ARE CLASSICAL MOLECULAR-DYNAMICS CALCULATIONS ACCURATE FOR STATE-TO-STATE TRANSITION-PROBABILITIES IN THE H+D2 REACTION

We present converged quantum dynamics for the H + D2 reaction at a total energy high enough to produce HD in the v′ = 3, j′ = 7 vibrational-rotational state and for total angular momenta J = 0, 1, and 2. We compare state-to-state partial cross sections for H + D2 (v = 0-2, j = 0, J = 0-2) → HD (v′ = 0-2, j′) + H and H + D2 (v = l, j = 6, J = 0-2) → HD (v′ = 0-2, j′) + H as calculated from classical trajectory calculations with quantized initial conditions, i.e., a "quasiclassical" trajectory (QCT) simulation, to the results of converged quantum dynamics calculations involving up to 654 coupled channels. Final states in the QCT calculations are assigned by the quadratic smooth sampling (QSS) method. Since the quasiclassical and quantal calculations are carried out with the same potential energy surface, the comparison provides a direct test of the accuracy of the quasiclassical simulations as a function of the initial vibrational-rotational state and the final vibrational-rotational state. The test of the QCT-QSS method against quantum mechanics for the four initial states considered yields the following conclusions (since the v′ = 3 cross sections are all very small, we consider only v′ = 0, 1, and 2 for these comparisons). QCT-QSS partial cross sections summed over v′ and j′ are accurate to 2-5%. QCT-QSS partial cross sections summed over j′ for specified v′ are accurate to 5-10% for v′ = 0, 8-17% for v′ = 1, and 7-29% for v′ = 2, with an average error of these 12 partially summed cross sections of 13%. The ratio of the partial cross section for producing v′ = 0 to that for producing v′ = 1 is accurate to 2-23%, and the (v′ = l)/(v′ = 2) ratio is accurate to 2-54%; the average error in these eight ratios is 26%. The average value of j′ in a given j′ manifold is accurate to 2-37% with average error of 17% for initial states with j = 0, but it is accurate to 1 -4% with an average error of only 2% for the initial state with j = 6. The root-mean-square width of the j′ distribution for a given v′ is accurate to 1-29% with an average error of 12%, where we have included both j = 0 and j = 6 initial states in this comparison since the j = 6 results are not more accurate for this product attribute. The peak in the QCT-QSS j′ distributions for a given j′ agrees (within sampling statistics) with the accurate quantal peak position in all eight cases for v′ = 0 and v′ = 1 but in only two of four cases for v′ = 2. Fully resolved state-to-state cross sections show larger errors than the partially summed ones in many cases, and in general the quantal product state distributions have more structure than the QCT-QSS ones, even though the quantal oscillations are partially damped by summing over three to five total angular momentum/parity blocks. We conclude that classical mechanics, although very accurate for the reaction cross section summed over all final states and qualitatively correct for product state distributions, shows significant quantitative errors on the order of 20% for partially summed cross sections and low moments of the product distribution, with larger errors in some cases for individual state-to-state cross sections. © 1990 American Chemical Society.