# A topological classification of molecules and chemical reactions with a perplectic structure

## TL;DR

This paper introduces a topological classification framework for molecules and chemical reactions based on a perplectic structure and $ ext{Z}_2$ invariants, linking topological properties to reaction feasibility.

## Contribution

It proposes a novel topological classification method for molecules and reactions using a perplectic structure and applies it to chemical reactions with symmetry considerations.

## Key findings

- Reactions occur when reactants and products are topologically deformable into each other.
- Reactions requiring a change in topological invariants are not observed experimentally.
- Topological invariants influence reaction pathways and feasibility.

## Abstract

In this paper, a topological classification of molecules and their chemical reactions is proposed on a single particle level . We consider zero-dimensional electronic Hamiltonians in a real-space tight-binding basis with spinless time-reversal symmetry and an additional spatial reflection symmetry. The symmetry gives rise to a perplectic structure and suggests a $\mathbb{Z}_2$ invariant in form of a pfaffian, which can be captured by an entanglement cut. We apply our findings to a class of chemical reactions studied by Woodward and Hoffmann, where a reflection symmetry is preserved along a one-dimensional reaction path and argue that the topological classification should contribute to the rate constants of these reactions. More concretely, we find that a reaction takes place experimentally whenever the reactants and products can be adiabatically deformed into each other, while reactions that require a change of topological invariants have not been observed experimentally.