Shape resonance determined from angular distribution in D2 (v = 2, j = 2) + He → D2 (v = 2, j = 0) + He cold scattering

Stereodynamic control of nonadiabatic processes in low-energy Be+(2P) + H2 (v = 0, j = 2) collisions

Controlling the relative arrangement of colliding molecules is crucial for determining the dynamical outcomes of chemical processes and has emerged as a hot spot of experimental research. Here, the quantum scattering calculations are conducted to investigate the stereodynamic control in collisions between Be+(2P) and H2 (v = 0, j = 2), which undergo nonadiabatic transitions to the electronic ground state. Stereodynamic preparation is achieved by controlling the initial alignment of the H2 bond axis relative to the scattering frame. For product BeH+ in the reactive process, the differential cross sections (DCSs) are significantly enhanced in the forward and sideways hemispheres when the alignment angle β is 60°. For the product H2 in the quenching channel, the β = 0° preparation can result in a more than one-fold increase in the DCS at a polar scattering angle of 0°. Furthermore, varying the alignment angle β also has noteworthy effects on the rotational-state distributions of BeH+ products. Specifically, β = 0° preparation can induce the disappearance of the bimodal distribution of rotational states at a collision energy of 0.05 eV.

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.

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.

Experimental study of rotational relaxation for D2(1,12) in collisions with N2

The rotational relaxation behavior of D2(1,12) in a D2-N2 mixture was investigated using coherent anti-Stokes Raman scattering (CARS) technique. The rovibrational level v = 1 and J = 12 of D2 was selectively excited through stimulated Raman pumping while monitoring the temporal evolution of population for D2(1, J ≤ 12) molecules using time-resolved CARS spectroscopy. The results demonstrate that the rotational relaxation processes of D2(1,12) encompass both multi-quantum relaxation and continuous single-quantum relaxation. When α, the molar ratio of N2, is less than 0.5, D2(1,12) predominantly undergoes a single quantum relaxation process transition. However, when α ≥ 0.5, the multi-quantum relaxation mechanism gradually predominates. The total rotational relaxation rate coefficients of D2(1,12) collisions with N2 and D2 at 295 K were determined to be 3.974 × 10-14 and 1.179 × 10-14 cm3 s-1, respectively. The temperature dependence of rotational relaxation rate of D2(1,12) was investigated within the temperature range of 295-453 K. With increasing temperature, the dominant relaxation process exhibited an accelerated behavior, while the minor relaxation process remained largely unaffected. The rotational temperature of the D2 molecule at various N2 molar ratios was determined through the utilization of Boltzmann plots. The rotational temperature undergoes a rapid decline within 2 μs, corresponding to the near-resonant rotation-vibration relaxation process of D2(1,12) collisions with N2. The system reaches a quasi-equilibrium state when the delay time is 3 μs. The findings of this study can serve as a valuable empirical basis for further validation of the kinetic theory and simulation.

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.

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.

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.

Quantum-Controlled Collisions of H2 Molecules

The amount of information that can be obtained from a scattering experiment depends upon the precision with which the quantum states are defined in the incoming channel. By precisely defining the incoming states and measuring the outgoing states in a scattering experiment, we set up the boundary condition for experimentally solving the Schrödinger equation. In this Perspective we discuss cold inelastic scattering experiments using the most theoretically tractable H₂ and its isotopologues as the target. We prepare the target in a precisely defined rovibrational (v, j, m) quantum state using a special coherent optical technique called the Stark-induced adiabatic Raman passage (SARP). v and j represent the quantum numbers of the vibrational and rotational energy levels, and m refers to the projection of the rotational angular momentum vector j on a suitable quantization axis in the laboratory frame. Selection of the m quantum numbers defines the alignment of the molecular frame, which is necessary to probe the anisotropic interactions. For us to achieve the collision temperature in the range of a few degrees Kelvin, we co-expand the colliding partners in a mixed supersonic beam that is collimated to define a direction for the collision velocity. When the bond axis is aligned with respect to a well-defined collision velocity, SARP achieves stereodynamic control at the quantum scale. Through various examples of rotationally inelastic cold scattering experiments, we show how SARP coherently controls the dynamics of anisotropic interactions by preparing quantum superpositions of the orientational m states within a single rovibrational (v, j) energy state. A partial wave analysis, which has been developed for the cold scattering experiments, shows dominance of a resonant orbital that leaves its mark in the scattering angular distribution. These highly controlled cold collision experiments at the single partial wave limit allow the most direct comparison with the results of theoretical computations, necessary for accurate modeling of the molecular interaction potential.

Quantum Controlled Cold Scattering Challenges Theory

Our previous rotationally inelastic cold scattering experiments between state prepared D₂ (v = 2, j = 2, m = 0) and He disagreed with theory, raising serious concerns about either our understanding of the anisotropic potential or the accuracy of the measurement. To further interrogate interactions between molecular hydrogen and atomic helium, we study the Δj = 1and Δj = 2 rotational relaxation of HD (v = 2, j = 2, m = 0) by collision with He. The two rotational transitions probe different anisotropic components of the van der Waals potential. Our state resolved scattering study shows that these two transitions are mediated by two different shape resonances l = 1 for Δj = 1 and l = 2 for Δj = 2. The strong l = 1 resonance dominates the Δj = 1 scattering, agreeing with theory. However, the dominance of the weaker l = 2 resonance in the Δj = 2 transition, which matches our earlier D₂-He result, contradicts theoretical calculations. The continued contradiction, when we expect one-to-one correspondence between our stereodynamically controlled scattering experiment and theoretical calculations, makes us question the accuracy of the weaker anisotropic part of the H₂-He interaction potential.

Coherent Preparation of Highly Vibrating and Rotating D2 Molecules

Highly vibrationally and rotationally excited hydrogen molecules are of immense interest for understanding and modeling the physics and chemistry of the cold interstellar medium. Using a sequence of two Stark-induced adiabatic Raman passages, we demonstrate the preparation of rotationally excited D₂ molecules in the fourth excited vibrational level within its ground electronic state. The nearly complete population transfer to the target state is confirmed by observing both the threshold behavior as a function of the laser power and the depletion of the intermediate level. The vibrational excitation reported here opens new possibilities in the study of the much debated four-center reaction between a pair of hydrogen molecules. Additionally, these rovibrationally excited molecules could be potentially used to generate the high-intensity D^- ion beams considered essential for D-T thermonuclear fusion by enhancing the cross section for dissociative electron attachment by 5 orders of magnitude compared to that of the ground state.

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.

Stereodynamical Control of Cold Collisions of Polyatomic Molecules with Atoms

Scattering between atomic and/or molecular species can be controlled by manipulating the orientation or alignment of the collision partners. Such stereodynamics is particularly pronounced at cold (∼1 K) collision temperatures because of the presence of resonances. Comparing to the extensively studied atomic and diatomic species, polyatomic molecules with strong steric anisotropy could provide a more sophisticated platform for studying such stereodynamics. Here, we provide the quantum mechanical framework for understanding state-to-state stereodynamics in rotationally inelastic scattering of polyatomic molecules with atoms and apply it to cold collision of oriented H₂O with He on a highly accurate potential energy surface. It is shown that strong stereodynamical control can be achieved near 1 K via shape resonances. Furthermore, quantum interference in scattering of a coherently prepared initial state of the H₂O species is explored, which is shown to be significant.

Quantum mechanical double slit for molecular scattering

[Figure: see text].

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.