Abstract
We propose a definitive expression to evaluate electrostatic energies under periodic conditions, starting from the Yukawa potential with a finite range and summing up positive and negative contributions separately. We find a dimension-dependent function that can be used to solve problems concerning divergences and ambiguities in the direct sum of Coulomb potentials. The infinite-range limit of this function leads to a universal constant independent of lattice structure, which reveals the origin of ambiguities from conditionally convergent series in the sum of Coulomb potentials.
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