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

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.