Full-potential KKR within the removed-sphere method: A practical and accurate solution to the Poisson equation

Abstract

Here an efficient and accurate generalization of the removed-sphere method (RSM) to solve the Poisson equation for total charge density in a solid with space-filling convex Voronoi polyhedra (VPs) and any symmetry is presented. The generalized RSM avoids the use of multipoles and VP shape functions for cellular integrals, which have associated ill-convergent large, double-internal L sums in spherical-harmonic expansions, so that fast convergence in single-L sums is reached. Our RSM adopts full Ewald formulation to work for all configurations or when symmetry breaking occurs, such as for atomic displacements or elastic constant calculations. The structure-dependent coefficients A L that define RSM can be calculated once for a fixed structure and speed up the whole self-consistent-field procedure. The accuracy and rapid convergence properties are confirmed using two analytic models, including the Coulomb potential and energy. We then implement the full-potential RSM using the Green's function Korringa-Kohn-Rostoker (KKR) method for real applications and compare the results with other first-principle methods and experimental data, showing that they are equally as accurate.