Note: A pairwise form of the Ewald sum for non-neutral systems

TL;DR

This paper presents a pairwise Ewald sum formulation for non-neutral systems, enabling unambiguous Coulomb energy calculations that are independent of the screening parameter, thus improving accuracy in periodic charge simulations.

Contribution

It introduces an exact pairwise form of the Ewald sum applicable to non-neutral systems, addressing ambiguities caused by the screening factor.

Findings

Provides a well-defined pairwise Ewald sum for non-neutral systems.

Removes dependence on the Ewald screening factor.

Enables more accurate Coulomb energy calculations in periodic systems.

Abstract

Using an example of a mixed discrete-continuum representation of charges under the periodic boundary condition, we show that the exact pairwise form of the Ewald sum, which is well-defined even if the system is non-neutral, provides a natural starting point for deriving unambiguous Coulomb energies that must remove all spurious dependence on the choice of the Ewald screening factor.