A theory of special points in two-dimensional solid-state calculations

Abstract

A theory of special points in solid-state calculations is developed using a finite-dimensional function space. This generalizes many of the ideas of the present authors about Gaussian-type cubature since the special points are identified with the grid points of a quadrature. The theory is applied to planar square lattices with C4v symmetry. By the systematic use of symmetry, substantial grids of points can be calculated economically. The accuracy of the sets of points is discussed and a redefinition of accuracy offered. Examples are given, some of which agree with those already known, but a new category of skew direct product grids is introduced which enables a large number of suitable grids to be generated. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 601–615, 1999