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In the late 1970s Meyer and Miller (MM) [J. Chem. Phys. 1979, 70, 3214.] presented a classical Hamiltonian corresponding to a finite set of electronic states of a molecular system (i.e., the various potential energy surfaces and their couplings), so that classical trajectory simulations could be carried out by treating the nuclear and electronic degrees of freedom (DOF) in an equivalent dynamical framework (i.e., by classical mechanics), thereby describing nonadiabatic dynamics in a more unified manner. Much later Stock and Thoss (ST) [Phys. Rev. Lett. 1997, 78, 578.] showed that the MM model is actually not a "model", but rather a "representation" of the nuclear-electronic system; i.e., were the MMST nuclear-electronic Hamiltonian taken as a Hamiltonian operator and used in the Schrodinger equation, the exact (quantum) nuclear-electronic dynamics would be obtained. In recent years various initial value representations (IVRs) of semiclassical (SC) theory have been used with the MMST Hamiltonian to describe electronically nonadiabatic processes. Of special interest is the fact that, though the classical trajectories generated by the MMST Hamiltonian (and which are the "input" for an SC-IVR treatment) are "Ehrenfest trajectories", when they are used within the SC-IVR framework, the nuclear motion emerges from regions of nonadiabaticity on one potential energy surface (PES) or another, and not on an average PES as in the traditional Ehrenfest model. Examples are presented to illustrate and (hopefully) illuminate this behavior.

Electronically Nonadiabatic Dynamics via Semiclassical Initial Value Methods