Finite-size effects of Kirkwood–Buff integrals from molecular simulations

The modelling of thermodynamic properties of liquids from local density fluctuations is relevant to many chemical and biological processes. The Kirkwood–Buff (KB) theory connects the microscopic structure of isotropic liquids with macroscopic properties such as partial derivatives of activity coefficients, partial molar volumes and compressibilities. Originally, KB integrals were formulated for open and infinite systems which are difficult to access with standard Molecular Dynamics (MD) simulations. Recently, KB integrals for finite and open systems were formulated (J Phys Chem Lett. 2013;4:235). From the scaling of KB integrals for finite subvolumes, embedded in larger reservoirs, with the inverse of the size of these subvolumes, estimates for KB integrals in the thermodynamic limit are obtained. Two system size effects are observed in MD simulations: (1) effects due to the size of the simulation box and the size of the finite subvolume embedded in the simulation box, and (2) effects due to computing radial distribution functions (RDF) from a closed and finite system. In this study, we investigate the two effects in detail by computing KB integrals using the following methods: (1) Monte Carlo simulations of finite subvolumes of a liquid with an analytic RDF and (2) MD simulations of a WCA mixture for various simulation box sizes, but at the same thermodynamic state. We investigate the effect of the size of the simulation box and quantify the differences compared to KB integrals computed in the thermodynamic limit. We demonstrate that calculations of KB integrals should not be extended beyond half the size of the simulation box. For finite-size effects related to the RDF, we find that the Van der Vegt correction (J Chem Theory Comput. 2013;9:1347) yields the most accurate results.