Exact treatment of Poisson’s equation in solids with space-filling cells

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Abstract
We present a new, rigorous treatment of Poisson’s equation in solids with no shape approximation to the potential. In contrast to existing techniques, this method allows the unified treatment of periodic solids, as well as materials containing imperfections such as substitutional or interstitial impurities and disordered alloys. Explicit expressions for the potential and the Coulomb part of the energy are given. The validity and utility of this approach is demonstrated by numerical calculations.