Figure (left) reports the nuclear kinetic energy along the two nuclear directions r (upper panel) and θ (lower panel) as function of time. We observe that the nuclear kinetic energy in Ehrenfest is too small compared to the reference along both coordinates, which is probably due to the fact that the potential energy is overestimated already after about 35 fs. Specifically, in Ehrenfest the potential energy is the average of the electronic adiabatic energies weighted by the populations. Then, since in particular the population of S 1 is overestimated at the expenses of S 0 , it is not surprising that the kinetic energy is small (in Ehrenfest the classical total energy is conserved along each trajectory). TSHED does indeed a good job in reproducing the exact kinetic energy, while CTTSH overestimates the kinetic energy along both directions. In CTTSH, this happens for the opposite reason if compared to Ehrenfest, as in CTTSH the ground state population is overestimated at the expenses of S 1 . Instabilities in the nuclear kinetic energy can be observed in CTMQC, which are slightly kept under control in CTMQC-E.