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Introduction to Relativistic Quantum Chemistry Book

Introduction to Relativistic Quantum Chemistry
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 has a rating of 4 stars
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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
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  • Introduction to Relativistic Quantum Chemistry
  • Written by author Kenneth G. Dyall
  • Published by Oxford University Press, USA, January 2007
  • 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
  • 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
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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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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

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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

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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

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