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

Y Zhang and A Otani and EJ Maginn, JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 11, 3537-3546 (2015).

DOI: 10.1021/acs.jctc.5b00351

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(cuV), 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.

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