Ewald sums for Yukawa potentials in quasi-two-dimensional systems

TL;DR

This paper derives Ewald sums for Yukawa potentials in systems with two-dimensional periodicity, extending previous three-dimensional formulations using Parry's method for Coulomb interactions.

Contribution

It introduces a new derivation of Ewald sums for Yukawa potentials in quasi-two-dimensional systems based on Parry's method.

Findings

Provides explicit Ewald sum formulas for Yukawa potentials in 2D periodic systems

Extends previous 3D Ewald sums to quasi-2D systems

Facilitates accurate simulations of Yukawa interactions in layered materials

Abstract

In this note, we derive Ewald sums for Yukawa potential for three dimensional systems with two dimensional periodicity. This sums are derived from the Ewald sums for Yukawa potentials with three dimensional periodicity [G. Salin and J.-M. Caillol, J. Chem. Phys. {\bf 113}, 10459 (2000)] by using the method proposed by Parry for the Coulomb interactions [D.E. Parry, Surf. Sci. {\bf 49}, 433 (1975); {\bf 54}, 195 (1976)].