Glories, hidden rainbows and nearside-farside interference effects in the angular scattering of the state-to-state H + HD → H2 + D reaction

A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H2 → FH + H reaction at Etrans = 62.09 meV

The aim of the present paper is to bring clarity, through simplicity, to the important and long-standing problem: does a resonance contribute to the forward-angle scattering of the F + H2 reaction? We reduce the problem to its essentials and present a well-defined, yet rigorous and unambiguous, investigation of structure in the differential cross sections (DCSs) of the following three state-to-state reactions at a translational energy of 62.09 meV: F + H2(vi = 0, ji = 0, mi = 0) → FH(vf = 3, jf = 0, 1, 2, mf = 0) + H, where vi, ji, mi and vf, jf, mf are the initial and final vibrational, rotational and helicity quantum numbers respectively. Firstly, we carry out quantum-scattering calculations for the Fu-Xu-Zhang potential energy surface, obtaining accurate numerical scattering matrix elements for indistinguishable H2. The calculations use a time-independent method, with hyperspherical coordinates and an enhanced Numerov method. Secondly, the following theoretical techniques are employed to analyse structures in the DCSs: (a) full and Nearside-Farside (NF) partial wave series (PWS) and local angular momentum theory, including resummations of the full PWS up to second order. (b) The recently introduced "CoroGlo" test, which lets us distinguish between glory and corona scattering at forward angles for a Legendre PWS. (c) Six asymptotic (semiclassical) forward-angle glory theories and three asymptotic farside rainbow theories, valid for rainbows at sideward-scattering angles. (d) Complex angular momentum (CAM) theories of forward and backward scattering, with the Regge pole positions and residues computed by Thiele rational interpolation. Thirdly, our conclusions for the three PWS DCSs are: (a) the forward-angle peaks arise from glory scattering. (b) A broad (hidden) farside rainbow is present at sideward angles. (c) A single Regge pole contributes to the DCS across the whole angular range, being most prominent at forward angles. This proves that a resonance contributes to the DCSs for the three transitions. (d) The diffraction oscillations in the DCSs arise from NF interference, in particular, interference between the Regge pole and direct subamplitudes.

Unveiling Quantum Interference in the D+ + H2 Nonadiabatic Reaction Dynamics at Low Collision Energies

Fully converged nonadiabatic dynamics calculations of the D+ + H2 → H+ + HD reaction are performed at low temperatures using the time-dependent wave packet approach based on a set of precise 3 × 3 diabatic potential energy surfaces (PESs) ( Phys. Chem. Chem. Phys., 2021, 23, 7735-7747, DOI: 10.1039/D0CP04100A). The D+ + H2 reaction is mediated by a dense manifold of resonances associated with the deep potential well on the ground-state PES. The calculated results show that the nonadiabatic coupling can affect the resonance positions, deviating from the expectation based solely on adiabatic considerations. Furthermore, significant forward-backward asymmetry in total differential cross sections (DCSs) is revealed, which is markedly influenced by nonadiabatic effects. The nonadiabatic effects not only affect the contribution of partial waves in the reaction but also make the interference patterns in the DCSs change significantly.

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

Out of the many major breakthroughs that the hydrogen-exchange reaction has led to, electronic nonadiabatic effects that are mainly due to the geometric phase has intrigued many. In this work we investigate such effects in the state-to-state dynamics of the H + H2 (v = 3, 4, j = 0) → H2 (v', j') + H reaction with a vibrationally excited reagent at energies corresponding to thermal conditions. The dynamical calculations are performed by a time-dependent quantum mechanical method both on the lower adiabatic potential energy surface (PES) and also using a two-states coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 1E' ground electronic manifold of the H3 system. The nonadiabatic couplings are considered here up to the quadratic term; however, the effect of the latter on the reaction dynamics is found to be very small. Adiabatic population analysis showed a minimal participation of the upper adiabatic surface even for the vibrationally excited reagent. A strong nonadiabatic effect appears in the state-to-state reaction probabilities and differential cross sections (DCSs). This effect is manifested as "out-of-phase" oscillations in the DCSs between the results of the uncoupled and coupled surface situations. The oscillations persist as a function of both scattering angle and collision energy in both the backward and forward scattering regions. The origins of these oscillations are examined in detail. The oscillations that appear in the forward direction are found to be different from those due to glory scattering, where the latter showed a negligibly small nonadiabatic effect. The nonadiabatic effects are reduced to a large extent when summed over all product quantum states, in addition to the cancellation due to integration over the scattering angle and partial wave summation.

Velocity-Selected Rotational State Distributions of Nitric Oxide Scattered off Graphene Revealed by Surface-Velocity Map Imaging

We report velocity-dependent internal energy distributions of nitric oxide molecules, NO, scattered off graphene supported on gold to further explore the dynamics of the collision process between NO radicals and graphene. These experiments were performed by directing a molecular beam of NO onto graphene in a surface-velocity map imaging setup, which allowed us to record internal energy distributions of the NO radicals as a function of their velocity. We do not observe bond formation but (1) major contributions from direct inelastic scattering and (2) a smaller trapping-desorption component where some physisorbed NO molecules have residence times on the order of microseconds. This is in agreement with our classical molecular dynamics simulations which also observe a small proportion of two- and multi-bounce collisions events but likewise a small proportion of NO radicals trapped at the surface for the entire length of the molecular dynamics simulations (a few picoseconds). Despite a collision energy of 0.31 eV, which would be sufficient to populate NO(v = 1), we do not detect vibrationally excited nitric oxide.

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

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) → H₂(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 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 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.