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

Journal of Computational Chemistry, vol. 44, pp. 1347–1359

Abstract

Abstract Analysis 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.

Authors 4

1. Adrian L. Usler corresponding Aachen Institute of Physical Chemistry

   RWTH Aachen University

   Affiliation as printed

   Institute of Physical Chemistry RWTH Aachen University Aachen Germany

   Institute of Physical Chemistry, RWTH Aachen University, Aachen, Germany

2. Dennis Kemp Aachen Institute of Physical Chemistry

   RWTH Aachen University

   Affiliation as printed

   Institute of Physical Chemistry RWTH Aachen University Aachen Germany

   Institute of Physical Chemistry, RWTH Aachen University, Aachen, Germany

3. Alexander Bonkowski Aachen Institute of Physical Chemistry

   RWTH Aachen University

   Affiliation as printed

   Institute of Physical Chemistry RWTH Aachen University Aachen Germany

   Institute of Physical Chemistry, RWTH Aachen University, Aachen, Germany

4. Roger A. De Souza corresponding Aachen Institute of Physical Chemistry

   RWTH Aachen University

   Affiliation as printed

   Institute of Physical Chemistry RWTH Aachen University Aachen Germany

   Institute of Physical Chemistry, RWTH Aachen University, Aachen, Germany