On mesh-based Ewald methods: Optimal parameters for two differentiation schemes

The particle-particle particle-mesh Ewald method for the treatment of long-range electrostatics under periodic boundary conditions is reviewed. The optimal Green’s function for exact (real-space differentiation), which differs from that for reciprocal-space differentiation, is given. Simple analytic formulas are given to determine the optimal Ewald screening parameter given a differentiation scheme, a real-space cutoff, a mesh spacing, and an assignment order. Simulations of liquid water are performed to examine the effect of the accuracy of the electrostatic forces on calculation of the static dielectric constant. A target dimensionless root-mean-square error of $10−4$ is sufficient to obtain a well-converged estimate of the dielectric constant.