Determination of collision mechanisms at low energies using four-vector correlations.

In molecular dynamics, a fundamental question is how the outcome of a collision depends on the relative orientation of the collision partners before their interaction begins (the stereodynamics of the process). The preference for a particular orientation of the reactant complex is intimately related to the idea of a collision mechanism and the possibility of control, as revealed in recent experiments. Indeed, this preference holds not only for chemical reactions involving complex polyatomic molecules, but also for the simplest inelastic atom-diatom collisions at cold collision energies. In this work, we report how the outcome of rotationally inelastic collisions between two D2 molecules can be controlled by changing the alignment of their internuclear axes under the same or different polarization vectors. Our results demonstrate that a higher degree of control can be achieved when two internuclear axes are aligned, especially when both molecules are relaxed in the collision. The possibility of control extends to very low energies, even to the ultracold regime, when no control could be achieved just by the alignment of the internuclear axis of one of the colliding partners.

Dynamical effects on the O(3P) + D2 reaction and its impact on the Λ-doublet population.

The O(3P) + D2 → OD(2Π) + D reaction presents the peculiarity of taking place on two different potential energy surfaces (PESs) of different symmetry, 3A' and 3A'', which become degenerate for collinear configurations where the saddle-point of the reaction is located. The degeneracy is broken for non-collinear approaches with the energy on the 3A' PES rising more abruptly with the bending angle, making the frequency of this mode higher on the 3A' state. Consequently, the 3A' PES should be less reactive than the 3A'' one. Nevertheless, quantum scattering calculations show that the cross section is higher on the 3A' PES for energies close to the classical reaction threshold and rotationless reactant. It is found that the differences between the reactivity on the two PESs are greater for low values of total angular momentum, where the centrifugal barrier is lower and contribute to the higher population of the Π(A') Λ-doublet states of OD at low collision energies. At high collision energies, the Π(A') Λ-doublet state is also preferentially populated. Analysis of the differential cross sections reveals that the preponderance for the Π(A') Λ-doublet at low energies comes from backward scattering, originating from the reaction on the 3A' PES, while at high energies, it proceeds from a different mechanism that leads to sideways scattering on the 3A'' PES and that populates the Π(A') manifold.

Universal behavior in complex-mediated reactions: Dynamics of S(1D) + o-D2 → D + SD at low collision energies.

Reactive and elastic cross sections and rate coefficients have been calculated for the S(1D) + D2(v = 0, j = 0) reaction using a modified hyperspherical quantum reactive scattering method. The considered collision energy ranges from the ultracold regime, where only one partial wave is open, up to the Langevin regime, where many of them contribute. This work presents the extension of the quantum calculations, which in a previous study were compared with the experimental results, down to energies in the cold and ultracold domains. Results are analyzed and compared with the universal case of the quantum defect theory by Jachymski et al. [Phys. Rev. Lett. 110, 213202 (2013)]. State-to-state integral and differential cross sections are also shown covering the ranges of low-thermal, cold, and ultracold collision energy regimes. It is found that at E/kB < 1 K, there are substantial departures from the expected statistical behavior and that dynamical features become increasingly important with decreasing collision energy, leading to vibrational excitation.

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.

Multi- and single-reference methods for the analysis of multi-state peroxidation of enolates.

In spite of being spin-forbidden, some enzymes are capable of catalyzing the incorporation of O2(Σg-3) to organic substrates without needing any cofactor. It has been established that the process followed by these enzymes starts with the deprotonation of the substrate forming an enolate. In a second stage, the peroxidation of the enolate formation occurs, a process in which the system changes its spin multiplicity from a triplet state to a singlet state. In this article, we study the addition of O2 to enolates using state-of-the-art multi-reference and single-reference methods. Our results confirm that intersystem crossing is promoted by stabilization of the singlet state along the reaction path. When multi-reference methods are used, large active spaces are required, and in this situation, semistochastic heat-bath configuration interaction emerges as a powerful method to study these multi-configurational systems and is in good agreement with PNO-LCCSD(T) when the system is well-represented by a single-configuration.

Unveiling shape resonances in H + HF collisions at cold energies.

Scattering resonances are pure quantum effects that appear whenever the collision energy matches the energy of a quasi-bound state of the intermolecular complex. Here we show that rotational quenching of HF(j = 1, 2) with H is strongly influenced by the presence of two resonance peaks, leading to up to a two-fold increase in the thermal rate coefficients at the low temperatures characteristic of the interstellar medium. Our results show that each resonance peak is formed by a cluster of shape resonances, each of them characterized by the same value of the orbital angular momentum but different values of the total angular momentum. The relative intensity of these resonances depends on the relative geometry of the incoming reactants, and our results predict that by changing the alignment of the HF rotational angular momentum it is possible to decompose the resonance peaks, disentangling the underlying resonance pattern and the contribution of different total angular momenta to the resonance.

Unexpected dynamical effects change the lambda-doublet propensity in the tunneling region for the O(3P) + H2 reaction.

One of the most relevant features of the O(3P) + H2 reaction is that it occurs on two different potential energy surfaces (PESs) of symmetries A' and A'' that correlate reactants and products. The respective saddle points, which correspond to a collinear arrangement, are the same for both PESs, whilst the barrier height rises more abruptly on the 3A' PES than on the 3A'' PES. Accordingly, the reactivity on the 3A'' PES should be always higher than on the 3A' PES. In this work, we present accurate quantum-scattering calculations showing that this is not always the case for rotationless reactants, where dynamical factors near the reaction threshold cause the 3A' PES to dominate at energies around the barrier. Further calculation of cross sections and Λ-doublet populations has allowed us to establish how the reaction mechanism changes from the deep tunneling regime to hyperthermal energies.

How reactant polarization can be used to change the effect of interference on reactive collisions.

It is common knowledge that integral and differential cross sections (DCSs) are strongly dependent on the spatial distribution of the molecular axis of the reactants. Hence, by controlling the axis distribution, it is possible to either promote or hinder the yield of products into specific final states or scattering angles. This idea has been successfully implemented in experiments by polarizing the internuclear axis before the reaction takes place, either by manipulating the rotational angular distribution or by the Stark effect in the presence of an orienting field. When there is a dominant reaction mechanism, characterized by a set of impact parameters and angles of attack, it is expected that a preparation that helps the system to reach the transition state associated with that mechanism will promote the reaction, whilst a different preparation would generally impair the reaction. However, when two or more competing mechanisms via interference contribute to the reaction into specific scattering angles and final states, it is not evident which would be the effect of changing the axis preparation. To address this problem, throughout this article we have simulated the effect that different experimental preparations have on the DCSs for the H + D2 reaction at relatively high energies, for which it has been shown that several competing mechanisms give rise to interference that shapes the DCS. To this aim, we have extended the formulation of the polarization dependent DCS to calculate polarization dependent generalized deflection functions of ranks greater than zero. Our results show that interference is very sensitive to changes in the internuclear axis preparation, and that the shape of the DCS can be controlled exquisitely.

New Stress Test for Ring Polymer Molecular Dynamics: Rate Coefficients of the O(3P) + HCl Reaction and Comparison with Quantum Mechanical and Quasiclassical Trajectory Results.

In the past decade, ring polymer molecular dynamics (RPMD) has emerged as a very efficient method to determine thermal rate coefficients for a great variety of chemical reactions. This work presents the application of this methodology to study the O(3P) + HCl reaction, which constitutes a stringent test for any dynamical calculation due to rich resonant structure and other dynamical features. The rate coefficients, calculated on the 3A' and 3A″ potential energy surfaces (PESs) by Ramachandran and Peterson [ J. Chem. Phys. 2003 , 119 , 9590 ], using RPMD and quasiclassical trajectories (QCT) are compared with the existing experimental and the quantum mechanical (QM) results by Xie et al. [ J. Chem. Phys. 2005 122 , 014301 ]. The agreement is very good at T > 600 K, although RPMD underestimates rate coefficients by a factor between 4 and 2 in the 200-500 K interval. The origin of these discrepancies lies in the large contribution from tunneling on the 3A″ PES, which is enhanced by resonances due to quasibound states in the van der Waals wells. Although tunneling is fairly well accounted for by RPMD even below the crossover temperature, the effect of resonances, a long-time effect, is not included in the methodology. At the highest temperatures studied in this work, 2000-3300 K, the RPMD rate coefficients are somewhat larger than the QM ones, but this is shown to be due to limitations in the QM calculations and the RPMD are believed to be more reliable.

The dynamics of the Hg + Br2 reaction: elucidation of the reaction mechanism for the Br exchange reaction.

In spite of its importance in the Hg atmospheric chemistry, the dynamics of the Hg + Br2 → HgBr + Br reaction is poorly understood. In this article, we have carried out a comprehensive study of the reaction mechanism of this reaction by means of quasiclassical trajectories (QCTs) on an existing ab initio potential energy surface (PES). The reaction has a non trivial dynamics, as a consequence of its large endothermicity, the presence of a deep potential well, and the competition between the Br exchange and the collision induced dissociation processes. Our calculations demonstrate that insertion is only relevant at energies just above the reaction threshold and that, at energies above 2.3 eV, HgBr formation typically takes place via a sort of frustrated dissociation. In order to compare directly with the results obtained in extensive cross molecular beam experiments for the homologous reaction with I2, angular distributions in the laboratory frame for Hg + Br2 have been simulated under similar experimental conditions. The lack of agreement at the highest energies considered suggests that either the two reactions have substantially different mechanisms or that calculations on a single PES cannot account for the dynamics at those energies.

Impact of the Long-Range Interaction on the Efficiency of the Li + ClH → LiCl + H Reaction.

Quantum and quasiclassical calculations have been performed to compute the low energy efficiency of the Li + ClH → LiCl + H reaction on some potential energy surfaces fitted to ab initio electronic energies using different functional forms. The outcomes of the calculations show marked differences at threshold and in the shape of the excitation function in seeming contrast with the height of the saddle to reaction and the width of the cone of acceptance. The differences in the computed reactive probability and cross section are rationalized in terms of the attractive/repulsive nature of the long-range interaction and the inability of trajectory techniques to deal with threshold effects. The vestiges of these features in the value of the thermal rate coefficients are also commented on.

Multiple scattering mechanisms causing interference effects in the differential cross sections of H + D2 → HD(v' = 4, j') + D at 3.26 eV collision energy.

Differential cross sections (DCSs) for the H + D2 → HD(v' = 4, j') + D reaction at 3.26 eV collision energy have been measured using the photoloc technique, and the results have been compared with those from quantum and quasiclassical scattering calculations. The quantum mechanical DCSs are in good overall agreement with the experimental measurements. In common with previous results at 1.97 eV, clear interference patterns which appear as fingerlike structures have been found at 3.26 eV but in this case for vibrational states as high as v' = 4. The oscillatory structure is prominent for low rotational states and progressively disappears as j' increases. A detailed analysis, similar to that carried out at 1.97 eV, shows that the origin of these structures could be traced to interferences between well defined classical mechanisms. In addition, at this energy, we do not observe the anomalous positive j'-θ trend found for the v' = 4 manifold at lower collision energies, thus reinforcing our explanation that the anomalous distribution for HD(v' = 4, j') at 1.97 eV only takes place for those states associated with low product recoil energies.

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.

Accurate Time-Dependent Wave Packet Calculations for the O(+) + H2 → OH(+) + H Ion-Molecule Reaction.

Accurate quantum reactive scattering time-dependent wave packet close-coupling calculations have been carried out to determine total reaction probabilities and integral cross sections for the O(+) + H2 → OH(+) + H reaction in a range of collision energies from 10(-3) eV up to 1.0 eV for the H2 rovibrational states (v = 0; j = 0, 1, 2) and (v = 1; j = 0) using the potential energy surface (PES) by Martínez et al. As expected for a barrierless reaction, the reaction cross section decays rapidly with collision energy, Ec, following a behavior that nearly corresponds to that predicted by the Langevin model. Rotational excitation of H2 into j = 1, 2 has a very moderate effect on reactivity, similarly to what happens with vibrational excitation below Ec ≈ 0.3 eV. However, at higher collision energies the cross section increases notably when H2 is promoted to v = 1. This effect is explained by resorting to the effective potentials in the entrance channel. The integral cross sections have been used to calculate rate constants in the temperature range 200-1000 K. A good overall agreement has been found with the available experimental data on integral cross sections and rate constants. In addition, time-independent quantum mechanical and quasi-classical trajectory (QCT) calculations have been performed on the same PES aimed to compare the various methodologies and to discern the detailed mechanism of the title reaction. In particular, the analysis of individual trajectories has made it possible to explain, in terms of the coupling between reagent relative velocity and the topography of the PES, the presence of a series of alternating maxima and minima in the collision energy dependence of the QCT reaction probabilities for the reactions with H2(v=0,1,j=0), which are absent in the quantum mechanical calculations.

Cold and ultracold dynamics of the barrierless D(+) + H2 reaction: Quantum reactive calculations for ∼R(-4) long range interaction potentials.

Quantum reactive and elastic cross sections and rate coefficients have been calculated for D(+) + H2 (v = 0, j = 0) collisions in the energy range from 10(-8) K (deep ultracold regime), where only one partial wave is open, to 150 K (Langevin regime) where many of them contribute. In systems involving ions, the ∼R(-4) behavior extends the interaction up to extremely long distances, requiring a special treatment. To this purpose, we have used a modified version of the hyperspherical quantum reactive scattering method, which allows the propagations up to distances of 10(5) a0 needed to converge the elastic cross sections. Interpolation procedures are also proposed which may reduce the cost of exact dynamical calculations at such low energies. Calculations have been carried out on the PES by Velilla et al. [J. Chem. Phys. 129, 084307 (2008)] which accurately reproduces the long range interactions. Results on its prequel, the PES by Aguado et al. [J. Chem. Phys. 112, 1240 (2000)], are also shown in order to emphasize the significance of the inclusion of the long range interactions. The calculated reaction rate coefficient changes less than one order of magnitude in a collision energy range of ten orders of magnitude, and it is found in very good agreement with the available experimental data in the region where they exist (10-100 K). State-to-state reaction probabilities are also provided which show that for each partial wave, the distribution of HD final states remains essentially constant below 1 K.

A semiclassical treatment of the ℓ-j correlation in atom-diatom collisions.

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.

The effect of the reactant internal excitation on the dynamics of the C(+) + H2 reaction.

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 reactive collision mechanism evinced: stereodynamical control of the elementary Br + H2 → H + HBr reaction.

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.

Reaction dynamics and mechanism of the Cl + HD(v = 1) reaction: a quantum mechanical study.

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.

Rotational alignment effects in NO(X) + Ar inelastic collisions: a theoretical study.

Rotational angular momentum alignment effects in the rotational inelastic scattering of NO(X) with Ar have been investigated by means of close-coupled quantum mechanical, quasi-classical trajectory, and Monte Carlo hard shell scattering calculations. It has been shown that the hard shell nature of the interaction potential at a collision energy of Ecoll = 66 meV is primarily responsible for the rotational alignment of the NO(X) molecule after collision. By contrast, the alternating trend in the quantum mechanical parity resolved alignment parameters with change in rotational state Δj reflects differences in the differential cross sections for NO(X) parity conserving and changing collisions, rather than an underlying difference in the collision induced rotational alignment. This suggests that the rotational alignment and the differential cross sections are sensitive to rather different aspects of the scattering dynamics. The applicability of the kinematic apse model has also been tested and found to be in excellent agreement with exact quantum mechanical scattering theory provided the collision energy is in reasonable excess of the well depth of the NO(X)-Ar potential energy surface.