Electron Correlations in Molecules and Solids

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Springer Science & Business Media, Jan 1, 1995 - Science - 480 pages
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Electron Correlations in Molecules and Solids bridges the gap between quantum chemistry and solid-state theory. In the first half of the text new concepts are developed for treating many-body and correlation effects, combining standard quantum chemical methods with projection techniques, Greens-function methods and Monte-Carlo techniques. The second half deals with applications of the theory to molecules, semiconductors, transition metals, heavy-fermion systems, and the new high-Tc superconducting materials.
  

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Contents

Introduction
1
The IndependentElectron Approximation
5
21 Starting Hamiltonian
6
22 Basis Functions and Basis Sets
8
23 SelfConsistent Field Approximation
10
24 Simplified SCF Calculational Schemes
18
25 Koopmans Theorem
24
26 Homogeneous Electron Gas
25
Homogeneous Metallic Systems
223
101 FermiLiquid Approach
224
102 Charge Screening and the RandomPhase Approximation
233
103 Spin Fluctuations
242
Transition Metals
253
111 Correlated Ground State
254
112 Excited States
262
113 Finite Temperatures
266

27 Local Exchange Potential The Xc Method
32
28 Shortcomings of the IndependentElectron Approximation
33
29 Unrestricted SCF Approximation
36
Density Functional Theory
39
31 ThomasFermi Method
40
32 HohenbergKohnSham Theory
41
33 LocalDensity Approximation
44
34 Results for Atoms Molecules and Solids
49
35 Extensions and Limitations
52
QuantumChemical Approach to Electron Correlations
61
41 Configuration Interactions
63
42 ManyBody Perturbation Theory
76
Cumulants Partitioning and Projections
81
51 Cumulant Representation
82
52 Projection and Partitioning Techniques
88
53 CoupledCluster Method
96
54 Comparison with Various Trial Wavefunctions
100
55 Simplified Correlation Calculations
103
Excited States
107
61 CI Calculations and Basis Set Requirements
108
62 Excitation Energies in Terms of Cumulants
110
63 Greens Function Method
112
64 Local Operators
126
FiniteTemperature Techniques
129
71 Approximations for Thermodynamic Quantities
130
72 FunctionalIntegral Method
138
73 Monte Carlo Methods
143
Correlations in Atoms and Molecules
151
81 Atoms
152
82 Hydrocarbon Molecules
156
83 Molecules Consisting of FirstRow Atoms
170
84 Strength of Correlations in Different Bonds
173
85 Polymers
177
86 Photoionization Spectra
183
Semiconductors and Insulators
189
91 GroundState Correlations
190
92 Excited States
202
Strongly Correlated Electrons
281
121 Molecules
284
122 Anderson Hamiltonian
288
123 Effective Exchange Hamiltonian
302
124 Magnetic Impurity in a Lattice of Strongly Correlated Electrons
311
125 Hubbard Hamiltonian
314
126 The t J Model
334
127 Slave Bosons in MeanField Approximation
341
128 Kanamoris tMatrix Approach
343
HeavyFermion Systems
347
131 The Fermi Surface and Quasiparticle Excitations
351
132 Model Hamiltonian and Slave Bosons
359
133 Application of the Noncrossing Approximation
365
134 Variational Wavefunctions
368
135 Quasiparticle Interactions
370
136 QuasiparticlePhonon Interactions Based on Strong Correlations
373
Superconductivity and the HighTc Materials
377
141 The Superconducting State
378
142 Electronic Properties of the HighTc Materials
394
143 Other Properties of the Cuprates
408
144 Heavy Fermions in Nd2xCexCuO4
417
Appendix
423
B Derivation of Several Relations Involving Cumulants
424
C Projection Method of Mori and Zwanzig
426
D CrossOver from Weak to Strong Correlations
428
E Derivation of a General Form for Ω
431
F Hunds Rule Correlations
432
G Cumulant Representation of Expectation Values and Correlation Functions
436
H Diagrammatic Representation of Certain Expectation Values
439
I Derivation of the Quasiparticle Equation
442
J CoherentPotential Approximation
444
K Derivation of the NCA Equations
447
L GroundState Energy of a Heisenberg Antiferromagnet on a Square Lattice
449
M The Lanczos Method
453
References
455
Subject Index
469
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