Statistical quantum studies on insertion atom–diatom reactions

The D(+) + H2 reaction: differential and integral cross sections at low energy and rate constants at low temperature

The D(+) + H2 reaction is investigated by means of a time independent quantum mechanical (TIQM) and statistical quantum mechanical (SQM) methods. Differential cross sections and product rotational distributions obtained with these two theoretical approaches for collision energies between 1 meV and 0.1 eV are compared to analyze the dynamics of the process. The agreement observed between the TIQM differential cross sections and the SQM predictions as the energy increases revealed the role played by the complex-forming mechanism. The importance of a good description of the asymptotic regions is also investigated by calculating rate constants for the title reaction at low temperature.

Dynamics of the D(+) + H2 → HD + H(+) reaction at the low energy regime by means of a statistical quantum method

The D(+) +H2(v = 0, j = 0, 1) → HD+H(+) reaction has been investigated at the low energy regime by means of a statistical quantum mechanical (SQM) method. Reaction probabilities and integral cross sections (ICSs) between a collisional energy of 10(-4) eV and 0.1 eV have been calculated and compared with previously reported results of a time independent quantum mechanical (TIQM) approach. The TIQM results exhibit a dense profile with numerous narrow resonances down to Ec ~ 10(-2) eV and for the case of H2(v = 0, j = 0) a prominent peak is found at ~2.5 × 10(-4) eV. The analysis at the state-to-state level reveals that this feature is originated in those processes which yield the formation of rotationally excited HD(v' = 0, j' > 0). The statistical predictions reproduce reasonably well the overall behaviour of the TIQM ICSs at the larger energy range (Ec ≥ 10(-3) eV). Thermal rate constants are in qualitative agreement for the whole range of temperatures investigated in this work, 10-100 K, although the SQM values remain above the TIQM results for both initial H2 rotational states, j = 0 and 1. The enlargement of the asymptotic region for the statistical approach is crucial for a proper description at low energies. In particular, we find that the SQM method leads to rate coefficients in terms of the energy in perfect agreement with previously reported measurements if the maximum distance at which the calculation is performed increases noticeably with respect to the value employed to reproduce the TIQM results.

New insights into the semiclassical Wigner treatment of photodissociation dynamics

The semiclassical Wigner treatment of Brown and Heller [J. Chem. Phys. 1981, 75, 186] is applied to direct triatomic (or triatomic-like polyatomic) photodissociations with the aim of accurately predicting final state distributions at relatively low computational cost, and having available a powerful interpretative tool. For the first time, the treatment takes rotational motions into account. The proposed formulation closely parallels the quantum description as far as possible. An approximate version is proposed, which is still accurate while numerically much more efficient. In addition to being weighted by usual vibrational Wigner distributions, final phase space states appear to be weighted by new rotational Wigner distributions. These densities have remarkable structures clearly showing that classical trajectories most contributing to rotational state j are those reaching the products with a rotational angular momentum close to [j(j + 1)](1/2) (in ℏ units). The previous methods involve running trajectories from the reagent molecule onto the products. The alternative backward approach [L. Bonnet, J. Chem. Phys., 2010, 133, 174108], in which trajectories are run in the reverse direction, is shown to strongly improve the numerical efficiency of the most rigorous method in addition to being state-selective, and thus, ideally suited to the description of state-correlated distributions measured in velocity imaging experiments. The results obtained by means of the previous methods are compared with rigorous quantum results in the case of Guo's triatomic-like model of methyl iodide photodissociation [J. Chem. Phys., 1992, 96, 6629] and close agreement is found. In comparison, the standard method of Goursaud et al. [J. Chem. Phys., 1976, 65, 5453] is only semi-quantitative.

Three-vector correlation in statistical reactions: the role of the triatomic parity

This article presents a methodology for the determination of the k-j-k' three-vector correlation assuming a statistical model for atom-diatom reactions; k and k' are the reagent-approach and product-recoil directions, respectively, and j is the rotational angular momentum of the reagent diatomic. Although the polarization of reagent angular momentum is in most cases negligible, conservation of the triatomic parity imposes a certain polarization for some combinations involving low reagent and product rotational states. Statistical and quantum-mechanical polarization-dependent differential cross sections were calculated for the barrierless D(+) + H(2)(v = 0,j) → HD(v' = 0,j') + H(+) reaction. The agreement between the two is in most cases excellent, confirming the statistical character of the reaction at low and moderate collision energies.

Ortho-para H₂ conversion by proton exchange at low temperature: an accurate quantum mechanical study

We report extensive, accurate fully quantum, time-independent calculations of cross sections at low collision energies, and rate coefficients at low temperatures for the H⁺ + H₂(v = 0, j) → H⁺ + H₂(v = 0, j') reaction. Different transitions are considered, especially the ortho-para conversion (j = 1 → j' = 0) which is of key importance in astrophysics. This conversion process appears to be very efficient and dominant at low temperature, with a rate coefficient of 4.15 × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ at 10 K. The quantum mechanical results are also compared with statistical quantum predictions and the reaction is found to be statistical in the low temperature regime (T < 100 K).

The O((1)D) + H2 (X (1)Σ+, v, j) → OH(X (2)Π, v', j') + H((2)S) reaction at low collision energy: when a simple statistical description of the dynamics works

In this communication, we highlight that statistical approaches for chemical reactions describe reasonably well the low energy dynamics of the title process. Consequently, such methods prove to be valuable to compute rate constants from low to room temperatures. Results are compared with experiment and recent precise quantum wave packet calculations [J. Phys. Chem. A, 2009, 113, 5285].

The method of Gaussian weighted trajectories. V. On the 1GB procedure for polyatomic processes

In recent years, many chemical reactions have been studied by means of the quasiclassical trajectory (QCT) method within the Gaussian binning (GB) procedure. The latter consists of "quantizing" the final vibrational actions in Bohr spirit by putting strong emphasis on the trajectories reaching the products with vibrational actions close to integer values. A major drawback of this procedure is that if N is the number of product vibrational modes, the amount of trajectories necessary to converge the calculations is ∼10(N)×larger than with the standard QCT method. Applying it to polyatomic processes is thus problematic. In a recent paper, however, Czakó and Bowman propose to quantize the total vibrational energy instead of the vibrational actions [G. Czakó and J. M. Bowman, J. Chem. Phys. 131, 244302 (2009)], a procedure called 1GB here. The calculations are then only ∼10 times more time consuming than with the standard QCT method, allowing thereby for considerable numerical saving. In this paper, we propose some theoretical arguments supporting the 1GB procedure and check its validity on model test cases as well as the prototype four-atom reaction OH+D(2)→HOD+D.

The dynamics of the O(1D) + HCl --> OH + Cl reaction at a 0.26 eV collision energy: a comparison between theory and experiment

The dynamics of the O((1)D) + HCl(v = 0, j = 0) --> Cl + OH reaction at a 0.26 eV collision energy has been investigated by means of a quasiclassical trajectory (QCT) and statistical quantum and quasiclassical methods. State-resolved cross sections and Cl atom velocity distributions have been calculated on two different potential energy surfaces (PESs): the H2 surface (Martinez et al. Phys. Chem. Chem. Phys. 2000, 2, 589) and the latest surface by Peterson, Bowman, and co-workers (PSB2) (J. Chem. Phys. 2000, 113, 6186). The comparison with recent experimental results reveals that the PSB2 PES manages to describe correctly differential cross sections and the velocity distributions of the departing Cl atom. The calculations on the H2 PES seem to overestimate the OH scattering in the forward direction and the fraction of Cl at high recoil velocities. Although the comparison of the corresponding angular distributions is not bad, significant deviations with a statistical description are found, thus ruling out a complex-forming mechanism as the dominant reaction pathway. However, for the ClO + H product channel, the QCT and statistical predictions are found to be in good agreement.

State-to-state quantum dynamics of O + O2 isotope exchange reactions reveals nonstatistical behavior at atmospheric conditions

The O + O(2) exchange reaction is a prerequisite for the formation of ozone in Earth's atmosphere. We report here state-to-state differential and integral cross sections for several O + O(2) isotope-exchange reactions obtained by dynamically exact quantum scattering calculations at collision energies relevant to atmospheric conditions. These reactions are shown to be highly nonstatistical, evidenced by dominant forward scattering and deviation of the integral cross section from the statistical limit. Mechanistic analyses revealed that the nonstatistical channel is facilitated by short-lived osculating resonances. The theoretical results provided an in-depth interpretation of a recent molecular beam experiment of the exchange reaction and shed light on the initial step of ozone recombination.

Study of the H+O2 reaction by means of quantum mechanical and statistical approaches: the dynamics on two different potential energy surfaces

The possible existence of a complex-forming pathway for the H+O(2) reaction has been investigated by means of both quantum mechanical and statistical techniques. Reaction probabilities, integral cross sections, and differential cross sections have been obtained with a statistical quantum method and the mean potential phase space theory. The statistical predictions are compared to exact results calculated by means of time dependent wave packet methods and a previously reported time independent exact quantum mechanical approach using the double many-body expansion (DMBE IV) potential energy surface (PES) [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)] and the recently developed surface (denoted XXZLG) by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. The statistical approaches are found to reproduce only some of the exact total reaction probabilities for low total angular momenta obtained with the DMBE IV PES and some of the cross sections calculated at energy values close to the reaction threshold for the XXZLG surface. Serious discrepancies with the exact integral cross sections at higher energy put into question the possible statistical nature of the title reaction. However, at a collision energy of 1.6 eV, statistical rotationally resolved cross sections managed to reproduce the experimental cross sections for the H+O(2)(v=0,j=1)-->OH(v(')=1,j('))+O process reasonably well.

A comparative study of the Si+O(2)-->SiO+O reaction dynamics from quasiclassical trajectory and statistical based methods

The dynamics of the singlet channel of the Si+O(2)-->SiO+O reaction is investigated by means of quasiclassical trajectory (QCT) calculations and two statistical based methods, the statistical quantum method (SQM) and a semiclassical version of phase space theory (PST). The dynamics calculations have been performed on the ground (1)A(') potential energy surface of Dayou and Spielfiedel [J. Chem. Phys. 119, 4237 (2003)] for a wide range of collision energies (E(c)=5-400 meV) and initial O(2) rotational states (j=1-13). The overall dynamics is found to be highly sensitive to the selected initial conditions of the reaction, the increase in either the collisional energy or the O(2) rotational excitation giving rise to a continuous transition from a direct abstraction mechanism to an indirect insertion mechanism. The product state properties associated with a given collision energy of 135 meV and low rotational excitation of O(2) are found to be consistent with the inverted SiO vibrational state distribution observed in a recent experiment. The SQM and PST statistical approaches, especially designed to deal with complex-forming reactions, provide an accurate description of the QCT total integral cross sections and opacity functions for all cases studied. The ability of such statistical treatments in providing reliable product state properties for a reaction dominated by a competition between abstraction and insertion pathways is carefully examined, and it is shown that a valuable information can be extracted over a wide range of selected initial conditions.

On the dynamics of the H+ +D2(v=0,j=0)-->HD+D + reaction: a comparison between theory and experiment

The H+ +D2(v=0,j=0)-->HD+D + reaction has been theoretically investigated by means of a time independent exact quantum mechanical approach, a quantum wave packet calculation within an adiabatic centrifugal sudden approximation, a statistical quantum model, and a quasiclassical trajectory calculation. Besides reaction probabilities as a function of collision energy at different values of the total angular momentum, J, special emphasis has been made at two specific collision energies, 0.1 and 0.524 eV. The occurrence of distinctive dynamical behavior at these two energies is analyzed in some detail. An extensive comparison with previous experimental measurements on the Rydberg H atom with D2 molecules has been carried out at the higher collision energy. In particular, the present theoretical results have been employed to perform simulations of the experimental kinetic energy spectra.

Mean potential phase space theory of chemical reactions

A nonconventional application of phase space theory to the insertion reactions A+H(2), with A=C((1)D) and S((1)D), is presented. Instead of approximating the potential energies of interaction between separated fragments by their isotropic long-range contributions, as in the original theory, the latter are replaced by the accurate potential energies averaged with respect to Jacobi angles. The integral and differential cross sections obtained from this mean potential phase space theory (MPPST) turn out to be in very satisfying agreement with the benchmark predictions of the time-independent and time-dependent statistical quantum methods. The formal and numerical simplicity of MPPST with respect to any approach combining statistical assumptions and dynamical calculations makes it a promising tool for studying indirect polyatomic reactions.

A statistical quasiclassical trajectory model for atom-diatom insertion reactions

A statistical model based on the quasiclassical trajectory method is presented in this work for atom-diatom insertion reactions. The basic difference between this and the corresponding statistical quantum model (SQM) lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar. In particular, it is shown that conservation of parity can be taken into account in a natural and precise way in the statistical quasiclassical trajectory (SQCT) model. Additionally, the SQCT model complies with the principle of detailed balance and overcomes the problem of the zero point energy in the products. As a test, the model is applied to the H3+ and H+D2 exchange reactions. The excellent agreement between the SQCT and SQM results, especially in the case of the differential cross sections, indicates that the effect of tunneling through the centrifugal barrier is negligible. The effect of ignoring quantum mechanical parity conservation is also investigated.