Relativistic Effects in Chemistry, Theory and

An exceptional introduction to one of chemistry's foremost analytical techniques, Relativistic Effects in Chemistry is also evidence of the still unending reverberations of Einstein's revolutionary theory.

KRISHNAN BALASUBRAMANIAN is Professor of Chemistry at Arizona State University. He has received the Alfred P. Sloan Fellowship, Camille and Henry Dreyfus teacher-scholar and Fulbright Research awards. He is an author of about 400 journal publications.

Preface

ix

1 Introduction

1

(30)

2 Special Relativity

31

(65)

2.1 Introduction

31

(2)

2.2 Galilean Transformations and Frames of Reference

33

(4)

2.3 The Michelson-Morley Experiment

37

(3)

2.4 Einstein's Axioms of Special Theory of Relativity

40

(2)

2.5 Relativistic Simultaneity

42

(3)

2.6 The Lorentz Transformations

45

(7)

2.6.1 Relativistic Inertial Frames and Derivation of the Transformations

45

(5)

2.6.2 Lorentz Transformation as a Rotation in Four-Dimensional Space

50

(2)

2.7 Properties of Lorentz Transformations

52

(1)

2.8 Space-Time Diagrams

53

(2)

2.9 Length Contraction

55

(1)

2.10 Time Dilation

56

(1)

2.11 Twin Paradox

57

(1)

2.12 Relativistic Transformation of Velocities

58

(2)

2.13 Relativistic Mass

60

(5)

2.14 Mass-Energy Equivalence

65

(3)

2.15 Relativistic Kinetic Energy and Momentum

68

(2)

2.16 Lorentz Transformation for Momentum and Energy

70

(2)

2.17 Relativistic Mechanics

72

(2)

2.18 Relativistic Force

74

(2)

2.19 Four-Dimensional Linear and Angular Momentum

76

(2)

2.20 Relativistic Electromagnetism

78

(11)

2.21 Group Theoretical Representation of Lorentz Transformations

89

(7)

3 Relativistic Quantum Mechanics

96

(101)

3.1 Introduction

96

(3)

3.2 The Klein-Gordon Equation

99

(2)

3.3 Solution of the Free-Particle Klein-Gordon Equation and Its Properties

101

(1)

3.4 The Klein-Gordon Equation for a Charged Particle in an Electromagnetic Field

102

(2)

3.5 Solution of Klein-Gordon Equation in a Coulombic Field

104

(4)

3.6 Nonrelativistic Limit of the Klein-Gordon Equation

108

(2)

3.7 The Dirac Equation

110

(9)

3.8 Solution of the Dirac Equation for a Free Electron

119

(5)

3.9 Relativistic One-Dimensional Barrier

124

(5)

3.10 Properties of the XXX Matrices

129

(3)

3.11 Relativistic Angular Momentum in Terms of Pauli Matrices

132

(7)

3.12 Dirac Equation for a Charged Particle in an Electromagnetic Field

139

(2)

3.13 Foldy-Wouthuysen Transformation of the Dirac Equation

141

(2)

3.14 Pauli Approximation to the Dirac Equation

143

(7)

3.15 Pauli Theory of the Hydrogen Atom

150

(9)

3.16 Exact Solution of the Dirac Equation for the Hydrogen Atom

159

(17)

3.17 Positrons and Negative Energy Solutions

176

(2)

3.18 Fine Structure and Lamb Shift

178

(2)

3.19 Breit Equations for Two-Electron Problem

180

(8)

3.20 Evaluation of the Breit-Pauli Terms for Heliumlike Atoms

188

(5)

3.20.1 Mass-Velocity Term

188

(1)

3.20.2 Retardation Correction and Darwin Correction

189

(1)

3.20.3 Spin-Orbit Correction

190

(2)

3.20.4 Spin-Spin Interaction for Helium

192

(1)

3.21 Breit-Pauli Approximation to the Multielectron Problem

193

(2)

3.22 Bethe-Salpeter Covariant Equation

195

(2)

4 Relativistic Quantum Chemistry

197

(20)

4.1 Relativistic Hamiltonians for Multielectron Systems

198

(3)

4.2 Computational Techniques for Molecules Containing Very Heavy Atoms

201

(7)

4.2.1 Ab initio Effective Core Potential Techniques

201

(7)

4.3 Ab Initio SCF, CASSCF, CI, and RCI Methods for the Electronic Structure of Molecules

208

(3)

4.4 Approximate Methods

211

(6)

4.4.1 Ligand Field Theory

211

(1)

4.4.2 Local Density Function (LDF) Method

211

(2)

4.4.3 Intermediate Neglect of Differential Overlap/Spin-Orbit CI Method (INDO/S-CI)

213

(4)

5 Double-Group Symmetry and the Classification of Relativistic Electronic States

217

(76)

5.1 Double-Group Symmetry

217

(4)

5.2 Double-Group of Diatomics

221

(1)

5.3 Nonrelativistic Classification of the Electronic States of Diatomics

222

(7)

5.4 Relativistic Treatment of Electronic States of a Diatomic and Use of the Double-Group Theory

229

(10)

5.5 Relativistic Wavefunctions for the Relativistic Electronic States of a Diatomic

239

(7)

5.6 Double Groups of Polyatomic Molecules

246

(30)

5.7 Correlation of Spin States in the Double Group and Enumeration of Relativistic States

276

(10)

5.8 Symmetry-Adapted Spin Functions for the Relativistic Electronic States

286

(7)

Index

293

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Relativistic Effects in Chemistry, Theory and Techniques and Relativistic Effects in Chemistry

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