Do Semiclassical Trajectory Theories Provide an Accurate Picture of Radiationless Decay for Systems with Accessible Surface Crossings?

We present quantum mechanical and semiclassical calculations of Feshbach funnel resonances that correspond to long-lived exciplexes in the à ²B₂ state of NaH₂. These exciplexes decay to the ground state, X̃ ²A₁, by a surface crossing in C_2v geometry. The quantum mechanical lifetimes and the branching probabilities for competing decay mechanisms are computed for two different NaH₂ potential energy matrices, and we explain the results in terms of features of the potential energy matrices. We compare the quantum mechanical calculations of the lifetimes and the average vibrational and rotational quantum numbers of the decay product, H₂, to two kinds of semiclassical trajectory calculations: the trajectory surface hopping method and the Ehrenfest self-consistent potential method (also called the time-dependent self-consistent field method). The trajectory surface hopping calculations use Tully's fewest switches algorithm and two different prescriptions for adjusting the momentum during a hop. Both the adiabatic and the diabatic representations are used for the trajectory surface hopping calculations. We show that the diabatic surface hopping calculations agree better with the quantum mechanical calculations than the adiabatic surface hopping calculations or the Ehrenfest calculations do for one potential energy matrix, and the adiabatic surface hopping calculations agree best with the quantum mechanical calculations for the other potential energy matrix. We test three criteria for predicting which representation is most accurate for surface hopping calculations. We compare the ability of the semiclassical methods to accurately reproduce the quantum mechanical trends between the two potential matrices, and we review other recent comparisons of semiclassical and quantum mechanical calculations for a variety of potential matrices. On the basis of the evidence so far accumulated, we conclude that for general three-dimensional two-state systems, Tully's fewest switches method is the most accurate semiclassical method currently available if (i) one uses the nonadiabatic coupling vector as the hopping vector and (ii) one propagates the trajectories in the representation that minimizes the number of surface hops.