Calculation of shape-truncation functions for Voronoi polyhedra

Abstract

The authors develop a new efficient method for calculating the shape-truncation functions of arbitrary Voronoi polyhedra by combining analytical and numerical techniques. Applications are presented for cells of cubic symmetry as well as for hexagonal close-packed (HCP) atomic polyhedra with different values of the c/a ratio. They also discuss an efficient way for performing three-dimensional integrations in electronic-structure calculations (e.g. solve Poisson's equation) using shape functions.