We remind that the classical populations F m (t) (thick lines) are calculated as F m (t) = N m (t)/N T , where N m (t) is the number of trajectories for which the active state at time t is m, while the electronic populations P m (t) are the averages over all trajectories of the state probabilities |C α m (t)| 2 . In general F m (t) ̸ = P m (t), and the difference is particularly relevant if decoherence effects are important and not accounted for, like in TSH, as shown on the left panel of Fig. . We note a remarkably good agreement across implementations of CT-TSH with respect to the electronic populations. However, the thawed Gaussian implementations seems to lose accuracy at long times if one considers the internal consistency. The partial failure of the thawed Gaussian option is due to the excessive increase of the σ i,ν widths in time. This is shown in Fig. , where we plot the mass-weighted average Σ =