Solution of Poisson’s equation: Beyond Ewald-type methods

Abstract

A general method for solving Poisson’s equation without shape approximation for an arbitrary periodic charge distribution is presented. The method is based on the concept of multipole potentials and the boundary value problem for a sphere. In contrast to the usual Ewald-type methods, this method has only absolutely and uniformly convergent reciprocal space sums, and treats all components of the charge density equivalently. Applications to band structure calculations and lattice summations are also discussed.