Reliable estimates of error in self-diffusivity from molecular simulations using statistical bootstrap

Abstract

In order to estimate the uncertainty in diffusion coefficients obtained from molecular simulations, the method of statistical bootstrapping has previously been proposed [17]. This method is efficient as it does not require running multiple simulations to obtain uncertainty estimates; instead, it relies on resampling trajectory data from a single simulation. However, atomic trajectories in a typical molecular simulation are correlated, especially at short timescales. Thus, the sufficient condition for the validity of resampling, namely independence of data, is not strictly met. We quantify the dependence of this error on simulation parameters, by running a large set of molecular dynamics simulations. Confidence intervals obtained from resampling and multiple independent simulations are compared. For short simulations, where correlation between trajectories is expected to be strongest, resampling systematically underestimates the uncertainty by a factor of about half. As simulation time is increased, the confidence intervals shrink, and begin to approach each other. It is found that estimates from statistical bootstrapping, and multiple independent simulations essentially converge, once the simulation time exceeds the average time required for a particle to traverse a distance equal to the length of the simulation box.