Part I Approximate Hartree-Fock Wavefunctions One-electron Properties and Electronic Structure of

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Part I Approximate Hartree-Fock Wavefunctions
One-electron Properties and Electronic
Structure of the Water Molecule
Part II Perturbation-Variational Calculation of the Nuclear
Spin-Spin Isotropic Coupling Constant in HD
Thesis by
Soe Aung
In Partial Fulfillment of the Requirements
For the Degree of
Doctor of Philosophy
California Institute of Technology
Pasadena, California
1969
(Submitted November 18, 1968)
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To my father and my mother
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ACKNOWLEDGMENTS
I would like to express my deep sense of gratitude to my
research supervisors, Professor Sunney I. Chan and Professor
Russell M. Pitzer, for invaluable guidance and patient encouragement
given me over the past four years. In particular, I am indebted to
Professors Chan and Pitzer for supervising Part I of this thesis
research, and to Professor Pitzer for supervising Part II. My
graduate education under their supervision covered an area far
broader than is evident in this thesis, however, and I shall take heed
of the idealistic yet practical examples which each of them has set in
his own way.
In connection with Part I of this thesis research, I am further
indebted to the persons named below:
Dr. W. E. Palke, for wise counsel and various favours,
particularly in regard to the modifications of the molecular integral
programs necessitated by the SCF calculations reported in Part I;
Professor W. A. Goddard, for encouragement and much
appreciated discussions given readily and unfailingly with contagious
enthusiasm, as a teacher gives unto his own student;
Dr. D. Eisenberg, for stimulating discussions based on his
encyclopaedic knowledge of the water molecule;
Mr. T. H. Dunning, for his adaptation of W. E. Palke 's
electron density map program and for advice on its use.
In connection with Part II of this thesis, I am indebted to
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Professor R. M. Pitzer for permission to describe his perturbation
variational theory of nuclear spin-spin coupling constants in advance
of publication.
In regard to my general education at Caltech, I would like to
acknowledge my considerable debt to the following persons:
Professor Richard M. Badger, for much encouragement given
very early in my period of graduate study, and for providing me with
an idea of the essential qualities of a dedicated scientist and scholar;
Professor V. McKoy, for advice and discussions given without
reservation over the past years;
My colleagues, past and present, particularly Dr. L. C.-T. Lin,
Dr. R. T. Iwamasa, Dr. T. E. Burke, and Mr. L. Lynds, for
advice and companionship;
Mr. Dana Roth, Chemistry Librarian, for numerous favours.
Finally, I am greatly indebted to the California Institute of
Technology, the U.S. Public Health Service, the National Science
Foundation, and the IBM Corporation for financial support during my
period of study at Caltech.
Typing of this thesis was done by Mrs. Harue Bierce.
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Abstract. Part I.
Several approximate Hartree-Fock SCF wavefunctions for the
ground electronic state of the water molecule have been obtained
using an increasing number of multicenter s, p, and d Slater-type
atomic orbitals as basis sets. The predicted charge distribution has
been extensively tested at each stage by calculating the electric dipole
moment, molecular quadrupole moment, diamagnetic shielding,
Hellmann-Feynman forces, and electric field gradients at both the
hydrogen and the oxygen nuclei. It was found that a carefully optimized
minimal basis set suffices to describe the electronic charge distri
bution adequately except in the vicinity of the oxygen nucleus. Our
calculations indicate, for example, that the correct prediction of the
field gradient at this nucleus requires a more flexible linear combi
nation of p-orbitals centered on this nucleus than that in the minimal
basis set. Theoretical values for the molecular octopole moment
components are also reported.
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Abstract. Part II.
The perturbation-variational theory of R. M. Pitzer for nuclear
spin-spin coupling constants is applied to the HD molecule. The zero
order molecular orbital is described in terms of a single ls Slater-
type basis function centered on each nucleus. The first-order molec
ular orbital is expressed in terms of these two functions plus one
-r
singular basis function each of the types er and e-r ln r centered on
one of the nuclei. The new kinds of molecular integrals were
evaluated to high accuracy using numerical and analytical means.
The value of the HD spin-spin coupling constant calculated with this
near-minimal set of basis functions is JHD = +96. 6 cps. This
represents an improvement over the previous calculated value of +120
cps obtained without using the logarithmic basis function but is still
considerably off in magnitude compared with the experimental measure-
ment of JHD = +43. 0 ± 0. 5 cps.
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TABLE OF CONTENTS
Part I: Approximate Hartree-Fock Wavefunctions, One-Electron
Properties, and Electronic Structure of the Water Molecule
1. INTRODUCTION
L 1 Previous ab initio calculations on the water molecule . 3
1. 2 Experimental measurements on the water molecule 7
1. 2. 1 Properties measured 7
1. 2. 2 Problems involved in some of the measure- 7
ment s
1. 3 Scope of this thesis research 10
2. HARTREE-FOCK THEORY 12
3. WAVEFUNCTIONS FOR THE WATER MOLECULE 14
3. 1 Computer programs 14
3. 2 Calculations 19
4. ELECTRONIC PROPERTIES 29
4. 1 Definitions and nature of one-electron properties 29
4. 2 Computation of one-electron properties 3 6
4. 3 Results and comparison with experiment 39
4. 4 Discussion of results 45
4. 4. 1 Energies 45
4. 4. 2 One-electron properties 47
4. 4. 2. 1 Oxygen field gradient 47
4. 4. 2. 2 Deuteron field gradient 56
4. 4. 2. 3 Hellmann-Feynman forces 56
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4. 4. 2. 4 Diamagnetic shieldings 56
4. 4. 2. 5 Dipole, quadrupole, and octopole 57
moments
5. ELECTRONIC STRUCTURE 59
5. 1 Contour maps 59
5. 2 Nature of the chemical bond 59
6. CONCLUSION 67
APPENDIX Implication of Stevenson and Townes' 73
Approximation concerning the 170 Effective
Spin-Rotational Constant in HD170
REFERENCES 77
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TABLE OF CONTENTS
Part II: Perturbation-Variational Calculation of the Nuclear
Spin-Spin Isotropic Coupling Constant in HD
Page
1. INTRODUCTION 86
1. 1 Discovery of nuclear spin-spin isotropic coupling 86
1. 2 Origin of the coupling 86
1. 3 Theoretical calculations of the coupling constant 90
1. 4 Object of this thesis research 93
2. THE PERTURBATION-VARIATIONAL APPROACH OF 97
R. M. PITZER
2.1 Basic idea 97
2.2 The equations for the first-order molecular 101
orbital coefficients
2.3 Rationalization and treatment of divergent 110
integrals
2.4 Cusp conditions on the first-order molecular 115
orbitals
3. APPLICATION TO THE HD MOLECULE 120
3.1 Basis functions 120
3.2 Evaluation of integrals 122
3. 2. 1 Divergent integrals 122
3.2.2 Finite integrals 122
3.3 Results and discussion 129
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4. CONCLUSION 140
APPENDIX A. The first-order wavefunction of the 141
hydrogen atom perturbed by Fermi
contact interaction
APPENDIX B. The Laplacian of in r 144
APPENDIX C. The second-order self-coupling energy 146
in HD
REFERENCES 148
PRO POSITIONS 150