Reliable Viscosity Calculation from Equilibrium Molecular Dynamics Simulations: A Time Decomposition Method

Equilibrium molecular dynamics is often used in conjunction with a Green–Kubo integral of the pressure tensor autocorrelation function to compute the shear viscosity of fluids. This approach is computationally expensive and is subject to a large amount of variability because the plateau region of the Green–Kubo integral is difficult to identify unambiguously. Here, we propose a time decomposition approach for computing the shear viscosity using the Green–Kubo formalism. Instead of one long trajectory, multiple independent trajectories are run and the Green–Kubo relation is applied to each trajectory. The averaged running integral as a function of time is fit to a double-exponential function with a weighting function derived from the standard deviation of the running integrals. Such a weighting function minimizes the uncertainty of the estimated shear viscosity and provides an objective means of estimating the viscosity. While the formal Green–Kubo integral requires an integration to infinite time, we suggest an integration cutoff time t cut, which can be determined by the relative values of the running integral and the corresponding standard deviation. This approach for computing the shear viscosity can be easily automated and used in computational screening studies where human judgment and intervention in the data analysis are impractical. The method has been applied to the calculation of the shear viscosity of a relatively low-viscosity liquid, ethanol, and relatively high-viscosity ionic liquid, 1-n-butyl-3-methylimidazolium bis­(trifluoromethane-sulfonyl)­imide ([BMIM]­[Tf2N]), over a range of temperatures. These test cases show that the method is robust and yields reproducible and reliable shear viscosity values.