Pseudopotential methods in condensed matter applications

The generalization from empirically determined screened pseudopotentials to self-consistently screened ab initio pseudopotentials had led to widespread use of the method in solid state applications. The method is reviewed here, beginning with the formal basis in density functional theory. Algorithms for solving the one-particle equations and evaluating the density functional expression for the energy are presented. Special attention is given to the developments in iteration to self-consistency, and to the implications of the variational nature of the energy. An extensive list is given of the broad range of applications of the self-consistent pseudopotential method for describing properties of condensed matter systems.