Electron Correlations in Molecules and SolidsSpringer Science & Business Media, 1995 - 480 Seiten 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. |
Inhalt
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 |
455 | |
469 | |
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Häufige Begriffe und Wortgruppen
ansatz antiferromagnetic approximation atom band basis set bond calculations charge fluctuations compute conduction electrons configurations consider contributions corr correlation energy corresponding Coulomb cumulants d³r defined denotes density described determined diagonal diagrams discussed in Sect doping doubly occupied effective eigenvalues elec electron correlations electron number electron system equation evaluated example exchange excitation energies expectation value expression Fermi energy Fermi surface fermions ferromagnetic Fulde ƒ electron given Green's function ground ground-state ground-state energy ground-state wavefunction H₁ Hamiltonian Hartree-Fock hole Hubbard Hund's rule hybrid impurity interaction interatomic correlations Kondo lattice magnetic matrix elements mean-field metals method molecules momentum obtain operators orbitals pair parameters perturbation phonons Phys potential PSCF quantum quasiparticle relation renormalized replaced semiconductors shown in Fig singlet Slater determinant spin strongly correlated electrons superconducting symmetry temperature theory tion tron valence electrons wavefunction