Cold state-selected molecular collisions and reactions

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.

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.

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.

ABC+D: A time-independent coupled-channel quantum dynamics program for elastic and ro-vibrational inelastic scattering between atoms and triatomic molecules in full dimensionality

We discuss the details of a time-independent quantum mechanical method and its implementation for full-dimensional non-reactive scattering between a closed-shell triatomic molecule and a closed-shell atom. By solving the time-independent Schrödinger equation within the coupled-channel framework using a log-derivative method, the state-to-state scattering matrix (S-matrix) can be determined for inelastic scattering involving both the rotational and vibrational modes of the molecule. Various approximations are also implemented. The ABC+D code provides an important platform for understanding an array of physical phenomena involving collisions between atoms and molecules.

Recent advances in quantum theory on ro-vibrationally inelastic scattering

Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.

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.

Time-dependent wave packet dynamics study of the resonances in the H + LiH+(v = 0, j = 0) → Li+ + H2 reaction at low collision energies

The depletion process of LiH⁺ by H collision plays an important role in the evolution of the early universe and astrophysical processes, including the eventual charge-states, abundances of atomic and molecular species and ensuing astrochemistry. Here, a quantum dynamics study on the H + LiH⁺(v = 0, j = 0) → Li⁺ + H₂ reaction is performed at the low collision energy range from 0.1 meV to 10 meV using the time-dependent wave packet method. A Feshbach resonance peak is observed near 0.8 meV collision energy on the total reaction probability curves. This resonance originates from the coupling with the v = 0, j = 1 energy level of the reactant LiH⁺, and it is dominated by the contributions of J = 0-4 partial waves. Another partial wave resonance is also found on the total integral cross section at 1.2 meV, which is closely connected to the opening of the J = 7 partial wave. The opening of the J = 7 partial wave generates a notable forward scattering peak, and the Feshbach resonance can promote both the forward and backward scatterings. Moreover, the total and product vibrational state-resolved rate coefficients for the temperature range of 1-100 K are also reported.

Long-range model of vibrational autoionization in core-nonpenetrating Rydberg states of NO

In high orbital angular momentum (ℓ ≥ 3) Rydberg states, the centrifugal barrier hinders the close approach of the Rydberg electron to the ion-core. As a result, these core-nonpenetrating Rydberg states can be well described by a simplified model in which the Rydberg electron is only weakly perturbed by the long-range electric properties (i.e., multipole moments and polarizabilities) of the ion-core. We have used a long-range model to describe the vibrational autoionization dynamics of high-ℓ Rydberg states of nitric oxide (NO). In particular, our model explains the extensive angular momentum exchange between the ion-core and the Rydberg electron that had been previously observed in vibrational autoionization of f (ℓ = 3) Rydberg states. These results shed light on a long-standing mechanistic question around these previous observations and support a direct, vibrational mechanism of autoionization over an indirect, predissociation-mediated mechanism. In addition, our model correctly predicts newly measured total decay rates of g (ℓ = 4) Rydberg states because for ℓ ≥ 4, the non-radiative decay is dominated by autoionization rather than predissociation. We examine the predicted NO⁺ ion rotational state distributions generated by vibrational autoionization of g states and discuss applications of our model to achieve quantum state selection in the production of molecular ions.

Full-Dimensional Global Potential Energy Surface for the KRb + KRb → K2Rb2* → K2 + Rb2 Reaction with Accurate Long-Range Interactions and Quantum Statistical Calculation of the Product State Distribution under Ultracold Conditions

A full-dimensional global potential energy surface (PES) for the KRb + KRb → K₂Rb₂* → K₂ + Rb₂ reaction is reported based on high-level ab initio calculations. The short-range part of the PES is fit with the permutationally invariant polynomial-neural network method, while the long-range parts of the PES in both the reactant and product asymptotes are represented by an asymptotically correct form. The long- and short-range parts are connected with intermediate-range parts to make them smooth. Within a statistical quantum model, this PES reproduces both the measured loss rates of ultracold KRb molecules and the K₂ and Rb₂ product state distributions, underscoring the important role of tunneling in ultracold chemistry. The PES also correctly predicts the lifetime of the K₂Rb₂* intermediate complex within the Rice-Ramsperger-Kassel-Marcus limit. It thus provides a reliable platform for future dynamical studies of the prototypical reaction.

Quantum reactive scattering calculations for the cold and ultracold Li + LiNa → Li2 + Na reaction

A first-principles based quantum dynamics study of the Li + LiNa(v = 0, j = 0) → Li₂(v^', j') + Na reaction is reported for collision energies spanning the ultracold (1 nK) to cold (1 K) regimes. A full-dimensional ab initio potential energy surface for the ground electronic state of Li₂Na is utilized that includes an accurate treatment of the long-range interactions. The Li + LiNa reaction is barrierless and exoergic and exhibits a deep attractive potential well that supports complex formation. Thus, significant reactivity occurs even for collision temperatures approaching absolute zero. The reactive scattering calculations are based on a numerically exact time-independent quantum dynamics methodology in hyperspherical coordinates. Total and rotationally resolved rate coefficients are reported at 56 collision energies and include all contributing partial waves. Several shape resonances are observed in many of the rotationally resolved rate coefficients and a small resonance feature is also reported in the total rate coefficient near 50 mK. Of particular interest, the angular distributions or differential cross sections are reported as a function of both the collision energy and scattering angle. Unique quantum fingerprints (bumps, channels, and ripples) are observed in the angular distributions for each product rotational state due to quantum interference and shape resonance contributions. The Li + LiNa reaction is under active experimental investigation so that these intriguing features could be verified experimentally when sufficient product state resolution becomes feasible for collision energies below 1 K.

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.

Ion-Molecule Reactions below 1 K: Strong Enhancement of the Reaction Rate of the Ion-Dipole Reaction He^{+}+CH_{3}F

The reaction between He^{+} and CH_{3}F forming predominantly CH_{2}^{+} and CHF^{+} has been studied at collision energies E_{coll} between 0 and k_{B}·10  K in a merged-beam apparatus. To avoid heating of the ions by stray electric fields, the reaction was observed within the orbit of a highly excited Rydberg electron. Supersonic beams of CH_{3}F and He(n) Rydberg atoms with principal quantum number n=30 and 35 were merged and their relative velocity tuned using a Rydberg-Stark decelerator and deflector, allowing an energy resolution of 150 mK. A strong enhancement of the reaction rate was observed below E_{coll}/k_{B}=1  K. The experimental results are interpreted with an adiabatic capture model that accounts for the state-dependent orientation of the polar CH_{3}F molecules by the Stark effect as they approach the He^{+} ion. The enhancement of the reaction rate at low collision energies is primarily attributed to para-CH_{3}F molecules in the J=1, KM=1 high-field-seeking states, which represent about 8% of the population at the 6 K rotational temperature of the supersonic beam.

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.

Investigation of the low-energy stereodynamics in the Ne(3P2) + N2, CO reactions

We report on an experimental investigation of the low-energy stereodynamics of the energy transfer reactions Ne(³P₂) + X, producing Ne(¹S) + X⁺ and [Ne-X]⁺ (X = N₂ or CO). Collision energies in the range 0.2 K-700 K are obtained by using the merged beam technique. Two kinds of product ions are generated by Penning and associative ionization, respectively. The intermediate product [Ne-X]⁺ in vibrationally excited states can predissociate into bare ions (X⁺). The experimental ratio of the NeX⁺ and X⁺ product ion yields is similar for both molecules at high collision energies but diverge at collision energies below 100 K. This difference is explained by the first excited electronic state of the product ions, which is accessible in the case of CO but lies too high in energy in the case of N₂.

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.

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.

General mathematical formulation of scattering processes in atom-diatomic collisions in the RmatReact methodology

Accurately modelling cold and ultracold reactive collisions occurring over deep potential wells, such as [Formula: see text], requires the development of new theoretical and computational methodologies. One potentially useful framework is the R-matrix method adopted widely for electron-molecule collisions which has more recently been applied to non-reactive heavy-particle collisions such as Ar-Ar. The existing treatment of non-reactive elastic and inelastic scattering needs to be substantially extended to enable modelling of reactive collisions: this is the subject of this paper. Herein, we develop the general mathematical formulation for non-reactive elastic and inelastic scattering, photoassociation, photodissociation, charge exchange and reactive scattering using the R-matrix method. Of particular note is that the inner region, of central importance to calculable R-matrix methodologies, must be finite in all scattering coordinates rather than a single scattering coordinate as for non-reactive scattering. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H₃⁺, H₅⁺ and beyond'.

Oriented Polar Molecules Trapped in Cold Helium Nanodropets: Electrostatic Deflection, Size Separation, and Charge Migration

Helium nanodroplets doped with polar molecules are studied by electrostatic deflection. This broadly applicable method allows even polyatomic molecules to attain subkelvin temperatures and nearly full orientation in the field. The resulting intense force from the field gradient strongly deflects even droplets with tens of thousands of atoms, the most massive neutral systems studied by beam "deflectometry." We use the deflections to extract droplet size distributions. Moreover, since each host droplet deflects according to its mass, spatial filtering of the deflected beam translates into size filtering of neutral fragile nanodroplets. As an example, we measure the dopant ionization probability as a function of droplet radius and determine the mean free path for charge hopping through the helium matrix. The technique will enable separation of doped and neat nanodroplets and size-dependent spectroscopic studies.

Restricted basis set coupled-channel calculations on atom-molecule collisions in magnetic fields

Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta J of the collision complex. We show that by restricting the total angular momentum basis to include only the states with helicities K ≤ K_max, it is possible to obtain accurate elastic and inelastic cross sections for low-temperature He + CaH, Li + CaH, and Li + SrOH collisions in the presence of an external magnetic field at a small fraction of the computational cost of the full coupled-channel calculations (where K is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field, with the minimal basis set (K_max = 0) producing quantitatively accurate results for, e.g., ultracold Li + CaH and Li + SrOH scattering at low magnetic fields, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in the magnetic field dependence of Li + CaH and Li + SrOH inelastic cross sections in the few partial wave-regime as well as indirect spin relaxation in He + CaH collisions. Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different K and the couplings between the rotational states of the same K induced by the anisotropy of the interaction potential.

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.

Quantum-state-controlled channel branching in cold Ne(3P2)+Ar chemi-ionization

A prerequisite to gain a complete understanding of the most basic aspects of chemical reactions is the ability to perform experiments with complete control over the reactant degrees of freedom. By controlling these, details of a reaction mechanism can be investigated and ultimately manipulated. Here, we present a study of chemi-ionization-a fundamental energy-transfer reaction-under completely controlled conditions. The collision energy of the reagents was tuned from 0.02 K to 1,000 K, with the orientation of the excited Ne atom relative to Ar fully specified by an external magnetic field. Chemi-ionization of Ne(³P₂) and Ar in these conditions enables a detailed investigation of how the reaction proceeds, and provides us with a means to control the branching ratio between the two possible reaction outcomes. The merged-beam experimental technique used here allows access to a low-energy regime in which the atoms dynamically reorient into a favourable configuration for reaction, irrespective of their initial orientations.

Molecules and the Eigenstate Thermalization Hypothesis

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N³, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

Low-temperature chemistry using the R-matrix method

Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.

Cold quantum-controlled rotationally inelastic scattering of HD with H2 and D2 reveals collisional partner reorientation

Molecular interactions are best probed by scattering experiments. Interpretation of these studies has been limited by lack of control over the quantum states of the incoming collision partners. We report here the rotationally inelastic collisions of quantum-state prepared deuterium hydride (HD) with H₂ and D₂ using a method that provides an improved control over the input states. HD was coexpanded with its partner in a single supersonic beam, which reduced the collision temperature to 0-5 K, and thereby restricted the involved incoming partial waves to s and p. By preparing HD with its bond axis preferentially aligned parallel and perpendicular to the relative velocity of the colliding partners, we observed that the rotational relaxation of HD depends strongly on the initial bond-axis orientation. We developed a partial-wave analysis that conclusively demonstrates that the scattering mechanism involves the exchange of internal angular momentum between the colliding partners. The striking differences between H₂/HD and D₂/HD scattering suggest the presence of anisotropically sensitive resonances.

Communication: General variational approach to nuclear-quadrupole coupling in rovibrational spectra of polyatomic molecules

A general algorithm for computing the quadrupole-hyperfine effects in the rovibrational spectra of polyatomic molecules is presented for the case of ammonia (NH₃). The method extends the general variational approach TROVE [J. Mol. Spectrosc. 245, 126-140 (2007)] by adding the extra term in the Hamiltonian that describes the nuclear quadrupole coupling, with no inherent limitation on the number of quadrupolar nuclei in a molecule. We applied the new approach to compute the nitrogen-nuclear-quadrupole hyperfine structure in the rovibrational spectrum of NH314. These results agree very well with recent experimental spectroscopic data for the pure rotational transitions in the ground vibrational and ν₂ states and the rovibrational transitions in the ν₁, ν₃, 2ν₄, and ν₁ + ν₃ bands. The computed hyperfine-resolved rovibrational spectrum of ammonia will be beneficial for the assignment of experimental rovibrational spectra, further detection of ammonia in interstellar space, and studies of the proton-to-electron mass variation.

Ab initio calculations of spectroscopic constants and vibrational state lifetimes of diatomic alkali-alkaline-earth cations

We investigate the lifetimes of vibrational states of diatomic alkali-alkaline-earth cations to determine their suitability for ultracold experiments where long decoherence time and controllability by an external electric field are desirable. The potential energy and permanent dipole moment curves for the ground electronic states of LiBe⁺, LiMg⁺, NaBe⁺, and NaMg⁺ are obtained using the coupled cluster with singles doubles and triples and multireference configuration interaction methods in combination with large all-electron cc-pCVQZ and aug-cc-pCV5Z basis sets. The energies and wave functions of all vibrational states are obtained by solving the Schrödinger equation for nuclei with the B-spline basis set method. To predict the lifetimes of vibrational states, the transition dipole moments, as well as the Einstein coefficients describing spontaneous emission, and the stimulated absorption and emission induced by black body radiation are calculated. Surprisingly, in all studied ions, the lifetimes of the highest excited vibrational states are similar to the lifetimes of the ground vibrational states indicating that highly vibrationally excited ions could be useful for the ultracold experiments requiring long decoherence time.

Development of a wavy Stark velocity filter for studying interstellar chemistry

Cold polar molecules are key to both the understanding of fundamental physics and the characterization of the chemical evolution of interstellar clouds. To facilitate such studies over a wide range of temperatures, we developed a new type of Stark velocity filter for changing the translational and rotational temperatures of velocity-selected polar molecules without changing the output beam position. The translational temperature of guided polar molecules can be significantly varied by exchanging the wavy deflection section with one having a different radius of the curvature and a different deflection angle. Combining in addition a temperature variable gas cell with the wavy Stark velocity filter enables to observe the translational and rotational temperature dependence of the reaction-rate constants of cold ion-polar molecule reactions over the interesting temperature range of 10-100 K.

Perspective: Advanced particle imaging

Since the first ion imaging experiment [D. W. Chandler and P. L. Houston, J. Chem. Phys. 87, 1445-1447 (1987)], demonstrating the capability of collecting an image of the photofragments from a unimolecular dissociation event and analyzing that image to obtain the three-dimensional velocity distribution of the fragments, the efficacy and breadth of application of the ion imaging technique have continued to improve and grow. With the addition of velocity mapping, ion/electron centroiding, and slice imaging techniques, the versatility and velocity resolution have been unmatched. Recent improvements in molecular beam, laser, sensor, and computer technology are allowing even more advanced particle imaging experiments, and eventually we can expect multi-mass imaging with co-variance and full coincidence capability on a single shot basis with repetition rates in the kilohertz range. This progress should further enable "complete" experiments-the holy grail of molecular dynamics-where all quantum numbers of reactants and products of a bimolecular scattering event are fully determined and even under our control.

Electrostatic Deflection of a Molecular Beam of Massive Neutral Particles: Fully Field-Oriented Polar Molecules within Superfluid Nanodroplets

Electric deflection measurements on liquid helium nanodroplets doped with individual polar molecules demonstrate that the cold superfluid matrix enables full orientation of the molecular dipole along the external field. This translates into a deflection force that is increased enormously by comparison with typical deflection experiments, and it becomes possible to measurably deflect neutral doped droplets with masses of tens to hundreds of thousands of Daltons. By using continuous fluxes of fully oriented polar molecules and measuring the deflection of the doped nanodroplet beam, this approach makes it possible to directly determine the dipole moments of internally cryogenically cold molecules. The technique is broadly and generally applicable, including to complex and biological molecules.

Unraveling Cold Molecular Collisions: Stark Decelerators in Crossed-Beam Experiments

In the last two decades, enormous progress has been made in the manipulation of molecular beams. In particular, molecular decelerators have been developed with which advanced control over neutral molecules in a beam can be achieved. By using arrays of inhomogeneous and time-varying electric (or magnetic) fields, bunches of molecules can be produced with a tunable velocity, narrow velocity spreads, and almost perfect quantum-state purity. These monochromatic or "tamed" molecular beams are ideally suited to be used in crossed-molecular-beam scattering experiments. Here, we review the first generation of these "cold and controlled" scattering experiments that have been conducted in the last decade and discuss the prospects for this emerging field of research in the years to come.

Production of high density molecular beams with wide velocity scanning

We describe modifications of a pulsed rotating supersonic beam source that improve performance, particularly increasing the beam density and sharpening the pulse profiles. As well as providing the familiar virtues of a supersonic molecular beam (high intensity, narrowed velocity distribution, and drastic cooling of rotation and vibration), the rotating source enables scanning the translational velocity over a wide range. Thereby, beams of any atom or molecule available as a gas can be slowed or speeded. Using Xe beams in the slowing mode, we have obtained lab speeds down to about 40 ± 5 m/s with density near 10(11) cm(-3) and in the speeding mode lab speeds up to about 660 m/s and density near 10(14) cm(-3). We discuss some congenial applications. Providing low lab speeds can markedly enhance experiments using electric or magnetic fields to deflect, steer, or further slow polar or paramagnetic molecules. The capability to scan molecular speeds facilitates merging velocities with a codirectional partner beam, enabling study of collisions at very low relative kinetic energies, without requiring either beam to be slow.

Cold and intense OH radical beam sources

We present the design and performance of two supersonic radical beam sources: a conventional pinhole-discharge source and a dielectric barrier discharge (DBD) source, both based on the Nijmegen pulsed valve. Both designs have been characterized by discharging water molecules seeded in the rare gases Ar, Kr, or Xe. The resulting OH radicals have been detected by laser-induced fluorescence. The measured OH densities are (3.0 ± 0.6) × 10(11) cm(-3) and (1.0 ± 0.5) × 10(11) cm(-3) for the pinhole-discharge and DBD sources, respectively. The beam profiles for both radical sources show a relative longitudinal velocity spread of about 10%. The absolute rotational ground state population of the OH beam generated from the pinhole-discharge source has been determined to be more than 98%. The DBD source even produces a rotationally colder OH beam with a population of the ground state exceeding 99%. For the DBD source, addition of O2 molecules to the gas mixture increases the OH beam density by a factor of about 2.5, improves the DBD valve stability, and allows to tune the mean velocity of the radical beam.

Observation of quantum dynamical resonances in near cold inelastic collisions of astrophysical molecules

Quantum resonances in inelastic collisions, predicted by theory and detected at low energies in a crossed-beam experiment, are reviewed.

This mini review summarizes experimental findings of quantum dynamical resonances in inelastic collisions at energies equivalent to temperatures of a few to a few tens of Kelvin, corresponding to physical conditions prevailing in dense molecular clouds of the interstellar medium. Information obtained is thus relevant to collision energy transfer modelling in such media. Crossed-beam scattering experiments performed at Bordeaux university for inelastic collisions of important astrophysical molecules such as CO with H₂ or He and O₂ with H₂ are described. The peaks that show up in the collision energy dependence of the state-to-state integral cross sections for the lowest rotational excitation transitions reveal the quantum nature of such processes. They are ascribed as shape and Feshbach resonances by comparison with the results of close coupling quantum mechanical calculations performed concomitantly on accurate potential energy surfaces.

Slowing and cooling of heavy or light (even with a tiny electric dipole moment) polar molecules using a novel, versatile electrostatic Stark decelerator

To meet some demands for realizing precise measurements of an electric dipole moment of electron (eEDM) and examining cold collisions or cold chemical physics, we have proposed a novel, versatile electrostatic Stark decelerator with an array of true 3D electric potential wells, which are created by a series of horizontally-oriented, U-shaped electrodes with time-sequence controlling high voltages (± HV) and two guiding electrodes with a constant voltage. We have calculated the 2D electric field distribution, the Stark shifts of the four lowest rotational sub-levels of PbF molecules in the X1(2)Π1/2(v = 0) electronic and vibrational ground states as well as the population in the different rotational levels. We have discussed the 2D longitudinal and transverse phase-space acceptances of PbF molecules in our decelerator. Subsequently, we have simulated the dynamic processes of the decelerated PbF molecules using the 3D Monte-Carlo method, and have found that a supersonic PbF beam with a velocity of 300 m s(-1) can be efficiently slowed to about 5 m s(-1), which will greatly enhance the sensitivities to research a parity violation and measure an eEDM. In addition, we have investigated the dependences of the longitudinal velocity spread, longitudinal temperature and bunching efficiency on both the number of guiding stages and high voltages, and found that after bunching, a cold packet of PbF molecules in the J = 7/2, MΩ = -7/4 state with a longitudinal velocity spread of 0.69 m s(-1) (corresponding to a longitudinal temperature of 2.35 mK) will be produced by our high-efficient decelerator, which will generate a high energy-resolution molecular beam for studying cold collision physics. Finally, our novel decelerator can also be used to efficiently slow NO molecules with a tiny electric dipole moment (EDM) of 0.16 D from 315 m s(-1) to 28 m s(-1). It is clear that our proposed new decelerator has a good slowing performance and experimental feasibility as well as wide applications in the field of precise measurements and cold molecule physics.

Electric dipole moments and chemical bonding of diatomic alkali-alkaline earth molecules

We investigate the properties of alkali-alkaline earth diatomic molecules in the lowest Σ(+) states of the doublet and quartet multiplicity by ab initio calculations. In all sixteen cases studied, the permanent electric dipole moment points in opposite directions for the two spin states. This peculiarity can be explained by molecular orbital theory. We further discuss dissociation energies and bond distances. We analyze trends and provide an empirically motivated model for the prediction of the permanent electric dipole moment for combinations of alkali and alkaline earth atoms not studied in this work.

Optoelectrical Cooling of Polar Molecules to Submillikelvin Temperatures

We demonstrate direct cooling of gaseous formaldehyde (H2CO) to the microkelvin regime. Our approach, optoelectrical Sisyphus cooling, provides a simple dissipative cooling method applicable to electrically trapped dipolar molecules. By reducing the temperature by 3 orders of magnitude and increasing the phase-space density by a factor of ∼10(4), we generate an ensemble of 3×10(5) molecules with a temperature of about 420  μK, populating a single rotational state with more than 80% purity.

Comb-assisted cavity ring-down spectroscopy of a buffer-gas-cooled molecular beam

We demonstrate continuous-wave cavity ring-down spectroscopy of a partially hydrodynamic molecular beam emerging from a buffer-gas-cooling source.

Spectral statistics of molecular resonances in erbium isotopes: How chaotic are they?

We perform a comprehensive analysis of the spectral statistics of the molecular resonances in (166)Er and (168)Er observed in recent ultracold collision experiments [Frisch et al., Nature (London) 507, 475 (2014)] with the aim of determining the chaoticity of this system. We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. The analysis of the short-range fluctuations as a function of the magnetic field points to a steady increase of chaoticity until B∼30 G. The repulsion parameter decreases for higher magnetic fields, an effect that can be interpreted as due to missing resonances. The analysis of long-range fluctuations allows us to be more quantitative and estimate a 20%-25% fraction of missing levels. Finally, a study of the distribution of resonance widths provides additional evidence supporting missing resonances of small width compared with the experimental magnetic field resolution. We conclude that further measurements with increased resolution will be necessary to give a final answer to the problem of missing resonances and the agreement with RMT.

Cold and Controlled Molecular Beams: Production and Applications

The field of cold molecules has become an important source of new insight in fundamental chemistry and molecular physics. High-resolution spectroscopy benefits from translationally and internally cold molecules by increased interaction times and reduced spectral congestion. Completely new effects in scattering dynamics become accessible with cold and controlled molecules. Many of these experiments use molecular beams as a starting point for the generation of molecular samples. This review gives an overview of methods to produce beams of cold molecules, starting from supersonic expansions or effusive sources, and provides examples of applications in spectroscopy and molecular dynamics studies.