Damped reaction field method and the accelerated convergence of the real space Ewald summation

TL;DR

This paper introduces a generalized reaction field method that accelerates the convergence of the real space Ewald sum for electrostatic calculations, providing a clearer electrostatic interpretation and identifying regimes for optimal parameter tuning.

Contribution

It extends the reaction field method to approximate the real space Ewald sum with improved convergence properties and clearer electrostatic significance.

Findings

Faster convergence of Coulomb energy compared to recent schemes

Identification of two regimes of convergence based on screening parameter

Optimal convergence achieved at a crossover point of regimes

Abstract

In this paper we study a general theoretical framework which allows to approximate the real space Ewald sum by means of effective force shifted screened potentials, together with a self term. Using this strategy it is possible to generalize the reaction field method, as a means to approximate the real space Ewald sum. We show that this method exhibits faster convergence of the Coulomb energy than several schemes proposed recently in the literature while enjoying a much more sound and clear electrostatic significance. In terms of the damping parameter of the screened potential, we are able to identify two clearly distinct regimes of convergence. Firstly, a reaction field regime corresponding to the limit of small screening, where effective pair potentials converge faster than the Ewald sum. Secondly, an Ewald regime, where the plain real space Ewald sum converges faster. Tuning the screening parameter for optimal convergence occurs essentially at the crossover. The implication is that effective pair potentials are an alternative to the Ewald sum only in those cases where optimization of the convergence error is not possible.