Benchmark Quantum Mechanical Calculations of Vibrationally Resolved Cross Sections and Rate Constants on ab Initio Potential Energy Surfaces for the F + HD Reaction: Comparisons with Experiments

Significant Isotope Effects from the Nonadiabatic Couplings in the Cl(2P) + HD(v = 0, j = 0) Reaction

The impact of non-Born-Oppenheimer couplings on the isotopic effects in the reaction of the Cl(2P) atom with the HD (v = 0, j = 0) molecule is investigated with our recently developed nonadiabatic time-independent quantum scattering methods, where the full open-shell characteristics are included in the six-state model, and also with the recently developed two-state model solving by time-independent methods, where part of the open-shell characteristic is included. The same reaction is also calculated with the simple adiabatic model using the lowest adiabatic potential energy surface. Compared with the results from different models, it is found that the reactivity of the Cl + HD → HCl + D channel is significantly overestimated in the adiabatic model. In contrast, the reactivity of the other channel agrees well with the nonadiabatic models. This is due to the van der Waals well in the reactant channel being changed a lot by including the nonadiabatic couplings. These quantum dynamics calculations suggest that sometimes the adiabatic model should be used with caution; otherwise, it may result in significant deviations for some reactions.

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.

Benchmark Quantum Kinetics at Low Temperatures toward Absolute Zero and Role of Entrance Channel Wells on Tunneling, Virtual States, and Resonances: The F + HD Reaction

This paper reports a study of the quantum reaction dynamics and kinetics of the F + HD reaction at low and ultralow temperatures, focusing on the range from the Wigner limit up to 50 K. Close coupling time-independent quantum reactive scattering calculations for the production of HF and DF molecules have been carried out on two potential energy surfaces differing in the description of the reaction entrance channel. This case is computationally more demanding than the cases of F with H₂ and D₂ ( De Fazio et al. Frontiers in Chemistry 2019 , 7 , 328 ) but offers a wider phenomenology regarding the roles of quantum mechanical effects of tunneling, of virtual states, and of resonances. The results show that at the temperatures in the cold and ultracold regimes small changes in the entrance channel long-range interaction induce surprising near threshold features. The presence of a virtual state close to the reactive threshold gives rise to a marked anti-Arrhenius behavior of the rate constants below 100 mK. This effect enhances reaction rates by about 2 orders of magnitude, making them of the same order as those at room temperature and confining the onset of the Wigner regime in the microkelvin region.

Orbiting resonances in the F + HD (v = 0, 1) reaction at very low collision energies. A quantum dynamical study

Time-independent, fully converged, quantum dynamical calculations have been performed for the F + HD (v = 0, j = 0) and F + HD (v = 1, j = 0) reactions on an accurate potential energy surface down to collision energies of 0.01 meV. The two isotopic exit channels, HF + D and DF + H, have been investigated. The calculations reproduce satisfactorily the Feshbach resonance structures for collision energies between 10 and 40 meV, previously reported in the literature for the HF + D channel. Contrary to the results of a former literature work, vibrational excitation of HD is found to enhance reactivity in all cases down to the lowest collision energy investigated. Shape-type orbiting resonances are found for collision energies lower than 2 meV. The resonances appear as peaks in the reaction cross sections that are associated to specific values of the total angular momentum, J. In contrast with the Feshbach resonances at higher energies, the orbiting resonance structure, which is caused by the van der Waals well of the entrance channel, is identical for the HF + D and DF + H exit channels. The orbiting resonance peaks for F + HD (v = 0) are very small, but those for F + HD (v = 1) could be observed, in principle, with a combination of Raman pumping and merged beams methods.

Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures

Integral cross sections and rate constants for the prototypical chemical reactions of the fluorine atom with molecular hydrogen and deuterium have been calculated over a wide interval of collision energy and temperature ranging from the sub-thermal (50 K) down to the ultra-cold regimes (0.5 mK). Rigorous close coupling time-independent quantum reactive scattering calculations have been carried out on two potential energy surfaces, differing only at long-range in the reactants' channel. The results show that tunnel, resonance and virtual state effects enhance under-barrier reactivity giving rise to pronounced deviations from the Arrhenius law as temperature is lowered. Within the ultra-cold domain (below 1 mK), the reactivity is governed by virtual state effects and by tunneling through the reaction barrier; in the cold regime (1 mK–1 K), the shape resonances in the entrance channel of the potential energy surface make the quantum tunneling contribution larger so enhancing cross sections and rate constants by about one order of magnitude; at higher temperatures (above 10 K), the tunneling pathway enhanced by the constructive interference between two Feshbach resonances trapped in the reaction exit channel competes with the thermally activated mechanism, as the energy gets closer to the reaction barrier height. The results show that at low temperatures cross sections and rate constants are extremely sensitive to small changes in the long-range intermolecular interaction in the entrance channel of the potential energy surface, as well as to isotopic substitution.

Quantum state-to-state study for (H−(D−),HD) collisions on two potential energy surfaces

Revealing the reaction mechanisms of the H⁻/D⁻ + HD reaction – an exact quantum dynamics study on two potential energy surfaces.

Dynamical resonances in chemical reactions

The transition state is a key concept in the field of chemistry and is important in the study of chemical kinetics and reaction dynamics.

Couplings and recouplings of four angular momenta: Alternative 9j symbols and spin addition diagrams

The Wigner 9j symbols of the first kind-also known as Fano X-coefficients-serve to connect different addition schemes of four angular momenta, widely known examples being the LS and the jj couplings in atomic, molecular, and nuclear spectroscopies. Here, we also consider alternative sequences of binary couplings of four angular momenta, which are dealt through the 9j symbols of the second kind, and are explicitly given by the pentagonal (or Biedenharn-Elliott) identity. These coefficients are essential ingredients in the quantum-mechanical treatments of rotational and polarization phenomena in reaction dynamics and photoinduced processes. We also emphasize the combinatorial structure underlying the extended construction of a previously introduced truncated icosahedral "abacus", and provide extensions useful for algebraical manipulations, semiclassical interpretations, and computational applications, including all the 120 addition schemes.