Scattering resonances in bimolecular collisions between NO radicals and H2 challenge the theoretical gold standard

Imaging Resonance Effects in C + H2 Collisions Using a Zeeman Decelerator

An intriguing phenomenon in molecular collisions is the occurrence of scattering resonances, which originate from bound and quasi-bound states supported by the interaction potential at low collision energies. The resonance effects in the scattering behavior are extraordinarily sensitive to the interaction potential, and their observation provides one of the most stringent tests for theoretical models. We present high-resolution measurements of state-resolved angular scattering distributions for inelastic collisions between Zeeman-decelerated C(3P1) atoms and para-H2 molecules at collision energies ranging from 77 cm-1 down to 0.5 cm-1. Rapid variations in the angular distributions were observed, which can be attributed to the consecutive reduction of contributing partial waves and effects of scattering resonances. The measurements showed excellent agreement with distributions predicted by ab initio quantum scattering calculations. However, discrepancies were found at specific collision energies, which most likely originate from an incorrectly predicted quasi-bound state. These observations provide exciting prospects for further high-precision and low-energy investigations of scattering processes that involve paramagnetic species.

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.

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.

Chemistry of a Light Impurity in a Bose-Einstein Condensate

Similar to an electron in a solid, an impurity in an atomic Bose-Einstein condensate (BEC) is dressed by excitations from the medium, forming a polaron quasiparticle with modified properties. This impurity can also undergo chemical recombination with atoms from the BEC, a process resonantly enhanced when universal three-body Efimov bound states cross the continuum. To study the interplay between these phenomena, we use a Gaussian state variational method able to describe both Efimov physics and arbitrarily many excitations of the BEC. We show that the polaron cloud contributes to bound state formation, leading to a shift of the Efimov resonance to smaller interaction strengths. This shifted scattering resonance marks the onset of a polaronic instability towards the decay into large Efimov clusters and fast recombination, offering a remarkable example of chemistry in a quantum medium.

Anisotropic dynamics of resonant scattering between a pair of cold aligned diatoms

The collision dynamics between a pair of aligned molecules in the presence of a partial-wave resonance provide the most sensitive probe of the long-range anisotropic forces important to chemical reactions. Here we control the collision temperature and geometry to probe the dynamics of cold (1-3 K) rotationally inelastic scattering of a pair of optically state-prepared D₂ molecules. The collision temperature is manipulated by combining the gating action of laser state preparation and detection with the velocity dispersion of the molecular beam. When the bond axes of both molecules are aligned parallel to the collision velocity, the scattering rate drops by a factor of 3.5 as collision energies >2.1 K are removed, suggesting a geometry-dependent resonance. Partial-wave analysis of the measured angular distribution supports a shape resonance within the centrifugal barrier of the l = 2 incoming orbital. Our experiment illustrates the strong anisotropy of the quadrupole-quadrupole interaction that controls the dynamics of resonant scattering.

A theoretical investigation into gallic acid pyrolysis

Thermodynamic and kinetic information on the first two steps of gallic acid pyrolysis, a decarboxylation followed by a dehydrogenation, is obtained based on density functional theory and quantum chemistry. For the kinetics, transition states are identified with the help of the climbing image nudged elastic band method. Both reactions exhibit two transition states. One of them is related to the rotation of OH groups, and the other one is related to the breaking and forming of bonds. The gallic acid pyrolysis as a whole is judged to be endothermal, and it changes from endergonic to exergonic between 500 and 750 K. The second reaction, the dehydrogenation of pyrogallol, is identified as the rate-determining step of gallic acid pyrolysis, with reaction rate constants below 1 s^-1 for temperatures below 1250 K.

Low-temperature reaction dynamics of paramagnetic species in the gas phase

Radicals are abundant in a range of important gas-phase environments. They are prevalent in the atmosphere, in interstellar space, and in combustion processes. As such, understanding how radicals react is essential for the development of accurate models of the complex chemistry occurring in these gas-phase environments. By controlling the properties of the colliding reactants, we can also gain insights into how radical reactions occur on a fundamental level. Recent years have seen remarkable advances in the breadth of experimental methods successfully applied to the study of reaction dynamics involving paramagnetic species-from improvements to the well-known crossed molecular beams approach to newer techniques involving magnetically guided and decelerated beams. Coupled with ever-improving theoretical methods, quantum features are being observed and interesting insights into reaction dynamics are being uncovered in an increasingly diverse range of systems. In this highlight article, we explore some of the exciting recent developments in the study of chemical dynamics involving paramagnetic species. We focus on low-energy reactive collisions involving neutral radical species, where the reaction parameters are controlled. We conclude by identifying some of the limitations of current methods and exploring possible new directions for the field.

Fano interference in quantum resonances from angle-resolved elastic scattering

Asymmetric spectral line shapes are a hallmark of interference of a quasi-bound state with a continuum of states. Such line shapes are well known for multichannel systems, for example, in photoionization or Feshbach resonances in molecular scattering. On the other hand, in resonant single channel scattering, the signature of such interference may disappear due to the orthogonality of partial waves. Here, we show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles also in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules with detection angle, in excellent agreement with theoretical predictions from full quantum scattering calculations. Using a model description for the partial wave interference, we can disentangle the resonant and background contributions and extract the relative phase responsible for the characteristic Fano-like profiles from our experimental measurements.

Active learning of potential-energy surfaces of weakly bound complexes with regression-tree ensembles

Several pool-based active learning (AL) algorithms were employed to model potential-energy surfaces (PESs) with a minimum number of electronic structure calculations. Theoretical and empirical results suggest that superior strategies can be obtained by sampling molecular structures corresponding to large uncertainties in their predictions while at the same time not deviating much from the true distribution of the data. To model PESs in an AL framework, we propose to use a regression version of stochastic query by forest, a hybrid method that samples points corresponding to large uncertainties while avoiding collecting too many points from sparse regions of space. The algorithm is implemented with decision trees that come with relatively small computational costs. We empirically show that this algorithm requires around half the data to converge to the same accuracy in comparison to the uncertainty-based query-by-committee algorithm. Moreover, the algorithm is fully automatic and does not require any prior knowledge of the PES. Simulations on a 6D PES of pyrrole(H₂O) show that <15 000 configurations are enough to build a PES with a generalization error of 16 cm^-1, whereas the final model with around 50 000 configurations has a generalization error of 11 cm^-1.

Velocity-tunable beam of continuously decelerated polar molecules for cold ion-molecule reaction studies

Producing high densities of molecules is a fundamental challenge for low-temperature, ion-molecule reaction studies. Traveling-wave Stark decelerators promise to deliver high density beams of cold, polar molecules but require non-trivial control of high-voltage potentials. We have overcome this experimental challenge and demonstrate continuous deceleration of ND₃ from 385 to 10 m/s, while driving the decelerator electrodes with a 10 kV amplitude sinewave. In addition, we test an alternative slowing scheme, which increases the time delay between decelerated packets of ND₃ and non-decelerated molecules, allowing for better energy resolution of subsequent reaction studies. We characterize this source of neutral, polar molecules suitable for energy-resolved reaction studies with trapped ions at cold translational temperatures. We also propose a combined apparatus consisting of the traveling-wave decelerator and a linear ion trap with a time-of-flight mass spectrometer and discuss to what extent it may achieve cold, energy-resolved, ion-neutral reactions.

The F + HD(v = 0, 1; j = 0, 1) reactions: stereodynamical properties of orbiting resonances

The excitation functions (reaction cross-section as a function of collision energy) of the F + HD(v = 0, 1; j = 0, 1) benchmark system have been calculated in the 0.01-6 meV collision energy interval using a time-independent hyperspherical quantum dynamics methodology. Special attention has been paid to orbiting resonances, which bring about detailed information on the three-atom interaction during the reactive encounter. The location of the resonances depends on the rovibrational state of the reactants HD(v,j), but is the same for the two product channels HF + D and DF + H, as expected for these resonances that are linked to the van der Waals well at the entrance. The resonance intensities depend both on the entrance and on the exit channels. The peak intensities for the HF + D channel are systematically larger than those for DF + H. Vibrational excitation leads to an increase of the peak intensity by more than an order of magnitude, but rotational excitation has a less drastic effect. It deceases the resonance intensity of the F + HD(v = 1) reaction, but increases somewhat that of F + HD(v = 0). Polarization of the rotational angular momentum with respect to the initial velocity reveals intrinsic directional preferences in the F + HD(v = 0, 1; j = 1) reactions that are manifested in the resonance patterns. The helicities (Ω = 0, Ω = ±1) possible for j = 1 contribute to the resonances, but that from Ω± 1 is, in general, dominant and in some cases exclusive. It corresponds to a preferential alignment of the HD internuclear axis perpendicular to the initial direction of approach and, thus, to side-on collisions. This work also shows that external preparation of the reactants, following the intrinsic preferences, would allow the enhancement or reduction of specific resonance features, and would be of great help for their eventual experimental detection.

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

We find an l = 2 shape resonance fingerprinted in the angular distribution of the cold (∼1 K) Δj = 2 rotationally inelastic collision of D₂ with He in a single supersonic expansion. The Stark-induced adiabatic Raman passage is used to prepare D₂ in the (v = 2, j = 2) rovibrational level with control of the spatial distribution of the bond axis of the molecule by magnetic sublevel selection. We show that the rate of Δj = 2 D₂-D₂ relaxation is nearly two orders of magnitude weaker than that of D₂-He. This suggests that the strong D₂-He scattering is caused by an orbiting resonance that is highly sensitive to the shape of the long-range potential.

Towards chemistry at absolute zero

The prospect of cooling matter down to temperatures that are close to absolute zero raises intriguing questions about how chemical reactivity changes under these extreme conditions. Although some types of chemical reaction still occur at 1 μK, they can no longer adhere to the conventional picture of reactants passing over an activation energy barrier to become products. Indeed, at ultracold temperatures, the system enters a fully quantum regime, and quantum mechanics replaces the classical picture of colliding particles. In this Review, we discuss recent experimental and theoretical developments that allow us to explore chemical reactions at temperatures that range from 100 K to 500 nK. Although the field is still in its infancy, exceptional control has already been demonstrated over reactivity at low temperatures.

Experimental and theoretical investigation of resonances in low-energy NO-H2 collisions

The experimental characterization of scattering resonances in low energy collisions has proven to be a stringent test for quantum chemistry calculations. Previous measurements on the NO-H₂ system at energies down to 10 cm^-1 challenged the most sophisticated calculations of potential energy surfaces available. In this report, we continue these investigations by measuring the scattering behavior of the NO-H₂ system in the previously unexplored 0.4 cm^-1-10 cm^-1 region for the parity changing de-excitation channel of NO. We study state-specific inelastic collisions with both para- and ortho-H₂ in a crossed molecular beam experiment involving Stark deceleration and velocity map imaging. We are able to resolve resonance features in the measured integral and differential cross sections. Results are compared to predictions from two previously available potential energy surfaces, and we are able to clearly discriminate between the two potentials. We furthermore identify the partial wave contributions to these resonances and investigate the nature of the differences between collisions with para- and ortho-H₂. Additionally, we tune the energy spreads in the experiment to our advantage to probe scattering behavior at energies beyond our mean experimental limit.

Determining the nature of quantum resonances by probing elastic and reactive scattering in cold collisions

Scattering resonances play a central role in collision processes in physics and chemistry. They help build an intuitive understanding of the collision dynamics due to the spatial localization of the scattering wavefunctions. For resonances that are localized in the reaction region, located at short separation behind the centrifugal barrier, sharp peaks in the reaction rates are the characteristic signature, observed recently with state-of-the-art experiments in low-energy collisions. If, however, the localization occurs outside of the reaction region, mostly the elastic scattering is modified. This may occur due to above-barrier resonances, the quantum analogue of classical orbiting. By probing both elastic and inelastic scattering of metastable helium with deuterium molecules in merged-beam experiments, we differentiate between the nature of quantum resonances-tunnelling resonances versus above-barrier resonances-and corroborate our findings by calculating the corresponding scattering wavefunctions.

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.

Time-independent quantum theory on vibrational inelastic scattering between atoms and open-shell diatomic molecules: Applications to NO + Ar and NO + H scattering

A full-dimensional rigorous quantum mechanical treatment of non-reactive inelastic scattering of an open-shell diatom [e.g., NO(²Π)] with a structureless and spinless atom is presented within the time-independent close-coupling framework. The inclusion of the diatomic vibrational degree of freedom allows the investigation of transitions between different vibrational manifolds, in addition to those between different rotational, spin-orbit, and Λ-doublet states. This method is applied to the scattering of vibrationally excited NO(²Π) with Ar and H (with its spin ignored). The former has negligible vibrational inelasticity, thanks to the weak interaction between the two collisional partners. This conclusion justifies the commonly used two-dimensional approximation in treating NO scattering with rare gas atoms. The latter, on the other hand, is shown to undergo significant vibrational relaxation, even in the ultra-cold regime, owing to a chemically bonded (HNO) complex on the lowest-lying singlet potential energy surfaces.

Manipulating beams of paramagnetic atoms and molecules using inhomogeneous magnetic fields

We review methods to manipulate the motion of pulsed supersonic atomic and molecular beams using time-independent and -dependent inhomogeneous magnetic fields. In addition, we discuss current and possible future applications and research directions.

Rotational-vibrational resonance states

Resonance states are characterized by an energy that is above the lowest dissociation threshold of the potential energy hypersurface of the system and thus resonances have finite lifetimes. All molecules possess a large number of long- and short-lived resonance (quasibound) states. A considerable number of rotational-vibrational resonance states are accessible not only via quantum-chemical computations but also by spectroscopic and scattering experiments. In a number of chemical applications, most prominently in spectroscopy and reaction dynamics, consideration of rotational-vibrational resonance states is becoming more and more common. There are different first-principles techniques to compute and rationalize rotational-vibrational resonance states: one can perform scattering calculations or one can arrive at rovibrational resonances using variational or variational-like techniques based on methods developed for determining bound eigenstates. The latter approaches can be based either on the Hermitian (L², square integrable) or non-Hermitian (non-L²) formalisms of quantum mechanics. This Perspective reviews the basic concepts related to and the relevance of shape and Feshbach-type rotational-vibrational resonance states, discusses theoretical methods and computational tools allowing their efficient determination, and shows numerical examples from the authors' previous studies on the identification and characterization of rotational-vibrational resonances of polyatomic molecular systems.

The Leiden Atomic and Molecular Database (LAMDA): Current Status, Recent Updates, and Future Plans

The Leiden Atomic and Molecular Database (LAMDA) collects spectroscopic information and collisional rate coefficients for molecules, atoms, and ions of astrophysical and astrochemical interest. We describe the developments of the database since its inception in 2005, and outline our plans for the near future. Such a database is constrained both by the nature of its uses and by the availability of accurate data: we suggest ways to improve the synergies among users and suppliers of data. We summarize some recent developments in computation of collisional cross sections and rate coefficients. We consider atomic and molecular data that are needed to support astrophysics and astrochemistry with upcoming instruments that operate in the mid- and far-infrared parts of the spectrum.

Roaming Reactions and Dynamics in the van der Waals Region

Roaming reactions were first clearly identified in photodissociation of formaldehyde 15 years ago, and roaming dynamics are now recognized as a universal aspect of chemical reactivity. These reactions typically involve frustrated near-dissociation of a quasibound system to radical fragments, followed by reorientation at long range and intramolecular abstraction. The consequences can be unexpected formation of molecular products, depletion of the radical pool in chemical systems, and formation of products with unusual internal state distributions. In this review, I examine some current aspects of roaming reactions with an emphasis on experimental results, focusing on possible quantum effects in roaming and roaming dynamics in bimolecular systems. These considerations lead to a more inclusive definition of roaming reactions as those for which key dynamics take place at long range.

Evidence of Nonrigidity Effects in the Description of Low-Energy Anisotropic Molecular Collisions of Hydrogen Molecules with Excited Metastable Helium Atoms

Cold collisions serve as a sensitive probe of the interaction potential. In the recent study of Klein et al. (Nature Phys.2017, 13, 35–38), the one-parameter scaling of the interaction potential was necessary to obtain agreement between theoretical and observed patterns of the orbiting resonances for excited metastable helium atoms colliding with hydrogen molecules. Here, we show that the effect of nonrigidity of the H₂ molecule on the resonant structure, absent in the previous study, is critical to predict the correct positions of the resonances in that case. We have complemented the theoretical description of the interaction potential and revised reaction rate coefficients by proper inclusion of the flexibility of the molecule. The calculated reaction rate coefficients are in remarkable agreement with the experimental data without empirical adjustment of the interaction potential. We have shown that even state-of-the-art calculations of the interaction energy cannot ensure agreement with the experiment if such an important physical effect as flexibility of the interacting molecule is neglected. Our findings about the significance of the nonrigidity effects can be especially crucial in cold chemistry, where the quantum nature of molecules is pronounced.

Cold and controlled chemical reaction dynamics

State-to-state chemical reaction dynamics, with complete control over the reaction parameters, offers unparalleled insight into fundamental reactivity.

Breakdown of energy transfer gap laws revealed by full-dimensional quantum scattering between HF molecules

Inelastic collisions involving molecular species are key to energy transfer in gaseous environments. They are commonly governed by an energy gap law, which dictates that transitions are dominated by those between initial and final states with roughly the same ro-vibrational energy. Transitions involving rotational inelasticity are often further constrained by the rotational angular momentum. Here, we demonstrate using full-dimensional quantum scattering on an ab initio based global potential energy surface (PES) that HF-HF inelastic collisions do not obey the energy and angular momentum gap laws. Detailed analyses attribute the failure of gap laws to the exceedingly strong intermolecular interaction. On the other hand, vibrational state-resolved rate coefficients are in good agreement with existing experimental results, validating the accuracy of the PES. These new and surprising results are expected to extend our understanding of energy transfer and provide a quantitative basis for numerical simulations of hydrogen fluoride chemical lasers.

Observation of Rainbows in the Rotationally Inelastic Scattering of NO with CH4

Using a combination of velocity-map imaging and resonance-enhanced multiphoton ionization detection with crossed molecular beam scattering, the dynamics of rotational energy transfer have been examined for NO in collisions with CH₄ at a mean collision energy of 700 cm^-1. The images of NO scattered into individual rotational (j_NO^') and spin-orbit (Ω) levels typically exhibit a single broad maximum that gradually shifts from the forward to the backward scattering direction with increasing rotational excitation (i.e., larger Δj_NO). The rotational rainbow angles calculated with a two-dimensional hard ellipse model show reasonable agreement with the observed angles corresponding to the maxima in the differential cross sections extracted from the images for higher Δj_NO transitions, but there are clear discrepancies for lower Δj_NO (in particular, final rotational levels with j_NO^' = 7.5 and 8.5). The sharply forward scattered angular distributions for these lower Δj_NO transitions better agree with the predictions of an L-type rainbow model. The more highly rotationally excited NO appears to coincide with low rotational excitation of the co-product CH₄, indicating a degree of rotational product-pair anticorrelation in this bimolecular scattering.

Orbiting resonances in the F + HD (v = 0, 1) reaction at very low collision energies. A quantum dynamical study

Time-independent, fully converged, quantum dynamical calculations have been performed for the F + HD (v = 0, j = 0) and F + HD (v = 1, j = 0) reactions on an accurate potential energy surface down to collision energies of 0.01 meV. The two isotopic exit channels, HF + D and DF + H, have been investigated. The calculations reproduce satisfactorily the Feshbach resonance structures for collision energies between 10 and 40 meV, previously reported in the literature for the HF + D channel. Contrary to the results of a former literature work, vibrational excitation of HD is found to enhance reactivity in all cases down to the lowest collision energy investigated. Shape-type orbiting resonances are found for collision energies lower than 2 meV. The resonances appear as peaks in the reaction cross sections that are associated to specific values of the total angular momentum, J. In contrast with the Feshbach resonances at higher energies, the orbiting resonance structure, which is caused by the van der Waals well of the entrance channel, is identical for the HF + D and DF + H exit channels. The orbiting resonance peaks for F + HD (v = 0) are very small, but those for F + HD (v = 1) could be observed, in principle, with a combination of Raman pumping and merged beams methods.

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.

Universal Probability Distributions of Scattering Observables in Ultracold Molecular Collisions

Currently, quantum dynamics theory cannot be used for quantitative predictions of molecular scattering observables at low temperatures because of two problems. The first problem is the extreme sensitivity of the low-temperature observables to details of potential energy surfaces (PESs) parametrizing the nuclear Schrödinger equation. The second problem is the large size of the basis sets required for the numerical integration of the Schrödinger equation for strongly interacting molecules in the presence of fields, which precludes the application of rigorous quantum theory to all but a few atom-molecule systems. Here, we show that, if the scattering problem is formulated as a probabilistic prediction, quantum theory can provide reliable results with exponentially reduced numerical effort. Specifically, we show that the probability distributions that an observable is in a certain range of values can be obtained by averaging the results of scattering calculations with much smaller basis sets than required for calculations of individual scattering cross sections. Moreover, we show that such distributions do not rely on the precise knowledge of the PES. This opens the possibility of making probabilistic predictions of experimentally relevant observables for a wide variety of molecular systems, currently considered out of reach of quantum dynamics theory. We demonstrate the approach by computing the probability for elastic scattering of CaH and SrOH molecules by Li atoms and SrF molecules by Rb atoms.

Design and construction of a multistage Zeeman decelerator for crossed molecular beams scattering experiments

Zeeman deceleration is a relatively new technique used to obtain full control over the velocity of paramagnetic atoms or molecules in a molecular beam. We present a detailed description of a multistage Zeeman decelerator that has recently become operational in our laboratory [Cremers et al., Phys. Rev. A 98, 033406 (2018)] and that is specifically optimized for crossed molecular beams scattering experiments. The decelerator consists of an alternating array of 100 solenoids and 100 permanent hexapoles to guide or decelerate beams of paramagnetic atoms or molecules. The Zeeman decelerator features a modular design that is mechanically easy to extend to arbitrary length and allows for solenoid and hexapole elements that are convenient to replace. The solenoids and associated electronics are efficiently water cooled and allow the Zeeman decelerator to operate at repetition rates exceeding 10 Hz. We characterize the performance of the decelerator using various beams of metastable rare gas atoms. Imaging of the atoms that exit the Zeeman decelerator reveals the transverse focusing properties of the hexapole array in the Zeeman decelerator.

Probing Nonadiabatic Effects in Low-Energy C(3 P j) + H2 Collisions

Nonadiabatic effects are of fundamental interest in collision dynamics. In particular, inelastic collisions between open-shell atoms and molecules, such as the collisional excitation of C(³ P _j) by H₂, are governed by nonadiabatic and spin-orbit couplings that are the sole responsible of collisional energy transfer. Here, we study collisions between carbon in its ground state C(³ P _j=0) and molecular hydrogen (H₂) at low collision energies that result in spin-orbit excitation to C(³ P _j=1) and C(³ P _j=2). State-to-state integral cross sections are obtained experimentally from crossed-beam experiments with a source of almost pure beam of C(³ P _j=0) and theoretically from highly accurate quantum calculations. We observe very good agreement between experimental and theoretical data that demonstrates our ability to model nonadiabatic dynamics. New rate coefficients at temperatures relevant to astrochemical modeling are also provided. They should lead to an increase of the abundance of atomic C(³ P) derived from the observations of interstellar clouds and a decrease of the efficiency of the cooling of the interstellar gas due to carbon atoms.