A general expression for the statistical error in a diffusion coefficient obtained from a solid‐state molecular‐dynamics simulation. Issue 14 (22nd February 2023)

• Record Type: Journal Article
• Authors: Usler, Adrian L.; Kemp, Dennis; Bonkowski, Alexander; De Souza, Roger A.
• Is Part Of: Journal of computational chemistry. Volume 44:Issue 14(2023)
• Page Start: 1347
• Page End: 1359
• Publication Date: 2023-02-22
• Subjects: diffusion -- kinetic Monte Carlo, kMC -- mean squared displacement, MSD -- molecular dynamics, MD -- statistical error; Chemistry -- Data processing -- Periodicals; 542.85
• DOI: 10.1002/jcc.27090
• Languages: English
• ISSNs: 0192-8651

Abstract

Abstract: Analysis of the mean squared displacement of species k, r k 2, 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 k 2 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. Abstract : Molecular‐dynamics (MD) simulations constitute an important technique for studying mass transport in the solid state. In this study, we investigated how different simulation parameters (e.g., time and cell size) determine the statistical error in the tracer diffusion coefficient obtained from an MD simulation. In addition, we distill the characteristics of the uncertainty into a mathematical expression that captures the interrelated influences of the simulation parameters.