  Electronic coherences are key to understanding and controlling photo-induced
molecular transformations. We identify a crucial quantum-mechanical feature of
electron-nuclear correlation, the projected nuclear quantum momenta, essential
to capture the correct coherence behavior. In simulations, we show that, unlike
traditional trajectory-based schemes, exact-factorization-based methods
approximate these correlation terms, and correctly capture electronic
coherences in a range of situations, including their spatial dependence, an
important aspect that influences subsequent electron dynamics and that is
becoming accessible in more experiments.
