Exact reaction dynamics by the hyperquantization algorithm: integral and differential cross sections for F + H2, including long-range and spin–orbit effects

Abstract

We present in this article a numerical investigation of the dynamics of the prototypical exchange reaction F + H₂ → HF + H applying an exact quantum mechanical method, the hyperquantization algorithm, which exploits discrete analogs of hyperspherical harmonics and whose accuracy is tested for both differential and integral cross sections. The calculations employ the potential energy surface by Stark and Werner, both in its original version (SW PES) and in two new versions, properly adapted to include the effects of the long-range interaction in the reactants' valley (SW-LR) and also those due to the spin–orbit interaction (SW-LR-SO). The features of the potential surfaces in the entrance channel have been modeled according to experimental information coming from total cross section measurements carried out in our laboratory. Computed integral and differential cross sections for H₂ in its ground vibrational state and for rotational states equal to 0, 1, 2 and 3 in the collision energy range 1.8–3.4 kcal mol⁻¹ are compared with previous results by other accurate quantum mechanical methods (J. F. Castillo, B. Hartke, H.-J. Werner, F. J. Aoiz, L. Bañares and B. Martínez-Haya, J. Chem. Phys., 1998, 109, 7224; M. H. Alexander, D. E. Manolopoulos and H.-J. Werner, J. Chem. Phys., 2000, 113, 11 084) and with several sets of experimental data (differential cross sections (D. M. Neumark, A. M. Wodkke, G. N. Robinson, C. C. Hayden and Y. T. Lee, J. Chem. Phys., 1985, 82, 3045), nascent rovibrational distributions (W. B. Chapman, B. W. Blackmon, S. Nizkorodov and D. J. Nesbitt, J. Chem. Phys., 1998, 109, 9306.) and total integral cross sections (F. Dong, S.-H. Lee and K. Liu, J. Chem. Phys., 2000, 113, 3633.)) to emphasize the role of intermediate and long-range forces on reaction dynamics. The effect of the modifications of the ground surface due to spin–orbit interaction is also discussed and perspectives for future improvements are pointed out, the main indication being that the effective reaction barrier appears to be lower with respect to that of the original SW PES.