Gaussian representations of covalent wave functions; silicon

Abstract

We represent the pseudo wave functions of silicon using Bloch sums of $s$, $p$, and $d$ Gaussians on atom sites. Maximal energy errors of 0.17 eV for the valence band and 0.28 eV for the two lowest conduction bands can be achieved with 18 states per atom. Localization to zeroth, first, and second neighbors is achieved with some contribution from third neighbors. The localization is similar to free atoms. $d$ states are needed in the valence band but are much more important in the conduction band. A four-state $s$, $p$ band fit is reasonable for the valence band but bad for the conduction band as found in earlier empirical work. We attribute the conduction-band errors to the need for $d$ functions. The Appelbaum-Hamann self-consistent pseudopotential is represented in Gaussian form with three coefficients. These coefficients could lead to a more efficient tight-binding parameterization scheme than the conventional overlap intergral method.