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We have characterized the stereodynamics of the H + LiH (v = 0, j = 0–1) reactive collisions leading to H2 formation through the quantum mechanical analysis of the k–j and k′–j′ vector correlations that describe the polarization of the reactants and products, respectively. Our results, which cover the collision energy interval between 10–4 and 1 eV, are unexpectedly complex given the apparent simplicity and featureless nature of the potential energy surface for the LiH2 system and point toward the existence of a dynamical barrier connected to the centrifugal barrier. Both reactants and products, in particular the second ones, display strong directional preferences in the cold region that indicate a bias for collinear approaching and departing geometries and are independent of the final state of the products. As more energy is available for the reaction, the polarization of reactants and products becomes weaker and strongly dependent on the final state. While stereodynamical control is feasible and signifi...

The dynamics of inelastic collisions between HF and H has been investigated in detail by means of time-independent quantum mechanical calculations on the LWA-78 potential energy surface ( Li , G. ; et al. J. Chem. Phys. 2007 , 127 , 174302 ). Reaction probabilities, differential cross sections, and three-vector correlations have been calculated and analyzed. Our results show that there are two competing collision mechanisms that correlate with low and high impact parameters and show very different stereodynamical preferences. The mechanism promoted by high impact parameters is the only one present at low collision energies. We also observe the presence of an apparent threshold in the inelastic cross section for relatively high initial HF rotational quantum numbers, which is associated with the larger energy difference between adjacent rotational quantum states with increasing rotation.

10 págs.; 10 figs.; 1 tab.; Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics, We have analyzed the influence of the rotational excitation on the H + D(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 products rovibrational distributions, so that most of the energy is released as recoil energy., The authors acknowledge funding by the Spanish Ministry of Science and Innovation (grant Consolider Ingenio 2010 CSD2009-00038). J.A., F.J.A. and P.G.J. acknowledge also funding by the Spanish Ministry of Economy and Competitiveness (grant CTQ2012-37404-C02), and V.J.H. acknowledges additional funding by the Spanish Ministry of Science and Innovation (FIS2013-48087-C2-1P) and by the European Research Council (ERC-2013-Syg-610256).

Within the framework of molecular quantum electrodynamics, response theory is employed to derive an expression for the retarded dispersion potential among N atoms or molecules each with arbitrary electric multipole polarisability. This approach first entails the evaluation of the electric displacement field due to all of the sources by solving Maxwell's equations. The dispersion energy shift is then given by taking the expectation value over the ground state of the total matter plus field system of the response of each body in turn through its generalised polarisability to the electric field due to the remaining N–1 bodies. It is shown how the general formula reduces to previously obtained results for the interaction of three electric dipole polarisable molecules, and for the energy shift between two or three species with arbitrary electric multipole polarisability characteristics.

Time-independent quantum mechanical calculations have been performed in order to characterize the dynamics and stereodynamics of Cl + HD reactive collisions. Calculations have been carried out at two different total energy values and for various initial states using the adiabatic potential energy surface by Bian and Werner [J. Chem. Phys. 2000, 112, 220]. Special attention has been paid to the reaction with HD(v = 1) for which integral and differential cross-sections have been calculated and the effect of vibrational vs translational energy on the reactivity has been examined. In addition, the reactant polarization parameters and polarization-dependent differential cross-sections have been determined. From these results, the spatial preferences of the reaction and the extent of the control of the cross sections achievable through a suitable preparation of the reactants have been also studied. The directional requirements are tighter for the HCl channel than for the DCl one. Formation of the products takes place preferentially when the rotational angular momentum of the HD molecule is perpendicular to the reactants approach direction. Cross-sections and polarization moments computed from the scattering calculations have been compared with experimental results by Kandel et al. [J. Chem. Phys. 2000, 112, 670] for the reaction with HD(v = 1) produced by stimulated Raman pumping. The agreement so obtained is good, and it improves the accordance found in previous calculations with other methodologies and potential energy surfaces.

Both experiment and theory recently showed that the H + D2(v = 0, j = 0) → HD(v' = 4, j') + D reactions at a collision energy of 1.97 eV display a seemingly anomalous HD product angular distribution that moves in the backward direction as the value of j' increases and the corresponding energy available for product recoil decreases. This behavior was attributed to the presence of a centrifugal barrier along the reaction path. Here, we show, using fully quantum mechanical calculations, that for low recoil energies, the collision mechanism is nearly independent of the HD internal state and the HD product becomes aligned, with its rotational angular momentum j' pointing perpendicular to the recoil momentum k'. As the kinetic energy to overcome this barrier becomes limited, the three atoms adopt a nearly collinear configuration in the transition-state region to permit reaction, which strongly polarizes the resulting HD product. These results are expected to be general for any chemical reaction in the low recoil energy limit.

This article raises and answers a question regarding the extent to which correlation between the angular momentum polarizations of reagents and products of a bimolecular collision is or is not uniform. The question is this: how markedly does product (j′) polarization change when reagent (j) polarization is changed? Using canonical collision mechanisms theory, and the operator-trigonometric concepts of maximal turning angle, antieigenvalue, and antieigenvector, the authors arrive at the following answer: barring complete or nearly complete insensitivity of the collision to steric effects, one should expect a high degree of nonuniformity in two-, three- or four-vector correlations involving j and j′.

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.

This article presents theoretical methods for the description of the directional effect of reactant rotation on the reactivity of atom-diatom systems and suggests an experiment that could be used to test theoretical predictions. The theory can be used in conjunction with both quantum reactive scattering and quasiclassical trajectory calculations, and is stated in general terms, which allows it to deal with arbitrary reactant polarizations. The illustrative results obtained for the benchmark H + D 2 reaction are also presented and show that under experimentally achievable conditions one can largely control reactive cross sections and product state distributions, while at the same time gaining valuable and at times surprising information on the reaction mechanism.

We have performed a dynamical study of the endothermic and barrierless C(+) + H2((1)Σg(+)) → CH(+)((1)Σg(+)) + H reaction for different initial rotational states of the H2(v = 0) and H2(v = 1) manifolds. The calculations have been carried out using quasiclassical trajectories and the Gaussian binning methodology on a recent potential energy surface [R. Warmbier and R. Schneider, Phys. Chem. Chem. Phys., 2011, 13, 10285]. Both state-selected integral cross sections as a function of the collision energy and rate coefficients, kv,j(T), have been determined. We show that rotational excitation of the reactants is as effective as vibrational excitation when it comes to increasing the reactivity, and that both types of excitation could contribute to explain the unexpectedly high abundance of CH(+) in the interstellar media. Such an increase in reactivity takes place by suppressing the reaction threshold when the internal energy is sufficient to overcome the endothermicity. Whenever this is the case, the excitation functions at collision energies Ecoll ≤ 0.1 eV display a ∝E(-1/2)coll dependence. However, the absolute values of the state selected kv=1(T) are one order of magnitude below the Langevin model predictions. The disagreement between the approximately derived experimental rate coefficients for v = 1 and those calculated by this and previous theoretical treatments is due to the neglect of the effect of the rotational excitation in the derivation of the former. In spite of the deep well present in the potential energy surface, the reaction does not show a statistical behaviour.

The dynamics of the asymmetric D + MuH (Mu = Muonium) reaction leading to Mu exchange, DMu + H, and H abstraction, DH + Mu, channels has been investigated using time-independent quantum mechanical (QM) calculations. Reaction probabilities, cross sections, cumulative reaction probabilities, and rate coefficients were determined for the two exit channels of the reaction. Quasiclassical trajectory (QCT) calculations were also performed in order to check the reliability of the method for this reaction and to discern the genuine quantum effects. Overall, the Mu exchange channel exhibits more structured reaction probabilities and cross sections with much larger rate coefficients than the H abstraction counterpart. Over the 100-1000 K temperature interval considered in this study, the QM rate coefficients for the Mu exchange vary between ≈5 × 10-15 and 2 × 10-11 cm 3 s-1 and those for the generation of DH + Mu between 2 × 10-18 and 3.5 × 10-12 cm3 s -1. In common with the rest of the isotopologues of the H + H 2 system, the height of the respective barriers in the collinear (symmetric stretch) vibrationally adiabatic potential energy curves matches the classical total energy threshold very accurately. Indeed, the lower and narrower vibrationally adiabatic collinear barrier as compared with that for the DH + Mu formation determines the preponderance of the DMu + H channel. Comparison of QM and QCT results and their analysis show that tunneling accounts for the reactivity at energies below the height of these barriers and that its effect on the rate coefficients becomes appreciable below 300 K. As expected, with growing temperature the contribution of tunneling to the global reactivity decreases markedly, but the rate coefficients are still much higher for the Mu exchange channel due to the effect of MuH rotational excitation that boosts the formation of DMu while diminishing the H abstraction channel that leads to DH formation. The analysis of the thermal cumulative reaction probabilities of the two channels indicates that at the lowest energies/temperatures the reaction into the DH + Mu channel takes place via 'leakage' from collisions proceeding along the DMu + H reaction path. © the Partner Organisations 2014., This work has been funded by the Spanish Ministry of Science and Innovation under grants CTQ2008-02578/BQU, CTQ2012-37404-C02, FIS2010-16455, and CSD2009-00038. JA acknowledges funding by the Junta de Castilla y León (grant SA244B12-1).

From a kinetics standpoint, reactive molecular collisions are the building blocks of the mechanisms of chemical reactions. In contrast, a dynamics standpoint reveals molecular collisions to have their own internal mechanisms, which are not mere theoretical abstractions: through suitable preparation of the reactants internal and stereochemical states, features of the mechanisms of a reactive molecular collision can be made evident and used as "handles" to control the reaction outcome. Using time-independent quantum dynamical calculations, we demonstrate this for the Br + H2(v = 0-1, j = 2) → H + HBr reaction in the 1.0-1.6 eV range of total energies. Despite its pronounced effect on reactivity, which is in agreement with the predictions from Polanyi rules, reactant vibration is found to have little effect on the mechanism of this endoergic, late-barrier reaction. Analysis of the correlations between directional reaction properties shows that the collision stereochemistry strongly depends on the total energy, but not on how this energy is partitioned between reactant translation and vibration. The stereodynamical preferences implied by the collision mechanisms determine how and to what extent one can control the reaction. Regarding the overall reaction, the extent of control is found to be large near the reaction threshold but not when the total energy is high. Regarding state-to-state reactions, the effect of reactant stereochemistry on the product rotational state distribution is found to be nontrivial and energy dependent.

The advent of very precise measurements of rate coefficients in reactions of muonium (Mu), the lightest hydrogen isotope, with H2 in its ground and first vibrational state and of kinetic isotope effects with respect to heavier isotopes has triggered a renewed interests in the field of muonic chemistry. The aim of the present article is to review the most recent results about the dynamics and mechanism of the reaction Mu+H2 to shed light on the importance of quantum effects such as tunnelling, the preservation of the zero point energy, and the vibrational adiabaticity. In addition to accurate quantum mechanical (QM) calculations, quasiclassical trajectories (QCT) have been run in order to check the reliability of this method for this isotopic variant. It has been found that the reaction with H2(v=0) is dominated by the high zero point energy (ZPE) of the products and that tunnelling is largely irrelevant. Accordingly, both QCT calculations that preserve the products’ ZPE as well as those based on the Ring ...

The dynamics and mechanism of the O((1)D) + HF → F + OH reaction have been studied through quasi-classical trajectory calculations carried out on the 1(1)A' Potential Energy Surface (PES) fitted by Gómez-Carrasco et al. [Chem. Phys. Lett., 2007, 435, 188]. The influence of the collision energy and the initial rovibrational state on the reaction has been considered. As a result of this study, we conclude that for v = 0 the reactive collisions take place exclusively through an indirect mechanism that involves a long-lived complex. Interestingly and somewhat unexpectedly for a barrierless reaction, vibrational excitation causes a large enhancement of the reactivity due to the concurrence of a direct abstraction mechanism. Unlike other reactions also taking place on a barrierless PES featuring deep wells, no insertion mechanism is observed in O((1)D) + HF reactive collisions.

We present a detailed theoretical investigation of the dynamics corresponding to the strongly endothermic Br + H(2) (v = 0-1, j = 0) → H + HBr reaction in the 0.85 to 1.9 eV total energy range. State-averaged and state-to-state results obtained through time-independent wave packet (TIWP) and time-independent quantum mechanical (TIQM) calculations and quasiclassical trajectories (QCT) are compared and analyzed. The agreement in the results obtained with both quantum mechanical results is very good overall. However, although QCT calculations reproduce the general features, their agreement with the QM results is sometimes only qualitative. The analysis of the mechanism based on state-averaged results turns out to be deceptive and conveys an oversimplified picture of the reaction consistent with a direct-rebound mechanism. Consideration of state-to-state processes, in contrast, unveils the existence of multiple mechanisms that give rise to a succession of maxima in the differential cross section (DCS). Such mechanisms correlate with different sets of partial waves and display similar collision times when analyzed through the time-dependent DCS.

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.

A detailed comparison of quantum mechanical (QM) and quasiclassical trajectory (QCT) integral and differential cross sections (DCSs) as well as opacity functions is presented in this work for the vibrationally inelastic collisions of H+D(2)(v=0,j=0)--H+D(2)(v(')=3,j(')) at 1.72 eV collision energy. These results are also compared with the experimental differential cross sections by Greaves et al. [Nature (London) 454, 88 (2008)]. The agreement between QCT and QM results is fairly good but some differences are appreciable, and it is shown that the experimental results are in a somewhat better agreement with the calculated QM DCS. The present results and their analysis confirm that the vibrational excitation takes place by elongation of the D-D bond in a "tug-of-war" mechanism, where the incoming H atom and one of the D atoms compete for the formation of a bond with the other D atom, as proposed by Greaves et al. It is also found that these collisions may give rise to the formation of short-lived collision complexes (tau(coll)=35-50 fs) that can be traced back to the presence of relatively deep wells in the potential surface when the original D-D bond is stretched. The analysis of the trajectories into v(')=3 reveals that most of them cross at least twice the reaction barrier via a recrossing mechanism.

This article considers the extent to which one can control the reactivity of atom–diatom systems through reactant polarisation. Three different limits for reactivity manipulation are defined: “absolute” limits that do not depend on the reaction dynamics but can only be obtained for particular combinations of quantum numbers, “unconstrained” limits that depend on dynamics but not on constraints imposed by any particular experimental setup, and “constrained” limits that depend on dynamics and also on the constraints imposed by a particular experimental setup. Methods for calculation of these limits are presented and applied to the benchmark F + H2 reaction. The variations of the maximum and minimum reactivity one can obtain are analysed in terms of reaction mechanisms and steric constraints. Tables listing the minimum and maximum values of angular momentum polarisation moments of rank up to 4, and integer and half-integer quantum numbers up to 5, are also presented.

The explicit consideration of the vector correlations is an essential step when it comes to determining the mechanism of chemical reactions. Usual vector correlations involve initial and final relative velocity vectors and rotational angular momenta. However, the correlation between the orbital, ℓ, and rotational, j, angular momenta has seldom received any attention. In this article, we present a semiclassical methodology capable of describing the ℓ-j correlation that may serve as a connection between the quantum and quasiclassical treatments. Using the scattering matrix in the orbital angular momentum representation, the ℓ-j correlation is expressed as a probability density function of the angle formed by both vectors. This technique is exemplified through the H + D2 reaction and its accuracy is appraised by comparing with results derived from calculations based on quasiclassical trajectories.

While Cl + H(2) reactive collisions have been a subject of numerous experimental and theoretical studies, inelastic collisions leading to rotational energy transfer and/or vibrational excitation have been largely ignored. In this work, extensive quantum mechanical calculations covering the 0.5-1.5 eV total energy range and various initial rovibrational states have been carried out and used to perform a joint study of inelastic and reactive Cl + H(2) collisions. Quasiclassical trajectories calculations complement the quantum mechanical results. The analysis of the inelastic transition probabilities has revealed the existence of two distinct dynamical regimes that correlate with low and high impact parameters, b, and are neatly separated by glory scattering. It has been found that while high-b collisions are mainly responsible for |Δj| = 2 transitions which dominate the inelastic scattering, they are very inefficient in promoting higher |Δj| transitions. The effectiveness of this type of collision also drops with rotational excitation of H(2). In contrast, reactive scattering, that competes with |Δj| 2 inelastic transitions, is exclusively caused by low-b collisions, and it is greatly favored when the reactants get rotationally excited. Previous studies focusing on the reactivity of the Cl + H(2) system established that the van der Waals well located in the entrance channel play a key role in determining the mechanism of the collisions. Our results prove this to be also a case for inelastic processes, where the origin of the double dynamical regime can be traced back to the influence exerted by this well that shapes the topology of the entrance channel of the Cl-H(2) system.

The stereodynamics and mechanism of the F + HD(v = 0, j = 1) → HF (DF) + D (H) reactions have been thoroughly analysed at collision energies in the 0–160 meV range. Specifically, this study is focused on (i) the comparison between the stereodynamics of the collisions leading to HF and DF formation, and (ii) the stereodynamical fingerprints of the resonance that occurs at low collision energies in the HF channel and whose manifestation in the total cross section is greatly diminished for initial j > 0. While previous studies were limited to the analysis of integral cross sections (ICS), differential cross sections (DCS) and reaction probabilities, in the present work we have included the analysis of vectorial quantities such as the direction of the initial rotational angular momentum and internuclear axis, and their effect on reactivity. In particular, polarisation parameters (PP) and polarisation dependent differential cross sections (PDDCS), quantities that describe how the intrinsic HD rotational angular momentum and molecular axis polarisations contribute to reaction, are calculated and examined. The evolution of the PPs with the collision energy differs markedly between the two reaction channels. For the DF channel, the PP values are small and change very little in the energy range in which DF formation is appreciable. In contrast, rapid fluctuations in the magnitude and sign of the PPs are observed in the HF channel at low collision energies in and around the resonance. As the collision energy increases, direct (non-resonant) scattering prevails, and the various quantities are reasonably well accounted for by the QCT calculations, as in the case of the DF channel. The intrinsic directional information has been used to access the extent of control that can be achieved through polarisation of the HD molecule prior to collision. It was found that the same extrinsic preparation leads to very different outcomes on the HF channel DCS when the collision energy is close to the resonance. It is also shown that polarisation of the HD internuclear axis along the initial relative velocity enhances the effect of the resonance and allows its clear identification. Finally, the effect of different extrinsic preparations on the angle–velocity DCS is found to be strong, thus allowing considerable control of product angular distributions.

This article analyses the mechanisms of inelastic and reactive H + D(2)(v = 0, j = 2) collisions that result in highly vibrationally excited products when the collision energy is 1.70 eV. The analytical method is entirely quantum mechanical and focuses on correlations between the polarization of the reactant molecule and the direction of product scattering. Two viewpoints are used. The "intrinsic" viewpoint reveals the reactant polarizations that lead to the largest cross section at each value of the scattering angle (the angle between the reactant-approach and product-recoil directions); the "extrinsic" viewpoint reveals how the dependence of the collision cross section on the scattering angle changes when the reactant polarization is fixed at each one of a set of experimentally feasible alternatives. Comparison of processes correlating with the same range of impact parameters is also used, to facilitate isolation and identification of directional effects. When products are scattered in the backward and sideways regions, the results for inelastic and reactive collisions are rather similar. When products are scattered in the forward region, the results for inelastic and reactive collisions are clearly different: a side-on collision geometry that largely increases the inelastic cross section hardly affects the reactive cross section. This feature is the quantum mechanical signature of the so-called "tug-of-war" mechanism.

This article introduces a definition of the concept of elementary reaction mechanism that, while conforming to the traditional view of reaction mechanisms as dynamical processes whereby reagents are transformed into products, sharpens it by requiring reagent and product states to be completely specified and fully correlated. This leads to well-defined mathematical requirements for classification of a dynamical process as a reaction mechanism and also to a straightforward mathematical procedure for the determination of a special class of independent collision mechanisms that are dubbed "canonical". Canonical mechanisms result from an exact decomposition of the differential cross section of the reaction and form a complete orthogonal basis in terms of which all reaction mechanisms can be described. Examples involving the benchmark F + H2 and D + H2 reactions at energies ranging from ultralow to hyperthermal illustrate how canonical and other reaction mechanisms can be visualised and also how analysis of a reaction in terms of its canonical mechanisms can provide insight into its dynamics.

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.