As will be discussed below, analytic derivative coupling vectors are useful for nonadiabatic molecular dynamics simulations. The h JK vectors are also very useful for locating MECPs, because they facilitate the use of more efficient branching-plane updating methods, in which the branching space (spanned by g JK and h JK ) is projected out of the gradient so that optimization proceeds entirely within the seam space. As compared to MECP-optimization algorithms that do not require h JK vectors, such as penaltyfunction methods or approximate branching-plane updating, the use of an exact branching-plane updating method requires far fewer optimization steps. When programmed efficiently, evaluation of h JK requires only modest overhead on top of the TDDFT gradient calculation that is already required to compute ∇R E J and ∇R E K , because solution of coupled-perturbed equations is required in either case. Timing data confirm that the overhead for computing h JK amounts to no more than 10-20% on top of the cost of TDDFT analytic gradients. 21,64