Figure shows the electronic populations and total energy deviation as a function of time computed with SH-EDC, CTMQC and CTMQC-E, along with the MCTDH benchmark extracted from Ref. [ 65]. We observe that SH-EDC largely underestimates the rate of population transfer from D 2 to D 0 and cannot describe the fast initial decay of the D 0 population. Instead, CTMQC captures the initial decay very accurately, following the MCTDH populations very closely up until 30 fs. Afterwards, it slightly deviates from the MCTDH reference and plateaus before continuing to decrease at the same rate. Overall the D 2 to D 0 population transfer is underestimated and some population is transferred to the high energy D 3 state, not observed in MCTDH or SH-EDC. Applying the energy correction in CTMQC-E yields worse population behavior than CTMQC, underestimating the D 2 to D 0 transfer and provides a relatively small improvement over SH-EDC. Nonetheless, the top panel of Figure confirms that the drift in total energy observed in CTMQC is reduced in CTMQC-E. As in the other cases, we see that the improved energy conservation improves the nuclear observables: in Figure we plot the values of the C-N, C=O and C=C bond lengths as a function of time obtained with CTMQC, CTMQC-E and SH-EDC, together with the MCTDH reference values. These bonds are related to the important modes included in the linear vibronic coupling model. In some cases, e.g., for the C=N and C=O bonds, after around 20 fs CTMQC deviates from the MCTDH reference predicting oscillations with larger amplitudes, reminiscent of our observations reported for the bond-length-alternation coordinate in PSB3. The energy correction in CTMQC-E reduces the oscillations and yields better energy conservation.