When using the MTS implementation described in algorithm 2 in combination with a TSH algorithm, one has to decide how to hop from one electronic state to another. In order to get trajectories of high accuracy, it would be beneficial to consider electronic transitions based on Tully's FS criterion in eq. ( ) calculated with the MTS high level functional. In the following, this type of calculation (with a velocity Verlet algorithm) will actually be used as a reference. However, when using an MTS algorithm, if the outer time step ∆t becomes large, some parts of the PES where the transition probabilities are high might be treated only by the low level functional and the transitions would be missed at the high level.