Multiple charge spreading as a generalization of the Bertaut approach to lattice summation of Coulomb series in crystals

TL;DR

This paper generalizes the Bertaut charge spreading method for lattice Coulomb series in crystals to multiple spreading functions, improving convergence and providing a unified framework for different spreading types.

Contribution

It introduces a generalized multiple spreading approach that extends Bertaut's method, allowing for consistent calculations of electrostatic potentials with various spreading functions.

Findings

Multiple spreading enhances convergence of Coulomb series.

Gaussian spreading functional remains invariant under multiple spreading.

Exponential spreading offers different convergence properties compared to Gaussian.

Abstract

The Bertaut approach associated with charge spreading so as to enhance the rate of convergence of Coulomb series in crystals is extended to the case of an arbitrary multiple spreading with a given initial spreading function. It is shown that the effect of spreading may in general be treated as a uniform transformation of space, providing that zero mean potential as a universal spatial property is sustained. As a result, electrostatic potentials driven by different orders of multiple spreading can be obtained from the same energy functional in a consistent manner. It is found that the effect of multiple spreading gives rise to more advanced forms described, for example, by simple exponential decrease, but the functional description based on a Gaussian spreading turns out to be invariant. In addition, the effects of a multiple charge spreading based on simple exponential and Gaussian spreading functions are compared as typical of molecular calculations.