................................................. 1 Context ............................................................................................................................ 1 Motivation ....................................................................................................................... 6 Outline ............................................................................................................................. 7 2. METHODS .............................................................................................................................................. 9 The OLCAO Method .................................................................................................... 10 The Visualization ToolKit............................................................................................. 14 Paraview ........................................................................................................................ 16 Program ......................................................................................................................... 17 3. RESULTS AND DISCUSSION ......................................................................................................... 21 Model Systems .............................................................................................................. 21 Carborane C2H10B12 ................................................................................................... 23 α-Rhombohedral Boron ............................................................................................. 24 β-Rhombohedral Boron ............................................................................................. 25 γ-Boron ...................................................................................................................... 27 α-Tetragonal Boron 51 .............................................................................................. 28 β-Tetragonal Boron 190 ............................................................................................ 29 vi Boron Carbide B11C-CBC ......................................................................................... 30 Amorphous Hydrogenated Boron Carbide a-BxC:Hy ................................................ 31 4. CONCLUSIONS AND FUTURE WORK ....................................................................................... 39 Conclusion..................................................................................................................... 39 Future Work .................................................................................................................. 39 APPENDIX ................................................................................................................................................ 41 Created and Altered Scripts and Programs ................................................................... 41 bond3C.F90 ............................................................................................................... 41 insert3cbo .................................................................................................................. 41 makeBOND ............................................................................................................... 42 Custom Paraview Filter ............................................................................................. 43 REFERENCES .......................................................................................................................................... 44 VITA ........................................................................................................................................................... 48 vii LIST OF ILLUSTRATIONS Figure 1 Atomic structure of dodecaborane B12H12 .............................................................4 Figure 2 (A)-(C) Schematic, stereographic, and broad views of α-rhombohedral boron; (D) Bonding charge contours from [6] ........................................................................5 Figure 3 Sample VTK legacy polydata output ..................................................................16 Figure 4 Paraview rendering of Figure 3 ...........................................................................17 Figure 5 Old process of bond visualization .......................................................................19 Figure 5 New process of visualization ...............................................................................20 Figure 6 Traditional visualizations of ortho, para, and meta-carboranes. .........................23 Figure 7 Carboranes new visualization: ortho, para, and meta ..........................................24 Figure 8 Alpha boron traditional visualization ..................................................................24 Figure 9 Alpha boron new visualization ............................................................................25 Figure 10 Beta boron traditional visualization...................................................................25 Figure 11 Beta boron new visualization ............................................................................26 Figure 12 Gamma boron traditional visualization .............................................................27 Figure 13 Gamma boron new visualization .......................................................................27 Figure 14 Alpha tetragonal boron traditional visualization ...............................................28 Figure 15 Alpha tetragonal boron new visualization .........................................................28 Figure 16 Beta tetragonal boron traditional visualization ..................................................29 Figure 17 Beta tetragonal boron new visualization ...........................................................29 Figure 18 Boron Carbide traditional visualization.............................................................30 Figure 19 Boron Carbide new visualization ......................................................................30 viii Figure 20 a-BC:H traditional visualization ........................................................................31 Figure 21 a-BC:H new visualization..................................................................................32
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