Unsupervised landmark analysis for jump detection in molecular dynamics simulations

Abstract

Molecular dynamics is a versatile and powerful method to study diffusion in solid-state ionic conductors, requiring minimal prior knowledge of equilibrium or transition states of the system's free energy surface. However, the analysis of trajectories for relevant but rare events, such as a jump of the diffusing mobile ion, is still rather cumbersome, requiring prior knowledge of the diffusive process in order to get meaningful results. In this work, we present a novel approach to detect the relevant events in a diffusive system without assuming prior information regarding the underlying process. We start from a projection of the atomic coordinates into a landmark basis to identify the dominant features in a mobile ion's environment. Subsequent clustering in landmark space enables a discretization of any trajectory into a sequence of distinct states. As a final step, the use of the smooth overlap of atomic positions descriptor allows distinguishing between different environments in a straightforward way. We apply this algorithm to ten Li-ionic systems and perform in-depth analyses of cubic ${\mathrm{Li}}_{7}{\mathrm{La}}_{3}{\mathrm{Zr}}_{2}{\mathrm{O}}_{12}$, tetragonal ${\mathrm{Li}}_{10}{\mathrm{GeP}}_{2}{\mathrm{S}}_{12}$, and the $\ensuremath{\beta}$-eucryptite ${\mathrm{LiAlSiO}}_{4}$. We compare our results to existing methods, underscoring strong points, weaknesses, and insights into the diffusive behavior of the ionic conduction in the materials investigated.