Introduction to relativistic quantum chemistry:
Gespeichert in:
Hauptverfasser: | , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York
Oxford University Press
[2007]
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | xiv, 530 Seiten |
ISBN: | 9780195140866 |
Internformat
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Datensatz im Suchindex
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adam_text | Titel: Introduction to relativistic quantum chemistry
Autor: Dyall, Kenneth G
Jahr: 2007
Contents
Notation Conventions, vii
I: Foundations
1 Introduction, 3
2 Basic Special Relativity, 6
2.1 Inertia! Frames and Newtonian Mechanics, 6
2.2 Relativistic Coordinate Transformations, 7
2.3 Transformation of Lengths and Relativistic Invariants, 9
2.4 Transformation of Velocities, 11
2.5 Transformation of Mass, 13
2.6 Relativistic Energy, 14
2.7 Relativistic Momentum, 15
3 Relativistic Electromagnetic Interactions, 17
3.1 The Maxwell Equations, 18
3.2 Potentials and Gauge Transformations, 19
3.3 The Relativistic Potential from a Moving Charge, 22
3.4 The Potential Experienced by a Moving Charge, 24
3.5 The Interaction of Two Charged Particles, 26
x CONTENTS
II: The Dirac Equation: Solutions and Properties
4 The Dirac Equation, 35
4.1 Quantization of the Nonrelativistic Hamiltonian, 36
4.2 Spin in the Nonrelativistic Hamiltonian, 37
4.3 The Dirac Equation, 39
4.4 The Time-Independent Dirac Equation, 44
4.5 The Dirac Wave Function, 45
4.6 Nonrelativistic Limit of the Dirac Equation, 49
5 Negative-Energy States and Quantum Electrodynamics, 54
5.1 Second Quantization, 57
5.2 Relativistic Second-Quantized Hamiltonians, 59
5.3 Definition of the Vacuum, 62
5.4 The Electron-Electron Interaction, 64
5.5 The Lamb Shift, 68
6 Relativistic Symmetry, 70
6.1 The Symmetry of the Relativistic One-Electron Atom, 71
6.2 Double Groups, 73
6.3 Spin and the SU{2) Group, 77
6.4 Spatial Rotations and the 50(3) Group, 80
6.5 Transformation of Operators, 84
6.6 Transformation of the Dirac Equation under SU(2)
and 50(3), 86
6.7 Space Inversion, 89
6.8 Reflections and Rotation-Inversions, 91
6.9 Time Reversal, 92
6.10 Lorentz Transformations and the Lorentz Group, 97
7 One-Electron Atoms, 100
7.1 Separation of Variables in the Dirac Equation, 100
7.2 Angular Wave Functions, 103
7.3 Solutions of the Radial Dirac Equation, 106
7.4 Behavior at Large r, 111
7.5 Behavior at Small r, 112
7.6 Nuclear Models, 115
8 Properties of Relativistic Mean-Field Theory, 118
8.1 Mean-Field Formalism in Second Quantization, 119
8.2 Structure of the Spinor Rotation Operator, 125
8.3 Relativistic Stationarity Conditions, 128
8.4 Projection and Bounds, 130
8.5 Many-Electron Theory, 131
CONTENTS xi
III: Four-Component Methodology
9 Operators, Matrix Elements, and Wave Functions under
Time-Reversal Symmetry, 135
9.1 Time Reversal and Kramers-Restricted Representation
of Operators, 136
9.2 Matrix Elements under Time Reversal, 142
9.3 Many-Particle States and Time Reversal, 144
10 Matrices and Wave Functions under Double-Group
Symmetry, 148
10.1 Time-Reversal and Point-Group Symmetry, 148
10.2 Time-Reversal Symmetry and Matrix Block Structure, 152
10.3 Symmetry of Spinor Components, 157
10.4 Symmetries of Two-Particle States, 162
10.5 Matrix Elements and Symmetry, 166
10.6 Time Reversal and Symmetry in the Many-Electron
Hamiltonian, 169
11 Basis-Set Expansions of Relativistic Electronic
Wave Functions, 174
11.1 The Dirac Equation in 2-Spinor Form, 175
11.2 Kinetic Balance, 176
11.3 Variational Bounds, 178
11.4 Matrix Dirac-Hartree-Fock Equations in a
2-Spinor Basis, 181
11.5 Kramers-Restricted 2-Spinor Matrix Dirac-Hartree-Fock
Equations, 184
11.6 Symmetry in the Kramers-Restricted Fock Matrix, 187
11.7 Kramers-Restricted Open-Shell Methods, 189
11.8 Expansion in Scalar Basis Sets, 192
11.9 Basis Set Choice and Design, 198
11.10 Comparison of Nonrelativistic and Relativistic SCF
Methods, 204
12 Correlation Methods, 207
12.1 The Reference State, 208
12.2 The No-Pair Approximation, 210
12.3 Integral Transformations, 211
12.4 Kramers-Restricted M0ller-Plesset Perturbation
Theory, 213
12.5 Kramers-Restricted Coupled-Cluster Expansions, 216
12.6 Open-Shell Kramers-Restricted Coupled-Cluster
Expansions, 219
12.7 Configuration Interaction Expansions, 221
x¡¡ CONTENTS
12.8 The Cost of Configuration Interaction Methods, 227
12.9 Relativistic Multiconfiguration Self-Consistent
Field Theory, 228
13 Molecular Properties, 233
13.1 Intrinsic Properties, 234
13.2 Electric Properties, 237
13.3 Gauge Invariance and Finite Basis Sets, 239
13.4 Magnetic Properties, 242
13.5 Second-Order Properties, 245
13.6 NMR Parameters, 248
13.7 Alternative Treatment of Magnetic Interactions, 250
13.8 Finite Nucleus Effects on Properties, 252
13.9 Parity-Violating Interactions, 255
14 Density Functional Approaches to Relativistic Quantum
Mechanics, 261
14.1 A Brief Review of Nonrelativistic Density Functional
Theory, 262
14.2 The Local Density and Local Exchange Approximations, 266
14.3 The Hohenberg-Kohn Theorem for Relativistic
N-Particle Systems, 268
14.4 Density Functional Theory and the Dirac-Coulomb
Hamiltonian, 270
IV: Approximations to the Dirac Equation
15 Spin Separation and the Modified Dirac Equation, 277
15.1 The Modified Dirac Equation, 278
15.2 Solutions of the Spin-Free Modified Dirac Equation, 281
15.3 Modified One-Electron Operators, 284
15.4 Modified Two-Electron Operators, 287
15.5 Practical Implications of Spin Separation, 291
16 Unitary Transformations of the Dirac Hamiltonian, 295
16.1 The Foldy-Wbuthuysen Transformation, 296
16.2 Approximate Foldy-Wouthuysen Transformations, 299
16.3 The Douglas-Kroll Transformation, 302
16.4 Two-Electron Terms and the Douglas-Kroll-Hess
Approximation, 308
16.5 Implementation of the Douglas-Kroll Transformation, 309
16.6 The Barysz-Sadlej-Snijders Transformation, 311
16.7 Transformation of Electric Property Operators, 313
16.8 Transformation of Magnetic Property Operators, 317
CONTENTS
17 Perturbation Methods, 322
17.1 The Pauli Hamiltonian, 323
17.2 The Breit-Pauli Hamiltonian, 327
17.3 Perturbative Treatment of the Lamb Shift, 331
17.4 Multiple Perturbation Theory for Many-Electron Systems
and Properties, 333
17.5 Direct Perturbation Theory, 336
17.6 Stationary Direct Perturbation Theory, 341
17.7 Stationary Direct Perturbation Theory for Many-Electron
Systems, 347
17.8 Direct Perturbation Theory of Properties, 350
18 Regular Approximations, 356
18.1 The CPD or ZORA Hamiltonian, 357
18.2 Perturbative Corrections to the ZORA Hamiltonian, 362
18.3 Nonperturbative Improvements of the ZORA Equation, 366
18.4 Many-Electron Systems, 371
18.5 Properties in the Regular Approximations, 377
19 Matrix Approximations, 381
19.1 The Matrix Elimination of the Small Components, 382
19.2 Properties of the NESC and UESC Equations, 385
19.3 Inclusion of the Two-Electron Terms, 388
19.4 Atom-Centered Approximations, 391
19.5 Properties in the Matrix Approximations, 394
20 Core Approximations, 396
20.1 The Frozen-Core Approximation, 398
20.2 The Generalized Philips-Kleinman Pseudopotential, 401
20.3 Shape-Consistent Pseudospinors and Pseudopotentials, 406
20.4 Energetics of Pseudopotentials, 409
20.5 Generation of Pseudopotentials, 413
20.6 Relativistic Effects in Pseudopotentials, 415
20.7 Model Potentials, 418
20.8 Energetics of Model Potentials, 420
20.9 Model Potential Implementation, 423
20.10 Relativistic Effects in Model Potentials, 424
20.11 Properties and Core Approximations, 425
21 Spin-Orbit Configuration Interaction Methods, 427
21.1 Breit-Pauli Spin-Orbit Operators, 428
21.2 Douglas-Kroll-Transformed Spin-Orbit Operators, 431
21.3 Spin-Orbit Operators for Model Potential and Pseudopotential
Methods, 434
21.4 Mean-Reid Approximations for Spin-Orbit Interaction, 435
xiv CONTENTS
21.5 Strategies for Spin-Orbit Methods, 439
21.6 One-Particle and Af-Particle Expansion Spaces, 441
21.7 One-Step Methods, 442
21.8 Two-Step Methods, 446
V: The Nature of the Relativistic Chemical Bond
22 Relativistic Effects on Molecular Bonding and Structure, 453
22.1 Relativistic Effects on Atomic Shell Structure, 453
22.2 Spin-Free Effects on Molecular Structure, 456
22.3 Spinor Bonds in Diatomic Molecules, 461
22.4 Hybridization and Bonding in Polyatomic Molecules, 465
22.5 Relativistic Effects on Properties, 467
22.6 A Final Warning, 470
Appendices
Appendix A: Four-Vector Quantities, 473
Appendix B: Vector Relations, 474
Appendix C: Elements of Group Theory, 476
Appendix D: Group Tables, 479
Appendix E: Change of Metric for Modified Wave
Functions, 483
Appendix F: Two-Electron Gauge Terms for the Modified
Dirac Operator, 486
Appendix G: The Second-Order Term of the Douglas-Kroll
Expansion, 489
Appendix H: Transformed Operators for Electric and Magnetic
Properties, 491
Appendix I: Gauge Term Contributions from the Breit Interaction
to the Breit-Pauli Hamiltonian, 495
Appendix J: Approximations in Relativistic Density Functional
Theory, 498
Appendix K: The Cowan-Griffin and Wood-Boring Equations, 501
Appendix L: Supplementary Reading, 503
Bibliography, 507
Index, 515
|
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author | Dyall, Kenneth G. Fægri, Knut Jr. 1946- |
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language | English |
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physical | xiv, 530 Seiten |
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spelling | Dyall, Kenneth G. Verfasser aut Introduction to relativistic quantum chemistry Kenneth G. Dyall, Knut Faegri, Jr. New York Oxford University Press [2007] © 2007 xiv, 530 Seiten txt rdacontent n rdamedia nc rdacarrier Quantenchemie (DE-588)4047979-1 gnd rswk-swf Relativistische Quantentheorie (DE-588)4177688-4 gnd rswk-swf Relativistische Quantentheorie (DE-588)4177688-4 s Quantenchemie (DE-588)4047979-1 s DE-604 Fægri, Knut Jr. 1946- Verfasser (DE-588)1251924131 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017443892&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Dyall, Kenneth G. Fægri, Knut Jr. 1946- Introduction to relativistic quantum chemistry Quantenchemie (DE-588)4047979-1 gnd Relativistische Quantentheorie (DE-588)4177688-4 gnd |
subject_GND | (DE-588)4047979-1 (DE-588)4177688-4 |
title | Introduction to relativistic quantum chemistry |
title_auth | Introduction to relativistic quantum chemistry |
title_exact_search | Introduction to relativistic quantum chemistry |
title_full | Introduction to relativistic quantum chemistry Kenneth G. Dyall, Knut Faegri, Jr. |
title_fullStr | Introduction to relativistic quantum chemistry Kenneth G. Dyall, Knut Faegri, Jr. |
title_full_unstemmed | Introduction to relativistic quantum chemistry Kenneth G. Dyall, Knut Faegri, Jr. |
title_short | Introduction to relativistic quantum chemistry |
title_sort | introduction to relativistic quantum chemistry |
topic | Quantenchemie (DE-588)4047979-1 gnd Relativistische Quantentheorie (DE-588)4177688-4 gnd |
topic_facet | Quantenchemie Relativistische Quantentheorie |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017443892&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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