Ewald summation evaluates long-range interactions in a periodically repeated system by separating rapidly convergent real-space and reciprocal-space contributions. For a Coulomb interaction, the identity splits a short-range term from a smooth long-range term.
The complementary-error-function term decays rapidly and is summed over nearby images. The smooth term is efficiently summed through Fourier modes, with a self-interaction correction removing the artificial screening contribution at each particle. The splitting parameter changes computational work rather than the converged physical answer. Net charge, the zero mode and the boundary convention must be handled explicitly; an arbitrary unqualified infinite Coulomb sum need not converge uniquely.[ref]
Die Berechnung optischer und elektrostatischer Gitterpotentiale by Paul Peter Ewald. Original lattice-potential construction
Articles by others on the same topic
Ewald summation is a mathematical technique used to compute the potential energy and forces in systems with periodic boundary conditions, commonly encountered in simulations of charged systems or dipolar systems in condensed matter physics, materials science, and molecular dynamics. The main challenge in these systems is that the Coulomb potential between charges, which falls off as \(1/r\), leads to divergent sums when calculated directly for an infinite periodic lattice.