论文标题
克利福德边界条件：Madelung常数的简单直接评估
Clifford boundary conditions: a simple direct-sum evaluation of Madelung constants
论文作者
论文摘要
我们提出了一种简单的直接和方法，用于有效评估周期性固体中的晶格总和。它由两个主要原则组成：i）创建一个具有克利福德圆环的超级电池，该拓扑是一个平坦，有限且无边界的多种多样； ii）克利福德圆环上两个点之间距离的距离通过将其定义为克利福德圆环的嵌入空间中的欧几里得距离，将距离的距离重新归一化。我们的方法不需要任何积分转换，也不需要对指控的任何重新归一化。我们通过将其应用于离子晶体Madelung常数的计算来说明我们的方法。我们表明，与无限尺寸系统的收敛是单调的，这使Madelung常数直接推断。我们能够以显着的精度恢复Madelung常数，并且几乎可以忽略不计的计算成本，即在笔记本电脑上几秒钟。
We propose a simple direct-sum method for the efficient evaluation of lattice sums in periodic solids. It consists of two main principles: i) the creation of a supercell that has the topology of a Clifford torus, which is a flat, finite and border-less manifold; ii) the renormalization of the distance between two points on the Clifford torus by defining it as the Euclidean distance in the embedding space of the Clifford torus. Our approach does not require any integral transformations nor any renormalization of the charges. We illustrate our approach by applying it to the calculation of the Madelung constants of ionic crystals. We show that the convergence towards the system of infinite size is monotonic, which allows for a straightforward extrapolation of the Madelung constant. We are able to recover the Madelung constants with a remarkable accuracy, and at an almost negligible computational cost, i.e., a few seconds on a laptop computer.
