Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H₂/D₂ reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H₂ and D₂) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H₂ and F + D₂ reactions are presented along with previous theoretical and experimental results.

Quantum Dynamics Studies of the Significant Intramolecular Isotope Effects on the Nonadiabatic Be+(2P) + HD → BeH+/BeD+ + D/H Reaction

Quantum time-dependent wave packet dynamics studies on the nonadiabatic Be⁺(²P) + HD → BeH⁺/BeD⁺ + D/H reaction are performed for the first time employing recently constructed diabatic potential energy surfaces. Strong intramolecular isotope effects and unusual results are presented, which are attributed to the dynamic effects of shallow wells induced by avoided crossing on the diagonal V₂₂^d surface. The BeH⁺ + D and BeD⁺ + H channels are dominated by high-J and low-J partial waves, respectively. The BeD⁺/BeH⁺ branching ratio is larger than 10 at low energy and gradually decreases with increasing collision energy. The BeH⁺ product is primarily distributed at low vibrational states, whereas there exists an obvious population inversion of vibrational states on the BeD⁺ product. The results of differential cross sections suggest that the formation of the BeH⁺ + D channel favors a direct reaction process, while the BeD⁺ + H channel is mainly generated by the complex-forming mechanism.

Beyond Born-Oppenheimer constructed diabatic potential energy surfaces for F + H2 reaction

First principles based beyond Born-Oppenheimer theory has been implemented on the F + H₂ system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin-orbit (SO) coupling effect on the collision process of the F + H₂ reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (1²A', 2²A', and 1²A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn-Teller (JT) type conical intersections between the two A' states translate along C_2v and linear geometries in F + H₂. In addition, A' and A″ states undergo Renner-Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H₂, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H₂ system.

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.

Theoretical Study of Barrierless Chemical Reactions Involving Nearly Elastic Rebound: The Case of S(1D) + X2, X = H, D

For some values of the total angular momentum consistent with reaction, the title processes involve nonreactive trajectories proceeding through a single rebound mechanism during which the internal motion of the reagent diatom is nearly unperturbed. When such paths are in a significant amount, the classical reaction probability is found to be markedly lower than the quantum mechanical one. This finding was recently attributed to an unusual quantum effect called diffraction-mediated trapping, and a semiclassical correction was proposed in order to take into account this effect in the classical trajectory method. In the present work, we apply the resulting approach to the calculation of opacity functions as well as total and state-resolved integral cross sections (ICSs) and compare the values obtained with exact quantum ones, most of which are new. As the title reactions proceed through a deep insertion well, mean potential statistical calculations are also presented. Seven values of the collision energy, ranging from 30 to 1127 K, are considered. Two remarkable facts stand out: (i) The corrected classical treatment strongly improves the accuracy of the opacity function as compared to the usual classical treatment. When the entrance transition state is tight, however, those trajectories crossing it with a bending vibrational energy below the zero point energy must be discarded. (ii) The quantum opacity function, particularly its cutoff, is finely reproduced by the statistical approach. Consequently, the total ICS is also very well described by the two previous approximate methods. These, however, do not predict state-resolved ICSs with the same accuracy, proving thereby that (i) one or several genuine quantum effects involved in the dynamics are missed by the corrected classical treatment and (ii) the dynamics are not fully statistical.

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 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.

Rainbows, supernumerary rainbows and interference effects in the angular scattering of chemical reactions: an investigation using Heisenberg's S matrix programme

Rainbow and supernumerary rainbow in the angular scattering of a state-to-state chemical reaction.

Complementarity between Quantum and Classical Mechanics in Chemical Modeling. The H + HeH+ → H2 + + He Reaction: A Rigourous Test for Reaction Dynamics Methods

In this work we present a dynamical study of the H + HeH+ → H2+ + He reaction in a collision energy range from 0.1 meV to 10 eV, suitable to be used in applicative models. The paper extends and complements a recent work [ Phys. Chem. Chem. Phys. 2014, 16, 11662] devoted to the characterization of the reactivity from the ultracold regime up to the three-body dissociation breakup. In particular, the accuracy of the quasi-classical trajectory method below the three-body dissociation threshold has been assessed by a detailed comparison with previous calculations performed with different reaction dynamics methods, whereas the reliability of the results in the high energy range has been checked by a direct comparison with the available experimental data. Integral cross sections for several HeH+ roto-vibrational states have been analyzed and used to understand the extent of quantum effects in the reaction dynamics. By using the quasi-classical trajectory method and quantum mechanical close coupling data, respectively, in the high and low collision energy ranges, we obtain highly accurate thermal rate costants until 15 000 K including all (178) the roto-vibrational bound and quasi-bound states of HeH+. The role of the collision-induced dissociation is also discussed and explicitly calculated for the ground roto-vibrational state of HeH+.

The H + HeH(+) → He + H2(+) reaction from the ultra-cold regime to the three-body breakup: exact quantum mechanical integral cross sections and rate constants

In this work, we present a quantum mechanical scattering study of the title reaction from 1 mK to 2000 K. Total integral cross sections and thermal rate constants are compared with previous theoretical and experimental data and with simpler theoretical models to understand the range of validity of the approximations used in the previous studies. The obtained quantum reactive observables have been found to be nearly insensitive to the roto-vibrational energy of the reactants at high temperatures. More sensitive to the reactant's roto-vibrational energy are the data in the cold and ultra-cold regimes. The implications of the new data presented here in the early universe scenario are also discussed and analyzed.

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially in the neighborhood of a reactive threshold.

Theoretical reaction kinetics astride the transition between moderate and deep tunneling regimes: the F + HD case

For the reaction between F and HD, giving HF + D and DF + H, the rate constants, obtained from rigorous quantum scattering calculations at temperatures ranging from 350 K down to 100 K, show deviations from the Arrhenius behavior that have been interpreted in terms of tunneling of either H or D atoms through a potential energy barrier. The interval of temperature investigated extends from above to below a crossover value Tc, a transition temperature separating the moderate and deep quantum tunneling regimes. Below Tc, the rate of the H or D exchange reaction is controlled by the prevalence of tunneling over the thermal activation mechanism. In this temperature range, Bell's early treatment of quantum tunneling, based on a semiclassical approximation for the barrier permeability, provides a reliable tool to quantitatively account for the contribution of the tunneling effect. This treatment is here applied for extracting from rate constants properties of the effective tunneling path, such as the activation barrier height and width. We show that this is a way of parametrizing the dependence of the apparent activation energy on temperature useful for both calculated and experimental rate constants in an ample interval of temperature, from above to below Tc, relevant for modelization of astrophysical and in general very low-temperature environments.

Insights into the semiclassical Wigner treatment of bimolecular collisions

The semiclassical Wigner treatment of bimolecular collisions, proposed by Lee and Scully on a partly intuitive basis [J. Chem. Phys. 73, 2238 (1980)], is derived here from first principles. The derivation combines Heller's ideas [J. Chem. Phys. 62, 1544 (1975); ibid. 65, 1289 (1976); ibid. 75, 186 (1981)], the backward picture of molecular collisions [L. Bonnet, J. Chem. Phys. 133, 174108 (2010)] and the microreversibility principle.

Resonances in the Ne + H2(+) → NeH(+) + H proton-transfer reaction

We investigated the oscillations found in the integral cross section of the title reaction, which are particularly evident for Ne + H2(+)(v0 = 2,j0 = 1) [essentially isoenergetic with NeH(+)(v' = 0,j' = 0) + H] at low collision energy (Ecol < 0.30 eV). We employed mainly an exact time-independent (TI) quantum dynamics method and used the best potential energy surface available. From analysis of TI initial state selected to all integral cross sections, state-to-state integral cross sections, and the corresponding differential cross sections (DCSs), we showed that the oscillations correspond to resonances. They arise from the influence of the global [Ne-H-H](+) (collinear) minimum on dynamics and probably correspond to Feshbach resonances. Besides, the forward-backward peaking DCS (which oscillates with Ecol) behavior observed could be a signature for this type of resonances. Finally, as most data on resonances in bimolecular reactions correspond to neutral systems, we hope that the present results will encourage experimentalists to re-examine this benchmark system.

The He + H2+ → HeH+ + H reaction: ab initio studies of the potential energy surface, benchmark time-independent quantum dynamics in an extended energy range and comparison with experiments

In this work we critically revise several aspects of previous ab initio quantum chemistry studies [P. Palmieri et al., Mol. Phys. 98, 1835 (2000); C. N. Ramachandran et al., Chem. Phys. Lett. 469, 26 (2009)] of the HeH(2)(+) system. New diatomic curves for the H(2)(+) and HeH(+) molecular ions, which provide vibrational frequencies at a near spectroscopic level of accuracy, have been generated to test the quality of the diatomic terms employed in the previous analytical fittings. The reliability of the global potential energy surfaces has also been tested performing benchmark quantum scattering calculations within the time-independent approach in an extended interval of energies. In particular, the total integral cross sections have been calculated in the total collision energy range 0.955-2.400 eV for the scattering of the He atom by the ortho- and para-hydrogen molecular ion. The energy profiles of the total integral cross sections for selected vibro-rotational states of H(2)(+) (v = 0,...,5 and j = 1,...,7) show a strong rotational enhancement for the lower vibrational states which becomes weaker as the vibrational quantum number increases. Comparison with several available experimental data is presented and discussed.

Dynamics of the S(1D2)+HD(j=0) reaction at collision energies approaching the cold regime: a stringent test for theory

We report integral cross sections for the S(1D2)+HD(j=0)→DS+H and HS+D reaction channels obtained through crossed-beam experiments reaching collision energies as low as 0.46 meV and from adiabatic time-independent quantum-mechanical calculations. While good overall agreement with experiment at energies above 10 meV is observed, neither the product channel branching ratio nor the low-energy resonancelike features in the HS+D channel can be theoretically reproduced. A nonadiabatic treatment employing highly accurate singlet and triplet potential energy surfaces is clearly needed to resolve the complex nature of the reaction dynamics.