Quasiclassical determination of reaction probabilities as a function of the total angular momentum

Quantum and Classical Dynamics of the N(2D) + N2 Reaction on Its Ground Doublet State N3(12A″) Potential Energy Surface

The initial state-selected dynamics of the N(²D) + N₂(X¹∑) → N₂(X¹∑) + N(²D) exchange reaction on its electronic ground doublet state N₃(1²A″) potential energy surface (PES) has been studied here by time-dependent quantum mechanics (TDQM) and quasi-classical trajectory (QCT) methods. Dynamical attributes such as total reaction probabilities, state-selected integral cross sections, and initial state-selected rate constants have been calculated. The presence of metastable quasi-bound complexes in the collision process is confirmed by substantial oscillatory structures in the reaction probability curves. Also, rotational excitations of reagent N₂ on the reactivity have been examined by calculating the probabilities for the two-body rotational angular momentum up to j = 10. We conclude that the reagent rotational excitation increases the reactivity. The TDQM results are compared with QCT results.

Reactive, Inelastic, and Dissociation Processes in Collisions of Atomic Nitrogen with Molecular Oxygen

Collisions of atomic nitrogen with molecular oxygen have been treated with the quasiclassical trajectory method (QCT) in order to obtain a complete database of vibrationally detailed cross sections and rate coefficients for reactive, inelastic, and dissociation processes. For reaction rate coefficients, the agreement with experimental and theoretical data in the literature is excellent on the whole available interval 300-5000 K, with reliable extension to 20,000 K. For the inelastic case and for dissociation, no comparisons are available; therefore, a study of QCT reliability is proposed. In the inelastic case, it is found that "purely inelastic" and "quasireactive" collisions show not only different mechanisms but also different QCT levels of reliability at low energy. For dissociation, similar considerations bring to the conclusion that for the present collisional system, the QCT method is appropriate on the whole energy range studied. Rate coefficients for all the processes studied are provided in the electronic form.

The F + HD(v = 0, 1; j = 0, 1) reactions: stereodynamical properties of orbiting resonances

The excitation functions (reaction cross-section as a function of collision energy) of the F + HD(v = 0, 1; j = 0, 1) benchmark system have been calculated in the 0.01-6 meV collision energy interval using a time-independent hyperspherical quantum dynamics methodology. Special attention has been paid to orbiting resonances, which bring about detailed information on the three-atom interaction during the reactive encounter. The location of the resonances depends on the rovibrational state of the reactants HD(v,j), but is the same for the two product channels HF + D and DF + H, as expected for these resonances that are linked to the van der Waals well at the entrance. The resonance intensities depend both on the entrance and on the exit channels. The peak intensities for the HF + D channel are systematically larger than those for DF + H. Vibrational excitation leads to an increase of the peak intensity by more than an order of magnitude, but rotational excitation has a less drastic effect. It deceases the resonance intensity of the F + HD(v = 1) reaction, but increases somewhat that of F + HD(v = 0). Polarization of the rotational angular momentum with respect to the initial velocity reveals intrinsic directional preferences in the F + HD(v = 0, 1; j = 1) reactions that are manifested in the resonance patterns. The helicities (Ω = 0, Ω = ±1) possible for j = 1 contribute to the resonances, but that from Ω± 1 is, in general, dominant and in some cases exclusive. It corresponds to a preferential alignment of the HD internuclear axis perpendicular to the initial direction of approach and, thus, to side-on collisions. This work also shows that external preparation of the reactants, following the intrinsic preferences, would allow the enhancement or reduction of specific resonance features, and would be of great help for their eventual experimental detection.

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.

Angular momentum-scattering angle quantum correlation: a generalized deflection function

A natural generalization of the classical deflection function, the functional dependence of the deflection angle on the angular momentum (or the impact parameter), is the joint probability density function of these two quantities, revealing the correlation between them. It provides, at a glance, detailed information about the reaction mechanisms and how changes in the impact parameter affect the product angular distribution. It is also useful to predict the presence of quantum phenomena such as interference. However, the classical angular momentum-scattering angle correlation function has a limited use whenever quantum effects become important. Rigorously speaking, there is not a quantum equivalent of the classical joint distribution, as the differential cross section depends on the coherences between the different values of J caused by the cross terms in the expansion of partial waves. In this article, we present a simple method to calculate a quantum analog of this correlation, a generalized deflection function that can shed light onto the reaction mechanism using just quantum mechanical results. Our results show that there is a very good agreement between the quantum and classical correlation functions as long as quantum effects are not all relevant. When this is not the case, it will also be shown that the quantum correlation function is most useful to observe the extent of quantum effects such as interference among different reaction mechanisms.

Time-Dependent Quantum Wave Packet Study of the Si + OH → SiO + H Reaction: Cross Sections and Rate Constants

The dynamics of the Si(³P) + OH(X²Π) → SiO(X¹Σ⁺) + H(²S) reaction is investigated by means of the time-dependent wave packet (TDWP) approach using an ab initio potential energy surface recently developed by Dayou et al. ( J. Chem. Phys. 2013 , 139 , 204305 ) for the ground X²A' electronic state. Total reaction probabilities have been calculated for the first 15 rotational states j = 0-14 of OH(v=0,j) at a total angular momentum J = 0 up to a collision energy of 1 eV. Integral cross sections and state-selected rate constants for the temperature range 10-500 K were obtained within the J-shifting approximation. The reaction probabilities display highly oscillatory structures indicating the contribution of long-lived quasibound states supported by the deep SiOH/HSiO wells. The cross sections behave with collision energies as expected for a barrierless reaction and are slightly sensitive to the initial rotational excitation of OH. The thermal rate constants show a marked temperature dependence below 200 K with a maximum value around 15 K. The TDWP results globally agree with the results of earlier quasi-classical trajectory (QCT) calculations carried out by Rivero-Santamaria et al. ( Chem. Phys. Lett. 2014 , 610-611 , 335 - 340 ) with the same potential energy surface. In particular, the thermal rate constants display a similar temperature dependence, with TDWP values smaller than the QCT ones over the whole temperature range.

Globally accurate potential energy surface for the ground-state HCS(X2A') and its use in reaction dynamics

A globally accurate many-body expansion potential energy surface is reported for HCS(X²A') by fitting a wealth of accurate ab initio energies calculated at the multireference configuration interaction level using aug-cc-pVQZ and aug-cc-pV5Z basis sets via extrapolation to the complete basis set limit. The topographical features of the present potential energy surface are examined in detail and is in good agreement with the raw ab initio results, as well as other theoretical results available in literatures. By utilizing the potential energy surface of HCS(X²A'), the dynamic studies of the C(³P) + SH(X²Π) → H(²S) + CS(X¹∑⁺) reaction has been carried out using quasi-classical trajectory method.

State-to-State Dynamics of the Ne + HeH(+) (v = 0, j = 0) → NeH(+)(v', j') + He Reaction

The dynamics of the Ne + HeH(+)(v = 0, j = 0) → NeH(+)(v', j') + He reaction was analyzed in detail at the state-to-state level. A time-independent quantum mechanical (TIQM) method was applied to calculate rovibrational distributions and differential cross sections (DCSs), in comparison with quasi-classical trajectory and statistical quantum predictions. Possible changes in the dynamical mechanisms that define the process were also investigated as a function of the collision energy. At the lowest energy regime, the TIQM results produce a noticeably different cross section in comparison with previously reported time-dependent wave packet results. Although the statistical methods reproduce some dynamical features, especially as the energy increases, the marked preference for the forward scattering direction on the DCSs suggests that the reaction mainly follows a direct mechanism.

Effects of reagent rotation on interferences in the product angular distributions of chemical reactions

Differential cross sections (DSCs) of the HD(v', j') product for the reaction of H atoms with supersonically cooled D2 molecules in a small number of initial rotational states have been measured at a collision energy of 1.97 eV. These DCSs show an oscillatory pattern that results from interferences caused by different dynamical scattering mechanisms leading to products scattered into the same solid angle. The interferences depend on the initial rotational state j of the D2(v = 0, j) reagent and diminish in strength with increasing rotation. We present here a detailed explanation for this behavior and how each dynamical scattering mechanism has a dependence on the helicity Ω, the projection of the initial rotational angular momentum j of the D2 reagent on the approach direction. Each helicity corresponds to a different internuclear axis distribution, with the consequence that the dependence on Ω reveals the preference of the different quasiclassical mechanisms as a function of approach direction. We believe that these results are general and will appear in any reaction for which several mechanisms are operative.

Influence of the Reactants Rotational Excitation on the H + D2(v = 0, j) Reactivity

We have analyzed the influence of the rotational excitation on the H + D2(v = 0, j) reaction through quantum mechanical (QM) and quasiclassical trajectories (QCT) calculations at a wide range of total energies. The agreement between both types of calculations is excellent. We have found that the rotational excitation largely increases the reactivity at large values of the total energy. Such an increase cannot be attributed to a stereodynamical effect but to the existence of recrossing trajectories that become reactive as the target molecule gets rotationally excited. At low total energies, however, recrossing is not significant and the reactivity evolution is dominated by changes in the collision energy; the reactivity decreases with the collision energy as it shrinks the acceptance cone. When state-to-state results are considered, rotational excitation leads to cold product's rovibrational distributions, so that most of the energy is released as recoil energy.

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.

Quantum, Statistical, and Quasiclassical Trajectory Studies For the Ne + HeH(+) → NeH(+) + He Reaction on the Ground Electronic State

Real wave packet, statistical quantum, and quasiclassical trajectory methods were employed to study the dynamics of Ne + HeH(+)(v0,j0) → He + NeH(+) reaction on an ab initio potential energy surface [J. Phys. Chem. A 2013, 117, 13070-13078]. Quantum and statistical quantum calculations were performed within the centrifugal sudden (CS) approximation as well as including the Coriolis coupling (CC). Dense oscillatory structures of the quantum reaction probabilities and fair agreement between quantum and statistical cross sections suggest a complex forming mechanism for the reaction. No significant differences between cross sections obtained within the CS and CC approaches are observed. Quasiclassical trajectory results give an excellent average description of the quantum CC results. At low collision energies, there is a substantial decrease in reactivity for the reaction upon rovibrational excitation. Initial state selected rate constants for the title reaction are calculated between 20 and 1000 K, and the calculated value at 300 K agrees quite well with the available experimental result. Reaction cross sections and rate constants are also compared with those calculated via the Langevin capture model for exothermic reactions.

Rate coefficients from quantum and quasi-classical cumulative reaction probabilities for the S(1D) + H2 reaction

Cumulative reaction probabilities (CRPs) at various total angular momenta have been calculated for the barrierless reaction S((1)D) + H(2) → SH + H at total energies up to 1.2 eV using three different theoretical approaches: time-independent quantum mechanics (QM), quasiclassical trajectories (QCT), and statistical quasiclassical trajectories (SQCT). The calculations have been carried out on the widely used potential energy surface (PES) by Ho et al. [J. Chem. Phys. 116, 4124 (2002)] as well as on the recent PES developed by Song et al. [J. Phys. Chem. A 113, 9213 (2009)]. The results show that the differences between these two PES are relatively minor and mostly related to the different topologies of the well. In addition, the agreement between the three theoretical methodologies is good, even for the highest total angular momenta and energies. In particular, the good accordance between the CRPs obtained with dynamical methods (QM and QCT) and the statistical model (SQCT) indicates that the reaction can be considered statistical in the whole range of energies in contrast with the findings for other prototypical barrierless reactions. In addition, total CRPs and rate coefficients in the range of 20-1000 K have been calculated using the QCT and SQCT methods and have been found somewhat smaller than the experimental total removal rates of S((1)D).

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.

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.

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.

Constraints at the transition state of the D + H2 reaction: quantum bottlenecks vs. stereodynamics

This article presents a quasiclassical trajectory method for the calculation of cumulative reaction probabilities by sampling of the helicity quantum number of the reagents (k). The method is applied to the D + H(2) reaction at various total angular momentum (J) values, and the helicity-resolved quasiclassical cumulative reaction probabilities are compared to their quantum mechanical counterparts. The agreement between the two sets of results is fairly good. In particular, k-dependent, J-independent reaction thresholds found with quantum methods are reproduced by the quasiclassical calculations. The shift of these thresholds with increasing k, which has been previously attributed to the quantum bottleneck states taking part in the reaction, is revisited and discussed also in terms of the reaction stereodynamics.

Cumulative reaction probabilities: A comparison between quasiclassical and quantum mechanical results

This article presents a quasiclassical trajectory (QCT) method for determining the cumulative reaction probability (CRP) as a function of the total energy. The method proposed is based on a discrete sampling using integer values of the total and orbital angular momentum quantum numbers for each trajectory and on the development of equations that have a clear counterpart in the quantum mechanical (QM) case. The calculations comprise cumulative reaction probabilities at a given total angular momentum J, as well as those summed over J. The latter are used to compute QCT rate constants. The method is illustrated by comparing QCT and exact QM results for the H+H2, H+D2, D+H2, and H+HD reactions. The agreement between QCT and QM results is very good, with small discrepancies between the two data sets indicating some genuine quantum effects. The most important of these involves the value of the CRP at low energies which, due to the absence of tunneling, is lower in the QCT calculations, causing the corresponding rate constants to be smaller. The second is the steplike structure that is clearly displayed in the QM CRP for J = 0, which is much smoother in the corresponding QCT results. However, when the QCT density of reactive states, i.e., the derivatives of the QCT CRP with respect to the energy, is calculated, a succession of maxima and minima is obtained which roughly resembles those found in the QM calculations, although the latter are considerably sharper. The analysis of the broad peaks in the QCT density of reactive states indicates that the distributions of collision times associated with the maxima are somewhat broader, with a tail extending to larger collision times, than those associated with the minima. In addition, the QM and QCT dynamics of the isotopic variants mentioned above are compared in the light of their CRPs. Issues such as the compliance of the QCT CRP with the law of microscopic reversibility, as well as the similarity between the CRPs for ortho and para species in the QM and QCT cases, are also addressed.

Local angular momentum-local impact parameter analysis: derivation and properties of the fundamental identity, with applications to the F+H2, H+D2, and Cl+HCl chemical reactions

The technique of local angular momentum-local impact parameter (LAM-LIP) analysis has recently been shown to provide valuable dynamical information on the angular scattering of chemical reactions under semiclassical conditions. The LAM-LIP technique exploits a nearside-farside (NF) decomposition of the scattering amplitude, which is assumed to be a Legendre partial wave series. In this paper, we derive the "fundamental NF LAM identity," which relates the full LAM to the NF LAMs (there is a similar identity for the LIP case). Two derivations are presented. The first uses complex variable techniques, while the second exploits an analogy between the motion of the scattering amplitude in the Argand plane with changing angle and the classical mechanical motion of a particle in a plane with changing time. Alternative forms of the fundamental LAM-LIP identity are described, one of which gives rise to a CLAM-CLIP plot, where CLAM denotes (Cross section) x LAM and CLIP denotes (Cross section) x LIP. Applications of the NF LAM theory, together with CLAM plots, are reported for state-to-state transitions of the benchmark reactions F+H2-->FH+H, H+D2-->HD+D, and Cl+HCl-->ClH+Cl, using as input both numerical and parametrized scattering matrix elements. We use the fundamental LAM identity to explain the important empirical observation that a NF cross section analysis and a NF LAM analysis provide consistent (and complementary) information on the dynamics of chemical reactions.

Mechanism and control of the F+H2 reaction at low and ultralow collision energies

This article uses theoretical methods to study the dependence on stereodynamical factors of the mechanism and reactivity of the F+H2 reaction at low and ultralow collision energies. The impact of polarization of the H2 reactant on total and state-to-state integral and differential cross sections is analyzed. This leads to detailed pictures of the reaction mechanism in the cold and ultracold regimes, accounting, in particular, for distinctions associated with the various product states and scattering angles. The extent to which selection of reactant polarization allows for external control of the reactivity and reaction mechanism is assessed. This reveals that even the simplest of reactant polarization schemes allows for fine, product state-selective control of differential and (for reactions involving more than a single, zero orbital angular momentum partial wave) integral cross sections.

Analysis of the H + D2reaction mechanism through consideration of the intrinsic reactant polarisation

The effect of reactant polarisation on the dynamics of the title reaction at collision energies up to 1.6 eV is analysed in depth. The analysis takes advantage of two novel theoretical concepts: intrinsic reaction properties and stereodynamical portraits. Exact quantum methods are used to determine the polarisation moments that quantify the intrinsic reactant polarisation at various levels of detail, including or not product state and/or scattering angle resolution. The data is then examined with the aid of stereodynamical portraits, which facilitate the rationalisation of the stereochemical effects that are relevant for the reaction dynamics. This allows for detailed characterisations of the so-called direct and delayed reaction mechanisms.