论文标题
改进的截止功能可用于短期电位和狼求和
Improved cutoff functions for short-range potentials and the Wolf summation
论文作者
论文摘要
提出了一类径向，多项式截止函数$ f _ {\ textrm {c} n}（r）$，用于短距离对电位或相关表达式。他们的衍生物达到$ n $和$ n+1 $在外部截止$ r_ \ textrm {c} $和内部半径$ r_ \ textrm {i} $上消失。此外，$ f _ {\ textrm {c} n}（r \ le r_ \ textrm {i}）= 1 $和$ f _ {\ textrm {c} n}（r \ ge r_ \ r_ \ r_ \ textrm {c}）= 0 $。结果表明，使用的订单$ n $可以在定性上影响结果：理想晶体的压力和大量模量不可避免地是不可行的，而密度分别为$ n = 0 $和$ n = 1 $。与标准切割程序相比，$ n = 2 $或$ n = 3 $的Lennard-Jones的能量和计算时间的系统错误减少了25 \％。事实证明，另一个截止函数有益于使用狼求和来计算库仑相互作用，狼的求和仅在局部电荷中立性遵守局部电荷中立性时显示出不正确的收敛。但是，对于所有研究的具有热噪声（离子晶体和液体）的同质系统，尽管在$ r_ \ textrm {c} $下是无限差异的，但经过改装的狼求和与原始总和相似。最后，讨论了如何使用狼求和，即使在不正确收敛的情况下，也可以使用数值精确的蒙特卡洛模拟的计算成本。
A class of radial, polynomial cutoff functions $f_{\textrm{c}n}(r)$ for short-ranged pair potentials or related expressions is proposed. Their derivatives up to order $n$ and $n+1$ vanish at the outer cutoff $r_\textrm{c}$ and an inner radius $r_\textrm{i}$, respectively. Moreover, $f_{\textrm{c}n}(r \le r_\textrm{i}) = 1$ and $f_{\textrm{c}n}(r\ge r_\textrm{c})=0$. It is shown that the used order $n$ can qualitatively affect results: stress and bulk moduli of ideal crystals are unavoidably discontinuous with density for $n=0$ and $n=1$, respectively. Systematic errors on energies and computing times decrease by approximately 25\% for Lennard-Jones with $n=2$ or $n=3$ compared to standard cutting procedures. Another cutoff function turns out beneficial to compute Coulomb interactions using the Wolf summation, which is shown to not properly converge when local charge neutrality is obeyed only in a stochastic sense. However, for all investigated homogeneous systems with thermal noise (ionic crystals and liquids), the modified Wolf summation, despite being infinitely differentiable at $r_\textrm{c}$, converges similarly quickly as the original summation. Finally, it is discussed how to reduce the computational cost of numerically exact Monte Carlo simulations using the Wolf summation even when it does not properly converge.
