Using real space pseudopotentials for the electronic structure problem

Abstract

This chapter describes the use of real Space pseudo potentials for the electronic structure problem. The pseudopotential model of condensed matter is one of the most promising developments within the of area computational materials science. It has led the way in providing a workable science framework for describing the properties of materials, while modern computers have provided the computational resources to implement the pseudopotential method. The pseudopotential concept treats matter as a sea of valence electrons moving in a background of ion cores. The cores are composed of nuclei and inert inner electrons. Within this model many of the complexities of an all-electron calculation are avoided. For example, a group IV element such as C with 6 electrons is treated in a similar fashion to Ge with 32 electrons as both elements have 4 valence electrons. The chapter illustrates that, as the pseudopotential binds only valence electron states, the resulting potential is weak and the Coulombic 1/r singularity at the nucleus is removed. Without the pseudopotential approximation, real space methods would be considerably more difficult to implement, if not impossible. Grids for the full potential must be spatially adapted to account for the rapid changes in the potential at the nuclear positions.