No description available.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1973. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1974. / Transcript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Molecular orbital calculations have been successively applied to mineralogical studies of equilibrium molecular geometry, electronic charge distributions, electronic spectra and bulk modulus calculations. To date, these studies have modelled bonding at atmospheric pressure. With the ever increasing interest in high pressure phases and mantle mineralogy, bonding studies of molecular groups at simulated high pressure can be an invaluable aid to understanding high pressure crystal chemistry, bond energetics and electronic spectra. This investigation tests the feasibility of various models to simulate pressure in ab initio SCF MO calculations on common metal-oxygen polyhedra. Pressure is simulated in the cluster, H₆Si₂O₇, by systematically stepping helium atoms directed^ along the Si-O bridging vectors toward the bridging oxygen. Changes in the Si-0 bond lengths, SiOSi angles and Si-0 force constants are monitored with increasing pressure. For an increase of 60 kbar pressure, the Si-0 bond length and SiOSi angle decrease 0.30% and 4.5%, respectively, which compares well with the 0.30% and 6.6% decrease observed in c-quartz for a similar increment of pressure. The linear correlation of Si-0 bond length and -sec(SiOSi), known to occur at one bar, holds at elevated pressure. In addition, the Si-0 stretching and SiOSi bending force constants show a percentage increase in the ratio 1:6 up to an estimated pressure of 140 kbar. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

V. Fock studied the hydrogen atom problem in momentum space by projecting the space onto a 4-dimensional hyper-sphere. He found that as a consequence of the symmetry of the problem in this space the eigen-functions are the R4 spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this chapter we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are the R3 spherical harmonics, Y1m, and the eigenvalues are determined only by the quantum number 1. These facts enable one to give a visualizable geometric discussion of the dynamical degeneracy.

No description available.

No description available.

by Chan Chun-Chung, Jerry. / The "59" in Co in title is superscript. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 157-170). / DESCRIPTIVE NOTE --- p.iii / Chapter CHAPTER ONE: --- A BRIEF SURVEY OF TRANSITION METAL NMR STUDIES --- p.1 / Chapter 1.0 --- Introduction --- p.1 / Chapter 1.1 --- Solution NMR Of Transition Metals --- p.2 / Chapter 1.1.1 --- Parametrization Model of Chemical Shifts --- p.4 / Chapter 1.2 --- Theoretical Calculation of the Chemical Shielding Constants of Transition Metals --- p.6 / Chapter 1.3 --- Solid State NMR of Transition Metals --- p.7 / Chapter 1.4 --- Scope of the Thesis --- p.9 / Chapter CHAPTER TWO: --- THEORY AND BACKGROUND --- p.10 / Chapter 2.0 --- Introduction --- p.10 / Chapter 2.1 --- The Origin of Chemical Shielding --- p.10 / Chapter 2.1.1 --- The Ramsey Shielding Tensor Equation with Gauge Origin Chosen at the Nucleus --- p.13 / Chapter 2.1.2 --- The Ramsey Shielding Tensor Equation with Arbitrary Gauge Origin --- p.20 / Chapter 2.1.3 --- The Physical Picture Associated with the Ramsey Shielding Equation --- p.21 / Chapter 2.2 --- Ab Initio Shielding Calculation --- p.24 / Chapter 2.2.1 --- Coupled Hartree-Fock Method --- p.25 / Chapter 2.2.2 --- Gauge Dependence Problem --- p.27 / Chapter 2.2.3 --- Post Hartree-Fock Methods --- p.29 / Chapter 2.3 --- Density Functional Theory --- p.30 / Chapter 2.3.1 --- The Hohenberg-Kohn Theorems --- p.30 / Chapter 2.3.2 --- The Kohn-Sham Approach --- p.35 / Chapter 2.3.3 --- Approximation to the Exchange- Correlation Energy --- p.37 / Chapter CHAPTER THREE: --- INTERPRETATION OF 59Co NMR SHIELDING USING THE HARD AND SOFT ACID-BASE CONCEPT -- INSIGHT INTO THE RELATIVE MAGNITUDE OF THE NEPHELAUXETIC AND THE SPETROCHEMICAL EFFECT --- p.39 / Chapter 3.0 --- Introduction --- p.39 / Chapter 3.1 --- Theory --- p.42 / Chapter 3.2 --- Evaluation of the Model --- p.45 / Chapter 3.3 --- Application to the Studies of trans-[Co(en)2X2](3+2n) + in Different Solvents and the Determination of the Spectrochemical Trend --- p.54 / Chapter 3.4 --- "Simultaneous Determination of the Nuclear Quadrupole Coupling Constant, Chemical Shift Anisotropy and Rotational Correlation Time in trans-Na[Co(acac)2(NO2)2]， trans- [Co(acac)2(NH3)2 ]I, trans-[Co(acac)2(CH3NH2)2]I and trans-[Co(acac)2(NH3)(NO2)]" --- p.59 / Chapter 3.5 --- Summary --- p.64 / Chapter CHAPTER FOUR: --- DENSITY FUNCTIONAL STUDY OF THE ELECTRONIC STRUCTURES OF [Co(NH3)5X](3+n)+ USING DIFFERENT POPULATION AND BONDING ANALYSIS METHODS --- p.66 / Chapter 4.0 --- Introduction --- p.66 / Chapter 4.1 --- Computational Details --- p.69 / Chapter 4.2 --- Bond Covalency Analysis of [Co(NH3)5X](3+n)+ --- p.71 / Chapter 4.2.1 --- Mayer Bond Order Analysis --- p.71 / Chapter 4.2.2 --- Natural Population Analysis --- p.73 / Chapter 4.2.3 --- Natural Bond Orbital Analysis --- p.76 / Chapter 4.2.4 --- Mulliken Population Analysis --- p.82 / Chapter 4.3 --- Summary --- p.86 / Chapter CHAPTER FIVE: --- DENSITY FUNCTIONAL STUDY OF 59Co CHEMICAL SHIELDING CONSTANTS --- p.87 / Chapter 5.0 --- Introduction --- p.87 / Chapter 5.1 --- SOS-DFPT-IGLO Calculations of 59Co NMR Shielding Parameters of Hexacoordinated Diamagnetic Co(III) Complexes --- p.90 / Chapter 5.1.1 --- Computational Details --- p.91 / Chapter 5.1.2 --- Basis Sets and XC Functional for 59Co Shielding Calculations --- p.92 / Chapter 5.1.2.1 --- 59Co NMR Shielding Calculation of [Co(CN)6]3- --- p.92 / Chapter 5.1.2.2 --- Nearest Neighbour Effect --- p.94 / Chapter 5.1.3 --- Comparison of the Calculated and Experimental 59Co Chemical Shift Anisotropy and Asymmetry Factor --- p.95 / Chapter 5.1.4 --- Comparison of the Calculated and Experimental 59Co Isotropic Chemical Shifts --- p.97 / Chapter 5.1.4.1 --- Reproducing the Experimental Trend by SOS-DFPT-IGLO? --- p.99 / Chapter 5.1.4.2 --- Local and Non-local Paramagnetic Shielding Contributions --- p.103 / Chapter 5.1.5 --- General Comments of the Calculated Results --- p.104 / Chapter 5.2 --- A Comparative Study of the Calculation of 59Co NMR Shielding Constants of Hexacoordinated Diamagnetic Co(III) Complexes Using SOS-DFPT-IGLO and Hybrid DFT-GIAO Methods --- p.105 / Chapter 5.2.1 --- Computational Details --- p.106 / Chapter 5.2.2 --- Comparison of DFT-IGLO-Becke/Perdew and DFT-GIAO-Becke/Perdew --- p.106 / Chapter 5.2.3 --- DFT-GIAO-B3LYP --- p.108 / Chapter 5.2.4 --- Summary --- p.111 / Chapter CHAPTER SIX: --- STUDY OF THE SHIELDING CONSTANTS OF DIAMAGNETIC HEXACOORDINATED Co(III) COMPLEXES BY POLYCRYSTALLINE 59Co NMR AND DENSITY FUNCTIONAL THEORY --- p.112 / Chapter 6.0 --- Introduction --- p.112 / Chapter 6.1 --- Solid State NMR Technique for Quadrupolar Nuclei --- p.112 / Chapter 6.2 --- Static Powder Lineshape Analysis --- p.114 / Chapter 6.2.1 --- Excitation of Quadrupolar Nuclei --- p.114 / Chapter 6.2.1.1 --- Selective and Partially Selective Excitation --- p.116 / Chapter 6.2.2 --- Spin Echo Pulse Sequence --- p.117 / Chapter 6.2.3 --- Lineshape Simulation --- p.120 / Chapter 6.3 --- Solid State 59Co NMR Study of Hexacoordinated Co(III) Complexes --- p.124 / Chapter 6.3.1 --- Experimental --- p.124 / Chapter 6.3.2 --- Simulation Details --- p.125 / Chapter 6.3.2.1 --- [Co(NH3)4CO3]NO3 --- p.127 / Chapter 6.3.2.2 --- [Co(en)2CO3]Cl and [Co(en)2NO3](NO3)2 --- p.130 / Chapter 6.3.2.3 --- cis-[Co(en)2(N02)2]NO3 and cis-[Co(en)2(N3)2]NO3 --- p.133 / Chapter 6.3.2.4 --- K3[Co(CN)6] --- p.133 / Chapter 6.3.2.5 --- "Co(acac)3， K3[Co(NO2)6] and [Co(en)3]X3 (X = C1, Br, I)" --- p.137 / Chapter 6.4 --- Dependence of 59Co Shielding Calculation on Basis Sets and Exchange Correlation Functional --- p.143 / Chapter 6.4.1 --- CSA and η calculations of [Co(NH3)4C03] Br --- p.144 / Chapter 6.4.2 --- CSA and η Calculations of [Co(NH3)6]C13 --- p.147 / Chapter 6.4.3 --- Shielding Calculations of Larger Co(III) Complexes at B3PW91/6311+G* Level --- p.149 / Chapter 6.5 --- Summary --- p.153 / Chapter CHAPTER SEVEN: --- CONCLUSION AND FUTURE WORK --- p.154 / BIBLIOGRAPHY --- p.157 / APPENDIX A MATHEMATICAL DETAILS FOR THE DERIVATION OF THE RAMSEY SHIELDING EQUATION --- p.171 / APPENDIX B ANALYSIS OF THE SIGN OF PARAMAGNETIC AND DIAMAGNETIC SHIELDING --- p.178 / APPENDIX C GENERALIZATION OF EQUATION [3.4] TO INCLUDE THE EFFECT OF π-BONDING --- p.181 / APPENDIX D GEOMETRY OPTIMIZATION OF CoH AND CoO --- p.183 / APPENDIX E A NON-LINEAR ITERATIVE LEAST SQUARE FITTING PROCEDURE FOR THE ANALYSIS OF SOLID STATE NMR STATIC SPECTRUM OF QUADRUPOLAR NUCLEUS --- p.187