It is also notable that in the azobenzene simulations reported in Ref. 29, a significant fraction of the LR-TDDFT trajectories had to be terminated and discarded due to convergence failure in the region of quasi-degeneracy, whereas none of the SF-TDDFT trajectories suffered this problem. This is likely a direct result of the more balanced treatment of the two states in the SF approach. Furthermore, the time-dependent energy gap E 1 -E 0 is observed to be much more oscillatory in the LR-TDDFT simulations, leading to much more frequent hopping events and concomitant oscillations in the populations of the two electronic states. At the SF-TDDFT level, the energy gap is less oscillatory, the population dynamics are smoother, and hopping events are relatively infrequent.