Electrostatic Energy of an Aggregate of Point Charges with Periodicity in a Uniform Background

Abstract

We propose a definitive expression for the electrostatic energy of an aggregate of point charges with periodicity in a uniform background. We correctly treat the long-range property of the Coulomb interaction on the basis of the Yukawa interaction. In the derivation, we define a dimension-dependent function which solves the divergence problem in the sum of Coulomb potentials. We also derive an expression for the sum of 1/r ν -type potentials. We recognize the validity of our expression for electrostatic energies, applying it to typical crystals in a uniform background, and show that electrostatic energies do not depend in a simple manner on the dimension of periodicity. We also investigate α-cluster matter as an example of Lennard-Jones systems.