Yukawa potentials in systems with partial periodic boundary conditions II : Lekner sums for quasi-two dimensional systems

TL;DR

This paper derives Lekner sums for quasi-two dimensional Yukawa systems and concludes they are unsuitable as an alternative to Ewald sums for such long-range potentials.

Contribution

It provides the first derivation of Lekner sums for Yukawa potentials in quasi-two dimensional systems and evaluates their effectiveness.

Findings

Lekner sums are not suitable for Yukawa potentials in quasi-2D systems.

Ewald sums remain the preferred method for these systems.

Lekner sums should not be used for Yukawa interactions in practice.

Abstract

Yukawa potentials may be long ranged when the Debye screening length is large. In computer simulations, such long ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we have provided Ewald sums for quasi-two dimensional systems with Yukawa interaction potentials [M. Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007) and M. Mazars, {\it Mol. Phys.}, Paper I]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two dimensional systems with Yukawa interaction potentials and we give some numerical tests for pratical implementations. The main result of this paper is to outline that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work : Lekner sums should not be used for quasi-two dimensional systems with Yukawa interaction potentials.