Cumulative reaction probabilities and transition state properties: a study of the H+ + H2 and H+ + D2 proton exchange...

Cumulative reaction probabilities (CRPs) have been calculated by accurate (converged, close coupling) quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical QCT (SQCT) methods for the H(+) + H(2) and H(+) + D(2) reactions at collision energies up to 1.2 eV and total angular momentum J = 0-4. A marked resonance structure is found in the QM CRP, most especially for the H(3)(+) system and J = 0. When the CRPs are resolved in their ortho and para contributions, a clear steplike structure is found associated with the opening of internal states of reactants and products. The comparison of the QCT results with those of the other methods evinces the occurrence of two transition states, one at the entrance and one at the exit. At low J values, except for the quantal resonance structure and the lack of quantization in the product channel, the agreement between QM and QCT is very good. The SQCT model, that reflects the steplike structure associated with the opening of initial and final states accurately, clearly tends to overestimate the value of the CRP as the collision energy increases. This effect seems more marked for the H(+) + D(2) isotopic variant. For sufficiently high J values, the growth of the centrifugal barrier leads to an increase in the threshold of the CRP. At these high J values the discrepancy between SQCT and QCT becomes larger and is magnified with growing collision energy. The total CRPs calculated with the QCT and SQCT methods allowed the determination of the rate constant for the H(+) + D(2) reaction. It was found that the rate, in agreement with experiment, decreases with temperature as expected for an endothermic reaction. In the range of temperatures between 200 and 500 K the differences between SQCT and QCT rate results are relatively minor. Although exact QM calculations are formidable for an exact determination of the k(T), it can be reliably expected that their value will lie between those given by the dynamical and statistical trajectory methods.