A fast and rigorous numerical tool to measure length-scale artifacts in molecular simulations

TL;DR

This paper introduces a fast numerical method to evaluate the quality factor based on the Bogoliubov inequality, helping to identify length-scale artifacts in molecular simulations with high efficiency and rigor.

Contribution

The work develops a novel numerical algorithm to compute the quality factor using the Bogoliubov inequality, enabling rigorous assessment of simulation box size effects in molecular systems.

Findings

Algorithm efficiently computes the quality factor.

Results are consistent with existing simulation data.

Method aids in detecting length-scale artifacts.

Abstract

The two-sided Bogoliubov inequality for classical and quantum many-body systems is a theorem that provides rigorous bounds on the free-energy cost of partitioning a given system into two or more independent subsystems. This theorem motivates the definition of a quality factor which directly quantifies the degree of statistical-mechanical consistency achieved by a given simulation box size. A major technical merit of the theorem is that, for systems with two-body interactions and a known radial distribution function, the quality factor can be computed by evaluating just two six-dimensional integrals. In this work, we present a numerical algorithm for computing the quality factor and demonstrate its consistency with respect to results in the literature obtained from simulations performed at different box sizes.