Convergence of Sampling Kirkwood-Buff Integrals of Aqueous Solutions with Molecular Dynamics Simulations

We discuss two methods for calculating Kirkwood-Buff integrals (KBIs) of aqueous cosolvent solutions from molecular simulations. The first method is based on computing running integrals over radial distribution functions obtained from NVT or NpT simulations. The second, more recent method, originally introduced by Schnell et al. (J. Phys. Chem. B2011, 115, 10911), obtains the KBIs from direct analysis of particle number fluctuations in small, open subvolumes embedded in a larger reservoir as provided by the NVT (NpT) simulation cell. The thermodynamic limit is taken in the first method by using the plateau-values of the running KBIs for large distances, while in the second method an analytical finite-size scaling relation is applied to the KBIs of subvolumes of variable size. We find that direct analysis of particle number fluctuations at small scales provides more precise estimates of KBIs for methanol-water and urea-water solutions. Converged KBIs could, however, not be obtained from nanosecond time scale molecular dynamics simulations with either of the two methods. Based on 0.1 μs simulation trajectories of small and large system sizes time-converged KBIs were obtained with both methods. The running integral method suffers, however, from stronger finite-size artifacts than the sub-box method, also when empirical finite-size tail corrections are applied to the radial distribution functions.