Entanglement entropy as a potential measure for non-adiabatic coupling

Molecular dynamics are most often described using a basis of states in which molecular electrons are separated from nuclei, the electronic states being parametrically dependent on the nuclear coordinates. Even in this basis, the electronic and nuclear wavefunctions can be completely separated only if the dependence of the electronic states on the nuclear configuration is truly adiabatic, implying that it can be expressed as a geometric phase factor. Thus, a measure of the entanglement of the electronic and nuclear wavefunctions could serve as a metric for non-adiabatic coupling in molecular dynamics. One such metric for bipartite systems is the entanglement entropy. Here we explore the link between the entanglement entropy of the electrons, S_el , and coupling between electrons and nuclei. Specifically, in the case of ro-electronic coupling in the B state of ammonia, we experimentally determine S_el and the Von Neumann Entropy S(θ,χ,t) as a function of molecular orientation and time. In this case, the results indicate that high entropy regions in the space of nuclear coordinates correlate with a more mixed electronic state, potentially provide a map of the degree of non-adiabatic coupling. We finally discuss the possibility of extending this to cases with strong vibronic coupling.