Application of Heisenberg's S matrix program to the angular scattering of the state-to-state F + H2 reaction

This paper makes two applications of Heisenberg's S matrix program (HSMP) to the differential cross section (DCS) of the benchmark reaction F + H2(vi = 0, ji = 0, mi = 0) → FH(vf = 3, jf = 3, mf = 0) + H, at a relative translational energy of 0.119 eV (total energy, 0.3872 eV), where v, j, m are vibrational, rotational, and helicity quantum numbers, respectively, for the initial and final states. (1) The first application employs a "weak" version of HSMP in which no potential energy surface (PES) is employed. It uses four simple S matrix parametrizations, two of which are piecewise continuous, and two are piecewise discontinuous, developed earlier by X. Shan and J. N. L. Connor (J. Phys. Chem. A 2012, 116, 11414-11426) for the state-to-state H + D2 reaction. We find that the small-angle DCS is reproduced for only θR ≲ 10° when compared with the DCS for a numerical S matrix obtained in a large-scale quantum scattering computation using a PES. Here θR is the reactive scattering angle. (2) In our second application, we ask the question "Can simple modifications to the parametrized S matrix be made in order to extend the agreement to larger angles?" To answer this question, we adopt a "hybrid" version of HSMP, as outlined by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392-8406), which indirectly uses PES information. We make simple Gaussian-type modifications to both the modulus and argument of the S matrix. We then obtain agreement between the DCSs for the modified and numerical S matrices up to θR ≲ 70°, a significant improvement compared with θR ≲ 10° for the unmodified parametrizations. We find that modifying the argument but not the modulus, or modifying the modulus but not the argument, fails to extend the agreement to larger angles. A semiclassical analysis is used to prove that the enhanced small-angle scattering for the "modified-modulus-modified-argument" parametrized S matrix is an example of a forward glory.