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Ab initio molecular dynamics (AIMD) simulation is widely employed in studying diffusion mechanisms and in quantifying diffusional properties of materials. However, AIMD simulations are often limited to a few hundred atoms and a short, sub-nanosecond physical timescale, which leads to models that include only a limited number of diffusion events. As a result, the diffusional properties obtained from AIMD simulations are often plagued by poor statistics. In this paper, we re-examine the process to estimate diffusivity and ionic conductivity from the AIMD simulations and establish the procedure to minimize the fitting errors. In addition, we propose methods for quantifying the statistical variance of the diffusivity and ionic conductivity from the number of diffusion events observed during the AIMD simulation. Since an adequate number of diffusion events must be sampled, AIMD simulations should be sufficiently long and can only be performed on materials with reasonably fast diffusion. We chart the ranges of materials and physical conditions that can be accessible by AIMD simulations in studying diffusional properties. Our work provides the foundation for quantifying the statistical confidence levels of diffusion results from AIMD simulations and for correctly employing this powerful technique.Ionic diffusion: Mapping the uncertaintyThe calculation of ionic diffusivity with ab initio molecular dynamics is often plagued by poor statistics; how accurate are the results? Due to computational limits only small systems and timescales can be modeled, limiting the number of diffusion events sampled. Here, Yifei Mo and colleagues at the University of Maryland outline best practice to obtain ionic diffusivity, as well as how to obtain statistical errors with this approach. They show linear behavior in diffusivity only happens for intermediate time intervals of the simulations. Moreover, variance of diffusivity is related to the total mean squared displacement of all ions, the statistical error reducing as the displacement increases. Accurate ionic diffusion calculations can only be performed for super-ionic conductors, or at high temperature, with implications for the reliability of calculations of diffusivity in other materials.

Statistical variances of diffusional properties from ab initio molecular dynamics simulations