A general expression for the statistical error in a diffusion coefficient obtained from a solid‐state molecular‐dynamics simulation

Abstract

AbstractAnalysis of the mean squared displacement of species , , as a function of simulation time constitutes a powerful method for extracting, from a molecular‐dynamics (MD) simulation, the tracer diffusion coefficient, . The statistical error in is seldom considered, and when it is done, the error is generally underestimated. In this study, we examined the statistics of curves generated by solid‐state diffusion by means of kinetic Monte Carlo sampling. Our results indicate that the statistical error in depends, in a strongly interrelated way, on the simulation time, the cell size, and the number of relevant point defects in the simulation cell. Reducing our results to one key quantity—the number of particles that have jumped at least once—we derive a closed‐form expression for the relative uncertainty in . We confirm the accuracy of our expression through comparisons with self‐generated MD diffusion data. With the expression, we formulate a set of simple rules that encourage the efficient use of computational resources for MD simulations.