In our previous work we showed how CTMQC-E correctly captures the kinetic energy along r , whose average increases in a monotonic way due to the wavepacket moving through the CI towards S 0 , while its oscillations decrease in amplitude as a result of a loss in vibrational coherence as the wavepacket spreads along θ . There we showed that, while CTMQC captures the initial behavior, it starts to deviate from the exact reference at around 80 fs. The lower panel of Figure shows the value of the momentum along the r coordinate (P r ) and the upper panel the corresponding variance (σ Pr ). We observe that all methods follow the trend of the expectation value of the momentum along r with SH-EDC slightly overdamping the oscillations around the average value towards the end of the simulated dynamics with respect to CTMQC, CTMQC-E and the QD reference. Despite this observable agreeing with QD, it is clear that CTMQC deviates from the reference at 90 fs since the variance of the momentum grows rapidly, as expected from the incorrect behavior of the kinetic energy along the r coordinate pointed out in Ref. [ 35]. With the redefined integrated force of CTMQC-E, this rapid growth is prevented, yielding a variance along r that follows closely the QD reference. To further illustrate this conclusion, we analyze some representative trajectories of the ensemble. Figure shows the values of the position and momenta along r for two trajectories. We observe how in CTMQC the momenta along r starts oscillating with high amplitudes after 150 fs which makes the r coordinate, in turn, fluctuate also far away from its average value. CTMQC-E dampens these oscillations and results in a kinetic energy along r (and a variance of the momentum along r ) that matches the QD calculations. C. Photo-relaxation dynamics through a 3-state CI: the Uracil cation radical