A semiclassical approach to the non-adiabatic dynamics problem involving three electronic states in linear triatomic systems

The local non-adiabatic dynamics near an accidental degeneracy of Sigma (+) = Pi type in a linear triatomic system has been investigated in the contex t of the semiclassical approximation. An exact analytical solution of the t ime-dependent semiclassical equations has been found for rectilinear trajec tories of the bending (pi) vibrational modes. The S-matrix and transition p robabilities associated with this three-state problem, which have a non-lan dau-Zener character, have been defined in analytical terms. The expressions obtained for the transition probabilities may be useful in the context of the trajectory surface hopping method.