平面界面静电场Ewald求和的严格误差界
Rigorous Error Bounds for Ewald Summation of Electrostatics at Planar Interfaces
摘要：
我们提出了一个严格的Ewald求和公式来计算三维系统的二维周期性平面界面中的静电相互作用。通过将具有显式阶数N2复杂度的原始Ewald2D表达式的求和公式的傅立叶部分重写为闭合形式的傅立叶积分，我们发现先前开发的静电层校正项和边界校正项都自然地产生于傅立叶积分部分的严格梯形求和的表达式。我们推导出精确的修正梯形求和的轮廓积分的形式提供精确的误差范围与给定的参数集的网格大小和系统长度。为了支持我们的分析结果，对板状模型离子晶体中的马德隆常数进行了数值计算。
英文摘要：
We present a rigorous Ewald summation formula to evaluate the electrostatic interactions in two-dimensionally periodic planar interfaces of three-dimensional systems. By rewriting the Fourier part of the summation formula of the original Ewald2D expression with an explicit order N2 complexity to a closed form Fourier integral, we find that both the previously developed electrostatic layer correction term and the boundary correction term naturally arise from the expression of a rigorous trapezoidal summation of the Fourier integral part. We derive the exact corrections to the trapezoidal summation in a form of contour integrals offering precise error bounds with given parameter sets of mesh size and system length. Numerical calculations of Madelung constants in model ionic crystals of slab geometry have been performed to support our analytical results.
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