Self-consistent formulation of the variational cellular method applied to periodic structures—results for sodium and silicon

The theoretical formulation of the self-consistent variational cellular method (SCVCM) has been developed in order to calculate the electronic structure of crystals with an arbitrary number of atoms per unit cell. Calculations for metallic sodium and silicon have been carried out. The electronic charge density within the atomic polyhedron was calculated assuming two regions, one corresponding to the inscribed sphere and the other corresponding to the interstitial region. The radial electronic charge density in the inscribed sphere was obtained by adding a limited number of contributions of Brillouin zone states using the “mean value point theory”, developed by Baldereschi and Chadi-Cohen. In the interstitial region, the electronic density was taken as of a constant value. The model can be extended to open structures by adding empty cells. Our results for sodium and silicon are in good agreement with those obtained by other methods. The self-consistent scheme proposed is accurate and fast enough to be applied to more complex structures.