We finally note that in the beginning of the simulation (where the perturbation has not yet induced any oscillations in the q 0 mode), ⟨q 1 ⟩ has a constant value in the reference simulation while small oscillations are observed in the same time-interval in the TD-ADGA and TD-ADGA rerun simulations. In the reference calculation, we expect the expectation value of q 1 to be constant in the beginning of the simulation because the initial wave function is a stationary state of the potential. This is not the case in the TD-ADGA and TD-ADGA rerun calculations, because the initial state is created from the reference potential and it is thus not exactly a stationary state for the TD-ADGA PES. Small oscillations in the ⟨q 0 ⟩ values are similarly observed in the TD-ADGA results, but these are visible seen in Fig. due to the larger scale on the y-axis.