论文标题
角度的系统推导 - 具有Ewald的电位
Systematic derivation of angular--averaged Ewald potential
论文作者
论文摘要
在这项工作中，我们提供了一个角度的逐步推导 - 具有无序库仑系统的数值模拟的Ewald电位。电势首先是由e。\，yakub和c。\，ronchi引入的，没有明确的推导。使用两种方法来找到电势的系列扩展的系数：基于Euler--Maclaurin和Poisson求和公式。每个系数的表达式表示为有限序列，其中包含jacobi theta函数的衍生物。在三维情况下，我们还证明了泊松和欧拉的形式等效 - 麦克拉林求和公式。角度 - 平均埃瓦尔德电位的有效性通过计算许多晶体晶格的Madelung常数的示例。
In this work we provide a step by step derivation of an angular--averaged Ewald potential suitable for numerical simulations of disordered Coulomb systems. The potential was first introduced by E.\,Yakub and C.\,Ronchi without a clear derivation. Two methods are used to find the coefficients of the series expansion of the potential: based on the Euler--Maclaurin and Poisson summation formulas. The expressions for each coefficient is represented as a finite series containing derivatives of Jacobi theta functions. We also demonstrate the formal equivalence of the Poisson and Euler--Maclaurin summation formulas in the three-dimensional case. The effectiveness of the angular--averaged Ewald potential is shown by the example of calculating the Madelung constant for a number of crystal lattices.
