For such a model system, reference results can be provided by solving exactly the TDSE. Turning to the trajectorybased calculations, in the pure state, the initial electronic state for all trajectories is described by {C Figure shows the electronic excited state population and the electronic coherence as functions of time. Surprisingly, we observe that starting with a pure state in Ehrenfest dynamics yields negligible net population transfer with the ground and excited state remaining coherent throughout the dynamics. This behavior is in stark contrast with the expected result predicted by the quantum dynamics (QD) simulation. On the other hand, CTMQC captures both the population and coherence behavior in very good agreement with the reference. Note that all methods miss the recoherence just after 90 fs that, unlike the other recoherences, occurs far from the nonadiabatic coupling region. Details on this mechanism are discussed in Ref. [262]. Let us focus on the first decoherence event occurring within the first 20 fs, during which the excited-state nuclear wavepacket moves away from the trapped ground state wavepacket before entering a region of strong nonadiabatic coupling. This situation represents the first step after a molecule gets excited via the laser pulse. Fig. shows time snapshots of the exact nuclear density and the spatiallyresolved energies (upper panel) and excited state populations (lower panel) during this event. We observe that Ehrenfest trajectories evolve in a mean-field surface which has 80% ground state character, and their electronic populations (and coherences) do not change away from regions of strong nonadiabaticity. Conversely, the quantum momentum term accounted for in the CTMQC equation of motion (15) induces both a branching of the electronic coefficients and a splitting of the trajectory distribution achieving decoherence. We now direct our attention to the mixed-state results, where both Ehrenfest and CTMQC capture the periodic population transfers, with Ehrenfest deviating from the reference at ∼120 fs. In terms of coherences, both methods cannot account for the initial decoherence, because in a mixed state the coherences are zero initially. However, after this first decoherence event, CTMQC captures the behavior of the indicator of coherence quite well, even though it misses the large recoherence at 90 fs as pointed out earlier; instead, Ehrenfest remains overcoherent after the first increase of coherece at ∼25fs. In summary, this work pointed out that the problem of the initialization of the electronic dynamics is critical when trajectory-based methods are used to simulate the dynamics triggered by an ultrashort laser pulse that creates an electronic wavepacket. We presented two strategies: a pure state and a mixed state. We tested these concepts in the simulation of the nonadiabatic dynamics of two-state electronic wavepacket in a one-dimensional model system. The pure state seems the natural choice for both Ehrenfest and CTMQC since all trajectories are associated to the same coherent superposition of electronic states. However, Ehrenfest performs very poorly, and if the mixed state is used instead, the population behavior greatly improves but the coherences, and consequently coherence-dependent observables such as the electronic current-density 142 , will be wrong from the very beginning. On the other hand, CTMQC starting from a pure state accurately captures both populations and coherences behavior. The quantum momentum is essential to capture those events at the spatially-resolved level, which is key to predict the right dynamics when regions of nonadiabatic electron-nuclear coupling are encountered.