Rate coefficients for the O + H2 and O + D2 reactions: how well ring polymer molecular dynamics accounts for tunelling.

We present here extensive calculations of the O(3P) + H2 and O(3P) + D2 reaction dynamics spanning the temperature range from 200 K to 2500 K. The calculations have been carried out using fully converged time-independent quantum mechanics (TI QM), quasiclassical trajectories (QCT) and ring polymer molecular dynamics (RPMD) on the two lowest lying adiabatic potential energy surfaces (PESs), 13A' and 13A'', calculated by Zanchet et al. [J. Chem. Phys., 2019, 151, 094307]. TI QM rate coefficients were determined using the cumulative reaction probability formalism on each PES including all of the total angular momenta and the Coriolis coupling and can be considered to be essentially exact within the Born-Oppenheimer approximation. The agreement between the rate coefficients calculated by using QM and RPMD is excellent for the reaction with D2 in almost the whole temperature range. For the reaction with H2, although the agreement is very good above 500 K, the deviations are significant at lower temperatures. In contrast, the QCT calculations largely underestimate the rate coefficients for the two isotopic variants due to their inability to account for tunelling. The differences found in the disagreements between RPMD and QM rate coefficients for the reactions for both the isotopologues are indicative of the ability of the RPMD method to accurately describe systems where tunelling plays a relevant role. Considering that both reactions are dominated by tunelling below 500 K, the present results show that RPMD is a very powerful tool for determining rate coefficients. The present QM rate coefficients calculated on adiabatic PESs slightly underestimate the best global fits of the experimental measurements, which we attribute to the intersystem crossing with the singlet 11A' PES.

Stereodynamical control of cold HD + D2 collisions.

We report full-dimensional quantum calculations of stereodynamic control of HD(v = 1, j = 2) + D2 collisions that has been probed experimentally by Perreault et al. using the Stark-induced adiabatic Raman passage (SARP) technique. Computations were performed on two highly accurate full-dimensional H4 potential energy surfaces. It is found that for both potential surfaces, rotational quenching of HD from with concurrent rotational excitation of D2 from is the dominant transition with cross sections four times larger than that of elastically scattered D2 for the same quenching transition in HD. This process was not considered in the original analysis of the SARP experiments that probed ΔjHD = -2 transitions in HD(vHD = 1, jHD = 2) + D2 collisions. Cross sections are characterized by an l = 3 resonance for ortho-D2(jD2 = 0) collisions, while both l = 1 and l = 3 resonances are observed for the para-D2(jD2 = 1) partner. While our results are in excellent agreement with prior measurements of elastic and inelastic differential cross sections, the agreement is less satisfactory with the SARP experiments, in particular for the transition for which the theoretical calculations indicate that D2 rotational excitation channel is the dominant inelastic process.

New Full-Dimensional Reactive Potential Energy Surface for the H4 System.

As the most abundant molecule in the universe, collisions involving H2 have important implications in astrochemistry. Collisions between hydrogen molecules also represent a prototype for assessing various dynamic methods for understanding fundamental few-body processes. In this work, we develop a new and highly accurate full-dimensional potential energy surface (PES) covering all reactive channels of the H2 + H2 system, which extends our previously reported H2 + H2 nonreactive PES [J. Chem. Theory Comput., 2021, 17, 6747] by adding 39,538 additional ab initio points calculated at the MRCI/AV5Z level in the reactive channels. The global PES is represented with high fidelity (RMSE = 0.6 meV for a total of 79,000 points) by a permutation invariant polynomial neural network (PIP-NN) and is suitable for studying collision-induced dissociation, single-exchange, as well as four-center exchange reactions. Preliminary quasi-classical trajectory studies on the new PIP-NN PES reveal strong vibrational enhancement of all reaction channels.

Quantum stereodynamics of cold molecular collisions.

Advances in quantum state preparations combined with molecular cooling and trapping technologies have enabled unprecedented control of molecular collision dynamics. This progress, achieved over the last two decades, has dramatically improved our understanding of molecular phenomena in the extreme quantum regime characterized by translational temperatures well below a kelvin. In this regime, collision outcomes are dominated by isolated partial waves, quantum threshold and quantum statistics effects, tiny energy splitting at the spin and hyperfine levels, and long-range forces. Collision outcomes are influenced not only by the quantum state preparation of the initial molecular states but also by the polarization of their rotational angular momentum, i.e., stereodynamics of molecular collisions. The Stark-induced adiabatic Raman passage technique developed in the last several years has become a versatile tool to study the stereodynamics of light molecular collisions in which alignment of the molecular bond axis relative to initial collision velocity can be fully controlled. Landmark experiments reported by Zare and coworkers have motivated new theoretical developments, including formalisms to describe four-vector correlations in molecular collisions that are revealed by the experiments. In this Feature article, we provide an overview of recent theoretical developments for the description of stereodynamics of cold molecular collisions and their implications to cold controlled chemistry.

Li + HF and Li + HCl Reactions Revisited I: QCT Calculations and Simulation of Experimental Results.

The Li + HF and Li + HCl reactions share some common features. They have the same kinematics, relatively small barrier heights, bent transition states, and are both exothermic when the zero point energy is considered. Nevertheless, the pioneering crossed beam experiments by Lee and co-workers in the 80s (Becker et al., J. Chem. Phys. 1980, 73, 2833) revealed that the dynamics of the two reactions differ significantly, especially at low collision energies. In this work, we present theoretical simulations of their results in the laboratory frame (LAB), based on quasiclassical trajectories and obtained using accurate potential energy surfaces. The calculated LAB angular distributions and time-of-flight spectra agree well with the raw experimental data, although our simulations do not reproduce the experimentally derived center-of-mass (CM) differential cross section and velocity distributions. The latter were derived by forward convolution fitting under the questionable assumption that the CM recoil velocity and scattering angle distribution were uncoupled, while our results show that the coupling between them is relevant. Some important insights into the reaction mechanism discussed in the article by Becker et al. had not been contrasted with those that can be extracted from the theoretical results. Among them, the correlation between the angular momenta involved in the reactions has also been examined. Given the kinematics of both systems, the reagent orbital angular momentum, l, is almost completely transformed into the rotation of the product diatom, j'. However, contrary to the coplanar mechanism proposed in the original paper, we find that the initial and final relative orbital angular momenta are not necessarily parallel. Both reactions are found to be essentially direct, although about 15% of the LiFH complexes live longer than 200 fs.

Stereodynamical Control of Cold Collisions between Two Aligned D_{2} Molecules.

Resonant scattering of optically state-prepared and aligned molecules in the cold regime allows the most detailed interrogation and control of bimolecular collisions. This technique has recently been applied to collisions of two aligned ortho-D_{2} molecules prepared in the j=2 rotational level of the v=2 vibrational manifold using the Stark-induced adiabatic Raman passage technique. Here, we develop the theoretical formalism for describing four-vector correlations in collisions of two aligned molecules and apply our approach to state-prepared D_{2}(v=2,j=2)+D_{2}(v=2,j=2)→D_{2}(v=2,j=2)+D_{2}(v=2,j=0) collisions, making possible the simulations of the experimental results from first principles. Key features of the experimental angular distributions are reproduced and attributed primarily to a partial wave resonance with orbital angular momentum ℓ=4.

Cold Collisions of Ro-Vibrationally Excited D2 Molecules.

The H2 + H2 system has long been considered a benchmark system for ro-vibrational energy transfer in bimolecular collisions. However, most studies thus far have focused on collisions involving H2 molecules in the ground vibrational level or in the first excited vibrational state. While H2 + H2/HD collisions have received wide attention due to the important role they play in astrophysics, D2 + D2 collisions have received much less attention. Recently, Zhou et al. [ Nat. Chem. 2022, 14, 658-663, DOI: 10.1038/s41557-022-00926-z] examined stereodynamic aspects of rotational energy transfer in collisions of two aligned D2 molecules prepared in the v = 2 vibrational level and j = 2 rotational level. Here, we report quantum calculations of rotational and vibrational energy transfer in collisions of two D2 molecules prepared in vibrational levels up to v = 2 and identify key resonance features that contribute to the angular distribution in the experimental results of Zhou et al. The quantum scattering calculations were performed in full dimensionality and using the rigid-rotor approximation using a recently developed highly accurate six-dimensional potential energy surface for the H4 system that allows descriptions of collisions involving highly vibrationally excited H2 and its isotopologues.

Role of Low Energy Resonances in the Stereodynamics of Cold He + D2 Collisions.

In recent experiments using the Stark-induced adiabatic Raman passage technique, Zhou et al. ( J. Chem. Phys. 2021, 154, 104309; Science 2021, 374, 960-964) measured the product's angular distribution for the collisions between He and aligned D2 molecules at cold collision energies. The signatures of the angular distributions were attributed to an [Formula: see text] = 2 resonance that governs scattering at low energies. A first-principles quantum mechanical treatment of this problem is presented here using a highly accurate interaction potential for the He-H2 system. Our results predict a very intense [Formula: see text] = 1 resonance at low energies, leading to angular distributions that differ from those measured in the experiment. A good agreement with the experiment is achieved only when the [Formula: see text] = 1 resonance is artificially removed, for example, by excluding the lowest energies present in the experimental velocity distribution. Our analysis revealed that neither the position nor the intensity of the [Formula: see text] = 1 resonance significantly changes when the interaction potential is modified within its predicted uncertainties. Energy-resolved measurements may help to resolve the discrepancy.

Stereodynamic control of cold rotationally inelastic CO + HD collisions.

Quantum control of molecular collision dynamics is an exciting emerging area of cold collisions. Co-expansion of collision partners in a supersonic molecular beam combined with precise control of their quantum states and alignment/orientation using Stark-induced Adiabatic Raman Passage allows exquisite stereodynamic control of the collision outcome. This approach has recently been demonstrated for rotational quenching of HD in collisions with H2, D2, and He and D2 by He. Here we illustrate this approach for HD(v = 0, j = 2) + CO(v = 0, j = 0) → HD(v' = 0, j') + CO(v' = 0, j') collisions through full-dimensional quantum scattering calculations at collision energies near 1 K. It is shown that the collision dynamics at energies between 0.01-1 K are controlled by an interplay of L = 1 and L = 2 partial wave resonances depending on the final rotational levels of the two molecules. Polarized cross sections resolved into magnetic sub-levels of the initial and final rotational quantum numbers of the two molecules also reveal a significant stereodynamic effect in the cold energy regime. Overall, the stereodynamic effect is controlled by both geometric and dynamical factors, with parity conservation playing an important role in modulating these contributions depending on the particular final state.

Controlling the Spin-Orbit Branching Fraction in Molecular Collisions.

The collision geometry, that is, the relative orientation of reactants before interaction, can have a large effect on how a collision or reaction proceeds. Certain geometries may prevent access to a given product channel, while others might enhance it. In this Letter, we demonstrate how the initial orientation of NO molecules relative to approaching Ar atoms determines the branching between the spin-orbit changing and the spin-orbit conserving rotational product channels. We use a recently developed quantum treatment to calculate differential and integral branching fractions, at any arbitrary orientation, from theoretical and experimental data points. Our results show that a substantial degree of control over the final spin-orbit state of the scattering products can be achieved by tuning the initial collision geometry.

Probing the location of the unpaired electron in spin-orbit changing collisions of NO with Ar.

Understanding the molecular forces that drive a reaction or scattering process lies at the heart of molecular dynamics. Here, we present a combined experimental and theoretical study of the spin-orbit changing scattering dynamics of oriented NO molecules with Ar atoms. Using our crossed molecular beam apparatus, we have recorded velocity-map ion images and extracted differential and integral cross sections of the scattering process in the side-on geometry. We observe an overall preference for collisions close to the N atom in the spin-orbit changing manifold, which is a direct consequence of the location of the unpaired electron on the potential energy surface. In addition, a prominent forward scattered feature is observed for intermediate, even rotational transitions when the atom approaches the molecule from the O-end. The appearance of this peak originates from an attractive well on the A' potential energy surface, which efficiently directs high impact parameter trajectories towards the region of high unpaired electron density near the N-end of the molecule. The ability to orient molecules prior to collision, both experimentally and theoretically, allows us to sample different regions of the potential energy surface(s) and unveil the associated collision pathways.

Non-adiabatic quantum dynamics of the electronic quenching OH(A2Σ+) + Kr.

We present the dynamics of the electronic quenching OH(A2Σ+) + Kr(1S) → OH(X2Π) + Kr(1S), with OH(A2Σ+) in the ground ro-vibrational state. This study relies on a new non-adiabatic quantum theory that uses three diabatic electronic states Σ+, Π', and Π'', coupled by one conical-intersection and nine Renner-Teller matrix elements, all of which are explicitly considered in the equation of the motion. The time-dependent mechanism and initial-state-resolved quenching probabilities, integral cross sections, thermal rate constants, and thermally-averaged cross sections are calculated via the real wavepacket method. The results point out a competition among three non-adiabatic pathways: Σ+ ↔ Π', Σ+ ↔ Π'', and Π' ↔ Π''. In particular, the conical-intersection effects Σ+-Π' are more important than the Renner-Teller couplings Σ+-Π', Σ+-Π'', and Π'-Π''. Therefore, Π' is the preferred product channel. The quenching occurs via an indirect insertion mechanism, opening many collision complexes, and the probabilities thus present many oscillations. Some resonances are still observable in the cross sections, which are in good agreement with previous experimental and quasi-classical findings. We also discuss the validity of more approximate quantum methods.

Steric Effects in the Inelastic Scattering of NO(X) + Ar: Side-on Orientation.

The rotationally inelastic collisions of NO(X) with Ar, in which the NO bond-axis is oriented side-on (i.e., perpendicular) to the incoming collision partner, are investigated experimentally and theoretically. The NO(X) molecules are selected in the |j = 0.5, Ω = 0.5, ε = -1, f⟩ state prior to bond-axis orientation in a static electric field. The scattered NO products are then state selectively detected using velocity-map ion imaging. The experimental bond-axis orientation resolved differential cross sections and integral steric asymmetries are compared with quantum mechanical calculations, and are shown to be in good agreement. The strength of the orientation field is shown to affect the structure observed in the differential cross sections, and to some extent also the steric preference, depending on the ratio of the initial e and f Λ-doublets in the superposition determined by the orientation field. Classical and quantum calculations are compared and used to rationalize the structures observed in the differential cross sections. It is found that these structures are due to quantum mechanical interference effects, which differ for the two possible orientations of the NO molecule due to the anisotropy of the potential energy surface probed in the side-on orientation. Side-on collisions are shown to maximize and afford a high degree of control over the scattering intensity at small scattering angles (θ < 90°), while end-on collisions are predicted to dominate in the backward scattered region (θ > 90°).

Competing Dynamical Mechanisms in Inelastic Collisions of H + HF.

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.

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.

New global potential energy surfaces of the ground 3A' and 3A″ states of the O(3P) + H2 system.

This paper presents two new adiabatic, global potential energy surfaces (PESs) for the two lowest 3A' and 3A″ electronic states of the O(3P) + H2 system. For each of these states, ab initio electronic energies were calculated for more than 5000 geometries using internally contracted multireference configuration interaction methods. The calculated points were then fitted using the ansatz by Aguado et al. [Comput. Phys. Commun. 108, 259 (1998)] leading to very accurate analytical potentials well adapted to perform reaction dynamics studies. Overall, the topographies of both PESs are in good agreement with the benchmark potentials of Rogers et al. [J. Phys. Chem. A 104, 2308 (2000)], but those presented in this work reproduce better the height and degeneracy of the two states at the saddle point. Moreover, the long range potential in the entrance channel does not require any cutoff. These features make the new PESs particularly suitable for a comparison of the dynamics on each of them. The new set of PESs was then used to perform quantum mechanics and quasiclassical trajectory calculations to determine differential and integral cross sections, which are compared to the experimental measurements by Garton et al. [J. Chem. Phys. 118, 1585 (2003)].

Side-impact collisions of Ar with NO.

In the realm of molecular collision dynamics, stereochemistry refers to the dependence of the collision outcome on the mutual orientation of the colliding partners. This may involve directed end-on collisions along a molecular bond axis or encounters in which the partner approaches the bond of an oriented molecule from the side. Using both experiment and theory, we show here that in the simplest case of an inelastic collision between an atom and a nearly homonuclear diatom, in which the two atoms have almost the same mass, the scattering dynamics are very distinct for impacts on either side of the molecule. By recording the direction of the scattered particles after the collision, we demonstrate that the intensity of products scattered in the forward direction, near parallel to the initial motion, can be substantially controlled and even maximized by altering the side-on orientation of the quantum state selected NO molecules that collide with Ar atoms. In addition, our findings provide valuable information about the preferred collision mechanism and reveal interesting quantum interference effects.