Abstract: In this talk, I will discuss notions of how strong correlations and topology can be found in molecular systems. Motivated by the concept of M\“obius aromatics in organic chemistry, I extend the recently introduced concept of fragile Mott insulators (FMIs) to ring-shaped molecules with repulsive Hubbard interactions threaded by a half-quantum of magnetic flux ($hc/2e$). In this context, a FMI is the insulating ground state of a finite-size molecule that cannot be adiabatically connected to a single Slater determinant (i.e., to a band insulator), provided that time-reversal and lattice translation symmetries are preserved. I establish a duality between Hubbard molecules with $4n$ and $4n+2$ sites, with $n$ integer. A molecule with $4n$ sites is an FMI in the absence of flux but becomes a band insulator in the presence of a half-quantum of flux, while a molecule with $4n+2$ sites is a band insulator in the absence of flux but becomes an FMI in the presence of a half-quantum of flux.
Based on these results, I propose a topological classification of molecules and their chemical reactions with and without many-body interactions. I 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 that 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. I argue that this topological classification has a universal contribution to the rate constants of chemical reactions and apply my theory to a class of reactions studied by Woodward and Hoffmann, where a reflection symmetry is preserved along a one-dimensional reaction path.