Special points for the evaluation of form factors and Fourier series representations in hexagonal crystals

Abstract

Efficient Gaussian type formulae are developed for evaluating the Fourier coefficients (form factors) of symmetrized plane waves for a hexagonal close-packed system in both real and reciprocal space ([Formula: see text] and [Formula: see text], respectively). These are the most efficient possible for a small number of sample points and represent a major advance over previous work on special point formulae. They will be particularly powerful for performing calculations of surface properties. The convergence of a Fourier series representation of energy bands is investigated by use of these formulae and found to converge slowly.