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

Author(s): Krishnan Balasubramanian (Arizona State Univ., Tempe)
ISBN10: 047130400X
ISBN13: 9780471304005
Cover: Hardcover
 
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SummaryTable of ContentsAuthor Biography
E = mc2 and the Periodic Table . . .

RELATIVISTIC EFFECTS IN CHEMISTRY

This century's most famous equation, Einstein's special theory of relativity, transformed our comprehension of the nature of time and matter. Today, making use of the theory in a relativistic analysis of heavy molecules, that is, computing the properties and nature of electrons, is the work of chemists intent on exploring the mysteries of minute particles.

The first work of its kind, Relativistic Effects in Chemistry details the computational and analytical methods used in studying the relativistic effects in chemical bonding as well as the spectroscopic properties of molecules containing very heavy atoms. The first of two independent volumes, Part A: Theory and Techniques describes the basic techniques of relativistic quantum chemistry. Its systematic five-part format begins with a detailed exposition of Einstein's special theory of relativity, the significance of relativity in chemistry, and the nature of relativistic effects, especially with molecules containing both main group atoms and transition metal atoms.

Chapter 3 discusses the fundamentals of relativistic quantum mechanics starting from the Klein-Gordon equation through such advanced constructs as the Breit-Pauli and Dirac multielectron Hamiltonian. Modern computational techniques, of importance with problems involving very heavy molecules, are outlined in Chapter 4. These include the relativistic effective core potentials, ab initio CASSCF, CI, and RCI techniques. Chapter 5 describes relativistic symmetry using the double group symmetry of molecules and the classification of relativistic electronic states and is of special importance to chemists or spectroscopists interested in computing or analyzing electronic states of molecules containing very heavy atoms.

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.
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
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.

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