Quantum entanglement between electronic and vibrational degrees of freedom in molecules

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with a tendency towards double welled potentials using model coupled harmonic diabatic potential-energy surfaces. The von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions in such a bipartite system. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local minima). However, in this region two distinct types of entanglement are found: (1) entanglement that arises purely from the degeneracy of energy levels in the two potential wells and which is destroyed by slight asymmetry, and (2) entanglement that involves strongly interacting states in each well that is relatively insensitive to asymmetry. These two distinct regions are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, semibullvalene, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.