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 ${\int }_0^{\infty }\text{d}rF(r)$, where $F(r)$ is a given oscillatory function, by a finite-range integral ${\int }_0^L\text{d}rF(r)W(r/L)$ 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 $F(r)=4\pi r^{2}h(r)$, and static structure factors, where $F(r)=(4\pi /q)r\sin (qr)h(r)$, $h(r)$ being the pair correlation function, shows that, in general, a choice $d\ne 3$ (e.g., $d=7$) for the embedding dimensionality may significantly reduce the error of the approximation ${\int }_0^{\infty }\text{d}rF(r)\simeq {\int }_0^L\text{d}rF(r)W(r/L)$.

8 pages, 7 figures; v2: static structure factor included

References in corpus (5)

• Size and shape dependence of finite volume Kirkwood-Buff integrals
• Exact bulk correlation functions in one-dimensional nonadditive hard-core mixtures
• Structural properties of the Jagla fluid
• Local and global properties of mixtures in one-dimensional systems. II. Exact results for the Kirkwood-Buff integral
• One-dimensional fluids with second nearest-neighbor interactions

Cited by in corpus (4)

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• Structural properties of additive binary hard-sphere mixtures
• Ensemble averaged Madelung energies of finite volumes and surfaces