Methods of molecular quantum mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
London <<[u.a.]>>
Acad. Press
1989
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| Edition: | 2. ed. |
| Series: | Theoretical chemistry
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 573 S. |
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Record in the Search Index
| _version_ | 1804140393140322304 |
|---|---|
| adam_text | Methods of Molecular
Quantum Mechanics
R MCWEENY
University of Pisa,
Pisa, Italy
SECOND EDITION
ACADEMIC PRESS
Harcourt Brace Jovanovich, Publishers
London San Diego New York Berkeley
Boston Sydney Tokyo Toronto
Contents
Preface to Second Edition v
Units xiv
1 Introductory Survey 1
1 1 Schrodinger s equation 1
1 2 Example: the helium atom 6
1 3 Example: the hydrogen molecule 17
Problems 1 21
2 Mathematical Methods 25
2 1 Complete set expansions 25
2 2 Vector spaces and matrices 29
2 3 The eigenvalue equation 34
2 4 Variation theory 40
2 5 Partitioning and perturbation methods 45
Problems 2 50
3 Many-Electron Wavefunctions 55
3 1 Antisymmetry and the Slater Method 55
3 2 Calculation of the energy: helium atom 58
3 3 Matrix elements between antisymmetrized products 61
3 4 Configuration interaction 66
3 5 An example: the hydrogen molecule 71
3 6 An alternative approach: Fock space 76
Problems 3 82
4 Spin and Permutation Symmetry 87
4 1 Spin eigenfunctions 87
4 2 Methods for constructing spin eigenfunctions 90
4 3 Permutation symmetry and its implications 97
4 4 Young tableaux 100
4 5 The standard irreps of SN 103
x CONTENTS
4 6 Connections between different bases 110
Problems 4 112
5 Digression: The Electron Distribution 115
5 1 Electron density functions - 115
5 2 Density matrices 119
5 3 Density functions for 1-determinant wavefunctions 125
5 4 Transition densities Generalizations 128
5 5 Localized orbitals Population analysis 133
5 6 Natural expansions 135
5 7 Molecular properties: An introduction 137
5 8 The pair function Electron correlation 142
5 9 Spin density 146
5 10 Other density functions 152
Problems 5 154
6 Self-Consistent Field Theory 159
6 1 Hartree-Fock theory The independent-particle model 159
6 2 Finite-basis approximations Closed-shell systems 166
6 3 Unrestricted Hartree-Fock theory 172
6 4 Some further properties of density matrices 175
6 5 Restricted HF theory An open-shell system 181
6 6 Other open-shell situations Ensemble averaging 187
6 7 States of given spin 194
6 8 Physical significance of MOs Localization 200
Problems 6 206
7 Valence Bond Theory 211
7 1 The Heitler-London calculation 211
7 2 Generalizations 215
7 3 Perfect pairing and resonance 216
7 4 One-configuration VB theory Non-orthogonal orbitals 223
7 5 Multiconfiguration VB theory Orthogonal orbitals 234
7 6 Multiconfiguration VB theory Non-orthogonal orbitals 239
77A non-variational method 247
Problems 7 251
8 Multiconfiguration SCF Theory 255
8 1 The optimization problem 255
8 2 Orbital variation Stationary-value conditions 256
8 3 Solution of the stationary-value equations 263
8 4 Gradient methods 267
CONTENTS xi
8 5 Use of the Brillouin-Levy-Berthier theorem 274
8 6 Variation of all parameters 278
Problems 8 282
9 Perturbation Theory and Diagram Techniques 285
9 1 Perturbation methods 285
9 2 The Hartree-Fock reference function 286
9 3 The cluster development 294
9 4 Diagrammatic perturbation theory 300
9 5 The linked-cluster (Goldstone s) theorem 309
9 6 Extensions of the diagrammatic approach 314
9 7 Generalizations 322
Problems 9 324
10 Large-Scale Cl and the Unitary-Group Approach 327
10 1 The general approach 327
10 2 Transformations and tensors 328
10 3 Irreducible bases in CI space 333
10 4 Generators of the unitary group The Hamiltonian 341
10 5 The matrix-eigenvalue problem Direct CI 347
Problems 10 352
11 Small Terms in the Hamiltonian Static Properties 357
11 1 Electric and magnetic interactions The classical approach 357
11 2 Relativistic effects: one particle 363
11 3 Relativistic treatment of many-particle systems 366
11 4 A variation-perturbation approach 371
11 5 Effect of a uniform electric field 377
11 6 Effect of a uniform magnetic field 381
11 7 Some spin-coupling effects (first-order) 386
11 8 Some spin-coupling effects (second-order) 394
11 9 Variational methods Coupled Hartree-Fock theory 404
11 10 Generalizations of CHF theory 410
Problems 11 415
12 Dynamic Properties and Response Theory 419
12 1 Preliminaries Linear response 419
12 2 Time-dependent variation theory 425
12 3 Free and forced oscillations 428
12 4 Significance of the response matrix 433
12 5 Time-dependent Hartree-Fock theory 435
12 6 Density-matrix form of TDHF theory 438
12 7 Multiconfiguration (MC) TDHF theory 442
Problems 12 446
xii CONTENTS
13 Propagator and Equation-of-Motion Methods 449
13 1 Preliminary notions 449
13 2 Propagators The polarization propagator 451
13 3 Propagators, Green s functions and density matrices 457
13 4 Some properties of the electron propagator 460
13 5 The calculation of propagators 464
13 6 Equation-of-morion (EOM) methods 475
Problems 13 481
14 Intermodular Forces 485
14 1 Weak interactions Generalized product functions 485
14 2 Variation theory for subsystems 491
14 3 Configuration interaction Interpretation of the terms 496
14 4 Long-range effects The dispersion energy 499
14 5 Non-orthogonality and short-range effects 507
14 6 Excited states and resonance interactions 514
Problems 14 517
Appendix 1: Atomic Orbitals 521
Appendix 2: Angular Momentum 527
Appendix 3: Symmetry and Group Concepts 531
Appendix 4: Relativistic terms in the Hamiltonian 545
References 553
Index 565
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| any_adam_object | 1 |
| author | McWeeny, Roy |
| author_facet | McWeeny, Roy |
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| discipline | Chemie / Pharmazie |
| edition | 2. ed. |
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| spelling | McWeeny, Roy Verfasser aut Methods of molecular quantum mechanics R. McWeeny 2. ed. London <<[u.a.]>> Acad. Press 1989 XV, 573 S. txt rdacontent n rdamedia nc rdacarrier Theoretical chemistry Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenchemie (DE-588)4047979-1 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Theoretische Chemie (DE-588)4185098-1 gnd rswk-swf Molekül (DE-588)4039972-2 gnd rswk-swf MO-Theorie (DE-588)4170580-4 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Molekül (DE-588)4039972-2 s DE-604 Quantenchemie (DE-588)4047979-1 s 1\p DE-604 MO-Theorie (DE-588)4170580-4 s 2\p DE-604 Quantenmechanik (DE-588)4047989-4 s 3\p DE-604 Theoretische Chemie (DE-588)4185098-1 s 4\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018398999&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | McWeeny, Roy Methods of molecular quantum mechanics Quantenmechanik (DE-588)4047989-4 gnd Quantenchemie (DE-588)4047979-1 gnd Quantentheorie (DE-588)4047992-4 gnd Theoretische Chemie (DE-588)4185098-1 gnd Molekül (DE-588)4039972-2 gnd MO-Theorie (DE-588)4170580-4 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4047979-1 (DE-588)4047992-4 (DE-588)4185098-1 (DE-588)4039972-2 (DE-588)4170580-4 |
| title | Methods of molecular quantum mechanics |
| title_auth | Methods of molecular quantum mechanics |
| title_exact_search | Methods of molecular quantum mechanics |
| title_full | Methods of molecular quantum mechanics R. McWeeny |
| title_fullStr | Methods of molecular quantum mechanics R. McWeeny |
| title_full_unstemmed | Methods of molecular quantum mechanics R. McWeeny |
| title_short | Methods of molecular quantum mechanics |
| title_sort | methods of molecular quantum mechanics |
| topic | Quantenmechanik (DE-588)4047989-4 gnd Quantenchemie (DE-588)4047979-1 gnd Quantentheorie (DE-588)4047992-4 gnd Theoretische Chemie (DE-588)4185098-1 gnd Molekül (DE-588)4039972-2 gnd MO-Theorie (DE-588)4170580-4 gnd |
| topic_facet | Quantenmechanik Quantenchemie Quantentheorie Theoretische Chemie Molekül MO-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018398999&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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