In Fig. , using the same color coding of Fig. for the different methods, we show the time-dependent trajectory-averaged normal mode coordinate q 46 , with shaded areas representing the standard deviation. The state specific position averages (SSPA), in S 1 (in darkblue) and in S 2 (in dark-red), according to Eq. ( ) are also shown as dotted-dashed lines. While the mean positions for all methods are nearly identical, the standard deviations and the SSPA reveal differences in the simulated dynamics. First, we see that the standard deviation for CTMQC is nearly twice as large as that of the other methods. Secondly, we see that the SSPA are quite distinct for every method. Let us start with the analysis of the lower panels of Fig. , where the TSH-based methods are shown. On the left, TSH-ED is presented, which has a clear splitting of the SSPAs of both states at ≈ 10 fs; after that, the SSPA of state S 2 oscillates quite steadily. This dynamics agrees well with our analysis of the adiabatic population in Fig. , since the main population transfer happens at the early times. Instead, in CTTSH, in phase ring distortion the mean position and the SSPAs almost coincide, but, we recall here that CTTSH has issues of internal consistency. On the other hand, CCTTSH does not show problems related to internal consistency, and, in fact, we observe similar dynamics as for TSH-ED in the SSPAs. In the upper panels, where MTE and CTMQC results are shown, we observe that in MTE the average position and the SSPAs are nearly identical, which is to be expected due to its mean-field character, whereas in CT-MQC, the coupled-trajectory corrections are responsible to yield different dynamics in the two states as they are expected to split the swarms of trajectories evolving in different states. However, it seems that the amplitude of the oscillations of the SSPA in S 2 is larger than TSH-ED and CCTTSH, causing larger standard deviations than the other methods.