Exact expressions for finite-volume Kirkwood-Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.

We show how density and energy fluctuations of small nonperiodic systems embedded in a reservoir can be used to determine macroscopic thermodynamic properties like the enthalpy density and the thermodynamic correction factor. For mixtures, the same formalism leads to a very convenient method to obtain so-called total correlation function integrals, also often referred to as Kirkwood-Buff integrals. Using finite size scaling, the properties obtained for small systems can be extrapolated to the macroscopic system limit provided that the system is sufficiently far from the critical point. As derived in our previous work (Chem. Phys. Lett. 2011, 504, 199-201), the finite size scaling is significant and depends on 1/L, where L is the length of the small system in one dimension. By considering a reservoir with an ensemble of embedded small systems, we can use the scaling arising from surface effects to determine properties for macroscopic systems by extrapolation. We demonstrate this method for the WCA and LJ fluids, as well a for a heterogeneous system, i.e., argon adsorbed in silicalite-1 zeolite.