Presumed versus real artifacts of the Ewald summation technique: The importance of dielectric boundary conditions

Abstract

AbstractDespite its widespread use the Ewald summation method has been criticized for introducing spatial periodicity in the simulation system. The question whether this leads to artifacts is rigorously addressed by comparing the electric field obtained with the Ewald method to that of an unmodified Coulomb potential. It is demonstrated that the Ewald potential ϕEW is a solution of the Poisson equation under toroidal (periodic) boundary conditions; however, ϕEW gives also rise to an implicit contribution analogous to a reaction field. This additional term is connected to the dielectric boundary conditions employed in the simulation, and we show how to adjust these in a physically meaningful manner by adding an explicit reaction field term. To verify the theoretical considerations and to study the effects which modifying the dielectric boundary conditions has on the properties of the simulated system, we calculate the static dielectric constant, the distance‐dependent G‐factor, and the relaxation time of the net dipole moment of SPC water. The commonly used tin‐foil boundary conditions (characterized by a formal dielectric constant \documentclass{article}\pagestyle{empty}\begin{document}$ \varepsilon _{{\rm{EW}}}^{{\rm{eff}}} $\end{document} = ∞) are found to overstabilize the correlation between dipoles at larger distances; therefore, we recommend to adjust the dielectric boundary conditions so that \documentclass{article}\pagestyle{empty}\begin{document}$ \varepsilon _{{\rm{EW}}}^{{\rm{eff}}} = \varepsilon _0 $\end{document}, where ϵ0 is the intrinsic static dielectric constant of the simulated system.