Application of the variational cellular method to periodic structures. Energy band of sodium

Abstract

The first application of the recently proposed variational cellular method (VCM) to periodic structures is reported. The method is applied to the determination of the electronic structure of metallic sodium. The results of these calculations, when compared with previous results obtained through other methods, lead to the conclusion that VCM is an accurate and fast method. Empty-lattice energy eigenvalues for the $\ensuremath{\Delta}$ symmetry line in a body-centered-cubic lattice are found to be correct to 0.001 Ry, when spherical harmonic components up to ${l}_{max}=4$ are used in the cellular expansions.