In Fig. , similarly to Fig. , we show the momentum along the normal coordinate q 46 , the associated standard deviation and the state specific momentum averages (SS-MAs) according to Eq. ( ). In addition, we report the total trajectory-averaged nuclear kinetic energy as function of time. We observe that the mean momenta and standard deviations for all methods are very similar. Only CTMQC stands out for the standard deviation which is larger than all other methods, leading to a steady increase of slightly more than 1 eV in the total kinetic energy, as shown in the top right panel of Fig. ; the kinetic energy in all other methods increases initially but then oscillates in a stable way until the end of the simulated dynamics. To further analyze the CTMQC and CCTTSH dynamics, we show in Fig. the value of the normal coordinate q 46 as function of time for all the trajectories in the swarm. In Fig. , (i) the trajectories are plotted semi-transparent to give an idea of the density at a given position and at a given time, and (ii) the trajectories are colored according the value of |C S2 | 2 , namely red refers to the trajectory fully in state S 2 , i.e., |C S2 | 2 = 1 blue to the trajectory fully in state S 1 , i.e., |C S2 | 2 = 0, and for all other values of |C S2 | 2 the colors are interpolated. Both in CTMQC and CCTTSH, the trajectories start out red, therefore, in state S 2 , and then turn blue as they switch state soon after via the CI. However, in CCTTSH, we see quite clearly a branching onto different states after t = 20 fs, with the swarm of red trajectories in S 2 showing different oscillations if compared to the blue trajectories in S 1 . Instead, with CTMQC, this branching is not very neat, and some trajectories manifest oscillations with large amplitudes in state S 2 alongside trajectories with reduced oscillations in state S 1 . Since the population of the electronic state S 2 is approximately the same in both methods (see Fig. ), the number of trajectories in S 2 is approximately the same in both methods. Therefore, it seems that in CTMQC the trajectories are accelerated, and this increases the nuclear kinetic energy and the standard deviation of the momentum. Finally, we briefly comment on the dynamics in DMABN initiated by populating fully the diabatic state 2, aiming to provide direct comparison with MCTDH results. In MTE and CTMQC, each trajectory of the swarm is initialized in a coherent superposition of S 1 (with 10% population) and S 2 (with 90% population) and we did not account for any relative phase between the two contributions. This initialization is not straightforward (and not recommended) in TSH-based methods as th results may strongly depend how the superposition is encoded , thus we only analyze here MTE and CT-MQC. The time trace of the diabatic population of state 2 is shown in Fig. . There, CTMQC seems to improve the dynamics of MTE and to yield a very good agreement with MCTDH, especially for short times.