Introduction to relativistic quantum chemistry / Kenneth G. Dyall, Knut Faegri, Jr.

Format:

Book

Author/Creator:

Dyall, Kenneth G., 1955-

Contributor:

Fgri, Knut, 1946-

Language:

English

Subjects (All):

Quantum chemistry.

Quantum field theory.

Physical Description:

xiv, 530 p. : ill.

Edition:

1st ed.

Place of Publication:

New York : Oxford University Press, 2007.

Summary:

This book introduces relativistic methods in quantum chemistry to non-experts and students. Its five sections cover classical relativity background; the Dirac equation; four-component methods, including symmetry, correlation, and properties; approximate methods, including perturbation theory, transformed Hamiltonians, regular approximations, matrix approximations, and pseudopotential methods; and an overview of relativistic effects on bonding.

Contents:

Cover

Title Page

Copyright Page

Preface

Notation Conventions

Contents

I: Foundations

1 Introduction

2 Basic Special Relativity

2.1 Inertial Frames and Newtonian Mechanics

2.2 Relativistic Coordinate Transformations

2.3 Transformation of Lengths and Relativistic Invariants

2.4 Transformation of Velocities

2.5 Transformation of Mass

2.6 Relativistic Energy

2.7 Relativistic Momentum

3 Relativistic Electromagnetic Interactions

3.1 The Maxwell Equations

3.2 Potentials and Gauge Transformations

3.3 The Relativistic Potential from a Moving Charge

3.4 The Potential Experienced by a Moving Charge

3.5 The Interaction of Two Charged Particles

II: The Dirac Equation: Solutions and Properties

4 The Dirac Equation

4.1 Quantization of the Nonrelativistic Hamiltonian

4.2 Spin in the Nonrelativistic Hamiltonian

4.3 The Dirac Equation

4.4 The Time-Independent Dirac Equation

4.5 The Dirac Wave Function

4.6 Nonrelativistic Limit of the Dirac Equation

5 Negative-Energy States and Quantum Electrodynamics

5.1 Second Quantization

5.2 Relativistic Second-Quantized Hamiltonians

5.3 Definition of the Vacuum

5.4 The Electron-Electron Interaction

5.5 The Lamb Shift

6 Relativistic Symmetry

6.1 The Symmetry of the Relativistic One-Electron Atom

6.2 Double Groups

6.3 Spin and the SU(2) Group

6.4 Spatial Rotations and the SO(3) Group

6.5 Transformation of Operators

6.6 Transformation of the Dirac Equation under SU(2) and SO(3)

6.7 Space Inversion

6.8 Reflections and Rotation-Inversions

6.9 Time Reversal

6.10 Lorentz Transformations and the Lorentz Group

7 One-Electron Atoms

7.1 Separation of Variables in the Dirac Equation

7.2 Angular Wave Functions

7.3 Solutions of the Radial Dirac Equation

7.4 Behavior at Large r.

7.5 Behavior at Small r

7.6 Nuclear Models

8 Properties of Relativistic Mean-Field Theory

8.1 Mean-Field Formalism in Second Quantization

8.2 Structure of the Spinor Rotation Operator

8.3 Relativistic Stationarity Conditions

8.4 Projection and Bounds

8.5 Many-Electron Theory

III: Four-Component Methodology

9 Operators, Matrix Elements, and Wave Functions under Time-Reversal Symmetry

9.1 Time Reversal and Kramers-Restricted Representation of Operators

9.2 Matrix Elements under Time Reversal

9.3 Many-Particle States and Time Reversal

10 Matrices and Wave Functions under Double-Group Symmetry

10.1 Time-Reversal and Point-Group Symmetry

10.2 Time-Reversal Symmetry and Matrix Block Structure

10.3 Symmetry of Spinor Components

10.4 Symmetries of Two-Particle States

10.5 Matrix Elements and Symmetry

10.6 Time Reversal and Symmetry in the Many-Electron Hamiltonian

11 Basis-Set Expansions of Relativistic Electronic Wave Functions

11.1 The Dirac Equation in 2-Spinor Form

11.2 Kinetic Balance

11.3 Variational Bounds

11.4 Matrix Dirac-Hartree-Fock Equations in a 2-Spinor Basis

11.5 Kramers-Restricted 2-Spinor Matrix Dirac-Hartree-Fock Equations

11.6 Symmetry in the Kramers-Restricted Fock Matrix

11.7 Kramers-Restricted Open-Shell Methods

11.8 Expansion in Scalar Basis Sets

11.9 Basis Set Choice and Design

11.10 Comparison of Nonrelativistic and Relativistic SCF Methods

12 Correlation Methods

12.1 The Reference State

12.2 The No-Pair Approximation

12.3 Integral Transformations

12.4 Kramers-Restricted Møller-Plesset Perturbation Theory

12.5 Kramers-Restricted Coupled-Cluster Expansions

12.6 Open-Shell Kramers-Restricted Coupled-Cluster Expansions

12.7 Configuration Interaction Expansions

12.8 The Cost of Configuration Interaction Methods.

12.9 Relativistic Multiconfiguration Self-Consistent Field Theory

13 Molecular Properties

13.1 Intrinsic Properties

13.2 Electric Properties

13.3 Gauge Invariance and Finite Basis Sets

13.4 Magnetic Properties

13.5 Second-Order Properties

13.6 NMR Parameters

13.7 Alternative Treatment of Magnetic Interactions

13.8 Finite Nucleus Effects on Properties

13.9 Parity-Violating Interactions

14 Density Functional Approaches to Relativistic Quantum Mechanics

14.1 A Brief Review of Nonrelativistic Density Functional Theory

14.2 The Local Density and Local Exchange Approximations

14.3 The Hohenberg-Kohn Theorem for Relativistic N-Particle Systems

14.4 Density Functional Theory and the Dirac-Coulomb Hamiltonian

IV: Approximations to the Dirac Equation

15 Spin Separation and the Modified Dirac Equation

15.1 The Modified Dirac Equation

15.2 Solutions of the Spin-Free Modified Dirac Equation

15.3 Modified One-Electron Operators

15.4 Modified Two-Electron Operators

15.5 Practical Implications of Spin Separation

16 Unitary Transformations of the Dirac Hamiltonian

16.1 The Foldy-Wouthuysen Transformation

16.2 Approximate Foldy-Wouthuysen Transformations

16.3 The Douglas-Kroll Transformation

16.4 Two-Electron Terms and the Douglas-Kroll-Hess Approximation

16.5 Implementation of the Douglas-Kroll Transformation

16.6 The Barysz-Sadlej-Snijders Transformation

16.7 Transformation of Electric Property Operators

16.8 Transformation of Magnetic Property Operators

17 Perturbation Methods

17.1 The Pauli Hamiltonian

17.2 The Breit-Pauli Hamiltonian

17.3 Perturbative Treatment of the Lamb Shift

17.4 Multiple Perturbation Theory for Many-Electron Systems and Properties

17.5 Direct Perturbation Theory

17.6 Stationary Direct Perturbation Theory.

17.7 Stationary Direct Perturbation Theory for Many-Electron Systems

17.8 Direct Perturbation Theory of Properties

18 Regular Approximations

18.1 The CPD or ZORA Hamiltonian

18.2 Perturbative Corrections to the ZORA Hamiltonian

18.3 Nonperturbative Improvements of the ZORA Equation

18.4 Many-Electron Systems

18.5 Properties in the Regular Approximations

19 Matrix Approximations

19.1 The Matrix Elimination of the Small Components

19.2 Properties of the NESC and UESC Equations

19.3 Inclusion of the Two-Electron Terms

19.4 Atom-Centered Approximations

19.5 Properties in the Matrix Approximations

20 Core Approximations

20.1 The Frozen-Core Approximation

20.2 The Generalized Philips-Kleinman Pseudopotential

20.3 Shape-Consistent Pseudospinors and Pseudopotentials

20.4 Energetics of Pseudopotentials

20.5 Generation of Pseudopotentials

20.6 Relativistic Effects in Pseudopotentials

20.7 Model Potentials

20.8 Energetics of Model Potentials

20.9 Model Potential Implementation

20.10 Relativistic Effects in Model Potentials

20.11 Properties and Core Approximations

21 Spin-Orbit Configuration Interaction Methods

21.1 Breit-Pauli Spin-Orbit Operators

21.2 Douglas-Kroll-Transformed Spin-Orbit Operators

21.3 Spin-Orbit Operators for Model Potential and Pseudopotential Methods

21.4 Mean-Field Approximations for Spin-Orbit Interaction

21.5 Strategies for Spin-Orbit Methods

21.6 One-Particle and N-Particle Expansion Spaces

21.7 One-Step Methods

21.8 Two-Step Methods

V: The Nature of the Relativistic Chemical Bond

22 Relativistic Effects on Molecular Bonding and Structure

22.1 Relativistic Effects on Atomic Shell Structure

22.2 Spin-Free Effects on Molecular Structure

22.3 Spinor Bonds in Diatomic Molecules.

22.4 Hybridization and Bonding in Polyatomic Molecules

22.5 Relativistic Effects on Properties

22.6 A Final Warning

Appendix A: Four-Vector Quantities

Appendix B: Vector Relations

Appendix C: Elements of Group Theory

Appendix D: Group Tables

Appendix E: Change of Metric for Modified Wave Functions

Appendix F: Two-Electron Gauge Terms for the Modified Dirac Operator

Appendix G: The Second-Order Term of the Douglas-Kroll Expansion

Appendix H: Transformed Operators for Electric and Magnetic Properties

Appendix I: Gauge Term Contributions from the Breit Interaction to the Breit-Pauli Hamiltonian

Appendix J: Approximations in Relativistic Density Functional Theory

Appendix K: The Cowan-Griffin and Wood-Boring Equations

Appendix L: Supplementary Reading

Bibliography

Index.

Notes:

Includes bibliographical references.

Description based on metadata supplied by the publisher and other sources.

Description based on publisher supplied metadata and other sources.

ISBN:

9786611158828

9780197561744

0197561748

9781429486156

1429486155

9781281158826

1281158828

9780198032304

0198032307

9780190286378

0190286377

OCLC:

476242480