Synopsis
1. Introduction.- 2. The Independent-Electron Approximation.- 2.1 Starting Hamiltonian.- 2.2 Basis Functions and Basis Sets.- 2.3 Self-Consistent Field Approximation.- 2.4 Simplified SCF Calculational Schemes.- 2.4.1 Semi-empirical SCF Methods.- 2.4.2 Pseudopotentials.- 2.5 Koopmans' Theorem.- 2.6 Homogeneous Electron Gas.- 2.7 Local Exchange Potential -The X? Method.- 2.8 Shortcomings of the Independent-Electron Approximation.- 2.9 Unrestricted SCF Approximation.- 3. Density Functional Theory.- 3.1 Thomas-Fermi Method.- 3.2 Hohenberg-Kohn-Sham Theory.- 3.3 Local-Density Approximation.- 3.4 Results for Atoms, Molecules, and Solids.- 3.5 Extensions and Limitations.- 4. Quantum-Chemical Approach to Electron Correlations.- 4.1 Configuration Interactions.- 4.1.1 Localized-Orbital Methods.- 4.1.2 Selection of Double Substitutions.- 4.1.3 Multireference CI.- 4.2 Coupled-Cluster Methods.- 4.3 Many-Body Perturbation Theory.- 5. The Projection Technique and Use of Local Operators.- 5.1 The Projection Technique.- 5.2 Local Operators.- 5.2.1 Physical Interpretation.- 5.2.2 Comparison with Other Methods.- 5.3 Simplified Correlation Calculations.- 6. Excited States.- 6.1 CI Calculations and Basis Set Requirements.- 6.2 Green's Function Method.- 6.2.1 Perturbation Expansions.- 6.2.2 The Projection method.- 6.3 Local Operators.- 7. Finite-Temperature-Techniques.- 7.1 The Statistical Operator.- 7.2 Functional-Integral Method.- 7.2.1 Static Approximation.- 7.3 Monte Carlo Methods.- 7.3.1 Sampling Techniques.- 7.3.2 Ground-State Energy.- 8. Correlations in Atoms and Molecules.- 8.1 Atoms.- 8.2 Hydrocarbon Molecules.- 8.2.1 Analytic Expressions for Correlation-Energy Contributions.- 8.2.2 Simplified Correlation Calculations.- 8.3 Molecules Consisting of First-Row Atoms.- 8.4 Strength of Correlations in Different Bonds.- 8.5 Polymers.- 8.5.1 Polyethylene.- 8.5.2 Polyacetylene.- 8.6 Photoionization Spectra.- 9. Semiconductors and Insulators.- 9.1 Ground-State Correlations.- 9.1.1 Semi-empirical Correlation Calculations.- 9.1.2 Ab Initio Calculations.- 9.2 Excited States.- 9.2.1 Role of Nonlocal Exchange.- 9.2.2 The Energy Gap Problem.- 9.2.3 Hedins's GW Approximation.- 10. Homogeneous Metallic Systems.- 10.1 Fermi-Liquid Approach.- 10.2 Charge Screening and the Random Phase Approximation.- 10.3 Spin Fluctuations.- 11. Transition Metals.- 11.1 Correlated Ground State.- 11.2 Excited States.- 11.3 Finite Temperatures.- 11.3.1 Single-Site Approximation.- 11.3.2 Two-Site Approximation.- 11.3.3 Beyond the Static Approximation.- 12. Strongly Correlated Electrons.- 12.1 Molecules.- 12.2 Kondo Effect.- 12.2.1 Variational Treatment of the Anderson Hamiltonian.- 12.2.2 Schrieffer-Wolff Transformation.- 12.2.3 Kondo Divergency.- 12.2.4 Fermi-Liquid Description.- 12.3 Hubbard Hamiltonian.- 12.3.1 The Limits of One Dimension and Infinite Dimensions.- 12.3.2 Hubbard's Solution.- 12.3.3 Gutzwiller's Wavefunction and Approximation.- 12.3.4 Slave Bosons in the Mean-Field Approximation.- 12.3.5 Kanamori's t-Matrix Approach.- 13. Heavy-Fermion Systems.- 13.1 The Fermi Surface and Quasiparticle Excitations.- 13.2 Model Hamiltonian and Slave Bosons.- 13.3 Noncrossing Approximation.- 13.4 Variational Wavefunctions.- 13.5 Quasiparticle Interactions.- 13.6 Quasiparticle-Phonon Interactions Based on Strong Correlations.- 14. Superconductivity and the High-Tc Materials.- 14.1 The Superconducting State.- 14.1.1 Pair States.- 14.1.2 BCS Groundstate.- 14.1.3 Pair Breaking.- 14.2 Electronic Structure of the High-Tc Materials.- 14.3 2D Heisenberg Antiferromagnet.- 14.3.1 Ground-State Energy.- 14.3.2 Motion of a Hole.- 14.4 Electronic Excitations in the Cu-O Planes.- Appendices.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
