ABSTRACT
Another approach to describing electron dynamics in molecules is based on time-dependent DFT (TDDFT).1 In the so-called real-time TDDFT approach, the time-dependent Kohn-Sham density is propagated according to the time-dependent Kohn-Sham equations. This introduces a nonadiabatic coupling vector that permits changes in electronic states.2 A corresponding mean eld approach, also known as Ehrenfest dynamics,3 is well suited for describing electron dynamics on the attosecond time scale. However, for the investigation of chemical processes, a serious drawback of Ehrenfest dynamics is its failure to recover adiabatic states asymptotically after a mixing of electron states. Thus, Ehrenfest dynamics is, in general, incompatible with the Born-Oppenheimer approximation, which is the basis for the denition of molecular structure in chemistry. As a result, potential energy surface (PES) hopping4 is often preferred for the description of nonadiabatic chemical processes. For ET reactions, constrained DFT (cDFT) can be used to describe PES hopping in its most elementary steps.
