Figure shows the excited state population (lower panel), the coherences (middle panel) and the total energy deviation (upper panel) for BMA obtained from CTMQC, CTMQC-E, SH-EDC and QD calculations. CTMQC-E and especially CTMQC both closely follow the exact S 1 population decay up to 6 fs and subsequent back-transfer from around 15 to 20 fs for a later decay from 20 to 24 fs. SH-EDC underestimates the repopulation of S 1 that starts at 15 fs. In terms of coherences all 3 trajectory-based methods predict the right trend qualitatively with CTMQC being closest to the reference quantum dynamics result. Concerning the total energy, CTMQC-E significantly corrects the violation of energy conservation displayed in the CTMQC calculation, with a small energy increase which is caused by two effects. First, for trajectories for which the denominator in Eq. ( ) becomes smaller than a fixed threshold, the accumulated force reverts to its original definition, which does not conserve energy. Second, even when the new definition is used, the quantum momentum computation may revert to the original quantum momentum Q 0 definition when a denominator involved in imposing Eq. ( ) becomes too small : our redefined force is guaranteed to conserve energy only when used in conjunction with the modified definition Q m . Although the electronic populations and coherences may be a little worse with CTMQC-E than in CTMQC, the violation of energy conservation of the latter adversely affects the nuclear dynamics. This can be seen in the distribution of classical-like trajectories plotted together with the quantum nuclear density in Figure . We observe at 20 fs that the position of some CTMQC trajectories diverge from the nuclear density exploring regions of large negative values of the x-coordinate, as a consequence of an increase in the total energy of the ensemble. Applying the correction to the accumulated force in CTMQC-E remarkably improves energy conservation and the trajectories follow closely the exact density.