Madelung constants for ionic crystals using the Ewald sum

Abstract

Ionic crystal configuration energies have always been one of the bugbears of computational thermodynamics due to the inherent long-range interactions. Unlike the van der Waals forcer associated with non-ionic compounds, it is not possible to utilize a long-range cutoff,' ionic interactions require summation over an infinitely large crystal lattice. The situation is further complicated by the fact that the resulting infinite series for an ordered crystal lattice is non-convergent. This means that a direct summation over the charged particles is not feasible. This paper develops and analyzas a powerful yet under utilized method for calculating these lattice energies, the Ewald sum. Not only is this a powerful and accurate of calculating the configuration energies of ionic crystals, it is also not dependent on existence of crystal structure. Hence this method is useful in any application involving Coulonbic interactions, including substances in the liquid phase. The general Ewald method is presented with some simplifying assumptions to produce a working equation amenable to computer evaluations and sample computations are made for NaCI and CsCI. Extensive discussion is presented on determining the optimum splitting parameter: A simple yet general FORTRAN program for calculating the Madelung constant for an ionic system of any phase is presented and a sensitivity analysis is performed