- Single Determinantal Approximations: Hartree–Fock, Optimized Effective Potential Theory, Density Functional Theory

All properties of atoms, molecules, and solids can be determined by solving the many-particle Schroedinger equation with external potential arising from the electric charges of the nuclei. The difculty is that the state of the physical system under consideration is described by a wave function that has as many position variables as that of the number of electrons. At rst sight, the situation looks hopeless because one atom may have a hundred of position variables, an organic molecule can have

13.1 Introduction .................................................................................................. 253 13.1.1 Many-Electron Schroedinger Equation ............................................ 255 13.1.2 Reduction of Variational Principles to Minimum Principles ........... 257 13.1.3 Preliminaries on Many-Particle Wave Functions ............................. 258 13.1.4 Second Quantization Representation for Fermions ..........................260 13.1.5 Field Operators ................................................................................. 263 13.1.6 Matrix Elements of Hamiltonian ......................................................265