Fulde Electron Correlations in Molecules and Solids

1991
ISBN: 978-3-642-97309-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 100, 422 Seiten, eBook

Reihe: Springer Series in Solid-State Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Fulde, Peter

Inhaltsverzeichnis

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.