The left pannel of Figure compares the trajectory-averaged electronic state populations obtained with CTMQC, CTMQC-E, CTTSH, Ehrenfest and TSHED with the corresponding quantum-dynamics benchmark. Let us first focus on the surface-hopping-based schemes, TSHED and CTTSH. At short times, these methods do not correctly capture the oscillations in the S 1 and S 2 populations, due to the well-known problem of frustrated hops. Essentially, since this short-time dynamics implies electronic transitions from a low-lying state to a highlying state, some trajectories do not have enough kinetic energy to compensate for the increase of potential energy, and conserve total energy. Conversely, Ehrenfest shows very good agreement with the quantum dynamics results at short times but deviates from the reference after 16 fs. On the other hand, CTMQC and CTMQC-E are able to capture the oscillations in the electronic populations within the first 16 fs of the dynamics, with CTMQC-E in much better agreement with the reference than CTMQC and Ehrenfest. At long times, CTMQC predicts the populations of the electronic states in quite good agreement with the reference and slightly better than CTMQC-E, even though it misses the oscillations in the populations of S 1 and S 2 . Interestingly, CTMQC-E predicts population transfer from the ground S 0 state to the S 1 state at 48 fs. CTTSH slightly overestimates the population of the ground state all along the dynamics, and in general it shows a behavior similar to TSHED. Note that for CTTSH we show as continuous lines the trajectory-averaged electronic populations, i.e α |C α j (t)| 2 /N tr (with j = S 0 , S 1 or S 2 ) and with dashed lines the fraction of trajectories whose dynamics is driven by the corresponding (active) PES. The discrepancy between the two estimates of the populations in CTTSH, could be likely attributed to the ocurrence of frustrated hops. Therefore, current studies on CTTSH are directed towards curing the issue of frustrated hops exploiting the coupled-trajectory nature of the algorithm. Note also that the issue of frustrated hops has been recently addressed by Maitra and coworkers in the independent-trajectory quantum trajectory surface hopping method based on the exact factorization (QTSH-XF) .