Let us now focus on the results for the butatriene cation in Figure . We observe that all trajectory-based methods underestimate the rapid S 1 population decay up to 20 fs. Interestingly, SH-EDC is the best performing method. CTMQC underestimates the initial population transfer event prior to 10 fs, and overestimates both the back-transfer at about 12 fs and a subsequent transfer around 20 fs. CTMQC-E on the other hand underestimates the initial population transfer but the subsequent two transfer events follow the trend of the exact more closely (the populations are shifted up due to the initial underestimate). Interestingly, all the trajectory-based methods miss the repopulation of the excited state at 36 fs. In terms of coherences, CTMQC and SH-EDC predict the QD trend with a decay in the coherence after the passage through the CI rising later at around 40 fs. CTMQC-E on the other hand, remains overcoherent. In terms of energy conservation, CTMQC-E improves energy conservation reducing the energy leakage of CTMQC, which impacts the nuclear dynamics. Figure shows the trajectory-averaged values of the nuclear coordinates as a function of time and the QD expectation values together with their corresponding variances. We observe that all trajectory-based methods capture the dynamics along x. In terms of the variance σ x all the trajectory-based methods show similar behavior up to 10 fs differing from the QD reference when the wavepacket funnels through the CI. CTMQC starts clearly deviating from the QD reference trend at 10 fs, growing rapidly due to a gain of the total energy of the ensemble. CTMQC-E corrects the behavior and shows similar variance than SH-EDC and both slightly over-dampen the oscillations on σ x . The increase in the total energy of the ensemble is manifested also in the dynamics along y . We observe that in CTMQC the average value of y deviates significantly from the QD reference showing a very large positive oscillation. CTMQC-E on the other hand overcompensates this behavior showing reduced oscillation on the opposite direction, while SH-EDC matches pretty well the QD reference in terms of both y and its varaince σ y . CTMQC-E shows reduced increase in the variance, while CTMQC underestimates it more initially before then showing an increase later on at 45fs. The CT contribution to the force on the nuclei appears to be responsible for the incorrect behavior in the y -coordinate, since this does not occur for CTTSH (not shown here).