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 fu nnel resonances that correspond to long-lived exciplexes in the (A) over ti lde B-2(2) State of NaH2. These exciplexes decay to the ground state, (X) o ver tilde (2)A(1), by a surface crossing in C-2v geometry. The quantum mech anical lifetimes and the branching probabilities for competing decay mechan isms 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 ave rage vibrational and rotational quantum numbers of the decay product, H-2, to two kinds of semiclassical trajectory calculations: the trajectory surfa ce hopping method and the Ehrenfest self-consistent potential method (also called the time-dependent self-consistent field method). The trajectory sur face hopping calculations use Tully's fewest switches algorithm and two dif ferent prescriptions for adjusting the momentum during a hop. Both the adia batic and the diabatic representations are used for the trajectory surface hopping calculations. We show that the diabatic surface hopping calculation s agree better with the quantum mechanical calculations than the adiabatic surface hopping calculations or the Ehrenfest calculations do for one poten tial energy matrix, and the adiabatic surface hopping calculations agree be st 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 se miclassical methods to accurately reproduce the quantum mechanical trends b etween the two potential matrices, and we review other recent comparisons o f semiclassical and quantum mechanical calculations for a variety of potent ial matrices. On the basis of the evidence so far accumulated, we conclude that for general three-dimensional two-state systems, Tully's fewest switch es 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.