We now assume we have reached a time where the TD-ADGA grid is no longer converged and thus the TD-ADGA procedure will calculate a number of SPs to obtain convergence of the grid. After these SPs have been calculated and a new PES have been fitted, we need to determine how we want to continue the dynamics simulation. As discussed in Section 2.4, we suggest a partial restart scheme and a full restart scheme for introducing the new PES. In the partial restart scheme we want the PES of the dynamics to be slowly and continuously updated from the previous PES (V bef ) to the updated PES (V upd ) in order to avoid non-physical behavior in the wave function propagation. In the full restart scheme, we simply restart the dynamics from scratch using the new PES. To update the PES during the wave function propagation in the partial restart scheme, the wave function is reset to a time before the PES was updated (t bef ) by overwriting the current wave function and its derivatives with the wave function and its derivatives at time t bef . In order not to save all wave function data during the propagation, the update of the potential is done between set time-intervals. These reset intervals are spaced with the time t reset and when the current time t of the simulation enters a new reset interval, t and all wave function information relevant for the time-propagation are saved. When new SPs have been placed by the TD-ADGA The propagation is reset to the time t 1 which is indicated by the horizontal line below. Initially the PES saved at time t 1 (V bef ) is used to propagate the wave function but during the propagation the PES is continuously updated until t upd = t 2 is reached at which point the PES is equal to V upd . b) The wave function is propagated through time and in the second update interval new SPs are requested by the TD-ADGA routine. The propagation is then reset to the initial time t 0 . Since we reset to the initial time the PES is updated directly to V upd and the propagation continues from the initial wave function.