ABSTRACT
The key problem in the structure of matter is to solve the Schrödinger equation for a system of N interacting electrons in the external Coulombic field created by a collection of atomic nuclei (and maybe some other external field). It is a very difficult problem in the many-body theory and, in fact, the exact solution is known only in the case of the uniform electron gas, for atoms with a small number of electrons, and for a few small molecules. These exact solutions are always numerical. At the analytic level, one always has to resort to approximations. However, the effort of devising schemes to solve this problem is really worthwhile because the knowledge of the electronic ground state of a system gives access to many of its properties; for example, relative stability of different structures/isomers, equilibrium structural information, mechanical stability and elastic properties, pressuretemperature (P-T) phase diagrams, dielectric properties, dynamical (molecular or lattice) properties such as vibrational frequencies and spectral functions, (nonelectronic) transport properties such as diffusivity, viscosity, ionic conductivity, and so forth. Excited electronic states (or the explicit time dependence) also give access to another wealth of measurable phenomena such as electronic transport and optical properties.
