Symmetrization Techniques in Relativistic OPW Energy Band Calculations

Abstract

Definite advantages can be attained by the use of crystalline symmetry properties in calculations of energy bands. In particular, dramatic savings in computer time and core storage requirements can be realized. In this paper, we give some observations relevant to the Orthogonalized-Plane-Wave (OPW) method. Many of these observations are equally relevant to other computational techniques. Mattheiss, Wood, and Switendick¹ have outlined the use of symmetry in the Augmented-Plane-Wave (APW) method. A well-known disadvantage of the OPW method is the slow convergence of the wave function expansion.² Our experience with group IV, III–V, and II–VI semiconducting crystals indicates that at least 229 plane waves must be used (usually many more) to obtain convergence. Hence, an eigenvalue problem of at least order 229 must be solved to find eigenvalues and eigenvectors. This is a time-consuming task on the computer. The problem is even more difficult in the relativistic OPW formalism where spin doubles the order of the matrices.