To give an idea of the performance of the exact factorization, we show in Fig. how CTMQC works in the situation described in Fig. . The delocalization of the distribution of trajectories is correctly reproduced by CTMQC, especially as it shown by the circles at the final simulated time t = 24 fs (green circles). Such a delocalization seems to appear more slowly than in the quantum dynamics, as the distribution of trajectories at t = 12 fs (blue circles) suggests. However, it is interesting to note how a single potential is able to yield different forces in different portions of space so as to induce the splitting of the distribution of trajectories (that is not possible to achieve in Ehrenfest while in surface hopping it is only possible by introducing the hopping idea). In this simple case, the TDPES can be calculated exactly, and it is shown in Fig. as crosses at times t = 0 (light-blue crosses), t = 12 fs (magenta crosses) and t = 24 fs (purple crosses). Only at the intermediate time shown in the figure, the distribution of CTMQC trajectories along the potential that drives their dynamics, i.e., the blue circles, does not follow the TDPES, i.e., the magenta crosses, confirming, as observed previously, that CTMQC trajectories reproduce the splitting of the nuclear density with some delay. Nonetheless, such a delay does not affect significantly the population of the excited state (lower panel in Fig. ) which perfectly agrees with the reference (gray line) all along the dynamics.