A semiclassical model for the calculation of nonadiabatic transition probabilities for classically forbidden transitions

A semiclassical surface hopping model is presented for the calculation of nonadiabatic transition probabilities for the case in which the avoided crossing point is in the classically forbidden regions. The exact potentials and coupling are replaced with simple functional forms that are fitted to the values, evaluated at the turning point in the classical motion, of the Born-Oppenheimer potentials, the nonadiabatic coupling, and their first few derivatives. For the one-dimensional model considered, reasonably accurate results for transition probabilities are obtained down to around 10 − 10 . The possible extension of this model to many dimensional problems is discussed. The fact that the model requires only information at the turning point, a point that the trajectories encounter would be a significant advantage in many dimensional problems over Landau-Zener type models, which require information at the avoided crossing seam, which is in the forbidden region where the trajectories do not go.