An Energy Band Interpolation Scheme, with Application to Body-centred Cubic Lithium

Abstract

AN interpolation scheme has been developed for the calculation of the energy bands in solids, using plane wave expansions of the wave functions and accurately known values of the energy-levels at high-symmetry points of the Brillouin zone. For valence electron states having the same symmetry as those of the ion cores, these expansions must be modified by the use of an additional repulsive pseudo-potential V _r. Of various suggested forms¹ of V _r, that found most useful was that of Gáspár² and Antončík³, an extension to metals of that derived for atoms by Gombás⁴. By using only a small number of terms in the expansions it was then found possible to reproduce the energy-levels at high-symmetry points with at least the accuracy to which they had been originally determined. The levels at a large number of general points of the zone were then calculated, and, in order to obtain the density of states N(E), these energy values were fitted by a symmetrized triple Fourier expansion of E(k _x,k _y,k _z).