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

Analysis of the mean squared displacement of species k, (r(2) (k)), as a function of simulation time t constitutes a powerful method for extracting, from a molecular-dynamics (MD) simulation, the tracer diffusion coefficient, D-* k. The statistical error in D* (k) is seldom considered, and when it is done, the error is generally underestimated. In this study, we examined the statistics of (r(2) (k))(t) curves generated by solid-state diffusion by means of kinetic Monte Carlo sampling. Our results indicate that the statistical error in D-* k 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 k particles that have jumped at least once-we derive a closed-form expression for the relative uncertainty in D-* k. 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.

Automated summary

Analysis of the mean squared displacement of species k as a function of simulation time allows the extraction of tracer diffusion coefficient from a molecular dynamics simulation. The statistical error in the diffusion coefficient is often underestimated. In this study, we examined the statistics of displacement curves generated by solid-state diffusion and derived a closed-form expression for the relative uncertainty in the diffusion coefficient.