In a trajectory-based description of the coupled electron-nuclear dynamics in the presence of nonadiabatic effects and described within the exact-factorization framework, nuclear dynamics from Eq. ( ) is approximated in terms of an ensemble of coupled trajectories. Their positions and momenta evolve according to Hamilton equations under the effect of the TDVP and TD-PES . In turn, the TDVP and TDPES are computed from the electronic wavefunction, which is expanded in the adiabatic basis, i.e., the basis of eigenstates of Ĥel (r, R). Equation ( ) yields evolution equations for the expansion coefficients, which are solved coupled to the nuclear Hamilton equations. This is the essence of the coupled-trajectory mixed quantum-classical (CT-MQC) algorithm . It has been abundantly described in the literature, therefore, we refer the interested reader to Refs. for in-depth discussions, and we recall here only the main ideas and equations.