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(ν‘, 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.
We present a new semiclassical method for electronically nonadiabatic collisions. The method is a variant of the time-dependent self-consistent-field method and is called continuous surface switching. The algorithm involves a self-consistent potential trajectory surface switching approach that is designed to combine the advantages of the trajectory surface hopping approach and the Ehrenfest classical path self-consistent potential approach without their relative disadvantages. Viewed from the self-consistent perspective, it corresponds to “on-the-fly histogramming” of the Ehrenfest method by a natural decay of mixing; viewed from the surface hopping perspective, it corresponds to replacing discontinuous surface hops by continuous surface switching. In this article we present the method and illustrate it for three multidimensional cases. Accurate quantum mechanical scattering calculations are carried out for these three cases by a linear algebraic variational method, and the accurate values of reactive probabilities, quenching probabilities, and moments of final vibrational and rotational distributions are compared to the results of continuous surface switching, the trajectory surface hopping method in two representations, the time-dependent self-consistent-field method, and the Miller–Meyer classical electron method to place the results of the semiclassical methods in perspective.
We present quantum mechanical and semiclassical calculations of Feshbach funnel resonances that correspond to long-lived exciplexes in the A ˜2B 2 state of NaH 2 . These exciplexes decay to the ground state, X ˜2A 1 , 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 NaH 2 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, H 2 , 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.
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