In Fig. , we compare results for the OP and MP protocols for the smallest time step we treated, dt c = 0.12 fs. Through t = 120 fs or so, we find that the population dynamics of state 84 are the same for both protocols, from which one must conclude that dt c = 0.12 fs is sufficiently small for the MP protocol to recover the correct overlap matrix at (■). However, at t = 122 fs (⋆), the population dynamics following the OP and MP protocol diverge for states 65 and 72, even for with a very small time step. This discrepancy arises because another crossing is encountered, whereby the interaction of states 63 and 65 disturbs the relative phase of state 72. This disturbance eventually leads to a big difference in population for long times (P 84 = 0.08 for the OP protocol versus P 84 = 0.21 for the MP protocol at t = 145 fs).