Electron Correlations in Molecules and Solids

ISBN-13: 9783540593645 / Angielski / Miękka / 1995 / 483 str.

Peter Fulde

Opis

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.

Spis treści

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 Xa 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 Local and Localized Orbitals.- 4.1.2 Selection of Double Substitutions.- 4.1.3 Multireference CI.- 4.2 Many-Body Perturbation Theory.- 5. Cumulants, Partitioning, and Projections.- 5.1 Cumulant Representation.- 5.1.1 Ground-State Energy.- 5.1.2 Perturbation Expansion.- 5.2 Projection and Partitioning Techniques.- 5.2.1 Coupled-Electron-Pair Approximations.- 5.2.2 Projections Based on Local Operators.- 5.2.3 Method of Increments.- 5.3 Coupled-Cluster Method.- 5.4 Comparison with Various Trial Wavefunctions.- 5.5 Simplified Correlation Calculations.- 6. Excited States.- 6.1 CI Calculations and Basis Set Requirements.- 6.2 Excitation Energies in Terms of Cumulants.- 6.3 Green’s Function Method.- 6.3.1 Perturbation Expansions.- 6.3.2 The Projection Method.- 6.4 Local Operators.- 7. Finite-Temperature Techniques.- 7.1 Approximations for Thermodynamic Quantities.- 7.1.1 Temperature Green’s Function.- 7.1.2 The Projection Method for T ? 0.- 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 Hedin’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-Sites Approximation.- 11.3.3 Beyond the Static Approximation.- 12. Strongly Correlated Electrons.- 12.1 Molecules.- 12.2 Anderson Hamiltonian.- 12.2.1 Calculation of the Ground-State Energy.- 12.2.2 Excited States.- 12.2.3 Noncrossing Approximation.- 12.3 Effective Exchange Hamiltonian.- 12.3.1 Schrieffer-Wolff Transformation.- 12.3.2 Kondo Divergency.- 12.3.3 Fermi-Liquid Description.- 12.4 Magnetic Impurity in a Lattice of Strongly Correlated Electrons.- 12.5 Hubbard Hamiltonian.- 12.5.1 Ground-State: Gutzwiller’s Wavefunction and Spin-Density Wave State.- 12.5.2 Excitation Spectrum.- 12.5.3 The Limits of One Dimension and Infinite Dimensions.- 12.6 The t — J Model.- 12.7 Slave Bosons in the Mean-Field Approximation.- 12.8 Kanamori’s t-Matrix Approach.- 13. Heavy-Fermion Systems.- 13.1 The Fermi Surface and Quasiparticle Excitations.- 13.1.1 Large Versus Small Fermi Surface.- 13.2 Model Hamiltonian and Slave Bosons.- 13.3 Application of the 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 Ground State.- 14.1.3 Pair Breaking.- 14.2 Electronic Properties of the High-Tc Materials.- 14.2.1 Electronic Excitations in the Cu-O Planes.- 14.2.2 Calculation of the Spectral Weight by Projection Techniques.- 14.2.3 Size of the Fermi Surface.- 14.3 Other Properties of the Cuprates.- 14.3.1 Loss of Antiferromagnetic Order.- 14.3.2 Optical Conductivity.- 14.3.3 Magnetic Response.- 14.4 Heavy Fermions in Nd2_xCexCuO4.- B. Derivation of Several Relations Involving Cumulants.- C. Projection Method of Mori and Zwanzig.- D. Cross-Over from Weak to Strong Correlations.- E. Derivation of a General Form for ??).- F. Hund’s Rule Correlations.- G. Cumulant Representation of Expectation Values and Correlation Functions.- H. Diagrammatic Representation of Certain Expectation Values.- I. Derivation of the Quasiparticle Equation.- J. Coherent-Potential Approximation.- K. Derivation of the NCA Equations.- L. Ground-State Energy of a Heisenberg Antiferromagnet on a Square Lattice.- M. The Lanczos Method.- References.

Blurb

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 Monto-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.