Ewald methods for inverse power-law interactions in tridimensional and quasi-two dimensional systems

TL;DR

This paper develops Ewald methods for inverse power-law interactions in quasi-two dimensional systems, deriving new analytical formulas and validating them with Monte Carlo simulations for electrolyte and plasma models.

Contribution

It introduces a novel analytical Fourier transform involving incomplete gamma functions for Ewald summations in quasi-2D systems, bridging 3D and 2D approaches.

Findings

Derived new Ewald summation formulas for quasi-2D systems.

Validated formulas with Monte Carlo simulations.

Provided energy calculations for electrolyte and plasma models.

Abstract

In this paper, we derive the Ewald method for inverse power-law interactions in quasi-two dimensional systems. The derivation is done by using two different analytical methods. The first uses the Parry's limit, that considers the Ewald methods for quasi-two dimensional systems as a limit of the Ewald methods for tridimensional systems, the second uses Poisson-Jacobi identities for lattice sums. Taking into account the equivalence of both derivations, we obtain a new analytical Fourier transform intregral involving incomplete gamma function. Energies of the generalized restrictive primitive model of electrolytes ($\eta$-RPM) and of the generalized one component plasma model ($\eta$-OCP) are given for the tridimensional, quasi-two dimensional and monolayers systems. Few numerical results, using Monte-Carlo simulations, for $\eta$-RPM and $\eta$-OCP monolayers systems are reported.