Modern quantum chemistry: introduction to advanced electronic structure theory
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Garden City, New York
Dover Publications
1996
|
| Edition: | Dover edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Unabridged, slightly corrected Dover republication of the revised first edition published by McGraw-Hill Publishing Company, New York, 1989 (originally published in 1982) |
| Physical Description: | xiv, 466 Seiten Illustrationen, Diagramme |
| ISBN: | 9780486691862 0486691861 |
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MARC
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| 100 | 1 | |a Szabo, Attila |d 1947- |e Verfasser |0 (DE-588)131701371 |4 aut | |
| 245 | 1 | 0 | |a Modern quantum chemistry |b introduction to advanced electronic structure theory |c Attila Szabo, Neil S. Ostlund |
| 250 | |a Dover edition | ||
| 264 | 1 | |a Garden City, New York |b Dover Publications |c 1996 | |
| 300 | |a xiv, 466 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Unabridged, slightly corrected Dover republication of the revised first edition published by McGraw-Hill Publishing Company, New York, 1989 (originally published in 1982) | ||
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| 650 | 4 | |a Quantum chemistry | |
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Record in the Search Index
| _version_ | 1804127266379137024 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
Preface to Revised Edition
ix
Preface
xi
Chapter
1.
Mathematical Review
1
1.1
Linear Algebra
2
1.1.1
Three-Dimensional Vector Algebra
2
1.1.2
Matrices
5
.3
Determinants
7
.4
A -Dimensional Complex Vector Spaces
9
.5
Change of Basis
13
.6
The Eigenvalue Problem
15
.7
Functions of Matrices
21
1.2
Orthogonal Functions, Eigenfunctions, and Operators
24
1.3
The Variation Method
31
1.3.1
The Variation Principle
31
1.3.2
The Linear Variational Problem
33
Notes
38
Further Reading
38
Chapter
2.
Many Electron Wave Functions and Operators
39
2.1
The Electronic Problem
40
2.1.1
Atomic Units
41
2.1.2
The Born-Oppenheimer Approximation
43
2.1.3
The Antisymmetry or
Pauli
Exclusion Principle
45
2.2 Orbitals,
Slater Determinants, and Basis Functions
46
2.2.1
Spin
Orbitals
and Spatial
Orbitals 46
2.2.2
Hartree
Products
47
Ш
¡V
MODERN
QUANTUM
CHEMISTRY
2.2.3
Slater Determinants
49
2.2.4
The Hartree-Fock Approximation
53
2.2.5
The Minimal Basis H2 Model
55
2.2.6
Excited Determinants
58
2.2.7
Form of the Exact Wave Function and Configuration Interaction
60
2.3
Operators and Matrix Elements
64
2.3.1
Minimal Basis H2 Matrix Elements
64
2.3.2
Notations for One- and Two-Electron Integrals
67
2.3.3
General Rules for Matrix Elements
бб
2.3.4
Derivation of the Rules for Matrix Elements
74
2.3.5
Transition from Spin
Orbitals
to Spatial
Orbitals 81
2.3.6
Coulomb and Exchange Integrals
85
2.3.7
Pseudo-Classical Interpretation of Determinantal Energies
87
2.4
Second Quantization
89
2.4.1
Creation and Annihilation Operators and Their
Anticommutation
Relations
89
2.4.2
Second-Quantized Operators and Their Matrix Elements
95
2.5
Spin-Adapted Configurations
97
2.5.1
Spin Operators
97
2.5.2
Restricted Determinants and Spin-Adapted Configurations
100
2.5.3
Unrestricted Determinants
104
Notes
107
Further Reading
107
Chapter
3.
The Hartree-Fock Approximation
108
3.1
The Hartree-Fock Equations
Ш
3.1.1
The Coulomb and Exchange Operators
112
3.1.2
The Fock Operator
114
3.2
Derivation of the Hartree-Fock Equations
115
3.2.1
Functional Variation
115
3.2.2
Minimization of the Energy of a Single Determinant
117
3.2.3
The Canonical Hartree-Fock Equations
120
3.3
Interpretation of Solutions to the Hartree-Fock Equations
123
3.3.1
Orbital Energies and Koopmans Theorem
123
3.3.2
Brillouin s Theorem
128
3.3.3
The Hartree-Fock Hamiltonian
130
3.4
Restricted Closed-Shell Hartree-Fock: The Roothaan Equations
131
3.4.1
Closed-Shell Hartree-Fock: Restricted Spin
Orbitals 132
3.4.2
Introduction of a Basis .-The Roothaan Equations
136
3.4.3
The Charge Density
138
3.4.4
Expression for the Fock Matrix
140
3.4.5
Orthogonalization of the Basis
142
TABLE
OF
CONTENTS
V
3.4.6
The SCF Procedure
145
3.4.7
Expectation Values and Population Analysis
149
3.5
Model Calculations on H2 and HeH+
152
3.5.1
The is Minimal STO-3G Basis Set
153
3.5.2
STO-3GH2
159
3.5.3
An SCF Calculation on STO-3G
НеН*
168
3.6
Polyatomic Basis Sets
180
3.6.1
Contracted Gaussian Functions
180
3.6.2
Minimal Basis Sets: STO-3G
184
3.6.3
Double
Zeta
Basis Sets: 4-31G
186
3.6.4
Polarized Basis Sets
:
6-31G· and 6-31G*·
189
3.7
Some Illustrative Closed-Shell Calculations
190
3.7.1
Total Energies
191
3.7.2
Ionüation
Potentials
194
3.7.3
Equilibrium Geometries
200
3.7.4
Population Analysis and
Dipole
Moments
203
3.8
Unrestricted Open-Shell Hartree-Fock:
The Pople-Nesbet Equations
205
3.8.1
Open-Shell
Hartree
Fock: Unrestricted Spin
Orbitals 206
3.8.2
Introduction of a Basis: The Pople-Nesbet Equations
210
3.8.3
Unrestricted Density Matrices
212
3.8.4
Expression for the Fock Matrices
214
3.8.5
Solution of the Unrestricted SCF Equations
215
3.8.6
Illustrative Unrestricted Calculations
216
3.8.7
The Dissociation Problem and its Unrestricted Solution
221
XT
♦
229
Notes
Further Reading
229
Chapter
4.
Configuration Interaction
231
4.1
Multiconfigurational Wave Functions and the
Structure of the Full
CI
Matrix
233
4.1.1
Intermediate Normalization and an Expression for
the Correlation Energy
237
4.2
Doubly Excited
CI
242
4.3
Some Illustrative Calculations
245
4.4
Natural
Orbitals
and the One-Particle Reduced Density Matrix
252
4.5
The Multiconfiguration Self-Consistent Field (MCSCF)
and Generalized Valence Bond (GVB) Methods
258
4.6
Truncated
CI
and the Size-Consistency Problem
261
VÍ
MODERN
QUANTUM CHEMISTRY
Notes
269
Further Reading
269
Chapter
5.
Pair and Coupled-Pair Theories
271
5.1
The Independent Electron Pair Approximation
(ΙΕΡΑ)
272
5.1.1
Invariance
under Unitary Transformations: An Example
277
5.1.2
Some Illustrative Calculations
284
5.2
Coupled-Pair Theories
286
5.2.1
The Coupled Cluster Approximation (CCA)
287
5.2.2
The Cluster Expansion of the Wave Function
290
5.2.3
Linear CCA and the Coupled Electron Pair
Approximation
(СЕРА)
292
5.2.4
Some Illustrative Calculations
296
5.3
Many-Electron Theories with Single Particle Hamiltonians
297
5.3.1
The Relaxation Energy via
CI,
ΙΕΡΑ,
CCA, and
СЕРА
303
5.3.2
The Resonance Energy of Polyenes in ffiickel Theory
309
Notes
318
Further Reading
319
Chapter
6.
Many-Body Perturbation Theory
320
6.1
Rayleigh-Schrödinger (RS)
Perturbation Theory
322
*6.2 Diagrammatic Representation of RS Perturbation Theory
327
6.2.1
Diagrammatic Perturbation Theory for
2
States
327
6.2.2
Diagrammatic Perturbation Theory for
N
States
335
6.2.3
Summation of Diagrams
336
6.3
Orbital Perturbation Theory: One-Particle Perturbations
338
*6.4 Diagrammatic Representation of Orbital Perturbation Theory
348
6.5
Perturbation Expansion of the Correlation Energy
350
6.6
The TV-Dependence of the RS Perturbation Expansion
354
*6.7 Diagrammatic Representation of the Perturbation
Expansion of the Correlation Energy
356
6.7.1
Hugenholtz Diagrams
356
6.7.2 Goldstone
Diagrams
362
6.7.3
Summation of Diagrams
368
6.7.4
What Is the Linked Cluster Theorem?
369
6.8
Some Illustrative Calculations
370
Notes
378
Further Reading
379
TABLE
OF
CONTENTS
VÜ
Chapter
7.
The One-Particle Many-Body Green s Function
380
7.1
Green s Functions in Single Particle Systems
381
7.2
The One-Particle Many-Body Green s Function
387
7.2.1
The Self-Energy
389
7.2.2
The Solution of the Dyson Equation
391
7.3
Application of the Formalism to H2 and HeH+
392
7.4
Perturbation Theory and the Green s Function Method
398
7.5
Some Illustrative Calculations
405
Notes
409
Further Reading
409
Appendix A. Integral Evaluation with Is Primitive
Gaussiana
410
Appendix
В.
Two-Electron Self-Consistent-FieW Program
417
Appendix
С
Analytic Derivative Methods and Geometry
Optimization by M.C. Zerner
437
Appendix D. Molecular Integrals for H2 as a Function of Bond
Length
459
Index
461
|
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| author | Szabo, Attila 1947- Ostlund, Neil S. |
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| discipline | Chemie / Pharmazie Physik Chemie |
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| id | DE-604.BV012613499 |
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| isbn | 9780486691862 0486691861 |
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| physical | xiv, 466 Seiten Illustrationen, Diagramme |
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| spelling | Szabo, Attila 1947- Verfasser (DE-588)131701371 aut Modern quantum chemistry introduction to advanced electronic structure theory Attila Szabo, Neil S. Ostlund Dover edition Garden City, New York Dover Publications 1996 xiv, 466 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Unabridged, slightly corrected Dover republication of the revised first edition published by McGraw-Hill Publishing Company, New York, 1989 (originally published in 1982) Configuratie-interactie gtt Elektronenstructuur gtt Green-functies gtt Hartree-Fock-benadering gtt Kwantumchemie gtt Química quântica larpcal Storingsrekening gtt Veel-deeltjes-systemen gtt Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Quantenchemie (DE-588)4047979-1 s DE-604 Ostlund, Neil S. Verfasser aut Erscheint auch als Online-Ausgabe 978-0-486-13459-8 (DE-604)BV043836411 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008567031&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 |
| spellingShingle | Szabo, Attila 1947- Ostlund, Neil S. Modern quantum chemistry introduction to advanced electronic structure theory Configuratie-interactie gtt Elektronenstructuur gtt Green-functies gtt Hartree-Fock-benadering gtt Kwantumchemie gtt Química quântica larpcal Storingsrekening gtt Veel-deeltjes-systemen gtt Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd |
| subject_GND | (DE-588)4047979-1 (DE-588)4151278-9 |
| title | Modern quantum chemistry introduction to advanced electronic structure theory |
| title_auth | Modern quantum chemistry introduction to advanced electronic structure theory |
| title_exact_search | Modern quantum chemistry introduction to advanced electronic structure theory |
| title_full | Modern quantum chemistry introduction to advanced electronic structure theory Attila Szabo, Neil S. Ostlund |
| title_fullStr | Modern quantum chemistry introduction to advanced electronic structure theory Attila Szabo, Neil S. Ostlund |
| title_full_unstemmed | Modern quantum chemistry introduction to advanced electronic structure theory Attila Szabo, Neil S. Ostlund |
| title_short | Modern quantum chemistry |
| title_sort | modern quantum chemistry introduction to advanced electronic structure theory |
| title_sub | introduction to advanced electronic structure theory |
| topic | Configuratie-interactie gtt Elektronenstructuur gtt Green-functies gtt Hartree-Fock-benadering gtt Kwantumchemie gtt Química quântica larpcal Storingsrekening gtt Veel-deeltjes-systemen gtt Quantum chemistry Quantenchemie (DE-588)4047979-1 gnd |
| topic_facet | Configuratie-interactie Elektronenstructuur Green-functies Hartree-Fock-benadering Kwantumchemie Química quântica Storingsrekening Veel-deeltjes-systemen Quantum chemistry Quantenchemie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008567031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT szaboattila modernquantumchemistryintroductiontoadvancedelectronicstructuretheory AT ostlundneils modernquantumchemistryintroductiontoadvancedelectronicstructuretheory |