Reproducing Reaction Route Map on the Shape Space from its Quotient by Complete Nuclear Permutation-Inversion group

TL;DR

This paper presents an algorithm to reproduce reaction route maps in shape space using symmetry group actions, applicable to complex molecules without needing configuration encoding, demonstrated on toy and realistic models.

Contribution

It introduces a novel algorithm for reproducing reaction route maps that leverages symmetry groups, applicable to complex molecules without configuration encoding.

Findings

Algorithm successfully reproduces RRMs in toy and realistic molecules.

Subgraphs related by symmetry group actions are shown to be isomorphic.

Provides a method to compute feasible symmetry transformations.

Abstract

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.