  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.
