An efficient technique to combine the surface-hopping algorithm with the exact factorization has been proposed by Min and coworkers and dubbed SHXF, i.e., surface hopping based on the exact factorization . The main idea at the basis of SHXF is to use the surface-hopping procedure to propagate independent nuclear trajectories adiabatically, with the fewest-switches probability for the hops, and, at the same, to "spawn" auxiliary trajectories on the electronic states that are nonadiabatically coupled to the active/force state. The auxiliary trajectories are essential for the calculation of the quantum momentum (14), similarly to what is done in the original CTMQC algorithm: the quantum momentum induces quantum decoherence effects in the electronic evolution equation, thus bypassing the overcoherence problem of standard fewestswitches surface hopping . SHXF is an interesting alternative to CTMQC and CTTSH, as it is computationally less demanding, due to the fact that for each physical trajectory, only a few auxiliary trajectories need to be generated in the vicinity of a region of strong coupling as long as such a region remains well localized in space. The auxiliary trajectories can be evolved according to "unphysical" forces, in the sense that they do not need to follow the adiabatic potentials and, in fact, are launched with constant velocity, chosen such that the difference in potential energy from the active surface is isotropically distributed in the coordinates; in addition, the auxiliary trajectories are removed from the algorithm as soon as they evolve far away from the physical trajectory.