Calculating Transport Coefficients from Biased Molecular Dynamics

Molecular simulation is a fantastic tool for understanding the link between atomic details and macroscopic properties. Determination of transport properties remains a challenge, due to the long time scales needed to obtain convergent results in commonly used methods, such as equilibrium molecular dynamics simulations combined with the Green-Kubo (GK) formalism. The long timescales over which autocorrelation functions must be measured for GK is especially exacerbated when dynamics are slow due to molecular complexity or proximity to a glass transition. Here, we explore the long-time behavior of transport properties by averaging over an ensemble of short-time trajectories calculated using the GK equation, each re-weighting the ensemble-average by calculating the effective free energy of the local configuration. We explore useful parameters for determining the cutoff time for the short simulations, and methods by which the weight can be efficiently computed. The technique is then applied to calculate shear viscosity for a set of idealized systems, including a Kob-Andersen mixture prepared near the glassy state.