arXiv subjects
Publications and source records attributed to Masamitsu Aoki.
We show that the second bounded cohomology of the free product of racks and quandles is infinite-dimensional as a real vector space. This is similar to the case of groups. As a corollary, we show that the second bounded cohomology of the free rack and the free quandle is infinite-dimensional. We also give another proof of this corollary using homogeneous group quasimorphisms.
This study develops an algorithm to reproduce reaction route maps (RRMs) in shape space from the outputs of potential search algorithms. To demonstrate this, GRRM is utilized as a potential search algorithm but the proposed algorithm should work with other potential search algorithms in principle. The proposed algorithm does not require any encoding of the molecular configurations and is thus applicable to complicated realistic molecules for which efficient encoding is not readily available. We show subgraphs of a RRM mapped to each other by the action of the symmetry group are isomorphic and also provide an algorithm to compute the set of feasible transformations in the sense of Longuet--Higgins. We demonstrate the proposed algorithm in toy models and in more realistic molecules. Finally, we remark on absolute rate theory from our perspective.
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.