In Fig. , we plot the relative adiabatic states and the electronic populations according to the OP and MP protocols for the first 105 fs of the trajectory. First, in subplot (a), notice that the energy surface for the J = 72 state (red line) has a trivial crossing with the J = 73 state around 46.5 fs; the electronic population makes a complete transition (72 → 73). In fact, there are three trivial crossings occurring before t = 65 fs. Importantly, for all of these trivial crossings, the initial electronic wavefunction begin and end on one adiabatic state. For this reason, we find that both the MP and OP protocols can capture the correct transition even with a large classical time step (such as dt c = 0.36 fs). Intuitively, this result is not surprising: the phase of the overlap matrix does not affect the electronic wavefunction propagation when the propagation involves just two states.