These methods are characterized by the fact that classical trajectories are used to mimic the quantum nuclear dynamics. A trajectory α is identified by a collection of 3N n coordinates, indicated henceforth with the symbol R α (t). Along each trajectory, and coupled to the nuclear evolution, the electronic time-dependent state of the system evolves nonadiabatically as a superposition of adiabatic states. In such a superposition, the expansion coefficients are indicated as C α l (t), for each electronic state l included and along each trajectory α. In TSH, the electronic coefficients evolve according to