Evjen's Method of Evaluating the Madelung Constant

Abstract

A convenient method of evaluating the Madelung series is first to group the terms into unit cells and then sum the contributions from the different cells. It is emphasized that even such a grouping, which involves neighboring terms only, may affect the sum. This happens, for example, with the CsCl type of lattice, if the unit cell chosen is the usual body-centered cube, whereas by choosing an oblique elementary cell containing one ion, the sum remains unaltered. A criterion is given for the choice of a suitable elementary cell.