Some of the trajectory-based approaches derived from the exact factorization framework allow propagating coupled electron-nuclear dynamics in the presence of nonadiabatic effects by approximating the nuclear dynamics described by Eq. 4 using an ensemble of coupled trajectories. When the positions and momenta of these trajectories evolve according to Hamilton equations of motion driven by the TDVP and TDPES, the coupled-trajectory mixed quantum-classical (CT-MQC) algorithm is obtained . CT-MQC requires the calculation of the non-adiabatic coupling (NAC) vectors at all times to evaluate the nuclear forces. This is clearly a computationally expensive procedure for medium to large-size molecules. Furthermore, CT-MQC does not guarantee energy conservation either along a single trajectory or over the ensemble . To circumvent these issues, CT-TSH has been introduced: nuclear forces are purely adiabatic, i.e., are obtained as the gradient of a BO PES, and energy conservation is imposed after each hop as in standard TSH along each trajectory. It should be noted that Min and coworkers have proposed alternative trajectory-based procedures derived from the exact factorization but based on independent or auxiliary trajectories .