Are Semiclassical Methods Accurate for Electronically Nonadiabatic Transitions between Weakly Coupled Potential Energy Surfaces?

We have performed a systematic series of semiclassical and quantum mechanical calculations of collisions of Br* (electronicaly excited Br) with H₂ in order to test four semiclassical methods against accurate quantum mechanical scattering calculations for the quenching probability and the electronically nonadiabatic reaction probability. The results are analyzed using four different methods of assigning final quantum numbers based on the final values of the semiclassical and classical trajectory variables, namely energy-nonconserving histogram analysis, energy-conserving histogram analysis, energy-nonconserving linear smooth sampling, and energy-conserving linear smooth sampling. We examine the use of both forward and reverse state-to-state probabilities to predict the quenching and reaction probabilities. The reaction and quenching probabilities are compared to the results of accurate quantum mechanical calculations, and the mean unsigned error is calculated for each combination of a semiclassical method and a final analysis algorithm. Our results indicate that Tully's fewest switches (TFS) trajectory-surface-hopping method and the Ehrenfest self-consistent-potential method show the best agreement with the accurate results, although none of the methods provides satisfactory agreement in the cases where the reaction or quenching probability is small. The TFS method is the only one that can be used to calculate the reaction probabilities for this system directly in the forward direction, and it is judged to be the best method overall for weakly coupled potential energy surfaces.