# Unsupervised landmark analysis for jump detection in molecular dynamics simulations

## TL;DR

This paper introduces an unsupervised method for detecting ion jumps in molecular dynamics simulations, enabling analysis without prior knowledge of the diffusive process, and applies it to various lithium-ion conductors.

## Contribution

The novel approach combines landmark-based projection, clustering, and atomic environment descriptors to identify and analyze jump events in ionic diffusion simulations.

## Key findings

- Successfully applied to ten lithium-ion systems
- Revealed detailed diffusive behaviors in specific materials
- Compared favorably with existing methods

## 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 conduct in-depth analyses of cubic Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$, tetragonal Li$_{10}$GeP$_{2}$S$_{12}$, and the $\beta$-eucryptite 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.