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.