A topological classification of molecules and chemical reactions with and without interactions

In this talk, we propose a topological classification of molecules and their chemical reactions with and without many-body interactions. We consider 0-dimensional molecular Hamiltonians in a real-space tight-binding basis with time-reversal symmetry and an additional spatial reflection symmetry. On a single particle level, the reflection symmetry gives rise to a perplectic structure which can be probed by a Wilson loop after a flux-insertion. The classification in terms of Wilson loops remains stable in the presence of many-body interactions, which can be explained by the presence of zeros of the interacting single particle Green's function.
We argue that this topological classification has a universal contribution to the rate constants of chemical reactions and apply our model to a class of chemical reactions studied by Woodward and Hoffmann, where a reflection symmetry is preserved along a one-dimensional reaction path.