Baldereschi Points for Some Noncubic Lattices

Abstract

A calculation of many physical properties of crystals requires the integration of the corresponding properties over the Brillouin zone. Examples include calculations of the valence electron charge density in solids, the total crystal energy, the selfconsistent crystalline potential, etc. The important method of integration has been introduced by Baldereschi /1/ and developed by Cohen et al. /2 to 4/. These authors have shown that the sum over a large number of uniformly distributed points in the Brillouin zone can be approximated quite well by using a very small number of carefully chosen representative points. Phillips /5/ has argued that these points may have physical significance over and above their mathematical significance a s "meanvalue" points. ,The formalism required to derive the Baldereschi points is a s follows. We denote by f( k) the periodic function whose integral is of interest, and express this integral a s the Brillouin-zone volume times the average value of f ( k):

Many special point scheme for noncubic lattices

“…Bashenov et al [3] have recently derived the single Baldereschi points for other noncubic lattices. However, there were some errors in their results, and the special point obtained by them satisfied equation (Gb) only up to m = 3.…”