Accurate Error Estimates and Optimal Parameter Selection in Ewald Summation for Dielectrically Confined Coulomb Systems

Dielectrically confined Coulomb systems are widely employed in molecular dynamics (MD) simulations. Despite extensive efforts in developing efficient and accurate algorithms for these systems, rigorous and accurate error estimates, which are crucial for optimal parameter selection for simulations, is still lacking. In this work, we present a rigorous error analysis in Ewald summation for electrostatic interactions in systems with two dielectric planar interfaces, where the polarization contribution is modeled by an infinitely reflected image charge series. Accurate error estimate is provided for the truncation error of image charge series, as well as decay rates of energy and force correction terms, as functions of system parameters such as vacuum layer thickness, dielectric contrasts, and image truncation levels. Extensive numerical tests conducted across several prototypical parameter settings validate our theoretical predictions. Additionally, our analysis elucidates the non-monotonic error convergence behavior observed in previous numerical studies. Finally, we provide an optimal parameter selection strategy derived from our theoretical insights, offering practical guidance for efficient and accurate MD simulations of dielectric-confined systems.