indirectly describes the excited states of a system without describing its excited state wave functions. However, the derivation of the TDDFT vibronic coupling theory is not trivial, since there are no electronic wave functions in TDDFT that are available for plugging into the defining equation of the vibronic coupling.

In 2000, Chernyak and Mukamel showed that in the complete basis set (CBS) limit, knowledge of the reduced transition density matrix between a pair of states (both at the unperturbed