Path Integral Approaches to Ion Diffusion

Classical ion diffusion theories rely on simplified hopping models lacking concerted motion. Molecular dynamics can capture correlations but requires extensive sampling. This fairly brute-force approach has become the standard way to calculate ion diffusion rates, recently accelerated with the use of machine learning force-fields trained against density functional theory calculations.<br/><br/>We revisit path integral techniques to bridge this gap. Integrating state-of-the-art graph neural network potentials [1] with the 1990s path-integral approach of Chakraborty et al. [2] offers an efficient route to model correlated transport, and understand the physical processes. Generally these more sophisticated mathematical models developed in the 70s to 90s, have mostly been neglected as attention has shifted to explicit simulation on fast computers.<br/><br/>We show how a semi-numerical path integral approach parameterised by lighter weight machine-learning force-field molecular dynamics, can describe and understand correlation effects in representative lithium, sodium, and halide ion conductors.<br/><br/>[1] Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J.P., Kornbluth, M., Molinari, N., Smidt, T.E. and Kozinsky, B., 2022. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature communications, 13(1), p.2453.<br/><br/>[2] Chakraborty, A.K., Bratko, D., Chandler, D., 1994. Diffusion of ionic penetrants in charged disordered media. J. Chem. Phys. 100, 1528–1541. https://doi.org/10.1063/1.466632