Kirkwood–Buff integrals of finite systems: Shape effects

Noura Dawass, Peter Krüger, Jean Marc Simon, Thijs J.H. Vlugt*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)
67 Downloads (Pure)


The Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.

Original languageEnglish
Pages (from-to)1573-1580
JournalMolecular Physics: an international journal at the interface between chemistry and physics
Issue number12
Publication statusPublished - 2018


  • Kirkwood–Buff integrals
  • small-systems thermodynamics


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