Towards a topological classification of molecules and chemical reactions

In this talk, I outline a topological classification of molecules and their chemical reactions, proposing that changes in topological invariants of molecules measure strong non-adiabatic couplings along the reaction path. As an example, we consider 0-dimensional molecular Hamiltonians in a real-space tight-binding basis with time-reversal symmetry and an additional spatial reflection symmetry. We develop a classification in terms of Wilson loops in the presence of many-body interactions, and propose that the topological properties can be explained by the presence of zeros of the interacting single particle Green's function.