Quantum chemistry and solid-state theory are two important related fields of research that have grown up with almost no cross communication. This book bridges the gap between the two. In the first half, new concepts for treating weak and strong correlations are developed, and standard quantum-chemical methods, as well as density functional, Green's function, functional integral, and Monte Carlo methods are discussed. The second half discusses applications of the theory to molecules, semiconductors, homogeneous metallic systems, transition metals, and strongly correlated systems such as heavy-fermion systems and the new high-Tc superconducting materials.
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ISBN-13
978-3-642-97309-3 (9783642973093)
DOI
10.1007/978-3-642-97309-3
Schweitzer Klassifikation
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.- 2.5 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.- 4.2 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.- 5.3 Simplified Correlation Calculations.- 6. Excited States.- 6.1 CI Calculations and Basis Set Requirements.- 6.2 Green's Function Method.- 6.3 Local Operators.- 7. Finite-Temperature-Techniques.- 7.1 The Statistical Operator.- 7.2 Functional-Integral Method.- 7.3 Monte Carlo Methods.- 8. Correlations in Atoms and Molecules.- 8.1 Atoms.- 8.2 Hydrocarbon Molecules.- 8.3 Molecules Consisting of First-Row Atoms.- 8.4 Strength of Correlations in Different Bonds.- 8.5 Polymers.- 8.6 Photoionization Spectra.- 9. Semiconductors and Insulators.- 9.1 Ground-State Correlations.- 9.2 Excited States.- 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.- 12. Strongly Correlated Electrons.- 12.1 Molecules.- 12.2 KondoEffect.- 12.3 Hubbard Hamiltonian.- 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.- 14.2 Electronic Structure of the High-Tc Materials.- 14.3 2D Heisenberg Antiferromagnet.- 14.4 Electronic Excitations in the Cu-O Planes.- Appendices.
