Nearside-Farside Analysis of the Angular Scattering for the State-to-State H + HD → H₂ + D Reaction: Nonzero Helicities

Abstract

We theoretically analyze the differential cross sections (DCSs) for the state-to-state reaction, H + HD( v i = 0, j i = 0, m i = 0) → H 2 ( v f = 0, j f = 1,2,3, m f = 1,.., j f ) + 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 j f = 0,1,2,3 and m f = 0, as reported by Xiahou C. Connor J. N. L. Xiahou C. Connor J. N. L. 34096934 Phys. Chem. Chem. Phys. 2021 23 13349 13369 . Motivation comes from the state-of-the-art experiments and simulations of Yuan Yuan 29686377 Nature Chem. 2018 10 653 658 who have measured, for the first time, fast oscillations in the small-angle region of the degeneracy-averaged DCSs for j f = 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 m f > 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.

Electronic nonadiabatic effects in the state-to-state dynamics of the H + H2 → H2 + H exchange reaction with a vibrationally excited reagent

“…39 Such a glory phenomenon has recently been observed experimentally in the forward scattering of H + HD ( v = 0, j = 0) → H 2 ( v ′ = 0, j ′ = 1, 3) + D reaction but at a collision energy much lower than the minimum of the seam of the CIs. 20,21,61 The negligible nonadiabatic effects in the forward scattering oscillations are found to be general for products having low j ′ quantum numbers, irrespective of the product vibrational manifold. A few more examples are given in Fig.…”

“…Moreover, this reaction has witnessed many new findings in reaction dynamics, e.g. , the time-delayed mechanism, 17 the appearance of Feshbach resonance below the reaction barrier, 18,19 glory scattering in the forward scattered differential cross sections (DCSs), 20,21 etc. Furthermore, it has been considered as a benchmark reactive system to explore the electronic nonadiabatic effects 22–33 and the geometric phase (GP) effects 27,34–48 in reaction dynamics.…”

“…Studies of this reaction have led to many rudimentary notions in chemical reaction dynamics, e.g., potential energy surfaces (PES), [1][2][3] the transition state, 4,5 reactive resonances, [6][7][8][9] the quantized bottleneck state (QBS) [10][11][12][13][14][15][16] etc. Moreover, this reaction has witnessed many new findings in reaction dynamics, e.g., the time-delayed mechanism, 17 the appearance of Feshbach resonance below the reaction barrier, 18,19 glory scattering in the forward scattered differential cross sections (DCSs), 20,21 etc. Furthermore, it has been considered as a benchmark reactive system to explore the electronic nonadiabatic effects [22][23][24][25][26][27][28][29][30][31][32][33] and the geometric phase (GP) effects 27,[34][35][36][37][38][39][40][41][42][43][44][45]<...…”