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 4:0
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
11.Transition metals
12.Strongly correlated electrons
13.Heavy-fermion systems
14.Superconductivity and the high-tc materials
Appendix
References
Subject index