Finite-size estimates of Kirkwood-Buff and similar integrals

Abstract

Recently, Krüger and Vlugt [Phys. Rev. E 97, 051301(R) (2018)] have proposed a method to approximate an improper integral $\int_0^\infty \text{d}r\, F(r)$, where $F(r)$ is a given oscillatory function, by a finite-range integral $\int_0^L \text{d}r\, F(r) W(r/L)$ with an appropriate weight function $W(x)$. The method is extended here to an arbitrary (embedding) dimensionality $d$. A study of three-dimensional Kirkwood-Buff integrals, where $F(r)=4πr^2h(r)$, and static structure factors, where $F(r)=(4π/q) r\sin(qr) h(r)$, $h(r)$ being the pair correlation function, shows that, in general, a choice $d\neq 3$ (e.g., $d=7$) for the embedding dimensionality may significantly reduce the error of the approximation $\int_0^\infty \text{d}r\, F(r)\simeq \int_0^L \text{d}r\, F(r) W(r/L)$.