Characterizing Reaction Route Map of Realistic Molecular Reactions Based on Weight Rank Clique Filtration of Persistent Homology

A reaction route map (RRM) constructed using the GRRM program is a collection of elementary reaction pathways, each of which comprises two equilibrium (EQ) geometries and one transition state (TS) geometry connected by an intrinsic reaction coordinate (IRC). An RRM can be mathematically represented by a graph with weights assigned to both vertices, corresponding to EQs, and edges, corresponding to TSs, representing the corresponding energies. In this study, we propose a method to extract topological descriptors of a weighted graph representing an RRM based on persistent homology (PH). The work of Mirth et al. [ J. Chem. Phys. 2021, 154, 114114], in which PH analysis was applied to the (3N - 6)-dimensional potential energy surface of an N atomic system, is related to the present method, but our method is practically applicable to realistic molecular reactions. Numerical assessments revealed that our method can extract the same information as the method proposed by Mirth et al. for the 0-th and 1-st PHs, except for the death of the 1-st PH. In addition, the information obtained from the 0-th PH corresponds to the analysis using the disconnectivity graph. The results of this study suggest that the descriptors obtained using the proposed method accurately reflect the characteristics of the chemical reactions and/or physicochemical properties of the system.