Quantum Mechanical and Quasiclassical Trajectory Surface Hopping Studies of the Electronically Nonadiabatic Predissociation of the à State of NaH₂

Fully coupled quantum mechanical scattering calculations and adiabatic uncoupled bound-state calculations are used to identify Feshbach funnel resonances that correspond to long-lived exciplexes in the à state of NaH₂, and the scattering calculations are used to determine their partial and total widths. The total widths determine the lifetimes, and the partial widths determine the branching probabilities for competing decay mechanisms. We compare the quantum mechanical calculations of the resonance lifetimes and the average final vibrational and rotational quantum numbers of the decay product, H₂(v′, j′), to trajectory surface hopping calculations carried out by various prescriptions for the hopping event. Tully's fewest switches algorithm is used for the trajectory surface hopping calculations, and we present a new strategy for adaptive stepsize control that dramatically improves the convergence of the numerical propagation of the solution of the coupled classical and quantum mechanical differential equations. We performed the trajectory surface hopping calculations with four prescriptions for the hopping vector that is used for adjusting the momentum at hopping events. These include changing the momentum along the nonadiabatic coupling vector (d), along the gradient of the difference in the adiabatic energies of the two states (g), and along two new vectors that we describe as the rotated-d and the rotated-g vectors. We show that the dynamics obtained from the d and g prescriptions are significantly different from each other, and we show that the d prescription agrees better with the quantum results. The results of the rotated methods show systematic deviations from the nonrotated results, and in general, the error of the nonrotated methods is smaller. The nonrotated TFS-d method is thus the most accurate method for this system, which was selected for detailed study precisely because it is more sensitive to the choice of hopping vector than previously studied systems.