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.

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.

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.

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.

Differential steric effects in the inelastic scattering of NO(X) + Ar: spin-orbit changing transitions.

Spin-orbit changing transitions for bond-axis oriented collisions of NO(X) with Ar have been investigated with full quantum state selection via a crossed molecular beam experiment at collision energies of 532 cm-1 and 651 cm-1. NO(X) molecules were selected in their ground rotational state (Ω = 0.5, j = 0.5, f) before being adiabatically oriented using a static electric field, such that either the N- or O-end of the molecule was directed towards the incoming Ar atom. After collision, NO(X, Ω' = 1.5, j', e) molecules were probed quantum state specifically using velocity-map ion imaging, coupled with resonantly enhanced multi-photon ionization. Differences were observed between the experimental ion images and differential cross sections for collisions occurring at the two ends of the molecule, with results that could largely be accounted for by quantum mechanical scattering calculations. The bond-axis oriented data for the spin-orbit changing collisions are compared with similar results obtained previously for spin-orbit conserving transitions, and for field free scattering of NO(X) with Ar.

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.

Λ-Doublet Propensities for Reactions on Competing A' and A″ Potential Energy Surfaces: O(3 P) + N2 and O(3 P) + HCl.

This work presents scattering calculations for the O(3 P) + N2(1Σ) → NO(2Π) + N(4S) and for the O(3 P) + HCl(1Σ) → OH(2Π) + Cl(2P) reactions with a focus on the prediction of the Λ-doublet populations in which NO and OH are produced. Both reactions can take place on two competing potential energy surfaces of symmetries 3 A' and 3 A″ that correlate reagents with products but with very distinct topographies. As a result, they exhibit very different dynamical behaviors and total reactivity. Using a method that relates the reaction yield on the two competing surfaces to the Λ-doublet populations through the explicit consideration of the stereodynamics of the reaction, we predict that the population of NO and OH on the two Λ-doublet sates is surprisingly similar for both systems. These results contradict the model that assumes that collisions on the 3 A' and 3 A″ would give rise to products in the Π( A') and Π( A″) states, respectively.

Experimental and theoretical studies of the Xe-OH(A/X) quenching system.

New multi-reference, global ab initio potential energy surfaces (PESs) are reported for the interaction of Xe atoms with OH radicals in their ground X2Π and excited A2Σ+ states, together with the non-adiabatic couplings between them. The 2A' excited potential features a very deep well at the collinear Xe-OH configuration whose minimum corresponds to the avoided crossing with the 1A' PES. It is therefore expected that, as with collisions of Kr + OH(A), electronic quenching will play a major role in the dynamics, competing favorably with rotational energy transfer within the 2A' state. The surfaces and couplings are used in full three-state surface-hopping trajectory calculations, including roto-electronic couplings, to calculate integral cross sections for electronic quenching and collisional removal. Experimental cross sections, measured using Zeeman quantum beat spectroscopy, are also presented here for comparison with these calculations. Unlike similar previous work on the collisions of OH(A) with Kr, the surface-hopping calculations are only able to account qualitatively for the experimentally observed electronic quenching cross sections, with those calculated being around a factor of two smaller than the experimental ones. However, the predicted total depopulation of the initial rovibrational state of OH(A) (quenching plus rotational energy transfer) agrees well with the experimental results. Possible reasons for the discrepancies are discussed in detail.

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.

Angular distributions for the inelastic scattering of NO(X2Π) with O2(X3Σg-).

The inelastic scattering of NO(X2Π) by O2(X3Σg-) was studied at a mean collision energy of 550 cm-1 using velocity-map ion imaging. The initial quantum state of the NO(X2Π, v = 0, j = 0.5, Ω=0.5, 𝜖 = -1, f) molecule was selected using a hexapole electric field, and specific Λ-doublet levels of scattered NO were probed using (1+1') resonantly enhanced multiphoton ionization. A modified "onion-peeling" algorithm was employed to extract angular scattering information from the series of "pancaked," nested Newton spheres arising as a consequence of the rotational excitation of the molecular oxygen collision partner. The extracted differential cross sections for NO(X) f→f and f→e Λ-doublet resolved, spin-orbit conserving transitions, partially resolved in the oxygen co-product rotational quantum state, are reported, along with O2 fragment pair-correlated rotational state population. The inelastic scattering of NO with O2 is shown to share many similarities with the scattering of NO(X) with the rare gases. However, subtle differences in the angular distributions between the two collision partners are observed.

An experimental study of OH(A2Σ+) + H2: Electronic quenching, rotational energy transfer, and collisional depolarization.

Zeeman quantum beat spectroscopy has been used to determine the thermal (300 K) rate constants for electronic quenching, rotational energy transfer, and collisional depolarization of OH(A2Σ+) by H2. Cross sections for both the collisional disorientation and collisional disalignment of the angular momentum in the OH(A2Σ+) radical are reported. The experimental results for OH(A2Σ+) + H2 are compared to previous work on the OH(A2Σ+) + He and Ar systems. Further comparisons are also made to the OH(A2Σ+) + Kr system, which has been shown to display significant non-adiabatic dynamics. The OH(A2Σ+) + H2 experimental data reveal that collisions that survive the electronic quenching process are highly depolarizing, reflecting the deep potential energy wells that exist on the excited electronic state surface.

Integral steric asymmetry in the inelastic scattering of NO(X2Π).

The integral steric asymmetry for the inelastic scattering of NO(X) by a variety of collision partners was recorded using a crossed molecular beam apparatus. The initial state of the NO(X, v = 0, j = 1/2, Ω=1/2, ϵ=-1,f) molecule was selected using a hexapole electric field, before the NO bond axis was oriented in a static electric field, allowing probing of the scattering of the collision partner at either the N- or O-end of the molecule. Scattered NO molecules were state selectively probed using (1 + 1') resonantly enhanced multiphoton ionisation, coupled with velocity-map ion imaging. Experimental integral steric asymmetries are presented for NO(X) + Ar, for both spin-orbit manifolds, and Kr, for the spin-orbit conserving manifold. The integral steric asymmetry for spin-orbit conserving and changing transitions of the NO(X) + O2 system is also presented. Close-coupled quantum mechanical scattering calculations employing well-tested ab initio potential energy surfaces were able to reproduce the steric asymmetry observed for the NO-rare gas systems. Quantum mechanical scattering and quasi-classical trajectory calculations were further used to help interpret the integral steric asymmetry for NO + O2. Whilst the main features of the integral steric asymmetry of NO with the rare gases are also observed for the O2 collision partner, some subtle differences provide insight into the form of the underlying potentials for the more complex system.

Influence of vibration in the reactive scattering of D + MuH: the effect of dynamical bonding.

The dynamics of the D + MuH(v = 1) reaction has been investigated using time-independent quantum mechanical calculations. The total reaction cross sections and rate coefficients have been calculated for the two exit channels of the reaction leading, respectively, to DMu + H and DH + Mu. Over the 100-1000 K temperature range investigated the rate coefficients for the DMu + H channel are of the order of 10(-10) cm(3) s(-1) and those for the DH + Mu channel vary between 1 × 10(-12) and 8 × 10(-11) cm(3) s(-1). These results point to a virtually barrierless reaction for the DMu + H channel and to the presence of a comparatively small barrier for the DH + Mu channel and are consistent with the profiles of their respective collinear vibrationally adiabatic potentials (VAPs). The effective barrier in the VAP of the DH + Mu channel is located in the reactant valley and, consequently, translation is found to be more efficient than vibration for the promotion of the reaction over a large energy interval in the post threshold region. Below this barrier, the DH + Mu channel can be accessible through an indirect mechanism implying crossing from the DMu + H pathway. The most salient feature found in the present study is revealed in the total reaction cross section for the DMu + H channel, which shows a sharp resonance caused by the presence of a deep well in the vibrationally adiabatic potential. This well has a dynamical origin, reminiscent of that found recently in the vibrationally bonded BrMuBr complex [Fleming, et al., Angew. Chem., Int. Ed., 2014, 53, 1], and is due to the stabilizing effect of the light Mu atom oscillating between the heavier H and D isotopes and to the bond softening associated with vibrational excitation of MuH.

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.

Stereodynamics in NO(X) + Ar inelastic collisions.

The effect of orientation of the NO(X) bond axis prior to rotationally inelastic collisions with Ar has been investigated experimentally and theoretically. A modification to conventional velocity-map imaging ion optics is described, which allows the orientation of hexapole state-selected NO(X) using a static electric field, followed by velocity map imaging of the resonantly ionized scattered products. Bond orientation resolved differential cross sections are measured experimentally for a series of spin-orbit conserving transitions and compared with quantum mechanical calculations. The agreement between experimental results and those from quantum mechanical calculations is generally good. Parity pairs, which have previously been observed in collisions of unpolarized NO with various rare gases, are not observed due to the coherent superposition of the two j = 1/2, Ω = 1/2 Λ-doublet levels in the orienting field. The normalized difference differential cross sections are found to depend predominantly on the final rotational state, and are not very sensitive to the final Λ-doublet level. The differential steric effect has also been investigated theoretically, by means of quantum mechanical and classical calculations. Classically, the differential steric effect can be understood by considering the steric requirement for different types of trajectories that contribute to different regions of the differential cross section. However, classical effects cannot account quantitatively for the differential steric asymmetry observed in NO(X) + Ar collisions, which reflects quantum interference from scattering at either end of the molecule. This quantum interference effect is dominated by the repulsive region of the potential.

The Cl + O3 reaction: a detailed QCT simulation of molecular beam experiments.

We have studied in detail the dynamics of the Cl + O3 reaction in the 1-56 kcal mol(-1) collision energy range using quasi-classical trajectory (QCT) calculations on a recent potential energy surface (PES) [J. F. Castillo et al., Phys. Chem. Chem. Phys., 2011, 13, 8537]. The main goal of this work has been to assess the accuracy of the PES and the reliability of the QCT method by comparison with the existing crossed molecular beam results [J. Zhang and Y. T. Lee J. Phys. Chem. A, 1997, 101, 6485]. For this purpose, we have developed a methodology that allows us to determine the experimental observables in crossed molecular beam experiments (integral and differential cross sections, recoil velocity distributions, scattering angle-recoil velocity polar maps, etc.) as continuous functions of the collision energy. Using these distributions, raw experimental data in the laboratory frame (angular distributions and time-of-flight spectra) have been simulated from first principles with the sole information on the instrumental parameters and taking into account the energy spread. A general good agreement with the experimental data has been found, thereby demonstrating the adequacy of the QCT method and the quality of the PES to describe the dynamics of this reaction at the level of resolution of the existing crossed beam experiments. Some features which are apparent in the differential cross sections have also been analysed in terms of the dynamics of the reaction and its evolution with the collision energy.