Model density approach to Ewald summations

The evaluation of the electrostatic potential is fundamental to the study of condensed phase systems. We discuss the calculation of the relevant lattice summations by Ewald-type techniques. A model charge density is introduced, that cancels multipole moments of the crystalline charge distribution up to a desired order, for accelerating convergence of the Ewald sums. The method is applicable to calculations of bulk systems, employing arbitrary unit cells in a classical or quantum context, and with arbitrary basis functions to represent the charge density. The efficacy of the method is demonstrated on the calculation of the fundamental gap of the gallium arsenide bulk semiconductor, as a prototype example, where significantly accelerated convergence is numerically confirmed, due to a reduction of the number of two-electron integrals that need to be computed. The approach clarifies a decades-old implementation in the CRYSTAL code.