Improved cutoff functions for short-range potentials and the Wolf summation

TL;DR

This paper introduces improved polynomial cutoff functions for short-range potentials, enhancing accuracy and efficiency in simulations, and explores their impact on the Wolf summation method for Coulomb interactions.

Contribution

The paper proposes a new class of cutoff functions with higher-order smoothness and demonstrates their benefits in reducing errors and computational costs in molecular simulations.

Findings

Systematic error reduction of ~25% in energies and times with n=2 or 3

Discontinuous stress and moduli for n=0 and 1

Modified Wolf summation improves Coulomb calculations under certain conditions

Abstract

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.