Excited-state, nonadiabatic molecular dynamics simulations are mostly based on trajectory surface hopping (TSH) methods, 22,95-100 most of which derive from Tully's seminal "fewest switches" algorithm, although modern variants incorporate some level of decoherence effects that are absent in Tully's original method. A notable exception (not based on Tully's algorithm) is the "multiple spawning" approach of Martínez and co-workers, which is an approximation to quantum wavepacket dynamics. The discussion below regarding the need for derivative coupling vectors is relevant to all of these methods. An example of a nonadiabatic dynamics algorithm that does not require derivative couplings is Zhu's "global switching" algorithm, which derives from Landau-Zener theory. It is worth recalling (as discussed above) that properly-coded TDDFT derivative couplings require only 10-20% additional computational overhead on top of a TDDFT analytic gradient calculation. Furche and co-workers report that TDDFT-based TSH simulations of the photodynamics of thymine, including the lowest three electronic states, require only 5× the cost of groundstate Born-Oppenheimer molecular dynamics, even with explicit calculation of derivative couplings. As such, the discussion here focuses on the more popular TSH-based approaches and it is assumed that vectors d JK are available for all pairs JK of energetically-accessible states.