Time-dependent Quantum Wave Packet Study of F+HCl and F+DCl Reactions

Ring-polymer molecular dynamical calculations for the F + HCl → HF + Cl reaction on the ground 12A' potential energy surface

The reaction kinetics of the heavy-light-heavy abstraction reaction F + HCl → HF + Cl on the ground electronic state potential energy surface (PES) is investigated theoretically by a recently developed ring polymer molecular dynamics (RPMD) approach. First, a new PES is developed by the permutation invariant polynomial neural network (PIP-NN) approach based on 30 620 points sampled over a large configuration space from the latest and most accurate Deskevich-Hayes-Takahashi-Skodje-Nesbitt (DHTSN) PES (J. Chem. Phys., 2006, 124, 224303). Excellent fitting performance was achieved with only 521 parameters. The PIP-NN PES is 11 times faster than the DHTSN PES. Besides, the first analytical derivatives with respect to the coordinates of the atoms have been obtained for the PIP-NN PES. The RPMD rate coefficients on the PIP-NN PES are calculated and compared with available theoretical and experimental results. It is found that the experimental rate coefficients are significantly larger than the theoretical results on the DHTSN PES, due to its overestimated reaction barrier. We conclude that a reliable PES for this important heavy-light-heavy reaction is highly desirable.

Product rotational angular momentum polarization of H+FCl (v=0-5; j=0, 3, 6, 9) → HF+Cl and HCl+F at Erel=0.5-20 kcal mol(-1)

The rotational angular momentum polarizations of product molecules of the title reactions on the ground potential energy surface 1 (2)A' of DHTSN [Deskevic et al. J Chem Phys 2006, 124, 224303] have been studied using the quasi-classical trajectory method. Reaction dynamic results of the HF product channel comparing with another channel of HCl with 100,000 trajectories can be accurately resolved. We show the value of the polar p(ϑr) in the range of 0° ≤ ϑr ≤ 180(°), azimuthal p(φr) in the range of 0° ≤ φr ≤ 360(°), and dihedral p(ϑr, φr) in the ranges of 0(°) ≤ ϑr ≤ 180(°) and 0(°) ≤ φr ≤ 360(°); the angular distributions of the product molecules HF and HCl at relative Erel = 0.5, 1, 2, 5, 10, 15, and 20 kcal mol(-1); and four polarization-dependent differential cross sections (PDDCSs) of HF and HCl at Erel = 0.5, 1, 2, 5, 10, and 15 kcal mol(-1). p(φr) distributions at v = 0-5, and j = 0, 3, 6, 9 at every Erel are plotted cylindrically together. The stereo dynamic transformation reaction dependent upon the rovibrational states of the reactant molecule FCl and its relative translational energies around 0.5-5 kcal mol(-1) can be significantly differentiated. Translational and rovibrational enhancements of the title reactions on both early barrier potential energy surfaces have been shown in great detail and clarified. Reaction mechanisms of forward and backward scattering of the product molecules HF and HCl, respectively, have been obtained. Graphical Abstract H + FCl → either HF + Cl (left) or HCl + F (right) is moving along a trajectory on the respective PES.

Quantum mechanical calculations of state-to-state cross sections and rate constants for the F + DCl → Cl + DF reaction

We present accurate state-to-state quantum wave packet calculations of integral cross sections and rate constants for the title reaction. Calculations are carried out on the best available ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged state-to-state reaction cross sections have been calculated for collision energies up to 0.5 eV and different initial rotational and vibrational excitations, DCl(v = 0, j = 0 - 1; v = 1, j = 0). Also, initial-state resolved rate constants of the title reaction have been calculated in a temperature range of 100-400 K. It is found that the initial rotational excitation of the DCl molecule does not enhance reactivity, in contract to the reaction with the isotopologue HCl in which initial rotational excitation produces an important enhancement. These differences between the isotopologue reactions are analyzed in detail and attributed to the presence of resonances for HCl(v = 0, j), absent in the case of DCl(v = 0, j). For vibrational excited DCl(v = 1, j), however, the reaction cross section increases noticeably, what is also explained by another resonance.

Relative efficacy of vibrational vs. translational excitation in promoting atom-diatom reactivity: rigorous examination of Polanyi's rules and proposition of sudden vector projection (SVP) model

To provide a systematic and rigorous re-examination of the well-known Polanyi's rules, excitation functions of several A + BC(v = 0, 1) reactions are determined using the Chebyshev real wave packet method on accurate potential energy surfaces. Reactions with early (F + H2 and F + HCl), late (Cl + H2), and central (H∕D∕Mu + H2, where Mu is a short-lived light isotope of H) barriers are represented. Although Polanyi's rules are in general consistent with the quantum dynamical results, their predictions are strictly valid only in certain energy ranges divided by a cross-over point. In particular, vibrational excitation of the diatomic reactant typically enhances reactivity more effectively than translational excitation at high energies, while reverse is true at low energies. This feature persists irrespective of the barrier location. A sudden vector projection model is proposed as an alternative to Polanyi's rules. It is found to give similar, but more quantitative, predictions about mode selectivity in these reactions, and has the advantage to be extendible to reactions involving polyatomic molecules.

Time-dependent wave packet quantum scattering and quasi-classical trajectory calculations of the H + FCl(v=0,j=0) → HF + Cl/HCl + F reaction

The dynamics of the title reaction are investigated using both time-dependent wave packet quantum scattering and quasi-classical trajectory (QCT) methods on adiabatic ground 1(2)A' potential energy surface (PES). Compared with the quantum results of reaction probabilities of H + FCl(J=0) → HF + Cl/HCl + F, the QCT method is proven feasible and further employed to produce integral cross sections and rate constants. Significant resonance structures are observed in the reaction probabilities using the quantum method; however, there are some undulations in the calculated QCT integral cross sections for both product channels. A comparison between the quantum mechanical coupled-channel (CC) calculation and centrifugal sudden approximation calculation reveals the very important role of Coriolis coupling effects in the quantum calculation. Comparisons between the calculated thermal rate constants for both reactions and the previous theoretical and experimental results have been done. HCl product formation is favored over the HF product in the reactive system. Finally, the HF products are found to be mainly forward scattering, and the HCl products are mainly backward scattering.

Accurate quantum wave packet calculations for the F + HCl → Cl + HF reaction on the ground 1(2)A' potential energy surface

We present converged exact quantum wave packet calculations of reaction probabilities, integral cross sections, and thermal rate coefficients for the title reaction. Calculations have been carried out on the ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged wave packet reaction probabilities at selected values of the total angular momentum up to a partial wave of J = 140 with the HCl reagent initially selected in the v = 0, j = 0-16 rovibrational states have been obtained for the collision energy range from threshold up to 0.8 eV. The present calculations confirm an important enhancement of reactivity with rotational excitation of the HCl molecule. First, accurate integral cross sections and rate constants have been calculated and compared with the available experimental data.

PRODUCT ROTATIONAL ANGULAR MOMENTUM POLARIZATION IN REACTIONS D + FCl(v = 0,j = 0) → DCl + F, DF + Cl

A comparative quasi-classical trajectory study on the product alignment and orientation of reactions D + FCl (v,j) → DCl + F , DF + Cl are carried out on a recently computed 12A′ ground-state surface reported by Deskevich et al. The reaction probabilities, integral and differential cross-sections as a function of collision energy are presented. The differential cross-sections and 〈P2(j′ ⋅ k)〉 are governed by different reaction mechanisms for these two reactions. P(θr) and P(ϕr) distributions of products DCl and DF at four selected collision energies of 5, 10, 16 and 30 kcal/mol indicate that DCl and DF product molecules are not only aligned, but also oriented along y-axis. By comparing the P(θr) and P(ϕr) distributions of reactions H + FCl (v = 0,j = 0) → HCl + F and H + FCl (v = 0,j = 0) → HF + Cl , mass factor has some influence on stereodynamics of the title reactions, but the features of PES should have major influence on the difference between dynamics of reactions D + FCl (v = 0,j = 0) → DCl + F and D + FCl (v = 0,j = 0) → DF + Cl .

THEORETICAL STUDY OF ABOVE THRESHOLD DISSOCIATION OF HD+ IN FEMTOSECOND LASER FIELDS

The above threshold dissociation (ATD) of the HD+ molecular ion in a linearly polarized femtosecond laser field is theoretically studied using three-dimensional time-dependent quantum wave packet method. Based on the Born–Oppenheimer approximation (BOA), calculations are performed on two electronic states, the ground state 1sσ and the excited state 2pσ. The energy-dependent distributions of the dissociated fragments, resulting from the ATD, are calculated by using an asymptotic-flow expression in the momentum space. The numerical results demonstrate that, in the laser field of wavelength λ = 800 nm and full-width at half-maximum (FWHM) τ = 30 fs , only two-photon dissociation is observable at a weaker pulse peak intensity, 5.0 × 1012 W cm -2, while at an intense intensity, 1.5 × 1015 W cm -2, the dissociated fragments resulting from four-photon absorption dominates over the photodissociation process. These results are consistent with the experimental observation of Orr et al. [Orr PA et al., Phys Rev Lett98:163001, 2007]. The ac Stark-shift caused by intense laser field will change the kinetic energies of the fragments. The ATD phenomena are quantitatively interpreted in terms of the concept of light-induced potential. The molecular rotation and alignment have some effects on the kinetic energy spectrum of the dissociated fragments. The molecular rotation reduces the ac Stark-shift and broadens the peaks of kinetic energy spectra of the dissociated fragments. However, the intense laser field can effectively align the molecule and is helpful to increase the ATD probability. The ATD spectrum is related to the initial quantum numbers J0 and M0 of the molecule. The ATD spectrum of HD+ is calculated at a limited thermal temperature.

Product rotational angular momentum polarization in the H+FCl(v=0-5, j=0, 3, 6, 9)→HF+Cl reaction

The product alignment and orientation of the title reaction on the ground potential energy surface of 1 (2)A' have been studied using the quasi-classical trajectory method. The calculations were carried out for case (a) at collision energies of 0.5-20 kcal mol(-1) with the initially rovibrational state of the reagent FCl molecule being at the v = 0 and j = 0 level to especially reveal in detail the dependence of the product integral cross section on collision energy. Further calculations at the collision energy of 15 kcal mol(-1) for case (b) at v = 0-5, and j = 0, and (c) at v = 0, and j = 3, 6, 9 initial states were carried out to reveal the effect of initially vibrational and rotational excitations on stereodynamics, respectively. Possessing final relative velocity k' (defined as a vector in the xz-plane), product alignment perpendicular to the reagent relative velocity vector k (defined as z- or parallel to the z-axis), for case (a) is found to be weaker at all collision energies, for case (b) is found to be vibrationally enhanced by the reactant molecule FCl, but for case (c), rather insensitive to initially rotational excitation. The rotational vector of product molecular orientation pointing to either negative or positive direction of the y-axis in the center of mass frame, e.g. origin of the coordinate system, is enhanced by collision energies regarding to 0.5-20 kcal mol(-1), while it becomes weaker at higher vibrational (v = 0-5) or rotational (j = 0, 3, 6, 9) excitation levels. Effects of collision energies and of rotational excitation at these collision energies, with 15 kcal mol(-1) as an example on the calculated PDDCSs are also shown and discussed. Detailed plots P(φ(r)) in the range of 0 ≤φ(r)≤ 360(o), and P(θ(r), φ(r)) in the ranges of 0 ≤θ(r)≤ 180° and 0 ≤φ(r)≤ 360° at collision energies 0.5-20 kcal mol(-1) have been presented. Overall, results of PDDCSs of the product alignment and product orientation at these collision energies in the title reaction are not very strongly distinguishable.