Validity of Phase Space Theory for Atom−Diatom Insertion Reactions

Quantum and statistical state-to-state studies of cold Ar + H2+ collisions

In this work we present new state-to-state integral scattering cross sections and initial-state selected rate coefficients for the 36Ar (1S) + H2+ (X2Σg+,v = 0,j) reactive system for collision energies up to 0.1 eV (with respect to the 36Ar (1S) + H2+ (X2Σg+,v = 0,j = 0) channel). To the best of our knowledge, these cross sections are the first fully state resolved ones that were obtained by performing time-independent quantum mechanical and quantum statistical calculations. For this purpose a new full-dimensional ground state 2A' adiabatic electronic potential energy surface was calculated at the MRCI+Q/aug-cc-pVQZ level of theory, which was fitted by means of machine learning methods. We find that a statistical quantum method and a statistical adiabatic channel model reproduce quantum mechanical initial-state selected cross sections fairly well, thus suggesting that complex-forming mechanisms seem to be playing an important role in the reaction dynamics of the reaction that was studied.

Benchmarking an improved statistical adiabatic channel model for competing inelastic and reactive processes

Inelastic collisions and elementary chemical reactions proceeding through the formation and subsequent decay of an intermediate collision complex, with an associated deep well on the potential energy surface, pose a challenge for accurate fully quantum mechanical approaches, such as the close-coupling method. In this study, we report on the theoretical prediction of temperature-dependent state-to-state rate coefficients for these complex-mode processes, using a statistical quantum method. This statistical adiabatic channel model is benchmarked by a direct comparison using accurate rate coefficients from the literature for a number of systems (H₂ + H⁺, HD + H⁺, SH⁺ + H, and CH⁺ + H) of interest in astrochemistry and astrophysics. For all of the systems considered, an error of less than factor 2 was found, at least for the dominant transitions and at low temperatures, which is sufficiently accurate for applications in the above mentioned disciplines.

Signature of shape resonances on the differential cross sections of the S(1D)+H2 reaction

Shape resonances appear when the system is trapped in an internuclear potential well after tunneling through a barrier. They manifest as peaks in the collision energy dependence of the cross section (excitation function), and in many cases, their presence can be observed experimentally. High-resolution crossed-beam experiments on the S(¹D) + H₂(j = 0) reaction in the 0.81-8.5 meV collision energy range reaction revealed non-monotonic behavior and the presence of oscillations in the reaction cross section as a function of the collision energy, as predicted by quantum mechanical (QM) calculations. In this work, we have analyzed the effect of shape resonances on the differential cross sections for this insertion reaction by performing additional QM calculations. We have found that, in some cases, the resonance gives rise to a large enhancement of extreme backward scattering for specific final states. Our results also show that, in order to yield a significant change in the state-resolved differential cross section, the resonance has to be associated with constructive interference between groups of partial waves, which requires not getting blurred by the participation of many product helicity states.

Experimental and theoretical studies of the N(2D) + H2 and D2 reactions

This study reports the first kinetic measurements of the N(²D) + H₂, D₂ reactions below 200 K.

Experimental and Theoretical Study of the O(1D) + HD Reaction

This work addresses the kinetics and dynamics of the gas-phase reaction between O(¹D) and HD molecules down to low temperature. Here, measurements were performed by using a supersonic flow (Laval nozzle) reactor coupled with pulsed laser photolysis for O(¹D) production and pulsed-laser-induced fluorescence for O(¹D) detection to obtain rate constants over the 50-300 K range. Additionally, temperature-dependent branching ratios (OD + H/OH + D) were obtained experimentally by comparison of the H/D atom atom yields with those of a reference reaction. In parallel, theoretical rate constants and branching ratios were calculated by using three different techniques; mean potential phase space theory (MPPST), the statistical quantum mechanical method (SQM), and ring polymer molecular dynamics (RPMD). Although the agreement between experimental and theoretical rate constants is reasonably good, with differences not exceeding 30% over the entire temperature range, the theoretical branching ratios derived by the MPPST and SQM methods are as much as 50% larger than the experimental ones. These results are presented in the context of earlier work, while the possible origins of the discrepancies between experiment and theory are discussed.

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.

A combined theoretical and experimental investigation of the kinetics and dynamics of the O(1D) + D2 reaction at low temperature

The O(¹D) + H₂ reaction is a prototype for simple atom-diatom insertion type mechanisms considered to involve deep potential wells. While exact quantum mechanical methods can be applied to describe the dynamics, such calculations are challenging given the numerous bound quantum states involved. Consequently, efforts have been made to develop alternative theoretical strategies to portray accurately the reactive process. Here we report an experimental and theoretical investigation of the O(¹D) + D₂ reaction over the 50-296 K range. The calculations employ three conceptually different approaches - mean potential phase space theory, the statistical quantum mechanical method and ring polymer molecular dynamics. The calculated rate constants are in excellent agreement over the entire temperature range, exhibiting only weak temperature dependence. The agreement between experiment and theory is also very good, with discrepancies smaller than 26%. Taken together, the present and previous theoretical results validate the hypothesis that long-lived complex formation dominates the reaction dynamics at low temperature.

Dynamics and resonances of the H(2S) + CH+(X1Σ+) reaction in the electronic ground state: a detailed quantum wavepacket study

Initial state-selected and energy resolved channel-specific reaction probabilities, integral cross sections and thermal rate constants of the H(²S) + CH⁺(X¹Σ⁺) reaction are calculated within the coupled states approximation by a time-dependent wave packet propagation method. The new ab initio global potential energy surface (PES) of the electronic ground state (1 ²A') of the system, recently reported by Li et al. [J. Chem. Phys., 2015, 142, 124302], is employed for this purpose. All partial wave contributions up to the total angular momentum J = 60 are considered to obtain the converged integral reaction cross section up to a collision energy of 1.0 eV. Thermal rate constants are calculated by averaging the reaction cross sections over the Boltzmann distribution of energies and compared with the available theoretical and experimental results for the temperature range 10-1000 K. Investigation of the channel-specific reaction attributes shows that the H abstraction (CH⁺ destruction) channel is highly favored over the H exchange channel. The effect of rotational and vibrational excitations of the CH⁺ reagent on the dynamics is also studied. The resonances formed during the course of the reaction are also identified by calculating the transition state spectrum and characterized in terms of the eigenfunctions and lifetimes. More than 260 vibrational levels are obtained and their eigenfunctions are calculated, which are represented in terms of the nodal assignments and the eigenenergies. They reveal both the local and hyperspherical behavior for the bound and quasibound states of the CH₂⁺ complex in the ground 1 ²A' surface. The lifetime analysis of the quasibound states indicates that the CH₂⁺ resonances survive for as long as ∼400 fs at high energies (E ∼ 2.0 eV) and are expected to decay faster with further increasing energy. Finally, the type of mechanism for the formation of the product (C⁺ + H₂) is elucidated.

An Empirical Dynamical Barrier for Statistical Theory of Low-Energy Reactive S(1D) + HD(j = 0), H2(j = 0) Collisions

A simple model potential is proposed to describe the dynamical barrier in the mean interaction potential at small distances between the reactants in S(¹D) + HD(¹Σ, v = 0, j = 0) reaction. The statistical theory of collision complex formation and complex decay is applied to calculate the total reaction cross sections and the cross sections for SH and SD productions in the range of low collision energies E_c = (0.4-60) meV. The results are compared with measured cross sections and results of hyperspherical close coupling calculations. As a check of consistency the same comparisons are presented for the case of S(¹D) + H₂(¹Σ, v = 0, j = 0) reaction.

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.

Capture and dissociation in the complex-forming CH + H2 → CH2 + H, CH + H2 reactions

The rate coefficients for the capture process CH + H(2)→ CH(3) and the reactions CH + H(2)→ CH(2) + H (abstraction), CH + H(2) (exchange) have been calculated in the 200-800 K temperature range, using the quasiclassical trajectory (QCT) method and the most recent global potential energy surface. The reactions, which are of interest in combustion and in astrochemistry, proceed via the formation of long-lived CH(3) collision complexes, and the three H atoms become equivalent. QCT rate coefficients for capture are in quite good agreement with experiments. However, an important zero point energy (ZPE) leakage problem occurs in the QCT calculations for the abstraction, exchange and inelastic exit channels. To account for this issue, a pragmatic but accurate approach has been applied, leading to a good agreement with experimental abstraction rate coefficients. Exchange rate coefficients have also been calculated using this approach. Finally, calculations employing QCT capture/phase space theory (PST) models have been carried out, leading to similar values for the abstraction rate coefficients as the QCT and previous quantum mechanical capture/PST methods. This suggests that QCT capture/PST models are a good alternative to the QCT method for this and similar systems.

Kinetic energy spectra in thermionic emission from small tungsten cluster anions: evidence for nonclassical electron capture

The delayed electron emission from small mass-selected anionic tungsten clusters W(n)(-) has been studied for sizes in the range 9 < or = n < or = 21. Kinetic energy spectra have been measured for delays of about 100 ns after laser excitation by a velocity-map imaging spectrometer. They are analyzed in the framework of microreversible statistical theories. The low-energy behavior shows some significant deviations with respect to the classical Langevin capture model, which we interpret as possibly due to the influence of quantum dynamical effects such as tunneling through the centrifugal barrier, rather than shape effects. The cluster temperature has been extracted from both the experimental kinetic energy spectrum and the absolute decay rate. Discrepancies between the two approaches suggest that the sticking probability can be as low as a few percent for the smallest clusters.

Phase space theory of evaporation in neon clusters: the role of quantum effects

Unimolecular evaporation of neon clusters containing between 14 and 148 atoms is theoretically investigated in the framework of phase space theory. Quantum effects are incorporated in the vibrational densities of states, which include both zero-point and anharmonic contributions, and in the possible tunneling through the centrifugal barrier. The evaporation rates, kinetic energy released, and product angular momentum are calculated as a function of excess energy or temperature in the parent cluster and compared to the classical results. Quantum fluctuations are found to generally increase both the kinetic energy released and the angular momentum of the product, but the effects on the rate constants depend nontrivially on the excess energy. These results are interpreted as due to the very few vibrational states available in the product cluster when described quantum mechanically. Because delocalization also leads to much narrower thermal energy distributions, the variations of evaporation observables as a function of canonical temperature appear much less marked than in the microcanonical ensemble. While quantum effects tend to smooth the caloric curve in the product cluster, the melting phase change clearly keeps a signature on these observables. The microcanonical temperature extracted from fitting the kinetic energy released distribution using an improved Arrhenius form further suggests a backbending in the quantum Ne(13) cluster that is absent in the classical system. Finally, in contrast to delocalization effects, quantum tunneling through the centrifugal barrier does not play any appreciable role on the evaporation kinetics of these rather heavy clusters.

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.

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.

Time dependent wave packet and statistical calculations on the H + O(2) reaction

The H + O(2)--> OH + O reaction has been theoretically investigated by means of an exact time dependent wave packet method and two statistical approaches: a recently developed statistical quantum model and phase-space theory. The exhaustive analysis of reaction probabilities at a zero total angular momentum would, in principle, reveal the existence of a complex-forming mechanism at low collision energies (E(c) = 1.15 eV), whereas deviations from a statistical behaviour at higher energies may be interpreted as the onset of a direct abstraction pathway which favours the production of highly excited rotational states of the OH fragment in its ground vibrational state. The good description by statistical means of previously measured product rotational distributions and excitation functions seems to support such an interpretation. However the statistical predictions clearly overestimate both existing and present exact quantum mechanical reaction probabilities and total cross sections, thereby precluding to conclude definitely the statistical nature of the collision. The exact time dependent method yields values of the integral cross sections in agreement with results by Goldfield and Meijer, and below the experimental findings.

On the theory of complex-forming chemical reactions: effect of parity conservation on the polarization of differential cross sections

For complex-forming triatomic reactions such as the prototypical insertion reactions intensively studied in the last few years, quantum mechanical differential cross sections (DCS) present sharp forward/backward polarization peaks when the reagent rotational angular momentum quantum number j is zero. Moreover, the size of the peaks decreases rapidly with increasing j values so that for j = 3, they are no longer visible. In contrast, the polarization peaks are always missing in the classical mechanical DCSs. Apart from the peaks, however, the quantum and classical DCSs are usually in good agreement. In a recent rapid communication, we showed that the fundamental reason for the previous differences in the quantum and classical scenarios is that parity conservation leads in quantum mechanics to an angular momentum constraint without equivalent in classical mechanics. We also proposed a parity-restoring approximation leading to an accurate semi-classical description of the peaks. While only the main lines of the demonstration were given in the communication, we report here the whole developments. We also analyse why the peaks disappear when the reagent diatom is rotationally excited. As a by-product of the previous developments, we finally discuss the possibility of a general statistico-dynamical semiclassical approach.

Cross sections and low temperature rate coefficients for the H + CH+reaction: a quasiclassical trajectory study

The H + CH(+) reaction is studied by quasiclassical trajectory (QCT) calculations, along with phase space theory (PST) and quantum rigid rotor calculations, employing a global single-valued potential energy surface recently derived by our group. We report QCT total cross sections for each of the three channels, for low collision energies and different reactant rotational quantum numbers. At the lowest collision energies, all cross sections exhibit a capture-like behaviour, as expected from a barrierless reaction. At higher energies, there are important dynamical effects coming from the opening of new channels in the inelastic and reactive exchange collisions. The inelastic cross sections turn out to largely increase, while the reactive abstraction cross sections are declining faster than predicted by the capture theory. A large value of the reactant rotational quantum number tends to suppress these dynamical effects. The QCT rate coefficients are reported for a temperature range from 1-700 K. Below 20 K, the abstraction and exchange QCT rate coefficients are almost constant, as predicted by the capture theory. Above this temperature, the abstraction rate coefficient declines, while the exchange and inelastic rate coefficients are increasing, due to the opening of new channels. A good agreement is observed between the experimental abstraction rate coefficient and the QCT and PST ones. The QCT inelastic results are also compared with those obtained from rigid rotor close coupling (CCRR) calculations in order to check the ability of this approach to provide a reliable estimate of the inelastic rate coefficients for a reactive system without a barrier. The laws of variation as a function of temperature are found to be very similar and the curves are parallel above 20 K. However, reaction is not allowed in the rigid rotor approximation, therefore the CCRR results are about twice as large as their QCT counterparts.

A detailed quantum mechanical and quasiclassical trajectory study on the dynamics of the H++H2→H2+H+ exchange reaction

The H+ + H2 exchange reaction has been studied theoretically by means of a different variety of methods as an exact time independent quantum mechanical, approximate quantum wave packet, statistical quantum, and quasiclassical trajectory approaches. Total and state-to-state reaction probabilities in terms of the collision energy for different values of the total angular momentum obtained with these methods are compared. The dynamics of the reaction is extensively studied at the collision energy of E(coll)=0.44 eV. Integral and differential cross sections and opacity functions at this collision energy have been calculated. In particular, the fairly good description of the exact quantum results provided by the statistical quantum method suggests that the dynamics of the process is governed by an insertion mechanism with the formation of a long-lived collision complex.

Parity conservation and polarization of differential cross sections in complex-forming chemical reactions

For complex-forming chemical reactions, such as atom-diatom insertion reactions, quantum scattering and quantum statistical calculations usually predict sharp forward/backward peaks in the Differential Cross Sections (DCS). Conversely, the corresponding classical calculations are unable to reproduce these peaks. We show here that the basic reason for such an intriguing failure is that parity conservation is ignored in classical mechanics. A by-product of the analysis is a simple parity-restoring approximation that might significantly increase the ability of classical mechanics to describe DCSs over the whole angular range for the title processes.