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.

翻译：介电约束库仑系统在分子动力学模拟中应用广泛。尽管已投入大量努力为这类系统开发高效精确的算法，但严格且精确的误差估计——这对于模拟的最优参数选择至关重要——仍然缺乏。本研究针对具有两个介电平面界面的系统中的静电相互作用，在Ewald求和方法中进行了严格的误差分析，其中极化贡献通过无限反射镜像电荷级数进行建模。我们为镜像电荷级数的截断误差，以及能量和力修正项的衰减速率，提供了精确的误差估计，这些估计是真空层厚度、介电对比度和镜像截断水平等系统参数的函数。在多个典型参数设置下进行的大量数值测试验证了我们的理论预测。此外，我们的分析阐明了先前数值研究中观察到的误差收敛非单调行为。最后，基于我们的理论见解，我们提出了一种最优参数选择策略，为介电约束系统的高效精确分子动力学模拟提供了实用指导。