An Alternative Construction of the Ewald Sum

Periodicity is a popular way to handle boundaries in atomistic simulations in the bulk. However, slowly decaying Coulomb interactions lead to ill-defined energies and forces. The Ewald sum is a common way of giving meaning to these terms, but its derivation, based on Fourier series, is not transparent. Described in this article is a derivation based on the limiting behaviour as the cutoff goes to infinity of a truncated and shifted Coulomb potential. This observation strengthens the case for the use of the original Ewald sum. And such a construction may offer advantages for computation and/or modelling.