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

摘要

In this paper we study a general theoretical framework which allows toapproximate the real space Ewald sum by means of effective force shiftedscreened potentials, together with a self term. Using this strategy it ispossible to generalize the reaction field method, as a means to approximate thereal space Ewald sum. We show that this method exhibits faster convergence ofthe Coulomb energy than several schemes proposed recently in the literaturewhile enjoying a much more sound and clear electrostatic significance. In termsof the damping parameter of the screened potential, we are able to identify twoclearly distinct regimes of convergence. Firstly, a reaction field regimecorresponding to the limit of small screening, where effective pair potentialsconverge faster than the Ewald sum. Secondly, an Ewald regime, where the plainreal space Ewald sum converges faster. Tuning the screening parameter foroptimal convergence occurs essentially at the crossover. The implication isthat effective pair potentials are an alternative to the Ewald sum only inthose cases where optimization of the convergence error is not possible.