In Section III, we discuss the performance of the trajectory-based methods in comparison to quantum -exact -results, based on various electronic and nuclear observables. We will show the electronic populations, ρ S l (t) = dr dθ |χ S l (r, θ, t)| 2 with l = 0, 1, 2 (B2) the nuclear kinetic energy along the two active coordinates, . In TSHED and in CTTSH, the electronic populations are estimated using the fraction of trajectories ρcl S l (t) = N S l (t) N tr aj (B8) to distinguish it from Eq. (B7), where N S l (t) is the number of trajectories in state S l at time t. In a surface-hopping scheme, internal consistency holds if ρcl S l (t) ρ cl S l (t) (with ρ cl S l (t) the trajectory-averaged value of |C α S l (t)| 2 ), and in general the "proper" quantities that should be compared to exact results is ρcl S l (t) from Eq. (B8). The dissociation probability is, instead, estimated by simply counting the number of trajectories that, at any time, are located at r α (t) > r cutoff independently of the value θ α (t).