Cl+HD (v=1; J=1,2) reaction dynamics: Comparison between theory and experiment

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.

Development of the Time-Independent Methods for the Cl + H2/F + HD Reaction Using Hyper-Spherical Coordinates Including (Full) Spin-Orbit Characteristics

Recently, a combined study of high-resolution molecular crossed beam experiment and accurate full-dimensional time-dependent theory, including full spin-orbit characteristics on the effect of electronic spin and orbital angular momenta in the F + HD reaction, was reported by some of us, focusing on the partial wave resonance phenomenon (Science 2021, 371, 936-940). It revealed that the time-dependent theory could explain all of the details observed in the high-resolution experiment. Here, we develop two time-independent close-coupling methods using hyperspherical coordinates, including the two-state model, where only a part of the spin-orbit characteristics is considered, and the six-state model, where the full spin-orbit characteristics is considered. With these two newly developed theoretical models and the adiabatic theoretical model, the detailed reaction dynamics of the F + HD (v = 0, j = 0) reaction and the Cl + H2 (v = 0, j = 0) reaction are investigated and compared. Some of the results are compared with the time-dependent quantum wave packet theory and the experimental observations, and good agreements have been obtained, which suggests the validity of the pure-procession approximation in the six-state model using different theoretical methods. This work demonstrates the ability of the reactive scattering theory including full spin-orbit characteristics for describing the reactions of a halogen atom plus hydrogen molecule and its isotopologues.

Significant Isotope Effects from the Nonadiabatic Couplings in the Cl(2P) + HD(v = 0, j = 0) Reaction

The impact of non-Born-Oppenheimer couplings on the isotopic effects in the reaction of the Cl(2P) atom with the HD (v = 0, j = 0) molecule is investigated with our recently developed nonadiabatic time-independent quantum scattering methods, where the full open-shell characteristics are included in the six-state model, and also with the recently developed two-state model solving by time-independent methods, where part of the open-shell characteristic is included. The same reaction is also calculated with the simple adiabatic model using the lowest adiabatic potential energy surface. Compared with the results from different models, it is found that the reactivity of the Cl + HD → HCl + D channel is significantly overestimated in the adiabatic model. In contrast, the reactivity of the other channel agrees well with the nonadiabatic models. This is due to the van der Waals well in the reactant channel being changed a lot by including the nonadiabatic couplings. These quantum dynamics calculations suggest that sometimes the adiabatic model should be used with caution; otherwise, it may result in significant deviations for some reactions.

Active stereo-control of the Cl + CH4(ν3 = 1) reaction: a three-dimensional perspective

The transition state in Cl + CH4 is of Cl-H-C collinear geometry. As the reactant CH4 is vibrationally excited by a linearly polarized infrared (IR) light to the antisymmetric-stretching state of ν3 = 1, all four C-H bonds are collectively excited and any one of the H-atoms can be reactive. Yet, a strong alignment of the excited CH4(ν3 = 1), as evidenced from the striking stereo-specificity in the Cl + CH4 reaction, was clearly revealed in a previous, exploratory study. Reported here is the full account of that investigation at two collisional energies of Ec = 4.8 and 2.7 kcal mol-1, using a crossed molecular-beam, product-imaging approach. By active control of the polarization direction of an IR laser under judiciously chosen beam-geometries, a complete set of polarization-dependent differential cross sections is disentangled from the CH3(00) product images. To our surprise, the quantitative results appear nearly identical to those obtained for the isotope-substituted reaction of Cl + CHD3(ν1 = 1) → HCl(ν) + CD3(00). A detailed discussion is presented to elucidate the underlying physics for such an intriguing similarity in stereo-reactivity between a spherical-top and a symmetric-top reactant.

Experimental and Theoretical Study of the Vibrationally Excited Reaction Cl + D2 (v = 1, j = 0) → DCl + D

Vibrationally excited reaction of Cl + D₂ (v = 1, j = 0) → DCl + D was investigated by a high-resolution crossed beam experiment, with D₂ molecules in the vibrationally excited state prepared by the scheme of stimulated Raman pumping. Differential cross sections (DCSs) were obtained at three collision energies of 4.03, 4.93, and 5.68 kcal/mol. Backward scattering is dominant for both DCl (v' = 0) and DCl (v' = 1) products, and no forward scattering signal was observed at these three collision energies. Collision-energy-dependent DCS in the backward scattering direction was measured at collision energies between 3.62 and 5.97 kcal/mol. Comparing with the DCSs from the vibrational ground state, it is found that the vibrational excitation of D₂ molecules significantly enhances the reactivity because of the later barrier nature of the reaction. No obvious oscillatory structure was found in the collision-energy-dependent DCS in the backward scattering direction, suggesting that the title reaction proceeds via a direct abstraction mechanism.

Dynamics study on the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction: insertion-abstraction mechanism

Time-dependent wave packet calculations are carried out for two reaction channels of the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction. The potential well on the excited state potential energy surface makes the reaction preferable to proceed through the insertion reaction path. The dominance of the NaD + H reaction channel and product rotational state distributions are found to be in agreement with the characteristics of typical adiabatic insertion reactions. However, significant forward scattering peaks in the differential cross sections (DCS) are found to be inconsistent with the forward-backward symmetric scattering characteristic of typical adiabatic insertion reactions, which indicate that the Na(3p) + HD reaction is dominated by a direct reaction mechanism. The comparison between adiabatic and non-adiabatic calculated DCSs reveals that the non-adiabatic couplings in the reaction could reduce the lifetime of the intermediate complex. Finally, the insertion-abstraction mechanism is put forward for the non-adiabatic Na(3p) + HD reaction.

Stereodynamical Control of a Quantum Scattering Resonance in Cold Molecular Collisions

Cold collisions of light molecules are often dominated by a single partial wave resonance. For the rotational quenching of HD (v=1, j=2) by collisions with ground state para-H_{2}, the process is dominated by a single L=2 partial wave resonance centered around 0.1 K. Here, we show that this resonance can be switched on or off simply by appropriate alignment of the HD rotational angular momentum relative to the initial velocity vector, thereby enabling complete control of the collision outcome.

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.

Extremely short-lived reaction resonances in Cl + HD (v = 1) → DCl + H due to chemical bond softening

The Cl + H2 reaction is an important benchmark system in the study of chemical reaction dynamics that has always appeared to proceed via a direct abstraction mechanism, with no clear signature of reaction resonances. Here we report a high-resolution crossed–molecular beam study on the Cl + HD (v = 1, j = 0) → DCl + H reaction (where v is the vibrational quantum number and j is the rotational quantum number). Very few forward scattered products were observed. However, two distinctive peaks at collision energies of 2.4 and 4.3 kilocalories per mole for the DCl (v′ = 1) product were detected in the backward scattering direction. Detailed quantum dynamics calculations on a highly accurate potential energy surface suggested that these features originate from two very short-lived dynamical resonances trapped in the peculiar H-DCl (v′ = 2) vibrational adiabatic potential wells that result from chemical bond softening. We anticipate that dynamical resonances trapped in such wells exist in many reactions involving vibrationally excited molecules.

A new perspective: imaging the stereochemistry of molecular collisions

The concept of the steric effect plays a central role in chemistry. This Perspective describes how the polarization of reactant molecules in space can be used to probe directly the steric effect, and highlights some of the new measurements that are made possible by coupling reactant orientation and alignment with ion imaging techniques.

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.

QUASI-CLASSICAL TRAJECTORY STUDY OF THE REACTION PROBABILITY AND CROSS SECTION OF THE REACTION LiH + H

Based on the new accurate potential energy surface of the ground state of LiH2 system. Quasi-classical trajectory (QCT) calculations were carried out for the reaction LiH + H . The reaction probability of the title reaction for J = 0 has been calculated. The reaction cross sections were calculated as functions of the collision energy in the range 0.1–2.5 eV. The results were found to be well consistent with the previous real wave packet (RWP) and QCT results.

Highly Efficient Pumping of Vibrationally Excited HD Molecules via Stark-Induced Adiabatic Raman Passage

A primary prerequisite to study reactivity of vibrationally excited species is to efficiently prepare reacting species in a well-defined vibrational level. Efficient pumping of IR active vibrational modes in a molecule can be achieved by direct IR absorption. For vibrational modes that are only Raman active, however, efficient preparation of vibrationally excited states in those modes is not easily attainable. In this work, we have shown that highly efficient preparation of the HD(v = 1) state using the Stark-induced adiabatic Raman passage (SARP) scheme is feasible. As high as 91% population transfer from v = 0 to 1 of HD has been demonstrated in our experiment. This method provides new opportunities for future experimental studies on the dynamics of vibrational state molecules, especially H2, in both gas-phase and beam-surface reactions.

Dynamical regimes on the Cl + H2 collisions: inelastic rainbow scattering

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.

False estimates of stimulated Raman pumping efficiency caused by the optical Stark effect

One technique for measuring the fraction of molecules pumped to the excited state in stimulated Raman pumping (SRP) is to record the depletion of molecules in the lower state by resonance enhanced multiphoton ionization (REMPI). The presence of electric fields on the order of 10(7) V/cm arising from the pulsed SRP laser beams is sufficient to shift the line position of the REMPI transition to such an extent that the estimate of the pumping efficiency is overestimated unless this shift is accounted for.

Quantum mechanical limits to the control of atom-diatom chemical reactions through the polarisation of the reactants

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.

Observing the stereodynamics of chemical reactions using randomly oriented molecular beams

A new method is demonstrated to study the stereodynamics of simple chemical reactions that does not require the use of oriented (or aligned) molecular beams or measurements of the orientation state of product molecules. Instead, it is shown that by numerically combining accurate measurements of the state-to-state differential cross section for two or more rotational states of the reagent molecule, the separate contribution from the individual helicity states can be extracted. New molecular beam experiments are conducted for the D+H(2)-->HD+H reaction that confirm the validity of the method.

Reactive scattering dynamics in atom+polyatomic systems: F+C2H6-->HF(v,J)+C2H5

State-to-state scattering dynamics of F+C2H6-->HF(v,J)+C2H5 have been investigated at Ecom=3.2(6) kcalmol under single-collision conditions, via detection of nascent rovibrationally resolved HF(v,J) product states with high-resolution infrared laser absorption methods. State-resolved Doppler absorption profiles are recorded for multiple HF(v,J) transitions originating in the v=0,1,2,3 manifold, analyzed to yield absolute column-integrated densities via known HF transition moments, and converted into nascent probabilities via density-to-flux analysis. The spectral resolution of the probe laser also permits Doppler study of translational energy release into quantum-state-resolved HF fragments, which reveals a remarkable linear correlation between (i) HF(v,J) translational recoil and (ii) the remaining energy available, Eavail=Etot-E(HF(v,J)). The dynamics are interpreted in the context of a simple impulsive model based on conservation of linearangular momentum that yields predictions in good agreement with experiment. Deviations from the model indicate only minor excitation of ethyl vibrations, in contrast with a picture of extensive intramolecular vibrational energy flow but consistent with Franck-Condon excitation of the methylene CH2 bending mode. The results suggest a relatively simple dynamical picture for exothermic atom+polyatomic scattering, i.e., that of early barrier dynamics in atom+diatom systems but modified by impulsive recoil coupling at the transition state between translationalrotational degrees of freedom.

How Reactants Polarization Can Be Used to Change and Unravel Chemical Reactivity

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 + D2 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.

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl(2P)+H2→HCl(X̃ 1Σg+)+H(2S) reaction

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.

On the role of van der Waals interaction in chemical reactions at low temperatures

It is shown that van der Waals interaction potential plays a crucial role in chemical reactions at low temperatures. By taking the Cl+HD reaction as an illustrative example, we demonstrate that quasibound states of the van der Waals potential preferentially undergo chemical reaction rather than vibrational predissociation. Prereaction occurs even when the wave functions of the quasibound states peak far out into the entrance channel, outside the region of the van der Waals well. It is found that chemical reaction dominates over nonreactive vibrational quenching in collisions of vibrationally excited HD molecules with ground state chlorine atoms at ultracold temperatures.

Quantum scattering calculations on chemical reactions

This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described.

Scattering resonances in the simplest chemical reaction

Recent studies of state-resolved angular distributions show the participation of reactive scattering resonances in the simplest chemical reaction. This review is intended for those who wish to learn about the state-of-the-art in the study of the H + H2 reaction family that has made this breakthrough possible. This review is also intended for those who wish to gain insight into the nature of reactive scattering resonances. Following a tour across several fields of physics and chemistry where the concept of resonance has been crucial for the understanding of new phenomena, we offer an operational definition and taxonomy of reactive scattering resonances. We introduce simple intuitive models to illustrate each resonance type. We focus next on the last decade of H + H2 reaction dynamics. Emphasis is placed on the various experimental approaches that have been applied to the search for resonance behavior in the H + H2 reaction family. We conclude by sketching the road ahead in the study of H + H2 reactive scattering resonances.

Direct measurement of the preferred sense of NO rotation after collision with argon

The preferred sense of product molecule rotation (clockwise or counterclockwise) in a bimolecular collision system has been measured. Rotationally inelastic collisions of nitric oxide (NO) molecules with Ar atoms were studied by combining crossed molecular beams, circularly polarized resonant multiphoton ionization probing, and velocity-mapped ion imaging detection. The observed sense of NO product rotation varies with deflection angle and is a strong function of the NO final rotational state. The largest preferences for sense of rotation are observed at the highest kinematically allowed product rotational states; for lower rotational states, the variation with deflection angle becomes oscillatory. Quantum calculations on the most recently reported NO-Ar potential give good agreement with the observed oscillation patterns in the sense of rotation.