Three-dimensional quantum mechanical studies of the H+H2 reactive scattering

Abstract

A three-dimensional quantum mechanical study is made of H+H2 reactive scattering. The differential and total cross sections as well as the S-matrix elements are obtained from the adiabatic distorted wave model and the Porter–Karplus semiempirical potential surface. With the initial molecule in the ground rotational state, the energy dependence, rotational state dependence, and other properties of the reaction probabilities and of the cross sections for transitions to all possible states of the product molecule are determined. The reactive scattering from the threshold to 0.5 eV is predominantly backward. The 0→0 rotational transition contributes only a small fraction to the total reactive cross section; however, most product molecules prefer rotational states that are considerably lower than the highest one allowed by energy conservation. The reaction probability is found to be a smoothly decreasing function of the total angular momentum of the system. These results are very similar to our previous results for the D+H2 reaction except the threshold energy for the H+H2 is higher and the magnitude of the cross section for the reaction of the D+H2 is larger. A systematic study of the effects of the Pauli exclusion principle on cross sections of the scattering of three identical particles shows that in order to obtain the ’’observable’’ cross sections, the unsymmetrized results of the H+H2 and D+D2 reactions have to be multiplied by various ’’strange’’ numerical factors. These observable cross sections are compared with three different sets of close coupling results on the same potential surface. Our results are in close agreement with those of Kuppermann and Schatz and are in substantial disagreement with those of Wolken and Karplus. Our results near the threshold and at 0.5 eV are similar to those of Elkowitz and Wyatt but there are significant differences in energy dependence in the intermediate region. The present results are also compared with the three-dimensional classical trajectory results. The most significant quantum effect is caused by the spin statistics. Dynamically, there are excellent qualitative and quantitative agreements in many respects between the quantum and classical results, although the present quantum cross sections rise above the classical values at incident energies greater than 0.4 eV.