Persistent Homology of Reaction Route Map*

Chemical reactions are governed by the potential energy surface (PES), the function of Euclidian coordinates of N atoms. In a chemical sense, local minima, or equilibrium structures (EQs), of PES correspond to stable conformers, which share the atomic constitution, but have different structures with each other. The first-order saddle point, connecting two EQs, is known as the transition state (TS) of chemical reaction converting these EQs. The potential energies of EQs and TSs on PES primarily determine the entire reaction properties.

Recently, the development of the GRRM program has made it possible to automatically construct reaction route maps (RRMs), which are collections of EQs and TSs on the PES. An RRM can be visualized as an energy-weighted network graph where nodes and edges correspond to EQs and TSs, respectively. Utilizing RRMs generated by GRRM has advanced our understanding of reaction mechanisms within various systems. However, most studies to date have focused only on subsets of TSs with low activation energies and their connected EQs, overlooking the whole structure. Focusing on the entire RRM could unveil new insights and values.

In this study, we extract features of RRMs using persistent homology, an analytical method based on topological "holes." Applying this method to RRMs of metal nanocluster systems, we discovered that clusters with similar compositions yield similar persistence diagrams (PDs). This finding suggests that it may be possible to predict reactivity based on RRMs. (edited)