The Poisson summation formula is used to calculate the effective interaction of charged particles in a three-dimensional system with periodicity in two dimensions. The interaction energy expression is identical to that obtained from the Berthaut approach for the Gaussian spreading function, and its correspondence with the results of the Rhee-Halley-Hautman-Rahman method is shown. The formalism based on the Poisson summation formula is used also to calculate the interaction energy of point-dipole moments.
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Grzybowski et al. (2000) studied this question.
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