Finite-size estimates of Kirkwood-Buff and similar integrals

Recently, Kr"uger and Vlugt [Phys. Rev. E 97, 051301® (2018)] have proposed a method to approximate an improper integral $\int_0^\infty $\text{d}$r, F®$,where$F®$ is a given oscillatory function, by a finite-range integral ${\int }_0^L\text{d}rF(r)W(r\mathrm{/}L)$ 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 $F(r)=4\pi r^{2}h(r)$, and static structure factors, where $F®=(4\pi/q) r\sin(qr) h®$,$h®$ being the pair correlation function, shows that, in general, a choice $d\mathrm{\ne }3$ (e.g., $d=7$) for the embedding dimensionality may significantly reduce the error of the approximation $\int_0^\infty $\text{d}$r, F®\simeq \int_0^L $\text{d}$r, F® W(r/L)$.