It is important to mention here that, in general, the outcome of a nonadiabatic quantum molecular-dynamics simulation strongly depends not only on the algorithm used to propagate nuclear and electronic dynamics, but also (i) on the choice of the initial conditions, (ii) on the representation used for the electronic problem, and, perhaps mainly, (iii) on the electronic-structure approach employed to determine electronic properties on-the-fly along the trajectories 200 . Since the application of the exact factorization in the domain of photochemistry is independent of point (iii), below, we will briefly discuss only points (i) and (ii), as they have been analyzed precisely in the framework of the exact factorization . In relation to point (iii) above, some ideas have been developed in the context of the time-independent formulation of the exact factorization by Requist and Gross in Ref. [120]. There, it was proposed that the electronic equation, equivalent to Eq. ( ) but for the stationary solutions of the electron-nuclear Hamiltonian, is expressed and solved using density functional theory and some test studies were reported . In addition, Min and coworkers recently recast the exact factorization in such a way that a trajectory-based scheme can be made operational in combination with real-time time-dependent density functional theory .