Band structure of silicon by the self-consistent variational cellular method

The self-consistent formulation of the variational cellular method has been developed in order to calculate the electronic structure of crystals with an arbitrary number of atoms per unit cell. Applications for silicon have been carried out. Silicon, chosen here as a test case, is treated as a face-centered cubic lattice with four “atoms” per unit cell by adding empty cells. The electronic charge density was taken muffin-tin, assuming a constant value in the interstitial region between the inscribed sphere and the Wigner–Seitz polyhedrum. The spherical symmetric 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. Our results are in good agreement with those obtained by other methods.