[220] and compared to the BO approximation, by calculating and analyzing the nuclear density, the TDPES and the TDVP of the exact factorization. Overall, the observations allowed to discard all traces of singularities or destructive interferences related to topological-phase effects. As an example, let us discuss here the TDPES in Fig. , which is shown as colour map at three times along the dynamics. First, in the left panel, the nuclear density (depicted as black contour lines) approaches the location of the conical intersection (indicated by a red cross at the origin X,Y = 0, 0) at 0.24 ms; then, in the central panel, the density has reached the location of the conical intersection at 0.69 ms; finally, at 1.35 ms, the density has passed the origin X,Y = 0, 0 and exhibits a depletion along the line X > 0,Y = 0. In particular at this last time, it is interesting to observe that the TDPES develops a barrier-like feature along Y = 0 for X > 0. However, while the height and width of this barrier change over time, it remains finite and does not diverge. Thus, this barrier induces a depletion of the nuclear density along Y = 0 but cannot cause a node in the corresponding nuclear wavefunction. Indeed, a finite (strictly larger than 10 -5 ), yet small, amount of nuclear density is always present in the region X > 0,Y = 0, attesting to the fact that there is no nodal line formed and thus, no topological-phase effect induced in the nuclear dynamics.