# Finding reaction pathways with optimal atomic index mappings

## TL;DR

This paper introduces a novel method using a permutation-invariant penalty function and Minima Hopping to efficiently find reaction pathways and intermediate states in complex molecular reactions, reducing computational effort.

## Contribution

It proposes a new approach combining a permutation-invariant bias and global optimization to identify reaction pathways with fewer intermediate states.

## Key findings

- Successfully applied to LJ38 benchmark system, identifying relevant intermediate states.
- Reduced the number of states needed to find the lowest energy pathway compared to previous methods.
- Applied to C60 and C20H20, revealing valuable synthesis pathways.

## Abstract

Finding complex reaction and transformation pathways, involving many intermediate states, is in general not possible on the DFT level with existing simulation methods due to the very large number of required energy and force evaluations. This is due to a large extent to the fact that for complex reactions, it is not possible to determine which atom in the educt is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. By using a penalty function that is invariant under index permutations, we can bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker whose global minimum is the product. By performing a Minima Hopping based global optimization on this biased potential energy surface we can rapidly find intermediate states that lead into the global minimum. Based on this information we can then extract the full reaction pathway. We first demonstrate for a benchmark system, namely LJ38 that our method allows to preferentially find intermediate states that are relevant for the lowest energy reaction pathway and that we, therefore, need a much smaller number of intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, C60 and C20H20 and show that the found reaction pathway contains valuable information on how the system can be synthesized.