Apparent density fluctuations in N-constant ensemble simulations

TL;DR

This paper demonstrates that local particle number fluctuations in N-constant ensemble simulations can accurately predict fluid compressibility and are equivalent to grand canonical ensemble results, impacting how radial distribution functions are interpreted.

Contribution

It shows that local fluctuations in constant N simulations can be used to compute compressibility and are equivalent to grand canonical ensemble results, clarifying the interpretation of radial distribution functions.

Findings

Apparent density fluctuations produce accurate compressibility estimates.

Radial distribution functions in N-constant and grand canonical ensembles are equivalent.

Implications for calculating Kirkwood-Buff integrals are discussed.

Abstract

In computer simulations performed in constant number of particles ensembles, although the total number of particles N contained in the simulation box does not fluctuate, hence giving a zero apparent compressibility, there are still local fluctuations in the number of particles. It is shown herein that these apparent fluctuations produce a compressibility that can be computed from the calculated radial distribution function, and which matches to a great accuracy the compressibility of the fluid for the open system. This statement implies that the radial distribution function evaluated in simulation of constant number of particles is identical to that evaluated in the grand canonical ensemble, for the entire distance range within half-box width. This is illustrated for the hard sphere and Lennard-Jones fluids and for molecular models of water. The origin of this apparent fluctuation is that the bulk of the remaining particles, outside the range over which the distribution function is calculated, act as a reservoir of particles for those within this range, thanks to the periodic boundary conditions. The implications on the calculation of the Kirkwood-Buff integrals are discussed.