Convergence peculiarities of lattice summation upon multiple charge spreading generalizing the Bertaut approach

TL;DR

This paper introduces a generalized multiple charge spreading method with polynomial functions to improve the convergence rate of Coulomb series in lattice summation, especially when charge overlaps occur, demonstrated on NaCl.

Contribution

It proposes a new class of confined spreading functions and analyzes their effectiveness in enhancing convergence compared to traditional methods.

Findings

Multiple spreading significantly improves convergence when charge overlaps occur.

Optimization of spreading parameters enhances computational efficiency.

Demonstrated effectiveness on a NaCl lattice model.

Abstract

Within investigating the multiple charge spreading generalizing the Bertaut approach, a set of confined spreading functions with a polynomial behaviour, but defined so as to enhance the rate of convergence of Coulomb series even upon a single spreading, is proposed. It is shown that multiple spreading is ultimately effective especially in the case when the spreading functions of neighbouring point charges overlap. In the cases of a simple exponential and a Gaussian spreading functions the effect of multiplicity of spreading on the rate of convergence is discussed along with an additional optimization of the spreading parameter in dependence on the cut-off parameters of lattice summation. All the effects are demonstrated on a simple model NaCl structure.