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Notation Conventions vii
Foundations
Introduction 3
Basic Special Relativity 6
Inertial Frames and Newtonian Mechanics 6
Relativistic Coordinate Transformations 7
Transformation of Lengths and Relativistic Invariants 9
Transformation of Velocities 11
Transformation of Mass 13
Relativistic Energy 14
Relativistic Momentum 15
Relativistic Electromagnetic Interactions 17
The Maxwell Equations 18
Potentials and Gauge Transformations 19
The Relativistic Potential from a Moving Charge 22
The Potential Experienced by a Moving Charge 24
The Interaction of Two Charged Particles 26
The Dirac Equation: Solutions and Properties
The Dirac Equation 35
Quantization of the Nonrelativistic Hamiltonian 36
Spin in the Nonrelativistic Hamiltonian 37
The Dirac Equation 39
The Time-Independent Dirac Equation 44
The Dirac Wave Function 45
Nonrelativistic Limit of the Dirac Equation 49
Negative-Energy States and Quantum Electrodynamics 54
SecondQuantization 57
Relativistic Second-Quantized Hamiltonians 59
Definition of the Vacuum 62
The Electron-Electron Interaction 64
The Lamb Shift 68
Relativistic Symmetry 70
The Symmetry of the Relativistic One-Electron Atom 71
Double Groups 73
Spin and the SU(2) Group 77
Spatial Rotations and the SO(3) Group 80
Transformation of Operators 84
Transformation of the Dirac Equation under SU(2) and SO(3) 86
Space Inversion 89
Reflections and Rotation-Inversions 91
Time Reversal 92
Lorentz Transformations and the Lorentz Group 97
One-Electron Atoms 100
Separation of Variables in the Dirac Equation 100
Angular Wave Functions 103
Solutions of the Radial Dirac Equation 106
Behavior at Large r 111
Behavior at Small r 112
Nuclear Models 115
Properties of Relativistic Mean-Field Theory 118
Mean-Field Formalism in Second Quantization 119
Structure of the Spinor Rotation Operator 125
Relativistic Stationarity Conditions 128
Projection and Bounds 130
Many-Electron Theory 131
Four-Component Methodology
Operators, Matrix Elements, and Wave Functions under Time-Reversal Symmetry 135
Time Reversal and Kramers-Restricted Representation of Operators 136
Matrix Elements under Time Reversal 142
Many-Particle States and Time Reversal 144
Matrices and Wave Functions under Double-Group Symmetry 148
Time-Reversal and Point-Group Symmetry 148
Time-Reversal Symmetry and Matrix Block Structure 152
Symmetry of Spinor Components 157
Symmetries of Two-Particle States 162
Matrix Elements and Symmetry 166
Time Reversal and Symmetry in the Many-Electron Hamiltonian 169
Basis-Set Expansions of Relativistic Electronic Wave Functions 174
The Dirac Equation in 2-Spinor Form 175
Kinetic Balance 176
Variational Bounds 178
Matrix Dirac-Hartree-Fock Equations in a 2-Spinor Basis 181
Kramers-Restricted 2-Spinor Matrix Dirac-Hartree-Fock Equations 184
Symmetry in the Kramers-Restricted Fock Matrix 187
Kramers-Restricted Open-Shell Methods 189
Expansion in Scalar Basis Sets 192
Basis Set Choice and Design 198
Comparison of Nonrelativistic and Relativistic SCF Methods 204
Correlation Methods 207
The Reference State 208
The No-Pair Approximation 210
Integral Transformations 211
Kramers-Restricted Moller-Plesset Perturbation Theory 213
Kramers-Restricted Coupled-Cluster Expansions 216
Open-Shell Kramers-Restricted Coupled-Cluster Expansions 219
Configuration Interaction Expansions 221
The Cost of Configuration Interaction Methods 227
Relativistic Multiconfiguration Self-Consistent Field Theory 228
Molecular Properties 233
Intrinsic Properties 234
Electric Properties 237
Gauge Invariance and Finite Basis Sets 239
Magnetic Properties 242
Second-Order Properties 245
NMR Parameters 248
Alternative Treatment of Magnetic Interactions 250
Finite Nucleus Effects on Properties 252
Parity-Violating Interactions 255
Density Functional Approaches to Relativistic Quantum Mechanics 261
A Brief Review of Nonrelativistic Density Functional Theory 262
The Local Density and Local Exchange Approximations 266
The Hohenberg-Kohn Theorem for Relativistic N-Particle Systems 268
Density Functional Theory and the Dirac-Coulomb Hamiltonian 270
Approximations to the Dirac Equation
Spin Separation and the Modified Dirac Equation 277
The Modified Dirac Equation 278
Solutions of the Spin-Free Modified Dirac Equation 281
Modified One-Electron Operators 284
Modified Two-Electron Operators 287
Practical Implications of Spin Separation 291
Unitary Transformations of the Dirac Hamiltonian 295
The Foldy-Wouthuysen Transformation 296
Approximate Foldy-Wouthuysen Transformations 299
The Douglas-Kroll Transformation 302
Two-Electron Terms and the Douglas-Kroll-Hess Approximation 308
Implementation of the Douglas-Kroll Transformation 309
The Barysz-Sadlej-Snijders Transformation 311
Transformation of Electric Property Operators 313
Transformation of Magnetic Property Operators 317
Perturbation Methods 322
The Pauli Hamiltonian 323
The Breit-Pauli Hamiltonian 327
Perturbative Treatment of the Lamb Shift 331
Multiple Perturbation Theory for Many-Electron Systems and Properties 333
Direct Perturbation Theory 336
Stationary Direct Perturbation Theory 341
Stationary Direct Perturbation Theory for Many-Electron Systems 347
Direct Perturbation Theory of Properties 350
Regular Approximations 356
The CPD or ZORA Hamiltonian 357
Perturbative Corrections to the ZORA Hamiltonian 362
Nonperturbative Improvements of the ZORA Equation 366
Many-Electron Systems 371
Properties in the Regular Approximations 377
Matrix Approximations 381
The Matrix Elimination of the Small Components 382
Properties of the NESC and UESC Equations 385
Inclusion of the Two-Electron Terms 388
Atom-Centered Approximations 391
Properties in the Matrix Approximations 394
Core Approximations 396
The Frozen-Core Approximation 398
The Generalized Philips-Kleinman Pseudopotential 401
Shape-Consistent Pseudospinors and Pseudopotentials 406
Energetics of Pseudopotentials 409
Generation of Pseudopotentials 413
Relativistic Effects in Pseudopotentials 415
Model Potentials 418
Energetics of Model Potentials 420
Model Potential Implementation 423
Relativistic Effects in Model Potentials 424
Properties and Core Approximations 425
Spin-Orbit Configuration Interaction Methods 427
Breit-Pauli Spin-Orbit Operators 428
Douglas-Kroll-Transformed Spin-Orbit Operators 431
Spin-Orbit Operators for Model Potential and Pseudopotential Methods 434
Mean-Field Approximations for Spin-Orbit Interaction 435
Strategies for Spin-Orbit Methods 439
One-Particle and N-Particle Expansion Spaces 441
One-Step Methods 442
Two-Step Methods 446
The Nature of the Relativistic Chemical Bond
Relativistic Effects on Molecular Bonding and Structure 453
Relativistic Effects on Atomic Shell Structure 453
Spin-Free Effects on Molecular Structure 456
Spinor Bonds in Diatomic Molecules 461
Hybridization and Bonding in Polyatomic Molecules 465
Relativistic Effects on Properties 467
A Final Warning 470
Appendices
Four-Vector Quantities 473
Vector Relations 474
Elements of Group Theory 476
Group Tables 479
Change of Metric for Modified Wave Functions 483
Two-Electron Gauge Terms for the Modified Dirac Operator 486
The Second-Order Term of the Douglas-Kroll Expansion 489
Transformed Operators for Electric and Magnetic Properties 491
Gauge Term Contributions from the Breit Interaction to the Breit-Pauli Hamiltonian 495
Approximations in Relativistic Density Functional Theory 498
The Cowan-Griffin and Wood-Boring Equations 501
Supplementary Reading 503
Bibliography 507
Index 515
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Add Introduction to Relativistic Quantum Chemistry, This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a go, Introduction to Relativistic Quantum Chemistry to the inventory that you are selling on WonderClubX
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Add Introduction to Relativistic Quantum Chemistry, This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a go, Introduction to Relativistic Quantum Chemistry to your collection on WonderClub |