Real space pairwise electrostatic summation in a uniform neutralising background

TL;DR

This paper introduces a simple, efficient real-space method for calculating electrostatic energies in neutral ionic crystals, closely related to Wolf's method, with linear scaling and practical implementation advantages.

Contribution

A novel real-space approach for electrostatic energy calculation in neutral systems, offering simplicity, efficiency, and linear scaling, suitable for electronic structure methods.

Findings

Method is straightforward to implement.

Achieves linear computational scaling.

Closely related to Wolf's method.

Abstract

Evaluating the total energy of an extended distribution of point charges, which interact through the Coulomb potential, is central to the study of condensed matter. With near ubiquity, the summation required is carried out using Ewald's method, which splits the problem into two separately convergent sums; one in real space and the other in reciprocal space. Density functional based electronic structure methods require the evaluation of the ion-ion repulsive energy, neutralised by a uniform background charge. Here a purely real-space approach is described. It is straightforward to implement, computationally efficient and offers linear scaling. When applied to the evaluation of the electrostatic energy of neutral ionic crystals, it is shown to be closely related to Wolf's method.