The graph-theoretic minimum energy path problem for ionic conduction

A new computational method was developed to analyze the ionic conduction mechanism in crystals through graph theory. The graph was organized into nodes, which represent the crystal structures modeled by ionic site occupation, and edges, which represent structure transitions via ionic jumps. We proposed a minimum energy path problem, which is similar to the shortest path problem. An effective algorithm to solve the problem was established. Since our method does not use randomized algorithm and time parameters, the computational cost to analyze conduction paths and a migration energy is very low. The power of the method was verified by applying it to α-AgI and the ionic conduction mechanism in α-AgI was revealed. The analysis using single point calculations found the minimum energy path for long-distance ionic conduction, which consists of 12 steps of ionic jumps in a unit cell. From the results, the detailed theoretical migration energy was calculated as 0.11 eV by geometry optimization and nudged elastic band method. Our method can refine candidates for possible jumps in crystals and it can be adapted to other computational methods, such as the nudged elastic band method. We expect that our method will be a powerful tool for analyzing ionic conduction mechanisms, even for large complex crystals.