Brillouin-wigner Methods for Many-body Systems

by Hubac, Ivan; Wilson, Stephen

• ISBN13: 9789048133727
• ISBN10: 9048133726
• Format: Hardcover
• Copyright: 2009-11-01
• Publisher: Springer Verlag

Summary

In twenty-first-century science, computional modelling is a powerful tool for the study of matter on a nanoscale. It complements an increasing range of experimental probes providing new or more accurate measurements in nanoscience and nanotechnology.

Table of Contents

Preface	p. ix
Nomenclature	p. xv
Abbreviations	p. xvii
Atomic Units	p. xix
Introduction	p. 1
Preamble	p. 1
Historical Background	p. 5
Lennard-Jones' 1930 paper	p. 5
Brillouin's 1932 paper	p. 7
Wigner's 1935 paper	p. 8
Studies in perturbation theory	p. 10
Perturbation Theory	p. 12
Brilloun-Wigner perturbation theory	p. 12
Rayleigh-Schrbdinger perturbation theory	p. 14
Comparison of Brillouin-Wigner and Rayleigh-Schrödinger perturbation theories	p. 17
Advantages of the Brillouin-Wigner theory	p. 18
Disadvantages of the Brillouin-Wigner theory	p. 22
The Many-Body Problem	p. 25
Linear scaling	p. 25
The re-emergence of Brillouin-Wigner methods	p. 26
An overview	p. 32
References	p. 33
Brillouin-Wigner perturbation theory	p. 37
The Partitioning Technique	p. 37
The partitioning technique for a single-reference function	p. 38
Model function and projection operators	p. 38
An effective Hamiltonian	p. 39
The wave operator	p. 40
The reaction operator	p. 43
The partitioning technique for a multi-reference function	p. 44
Model functions and projection operators	p. 44
An effective Hamiltonian	p. 45
The wave operator	p. 47
The reaction operator	p. 48
Perturbation Expansions	p. 48
Single-reference function perturbation expansions	p. 48
Expansions of the inverse operator	p. 48
Rayleigh-Schrbdinger perturbation theory	p. 50
Brillouin-Wigner perturbation theory	p. 51
Generalized Brillouin-Wigner perturbation theory	p. 53
Derivation of Rayleigh-Schrödinger perturbation theory from the Brillouin-Wigner perturbation expansion	p. 56
Multi-reference function perturbation expansions	p. 58
Multi-reference Rayleigh-Schrödinger perturbation theory	p. 58
Multi-reference Brillouin-Wigner perturbation theory	p. 64
An n-state system	p. 66
References	p. 68
The many-body problem in atoms and molecules	p. 69
Linear Scaling in Many-Body Systems	p. 69
The exact electronic Schrödinger equation	p. 70
Independent particle models	p. 73
Many-body theories of electron correlation	p. 76
Many-Body Perturbation Theory	p. 77
Second-quantization formalism	p. 78
Second-quantization and the many-body problem	p. 78
Creation and annihilation operators and the occupation number representation	p. 81
Normal products, contractions and Wick's theorem	p. 87
Particle-hole formalism	p. 90
The Hamiltonian operator in normal form	p. 94
Many-body Rayleigh-Schrödinger perturbation theory	p. 94
The many-body problem and quasiparticles	p. 94
The algebraic approximation	p. 96
Many-body Rayleigh-Schrödinger perturbation theory	p. 98
Second-order contribution to the correlation energy	p. 101
Third-order contributions to the correlation energy	p. 108
Fourth-order contributions to the correlation energy	p. 109
Many-body perturbation theory	p. 110
Many-Body Theories for Atoms And Molecules	p. 113
The full configuration interaction method and limited configuration interaction	p. 114
Cluster expansions	p. 119
References	p. 129
Brillouin-Wigner methods for many-body systems	p. 133
Introduction	p. 133
Brillouin-Wigner Coupled Cluster Theory	p. 137
Single-reference Brillouin-Wigner coupled cluster theory	p. 137
Multi-reference Brillouin-Wignerxoupled cluster theory	p. 143
Multi-root formulation of multi-reference Brillouin-Wigner coupled cluster theory	p. 145
Multi-root multi-reference Brillouin-Wigner coupled cluster: Hilbert space approach	p. 148
Basic approximations employed in the multi-reference Brillouin-Wigner coupled cluster method	p. 152
Single-root formulation of the multi-reference Brillouin-Wigner coupled-cluster theory	p. 155
Single-root formulation of multi-reference Brillouin-Wigner perturbation theory	p. 156
Single-root multi-reference Brillouin-Wigner coupled cluster theory: Hilbert space approach	p. 158
Single-root multi-reference Brillouin-Wigner coupled cluster single- and double-excitations approximation	p. 159
Linear scaling corrections in Brillouin-Wigner coupled cluster theory	p. 162
Brillouin-Wigner Configuration Interaction Theory	p. 164
Single-reference Brillouin-Wigner configuration interaction theory	p. 167
Brillouin-Wigner perturbation theory and limited configuration interaction	p. 167
Rayleigh-Schrodinger perturbation theory and limited configuration interaction	p. 169
'Many-body' corrections for Brillouin-Wigner limited configuration interaction	p. 170
Multi-reference Brillouin-Wigner configuration interaction theory	p. 171
Multi-reference Brillouin-Wigner perturbation theory for limited configuration interaction	p. 171
A p-state system	p. 174
Multi-reference configuration interaction in Brillouin-Wigner form	p. 175
A posteriori Brillouin-Wigner correction to limited multi-reference configuration interaction	p. 176
Brillouin-Wigner Perturbation Theory	p. 177
Single-reference Brillouin-Wigner perturbation theory	p. 177
Multi-reference Brillouin-Wigner perturbation theory	p. 179
Multi-reference second-order Brillouin-Wigner perturbation theory	p. 179
A posteriori correction to multi-reference Brillouin-Wigner perturbation theory	p. 183
References	p. 184
Summary and prospects	p. 191
References	p. 197
Löwdin's studies in perturbation theory	p. 201
Proof of the time-independent Wick's theorem	p. 211
References	p. 213
Diagrammatic conventions	p. 215
Rayleigh-Schrbdinger perturbation theory	p. 221
References	p. 225
Index	p. 227;
Table of Contents provided by Ingram. All Rights Reserved.