Rapidly convergent pseudopotentials for crystalline systems

Abstract

A new formulation of the pseudopotential theory has been developed for crystalline systems. A Green function version of the plane-wave secular equation is the starting point for the reformulation, and the Ewald technique and a Ziman transformation are used to obtain a plane-wave representation in which the pseudo-potential matrix elements decay very rapidly as the wave vector increases. This reformulation explains the observation of Falicov and Golin that the conventional pseudopotential secular equation converges only very slowly and can give markedly worse agreement with the experimental data than a parameterized secular equation with rapidly decaying matrix elements. An explanation is offered for the fact that the empirical pseudopotential method is successful even for materials for which no pseudopotential exists. The reformulated pseudopotential appears to be ideally suited to calculating the physical properties of simple metals and non-polar semi-conductors.