Model density approach to Ewald summations

TL;DR

This paper introduces a model density method to improve the convergence of Ewald summations for electrostatic potential calculations in condensed systems, applicable to classical and quantum models.

Contribution

A novel charge density model that cancels multipole moments to accelerate Ewald sum convergence in bulk systems with arbitrary unit cells.

Findings

Significantly accelerated convergence in gallium arsenide calculations.

Clarifies a longstanding implementation in the CRYSTAL code.

Applicable to both classical and quantum charge density representations.

Abstract

The evaluation of the electrostatic potential is fundamental to the study of condensed phase systems. We discuss the calculation of the relevant lattice summations by Ewald-type techniques. A model charge density is introduced, that cancels multipole moments of the crystalline charge distribution up to a desired order, for accelerating convergence of the Ewald sums. The method is applicable to calculations of bulk systems, employing arbitrary unit cells in a classical or quantum context, and with arbitrary basis functions to represent the charge density. The efficacy of the method is demonstrated on the calculation of the fundamental gap of the gallium arsenide bulk semiconductor, as a prototype example, where significantly accelerated convergence is numerically confirmed. The approach clarifies a decades-old implementation in the CRYSTAL code.