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.

Correction: The Li + CaF → Ca + LiF chemical reaction under cold conditions.

Correction for 'The Li + CaF → Ca + LiF chemical reaction under cold conditions' by Humberto da Silva Jr et al., Phys. Chem. Chem. Phys., 2023, 25, 14193-14205, https://doi.org/10.1039/D3CP01464A.

The Li + CaF → Ca + LiF chemical reaction under cold conditions.

The calcium monofluoride (CaF) molecule has emerged as a promising candidate for precision measurements, quantum simulation, and ultracold chemistry experiments. Inelastic and reactive collisions of laser cooled CaF molecules in optical tweezers have recently been reported and collisions of cold Li atoms with CaF are of current experimental interest. In this paper, we report ab initio electronic structure and full-dimensional quantum dynamical calculations of the Li + CaF → LiF + Ca chemical reaction. The electronic structure calculations are performed using the internally contracted multi-reference configuration-interaction method with Davidson correction (MRCI + Q). An analytic fit of the interaction energies is obtained using a many-body expansion method. A coupled-channel quantum reactive scattering approach implemented in hyperspherical coordinates is adopted for the scattering calculations under cold conditions. Results show that the Li + CaF reaction populates several low-lying vibrational levels and many rotational levels of the product LiF molecule and that the reaction is inefficient in the 1-100 mK regime allowing sympathetic cooling of CaF by collisions with cold Li atoms.

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.

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.

Full-Dimensional Potential Energy Surface for Ro-vibrationally Inelastic Scattering between H2 Molecules.

We report a new full-dimensional potential energy surface (PES) for the inelastic scattering between ro-vibrationally excited H2 molecules. The new PES is based on 39,462 multi-reference configuration interaction points in dynamically relevant regions. The analytic form of the PES consists of a short-range term fit with the permutational invariant polynomial-neural network method and a long-range term with a physically correct asymptotic functional form accounting for both electrostatic and dispersion terms, which are connected smoothly with a switching function. The PES compares favorably with existing accurate PESs near the H2 equilibrium geometries but covers a much larger configuration space for H2 with up to 10 vibrational quanta. Full-dimensional quantum scattering calculations on the new PES reproduce the recent Stark-induced adiabatic Raman passage results for the HD(v = 1) + H2 scattering near 1 K, validating its accuracy. These calculations also revealed significant differences with existing PESs in describing scattering of vibrationally excited molecules, underscoring the ability of the new PES in handling such dynamics.

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.

Rainbow scattering in rotationally inelastic collisions of HCl and H2.

We examine rotational transitions of HCl in collisions with H2 by carrying out quantum mechanical close-coupling and quasi-classical trajectory (QCT) calculations on a recently developed globally accurate full-dimensional ab initio potential energy surface for the H3Cl system. Signatures of rainbow scattering in rotationally inelastic collisions are found in the state resolved integral and differential cross sections as functions of the impact parameter (initial orbital angular momentum) and final rotational quantum number. We show the coexistence of distinct dynamical regimes for the HCl rotational transition driven by the short-range repulsive and long-range attractive forces whose relative importance depends on the collision energy and final rotational state, suggesting that the classification of rainbow scattering into rotational and l-type rainbows is effective for H2 + HCl collisions. While the QCT method satisfactorily predicts the overall behavior of the rotationally inelastic cross sections, its capability to accurately describe signatures of rainbow scattering appears to be limited for the present system.

Non-adiabatic quantum interference in the ultracold Li + LiNa → Li2 + Na reaction.

Electronically non-adiabatic effects play an important role in many chemical reactions. However, how these effects manifest in cold and ultracold chemistry remains largely unexplored. Here for the first time we present from first principles the non-adiabatic quantum dynamics of the reactive scattering between ultracold alkali-metal LiNa molecules and Li atoms. We show that non-adiabatic dynamics induces quantum interference effects that dramatically alter the ultracold rotationally resolved reaction rate coefficients. The interference effect arises from the conical intersection between the ground and an excited electronic state that is energetically accessible even for ultracold collisions. These unique interference effects might be exploited for quantum control applications such as a quantum molecular switch. The non-adiabatic dynamics are based on full-dimensional ab initio potential energy surfaces for the two electronic states that includes the non-adiabatic couplings and an accurate treatment of the long-range interactions. A statistical analysis of rotational populations of the Li2 product reveals a Poisson distribution implying the underlying classical dynamics are chaotic. The Poisson distribution is robust and amenable to experimental verification and appears to be a universal property of ultracold reactions involving alkali metal dimers.

Stereodynamics of ultracold rotationally inelastic collisions.

Recent experiments on rotational quenching of HD in the v = 1, j = 2 rovibrational state in collisions with H2, D2, and He near 1 K have revealed strong stereodynamic preference stemming from isolated shape resonances. So far, the experiments and subsequent theoretical analyses have considered the initial HD rotational state in an orientation specified by the projection quantum number m or a coherent superposition of different m states. However, it is known that such stereodynamic control is generally not effective in the ultracold energy regime due to the dominance of the incoming s-wave (l = 0, partial wave). Here, we provide a detailed analysis of the stereodynamics of rotational quenching of HD by He with both m and m' resolution, where m' refers to the inelastically scattered HD. We show the existence of a significant m dependence in the m'-resolved differential and integral cross sections even in the ultracold s-wave regime with a factor greater than 60 for j = 2 → j' = 1 and a factor greater than 1300 for j = 3 → j' = 2 transitions. In the helicity frame, however, the integral cross section has no initial orientation (k) dependence in the ultracold energy regime, even resolving with respect to the final orientation (k'). The distribution of final rotational state orientations (k') is found to be statistical (uniform), regardless of the initial orientation.

Stereodynamics of rotationally inelastic scattering in cold He + HD collisions.

Stereodynamics of cold collisions has become a fertile ground for sensitive probe of molecular collisions and control of the collision outcome. A benchmark system for stereodynamic control of rotational transition is He + HD. This system was recently probed experimentally by Perreault et al. by examining quenching from j = 2 to j' = 0 state in the v = 1 vibrational manifold of HD. Here, through explicit quantum scattering calculations on a highly accurate ab initio interaction potential for He + H2, we reveal how a combination of two shape resonances arising from l = 1 and l = 2 partial waves controls the stereodynamic outcome rather than a single l = 2 partial wave attributed in the experiment. Furthermore, for collision energies below 0.5 cm-1, it is shown that stereodynamic preference for the integral cross section follows a simple universal trend.

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.

Globally Accurate Full-Dimensional Potential Energy Surface for H2 + HCl Inelastic Scattering.

A globally accurate full-dimensional potential energy surface (PES) for the inelastic scattering between H2 and HCl is developed on the basis of a large number of points calculated at the coupled-cluster singles, doubles, and perturbative triples level of theory. The machine-learned PES is trained with 42 417 ab initio points using the permutation invariant polynomial-neural network method, resulting in a root-mean-square fitting error of 5.6 cm-1. Both full- and reduced-dimensional quantum calculations for rotationally inelastic scattering are performed on this new PES and good agreement is obtained with previous quantum dynamical results on a reduced-dimensional model. Furthermore, strong resonances are identified at collision energies below 100 K, including cold conditions. This new PES provides a reliable platform for future studies of scattering dynamics with vibrationally excited collision partners in a wide range of collision energies extending to cold and ultracold conditions.

Unraveling the Stereodynamics of Cold Controlled HD-H_{2} Collisions.

Measuring inelastic rates with partial-wave resolution requires temperatures close to a Kelvin or below, even for the lightest molecule. In a recent experiment, Perreault, Mukherjee, and Zare [Nat. Chem. 10, 561 (2018).NCAHBB1755-433010.1038/s41557-018-0028-5] studied collisional relaxation of excited HD molecules in the v=1, j=2 state by para- and ortho-H_{2} at a temperature of about 1 K, extracting the angular distribution of scattered HD in the v=1, j=0 state. By state preparation of the HD molecules, control of the angular distribution of scattered HD was demonstrated. Here, we report a first-principles simulation of that experiment which enables us to attribute the main features of the observed angular distribution to a single L=2 partial-wave shape resonance. Our results demonstrate important stereodynamical insights that can be gained when numerically exact quantum scattering calculations are combined with experimental results in the few-partial-wave regime.

Importance of Geometric Phase Effects in Ultracold Chemistry.

It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scattering characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O2 reaction for total angular momentum quantum number J = 0-5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a "quantum switch" which can turn the reaction "on" or "off".

Ultracold collisions and reactions of vibrationally excited OH radicals with oxygen atoms.

We report a quantum dynamics study of O + OH (v = 1, j = 0) collisions on its ground electronic state, employing two different potential energy surfaces: the DIMKP surface by Kendrick and Pack, and the XXZLG surface by Xu et al. A time-independent quantum mechanical method based on hyperspherical coordinates has been adopted for the dynamics calculations. Energy-dependent probabilities and rate coefficients are computed for the elastic, inelastic, and reactive channels over the collision energy range E(coll) = 10(-10)-0.35 eV, for J = 0 total angular momentum. Initial state-selected reaction rate coefficients are also calculated from the J = 0 reaction probabilities by applying a J-shifting approximation, for temperatures in the range T = 10(-6)-700 K. Our results show that the dynamics of the collisional process and its outcome are strongly influenced by long-range forces, and chemical reactivity is found to be sensitive to the choice of the potential energy surface. For O + OH (v = 1, j = 0) collisions at low temperatures, vibrational relaxation of OH competes with reactive scattering. Since long-range interactions can facilitate vibrational relaxation processes, we find that the DIMKP potential (which explicitly includes van der Waals dispersion terms) favours vibrational relaxation over chemical reaction at low temperatures. On the DIMKP potential in the ultracold regime, the reaction rate coefficient for O + OH (v = 1, j = 0) is found to be a factor of thirteen lower than that for O + OH (v = 0, j = 0). This significantly high reactivity of OH (v = 0, j = 0), compared to that of OH (v = 1, j = 0), is attributed to enhancement caused by the presence of a HO(2) quasibound state (scattering resonance) with energy near the O + OH (v = 0, j = 0) dissociation threshold. In contrast, the XXZLG potential does not contain explicit van der Waals terms, being just an extrapolation by a nearly constant function at large O-OH distances. Therefore, long-range potential couplings are absent in calculations using the XXZLG surface, which does not induce vibrational relaxation as efficiently as the DIMKP potential. The XXZLG potential leads to a slightly higher reactivity (a factor of 1.4 higher) for O + OH (v = 1, j = 0) compared to that for O + OH (v = 0, j = 0) at ultracold temperatures. Overall, both potential surfaces yield comparable values of reaction rate coefficients at low temperatures for the O + OH (v = 1, j = 0) reaction.

Quantum calculations of H2-H2 collisions: from ultracold to thermal energies.

We present quantum dynamics of collisions between two para-H(2) molecules from low (10(-3) K) to high collision energies (1 eV). The calculations are carried out using a quantum scattering code that solves the time-independent Schrodinger equation in its full dimensionality without any decoupling approximations. The six-dimensional potential energy surface for the H(4) system developed by Boothroyd et al. [J. Chem. Phys. 116, 666 (2002)] is used in the calculations. Elastic, inelastic, and state-to-state cross sections as well as rate coefficients from T=1 K to 400 K obtained from our calculations are compared with available experimental and theoretical results. Overall, good agreement is obtained with previous studies.

Quantum dynamics of the O + OH --> H + O2 reaction at low temperatures.

We report quantum dynamics calculations of the O + OH --> H + O(2) reaction on two different representations of the electronic ground state potential energy surface (PES) using a time-independent quantum formalism based on hyperspherical coordinates. Calculations show that several excited vibrational levels of the product O(2) molecule are populated in the reaction. Rate coefficients evaluated using both PESs were found to be very sensitive to the energy resolution of the reaction probability, especially at temperatures lower than 100 K. It is found that the rate coefficient remains largely constant in the temperature range of 10-39 K, in agreement with the conclusions of a recent experimental study [Carty et al., J. Phys. Chem. A 110, 3101 (2006)]. This is in contrast with the time-independent quantum calculations of Xu et al. [J. Chem. Phys. 127, 024304 (2007)] which, using the same PES, predicted nearly two orders of magnitude drop in the rate coefficient value from 39 to 10 K. Implications of our findings to oxygen chemistry in the interstellar medium are discussed.