The numerical accuracy of truncated Ewald sums for periodic systems with long-range Coulomb interactions

Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. An analysis is presented of the errors arising from truncating the infinite real- and Fourier-space lattice sums in the Ewald formulation. An optimal choice is derived for the Fourier-space cutoff given a screening parameter η. It is found that the number of vectors in Fourier space required to achieve a given accuracy scales with η3. The proposed method can be used to determine computationally efficient parameters for Ewald sums, to assess the quality of Ewald-sum implementations, and to compare different implementations.