Abstract
We theoretically analyze the differential cross sections (DCSs) for the state-to-state reaction, H + HD(vi = 0, ji = 0, mi = 0) → H2(vf = 0, jf = 1,2,3, mf = 1,..,jf) + D, over the whole range of scattering angles, where v, j, and m are the vibrational, rotational, and helicity quantum numbers for the initial and final states. The analysis extends and complements previous calculations for the same state-to-state reaction, which had jf = 0,1,2,3 and mf = 0, as reported by XiahouC.; ConnorJ. N. L.Phys. Chem. Chem. Phys.2021, 23, 13349–1336934096934. Motivation comes from the state-of-the-art experiments and simulations of Yuan et al.Nature Chem.2018, 10, 653–65829686377 who have measured, for the first time, fast oscillations in the small-angle region of the degeneracy-averaged DCSs for jf = 1 and 3 as well as slow oscillations in the large-angle region. We start with the partial wave series (PWS) for the scattering amplitude expanded in a basis set of reduced rotation matrix elements. Then our main theoretical tools are two variants of Nearside-Farside (NF) theory applied to six transitions: (1) We apply unrestricted, restricted, and restrictedΔ NF decompositions to the PWS including resummations. The restricted and restrictedΔ NF DCSs correctly go to zero in the forward and backward directions when mf > 0, unlike the unrestricted NF DCSs, which incorrectly go to infinity. We also exploit the Local Angular Momentum theory to provide additional insights into the reaction dynamics. Properties of reduced rotation matrix elements of the second kind play an important role in the NF analysis, together with their caustics. (2) We apply an approximate N theory at intermediate and large angles, namely, the Semiclassical Optical Model of Herschbach. We show there are two different reaction mechanisms. The fast oscillations at small angles (sometimes called Fraunhofer diffraction/oscillations) are an NF interference effect. In contrast, the slow oscillations at intermediate and large angles are an N effect, which arise from a direct scattering, and are a “distorted mirror image” mechanism. We also compare these results with the experimental data.
Highlights
The H + H2 → H2 + H reaction and its isotopic variants are important benchmarks in the theory of chemical reaction dynamics
We can compare with the four full differential cross sections (DCSs) for the mf = 0 case shown in Figure 3 of XC1.6 We see that the mf = 0 and mf > 0 DCSs are alike, the main difference being (a) the mf = 0 DCSs are nonzero at θR = 0°,180° unlike the mf > 0 DCSs, (b) the angular regions separating the fast and slow oscillations are slowly varying for mf = 0, whereas there are pronounced minima we examine wthheenresΔmNf,>re0sΔ
The motivation comes from the experiments and simulations of Yuan et al.,[1] who have measured for the first time fast oscillations in the small-angle region of the DEGENERACY AVERAGED DIFFERENTIAL CROSS SECTIONS (daDCSs) for jf = 1 and 3 as well as slow oscillations in the large-angle region
Summary
The H + H2 → H2 + H reaction and its isotopic variants are important benchmarks in the theory of chemical reaction dynamics. An important experimental advance has been reported by Yuan et al.[1] for the H + HD → H2 + D reaction They have measured, for the first time, fast oscillations in the small-angle region of the degeneracy-averaged DCSs (abbreviated as daDCSs). We report the results (including resummations) of the unresNF decomposition for the Local Angular Momentum (LAM), since this provides important additional insights into the reaction dynamics.[13−16]. This paper is organized as follows: Section 2 summarizes the partial wave theory and explains our conventions and definitions for the DCSs and LAMs. This section includes a discussion of the caustic properties that we need and summarizes the unresNF, resNF, and resΔNF decompositions. These two papers illustrate the potency of the NF theory for divers applications
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