Cutoff Errors in the Ewald Summation Formulae for Point Charge Systems

Closed formulae for both real and reciprocal space parts of cutoff errors in the Ewald summation method in cubic periodic boundary conditions are derived. Such estimates are useful in tuning parameters in molecular simulations. Errors in both the electrostatic energy and forces are considered. The estimates apply to a disordered configuration of point charges and, with some limitations, also to point-charge molecular models. The accuracy of our estimates is tested and confirmed using simulated configurations of two systems (molten salt and diethylether) under a variety of conditions.