The electrostatic potential of a periodic lattice

TL;DR

This paper presents a method to compute the electrostatic potential of periodic lattices with extended charges using Cartesian multipole formalism, enabling efficient separation of long-range and contact potentials.

Contribution

It introduces a reciprocal space summation approach for calculating electrostatic potentials and energies in periodic lattices with arbitrary charge distributions.

Findings

Potential and energy expressed as convergent sums in reciprocal space

Separation of long-range and contact potentials achieved

Applicable to arbitrary extended charge distributions

Abstract

We calculate the electrostatic potential of a periodic lattice of arbitrary extended charges by using the Cartesian multipole formalism. This method allows the separation of the long-range potential from the contact potential (potential on the source). We write both the electrostatic potential and the interaction energy as convergent sums in the reciprocal space.