Size and shape dependence of finite volume Kirkwood-Buff integrals

TL;DR

This paper derives analytic formulas for finite volume Kirkwood-Buff integrals, revealing shape dependence and proposing a faster convergence method for infinite volume extrapolation in molecular simulations.

Contribution

It provides closed-form expressions for common simulation shapes and proves the shape dependence of the leading term in volume expansions.

Findings

Surface area to volume ratio influences finite volume integrals

New extrapolation method converges faster to infinite volume

Analytic relations derived for cubes and cuboids

Abstract

Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed in molecular simulations. When finite volume Kirkwood-Buff integrals are expanded over inverse system size, the leading term depends on shape only through the surface area to volume ratio. This conjecture is proved for arbitrary shapes and a general expression for the leading term is derived. From this, a new extrapolation to the infinite volume limit is proposed, which converges much faster with system size than previous approximations and thus significantly simplifies the numerical computations.