  Modeling the dynamics of non-bound states in molecules requires an accurate
description of how electronic motion affects nuclear motion and vice-versa. The
exact factorization (XF) approach offers a unique perspective, in that it
provides potentials that act on the nuclear subsystem or electronic subsystem,
which contain the effects of the coupling to the other subsystem in an exact
way. We briefly review the various applications of the XF idea in different
realms, and how features of these potentials aid in the interpretation of two
different laser-driven dissociation mechanisms. We present a detailed study of
the different ways the coupling terms in recently-developed XF-based mixed
quantum-classical approximations are evaluated, where either truly coupled
trajectories, or auxiliary trajectories that mimic the coupling are used, and
discuss their effect in both a surface-hopping framework as well as the
rigorously-derived coupled-trajectory mixed quantum-classical approach.
