Solution of Poisson’s equation for arbitrarily shaped overlapping or nonoverlapping charge densities in terms of multipole moments

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Abstract
The solution of Poisson’s equation in terms of a Green’s function expanded in spherical harmonics is presented. No restrictions are imposed on the charge density. An angular-momentum representation for the potential is obtained ready for application in self-consistent full-potential band-structure methods, which are based on a multicenter expansion of the one-electron Green’s function into spherical harmonics.