Electron-nuclear entanglement in the time-dependent molecular wavefunction

We address the problem of electron-nuclear entanglement in time-dependent molecular wavefunctions, key quantities of quantum nonadiabatic molecular dynamics. The most natural way of tackling this question consists in comparing the nonadiabatic dynamics obtained from time-dependent self-consistent field and the exact factorization of the time-dependent electron-nuclear wavefunction. Both approaches are based on a single-product Ansatz for the molecular wavefunction, with both a time-dependent electronic and nuclear wavefunction. In the former, however, electron-nuclear coupling is treated within the mean-field approximation, whereas in the latter the entanglement is completely accounted for. Based on a numerical model study, we analyze the nature of the electron-nuclear entanglement in the exact factorization.