Molecular hydrogen interacts more strongly when rotationally excited at low temperatures leading to faster reactions

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 hot molecules

In this Perspective, we review our recent work on rotationally inelastic collisions of highly vibrationally excited NO molecules prepared in single rotational and parity levels at v = 10 using stimulated emission pumping (SEP). This state preparation is employed in a recently developed crossed molecular beam apparatus where two nearly copropagating molecular beams achieve an intersection angle of 4° at the interaction region. This near-copropagating beam geometry of the molecular beams permits very wide tuning of the collision energy, from far above room temperature down to 2 K where we test the theoretical treatment of the attractive part of the potentials and the difference potential for the first time. We have obtained differential cross sections for state-to-state collisions of NO (v = 10) with Ar and Ne in both spin-orbit manifolds using velocity map imaging. Overall good agreement of the experimental results was seen with quantum mechanical close-coupling calculations done on both coupled-cluster and multi-reference configuration interaction potential energy surfaces. Probing cold collisions of NO carrying ∼2 eV of vibrational excitation allows us to test state-of-the-art theory in this extreme nonequilibrium regime.

Enhancing reactivity of SiO+ ions by controlled excitation to extreme rotational states

Optical pumping of molecules provides unique opportunities for control of chemical reactions at a wide range of rotational energies. This work reports a chemical reaction with extreme rotational excitation of a reactant and its kinetic characterization. We investigate the chemical reactivity for the hydrogen abstraction reaction SiO⁺ + H₂ → SiOH⁺ + H in an ion trap. The SiO⁺ cations are prepared in a narrow rotational state distribution, including super-rotor states with rotational quantum number (j) as high as 170, using a broad-band optical pumping method. We show that the super-rotor states of SiO⁺ substantially enhance the reaction rate, a trend reproduced by complementary theoretical studies. We reveal the mechanism for the rotational enhancement of the reactivity to be a strong coupling of the SiO⁺ rotational mode with the reaction coordinate at the transition state on the dominant dynamical pathway.

Symmetry Dependence of the Continuum Coupling in the Chemi-ionization of Li(22S1/2) by He(23S1, 23PJ)

In the literature, the chemi-ionization of Li in the 2²S_1/2 ground level by He in a metastable state is typically described as an electron transfer process in which an electron from the 2s orbital of Li is transferred to the 1s orbital of He while an electron from the 2s orbital of He is ejected. Therefore, one would not assume that the orbital of the valence electron of He strongly influences the coupling strength of the collision complex to the ionization continuum. However, we observe that the chemi-ionization rate is decreased when He is laser-excited from the metastable 2³S₁ level to the 2³P_J level (with J = 0, 1, 2). A semiclassical treatment of the reaction dynamics reveals a strong dependence of the ionization rate on the reaction-channel-specific ionization width functions to which the observed decrease of the rate coefficients can be related to. The results are relevant for the improved understanding and control of chemi-ionization processes in merged beams and in traps.

The topology of the reaction stereo-dynamics in chemi-ionizations

Details on the stereo-dynamic topology of chemi-ionizations highlight the role of the centrifugal barrier of colliding reactants: it acts as a selector of the orbital quantum number effective for reaction in a state-to-state treatment. Here, an accurate internally consistent formulation of the Optical interaction potentials, obtained by the combined analysis of scattering and spectroscopic experimental findings, casts light on structure, energy and angular momentum couplings of the precursor (pre-reactive) state controlling the stereo-dynamics of prototypical chemi-ionization reactions. The closest approach (turning point) of reagents, is found to control the relative weight of two different reaction mechanisms: (i) A direct mechanism stimulated by exchange chemical forces mainly acting at short separation distances and high collision energy; (ii) An indirect mechanism, caused by the combination of weak chemical and physical forces dominant at larger distances, mainly probed at low collision energy, that can be triggered by a virtual photon exchange between reagents.

Reaction of an Ion and a Free Radical near 0 K: He+ + NO → He + N+ + O

The reactions between ions and free radicals are among the fastest chemical reactions. They are predicted to proceed with large rates, even near 0 K, but so far, this prediction has not been verified experimentally. We report on measurements of the rate coefficient of the reaction between the ion He⁺ and the free radical NO at collision energies in the range between 0 and ∼ k_B·10 K. To avoid heating of the ions by stray electric fields, the reaction is observed within the large orbit of a Rydberg electron of principal quantum number n ≥ 30, which shields the ion from external electric fields without affecting the reaction. Low collision energies are reached by merging a supersonic beam of He Rydberg atoms with a supersonic beam of NO molecules and adjusting their relative velocity using a chip-based Rydberg-Stark decelerator and deflector. We observe a strong enhancement of the reaction rate at collision energies below ∼k_B·2 K. This enhancement is interpreted on the basis of adiabatic-channel capture-rate calculations as arising from the near-degenerate rotational levels of opposite parity resulting from the Λ-doubling in the X ²Π_1/2 ground state of NO. With these new results, we examine the reliability of broadly used approximate analytic expressions for the thermal rate constants of ion-molecule reactions at low temperatures.

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.

Real-time hydrogen molecular dynamics satisfying the nuclear spin statistics of a quantum rotor

Apparent presence of the nuclear-spin species of a hydrogen molecule, para-hydrogen and ortho-hydrogen, associated with the quantum rotation is a manifestation of the nuclear quantum nature of hydrogen, governing not only molecular structures but also physical and chemical properties of hydrogen molecules. It has been a great challenge to observe and calculate real-time dynamics of such molecularized fermions. Here, we developed the non-empirical quantum molecular dynamics method that enables real-time molecular dynamics simulations of hydrogen molecules satisfying the nuclear spin statistics of the quantum rotor. While reproducing the species-dependent quantum rotational energy, population ratio, specific heat, and H-H bond length and frequency, we found that their translational, orientational and vibrational dynamics becomes accelerated with the higher rotational excitation, concluding that the nuclear quantum rotation stemmed from the nuclear spin statistics can induce various kinds of dynamics and reactions intrinsic to each hydrogen species.

Coherent Raman spectroscopy on hydrogen with in-situ generation, in-situ use, and in-situ referencing of the ultrabroadband excitation

Time-resolved spectroscopy can provide valuable insights in hydrogen chemistry, with applications ranging from fundamental physics to the use of hydrogen as a commercial fuel. This work represents the first-ever demonstration of in-situ femtosecond laser-induced filamentation to generate a compressed supercontinuum behind a thick optical window, and its in-situ use to perform femtosecond/picosecond coherent Raman spectroscopy (CRS) on molecular hydrogen (H₂). The ultrabroadband coherent excitation of Raman active molecules in measurement scenarios within an enclosed space has been hindered thus far by the window material imparting temporal stretch to the pulse. We overcome this challenge and present the simultaneous single-shot detection of the rotational H₂ and the non-resonant CRS spectra in a laminar H₂/air diffusion flame. Implementing an in-situ referencing protocol, the non-resonant spectrum measures the spectral phase of the supercontinuum pulse and maps the efficiency of the ultrabroadband coherent excitation achieved behind the window. This approach provides a straightforward path for the implementation of ultrabroadband H₂ CRS in enclosed environment such as next-generation hydrogen combustors and reforming reactors.

Differential Cross Sections for Cold, State-to-State Spin-Orbit Changing Collisions of NO(v = 10) with Neon

Inelastic scattering processes have proven a powerful means of investigating molecular interactions, and much current effort is focused on the cold and ultracold regime where quantum phenomena are clearly manifested. Studies of collisions of the open shell nitric oxide (NO) molecule have been central in this effort since the pioneering work of Houston and co-workers in the early 1990s. State-to-state scattering of vibrationally excited molecules in the cold regime introduces challenges that test the suitability of current theoretical methods for ab initio determination of intermolecular potentials, and concomitant electronically nonadiabatic processes raise the bar further. Here we report measurements of differential cross sections for state-to-state spin-orbit changing collisions of NO (v = 10, Ω″ = 1.5, and j″ = 1.5) with neon from 2.3 to 3.5 cm^-1 collision energy using our recently developed near-copropagating beam technique. The experimental results are compared with those obtained from quantum scattering calculations on a high-level set of coupled cluster potential energy surfaces and are shown to be in good agreement. The theoretical results suggest that distinct backscattering in the 2.3 cm^-1 case arises from overlapping resonances.

Complex energies and transition dipoles for shape-type resonances of uracil anion from stabilization curves via Padé

Absorption of slow moving electrons by neutral ground state nucleobases has been known to produce resonance metastable states. There are indications that such metastable states may play a key role in DNA/RNA damage. Therefore, herein, we present an ab initio non-Hermitian investigation of the resonance positions and decay rates for the low lying shape-type states of the uracil anion. In addition, we calculate the complex transition dipoles between these resonance states. We employ the resonance via Padé (RVP) method to calculate these complex properties from real stabilization curves by analytical dilation into the complex plane. This method has already been successfully applied to many small molecular systems, and herein, we present the first application of RVP to a medium-sized system. The presented resonance energies are optimized with respect to the size of the basis set and compared with previous theoretical studies and experimental findings. Complex transition dipoles between the shape-type resonances are computed using the optimal basis set. The ability to calculate ab initio energies and lifetimes of biologically relevant systems paves the way for studying reactions of such systems in which autoionization takes place, while the ability to also calculate their complex transition dipoles opens the door for studying photo-induced dynamics of such biological molecules.

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.

Multipole-moment effects in ion-molecule reactions at low temperatures: part I - ion-dipole enhancement of the rate coefficients of the He+ + NH3 and He+ + ND3 reactions at collisional energies Ecoll/kB near 0 K

The energy dependence of the rates of the reactions between He+ and ammonia (NY3, Y = {H,D}), forming NY2+, Y and He as well as NY+, Y2 and He, and the corresponding product branching ratios have been measured at low collision energies Ecoll between 0 and kB·40 K using a recently developed merged-beam technique [Allmendinger et al., ChemPhysChem, 2016, 17, 3596]. To avoid heating of the ions by stray electric fields, the reactions are observed within the large orbit of a highly excited Rydberg electron. A beam of He Rydberg atoms was merged with a supersonic beam of ammonia using a curved surface-electrode Rydberg-Stark deflector, which is also used for adjusting the final velocity of the He Rydberg atoms, and thus the collision energy. A collision-energy resolution of about 200 mK was reached at the lowest Ecoll values. The reaction rate coefficients exhibit a sharp increase at collision energies below ∼kB·5 K and pronounced deviations from Langevin-capture behaviour. The experimental results are interpreted in terms of an adiabatic capture model describing the rotational-state-dependent orientation of the ammonia molecules by the electric field of the He+ atom. The model faithfully describes the experimental observations and enables the identification of three classes of |JKMp〉 rotational states of the ammonia molecules showing different low-energy capture behaviour: (A) high-field-seeking states with |KM| ≥ 1 correlating to the lower component of the umbrella-motion tunnelling doublet at low fields. These states undergo a negative linear Stark shift, which leads to strongly enhanced rate coefficients; (B) high-field-seeking states subject to a quadratic Stark shift at low fields and which exhibit only weak rate enhancements; and (C) low-field-seeking states with |KM| ≥ 1. These states exhibit a positive Stark shift at low fields, which completely suppresses the reactions at low collision energies. Marked differences in the low-energy reactivity of NH3 and ND3-the rate enhancements in ND3 are more pronounced than in NH3-are quantitatively explained by the model. They result from the reduced magnitudes of the tunnelling splitting and rotational intervals in ND3 and the different occupations of the rotational levels in the supersonic beam caused by the different nuclear-spin statistical weights. Thermal capture rate constants are derived from the model for the temperature range between 0 and 10 K relevant for astrochemistry. Comparison of the calculated thermal capture rate coefficients with the absolute reaction rates measured above 27 K by Marquette et al. (Chem. Phys. Lett., 1985, 122, 431) suggests that only 40% of the close collisions are reactive.

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.

Molecular hydrogen in agriculture

H₂ gas, usually in the form of H₂-saturated water, could play a useful role in improving many aspects of plant growth and productivity, including resistance to stress tolerance and improved post-harvest durability. Therefore, molecular hydrogen delivery systems should be considered as a valuable addition within agricultural practice. Agriculture and food security are both impacted by plant stresses, whether that is directly from human impact or through climate change. A continuously increasing human population and rising food consumption means that there is need to search for agriculturally useful and environment friendly strategies to ensure future food security. Molecular hydrogen (H₂) research has gained momentum in plant and agricultural science owing to its multifaceted and diverse roles in plants. H₂ application can mitigate against a range of stresses, including salinity, heavy metals and drought. Therefore, knowing how endogenous, or exogenously applied, H₂ enhances the growth and tolerance against numerous plant stresses will enhance our understanding of how H₂ may be useful for future to agriculture and horticulture. In this review, recent progress and future implication of H₂ in agriculture is highlighted, focusing on how H₂ impacts on plant cell function and how it can be applied for better plant performance. Although the exact molecular action of H₂ in plants remains elusive, this safe and easy to apply treatment should have a future in agricultural practice.

Uniform vs Partial Scaling within Resonances via Padé Based on the Similarities to Other Non-Hermitian Methods: Illustration for the Beryllium 1s22p3s State

Resonance via Padé (RVP) is an efficient method for calculating autoionization resonance states. It is based on the stabilization technique in which the basis set is scaled. The scaling can be uniform (i.e., all basis functions are scaled) or partial. Herein, we compare the two RVP scaling schemes for calculating an autoionization eigenvalue; moreover, the effect of freezing the core electrons is intertwined within this comparison. In order to study the different behavior of the RVP schemes, we associate each RVP scaling scheme with a complex contour of integration. Similarities between RVP and other non-Hermitian methods emerge from the generated contours, which suggest that RVP introduces similar outgoing boundary conditions as the complex scaling (CS), complex basis function (CBF), and reflection-free complex absorbing potential (RF-CAP) methods. A uniform-RVP contour, unlike a partial one, immediately penetrates the complex plane and influences the interaction region. Hence, uniform scaling within RVP destroys the description of the core electrons, as well as the description of the reference state, and yields less reliable results than partial scaling. The 1s²2p3s ¹P autoionization state of Be, at the equation-of-motion coupled-cluster level, is used as our case study model.

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.

Kinetic Isotope Effect in Low-Energy Collisions between Hydrogen Isotopologues and Metastable Helium Atoms: Theoretical Calculations Including the Vibrational Excitation of the Molecule

We present very accurate theoretical results of Penning ionization rate coefficients of the excited metastable helium atoms (⁴He(2³S) and ³He(2³S)) colliding with the hydrogen isotopologues (H₂, HD, D₂) in the ground and first excited rotational and vibrational states at subkelvin regime. The calculations are performed using the current best ab initio interaction energy surface, which takes into account the nonrigidity effects of the molecule. The results confirm a recently observed substantial quantum kinetic isotope effect (Nat. Chem. 2014, 6, 332-335) and reveal that the change of the rotational or vibrational state of the molecule can strongly enhance or suppress the reaction. Moreover, we demonstrate the mechanism of the appearance and disappearance of resonances in Penning ionization. The additional model computations, with the morphed interaction energy surface and mass, give better insight into the behavior of the resonances and thereby the reaction dynamics under study. Our theoretical findings are compared with all available measurements, and comprehensive data for prospective experiments are provided.

The H2+ + HD reaction at low collision energies: H3+/H2D+ branching ratio and product-kinetic-energy distributions

The fully state-selected reactions between H2+ molecules in the X+ 2Σg+(v+ = 0, N+ = 0) state and HD molecules in the X 1Σg+(v = 0, J = 0) state forming H3+ + D and H2D+ + H have been studied at collision energies Ecoll between 0 and kB·30 K with a resolution of about 75 mK at the lowest energies. H2 molecules in a supersonic beam were prepared in Rydberg-Stark states with principal quantum number n = 27 and merged with a supersonic beam of ground-state HD molecules using a curved surface-electrode Rydberg-Stark decelerator and deflector. The reaction between H2+ and HD was studied within the orbit of the Rydberg electron to avoid heating of the ions by stray electric fields. The reaction was observed for well-defined and adjustable time intervals, called reaction-observation windows, between two electric-field pulses. The first pulse swept all ions away from the reaction volume and its falling edge defined the beginning of the reaction-observation window. The second pulse extracted the product ions toward a charged-particle detector located at the end of a time-of-flight tube and its rising edge defined the end of the reaction-observation window. Monitoring and analysing the time-of-flight distributions of the H3+ and H2D+ products in dependence of the duration of the reaction-observation window enabled us to obtain information on the kinetic-energy distribution of the product ions and determine branching ratios of the H3+ + D and H2D+ + H reaction channels. The mean product-kinetic-energy release is 0.46(5) eV, representing 27(3)% of the available energy, and the H3+ + D product branching ratio is 0.225(20). The relative reaction rates correspond closely to Langevin capture rates down to the lowest energies probed experimentally (≈kB·50 mK).

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.

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.

Direct observation of a Feshbach resonance by coincidence detection of ions and electrons in Penning ionization collisions

Observation of molecular dynamics with quantum state resolution is one of the major challenges in chemical physics. Complete characterization of collision dynamics leads to the microscopic understanding and unraveling of different quantum phenomena such as scattering resonances. Here we present an experimental approach for observing molecular dynamics involving neutral particles and ions that is capable of providing state-to-state mapping of the dynamics. We use Penning ionization reaction between argon and metastable helium to generate argon ion and ground state helium atom pairs at separation of several angstroms. The energy of an ejected electron carries the information about the initial electronic state of an ion. The coincidence detection of ionic products provides a state resolved description of the post-ionization ion-neutral dynamics. We demonstrate that correlation between the electron and ion energy spectra enables us to directly observe the spin-orbit excited Feshbach resonance state of HeAr+. We measure the lifetime of the quasi-bound HeAr+ A2 state and discuss possible applications of our method.

A versatile molecular beam apparatus for cold/ultracold collisions

We have developed an apparatus capable of performing intrabeam and near-copropagating beam scattering experiments at collision energies from room temperature to below 1 K where interesting quantum phenomena can be observed. A detailed description of the major components of the apparatus, single and dual molecular beam valves, high speed chopper, and the discharge source, is presented. With the intrabeam scattering setup, a novel dual-slit chopper permits collision energies down to millikelvins with a collision energy spread of 20%. With the near-copropagating beam configuration, state-to-state differential cross sections for rotationally inelastic collisions of highly vibrationally excited NO molecules with Ar have been measured at broadly tunable energies documenting the versatility of the instrument. Future applications in stereodynamics and cold state-to-state collisions of vibrationally excited polyatomic molecules are briefly discussed.

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.

Universal crossed beam imaging studies of polyatomic reaction dynamics

Crossed-beam imaging studies of polyatomic reactions show surprising dynamics not anticipated by extrapolation from smaller model systems.

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.

Complexes of Alkali Metal Cations and Molecular Hydrogen: Potential Energy Surfaces and Bound States

Complexes between metal cations and molecular hydrogen are systems quite amenable for precise spectroscopic and theoretical studies, and at the same time, they are relevant for applications in hydrogen storage and astrochemistry. In this work, we report new intermolecular potential energy surfaces and rovibrational states calculations for complexes involving molecular hydrogen and alkaline metal cations, M⁺-H₂ (M⁺ = Na⁺, K⁺, Rb⁺, Cs⁺). The intermolecular potentials, formulated in an internally consistent way to emphasize differences in the properties of the systems, are represented by simple analytical expressions whose parameters have been optimized from comparison with accurate ab initio calculations. Properties of the low-lying bound states-binding energies, frequencies, and rotational constants-are compared with previous measurements or computations and an overall good agreement is achieved, supporting the reliability of the present formulation. Variations of these properties as a function of the cation size and isotopic substitution, with a proper sequence of ortho and para rotational levels, are also discussed.

Sub-Kelvin Stereodynamics of the Ne(^{3}P_{2})+N_{2} Reaction

We present an experimental study of the low-energy stereodynamics of the Ne(^{3}P_{2})+N_{2} reaction. Supersonic expansions of the two reactants are superposed in a merged beam experiment, where individual velocity control of the two beams allows us to reach average relative velocities of zero, yielding minimum collision energies around 60 mK. We combine the merged beam technique with the orientation of the metastable neon atoms and measure the branching between two reaction channels, Penning ionization and associative ionization, as a function of neon orientation and collision energy, covering the range 0.06-700 K. We find that we lose the ability to orient Ne below ≈100  K due to dynamic reorientation. Associative ionization products Ne-N_{2}^{+} predissociate with a probability of 30%-60% and that associative ionization is entirely due to reactions of the Ω=2 state, where the singly occupied p orbital of the Ne^{*} is oriented along the interatomic axis.

Interactions of benzene, naphthalene, and azulene with alkali-metal and alkaline-earth-metal atoms for ultracold studies

We consider collisional properties of polyatomic aromatic hydrocarbon molecules immersed into ultracold atomic gases and investigate intermolecular interactions of exemplary benzene, naphthalene, and azulene with alkali-metal (Li, Na, K, Rb, and Cs) and alkaline-earth-metal (Mg, Ca, Sr, and Ba) atoms. We apply the state-of-the-art ab initio techniques to compute the potential energy surfaces (PESs). We use the coupled cluster method restricted to single, double, and noniterative triple excitations to reproduce the correlation energy and the small-core energy-consistent pseudopotentials to model the scalar relativistic effects in heavier metal atoms. We also report the leading long-range isotropic and anisotropic dispersion and induction interaction coefficients. The PESs are characterized in detail, and the nature of intermolecular interactions is analyzed and benchmarked using symmetry-adapted perturbation theory. The full three-dimensional PESs are provided for the selected systems within the atom-bond pairwise additive representation and can be employed in scattering calculations. The present study of the electronic structure is the first step toward the evaluation of prospects for sympathetic cooling of polyatomic aromatic molecules with ultracold atoms. We suggest azulene, an isomer of naphthalene which possesses a significant permanent electric dipole moment and optical transitions in the visible range, as a promising candidate for electric field manipulation and buffer-gas or sympathetic cooling.

Differential Cross Sections for State-to-State Collisions of NO( v = 10) in Near-Copropagating Beams

State-to-state differential cross sections for rotationally inelastic collisions of vibrationally excited NO with Ar have been measured in a near-copropagating crossed beam experiment at collision energies of 530 and 30 cm^-1. Stimulated emission pumping (SEP) to prepare NO in specific rovibrational levels is coupled with direct-current slice velocity map imaging to obtain a direct measurement of the differential cross sections. The use of nearly copropagating beams to achieve low NO-Ar collision energies and broad collision energy tuning capability are also demonstrated. The experimental differential cross sections (DCSs) for NO in v = 10 in specific rotational and parity states are compared with the corresponding DCSs predicted for NO in v = 0 obtained from quantum mechanical close coupling calculations to highlight the differences between the NO( v = 10)-Ar and NO( v = 0)-Ar interaction potentials.

Quantum Effects in Cold Molecular Collisions from Spatial Polarization of Electronic Wave Function

The quantum phenomena of electronic and nuclear resonances are associated with structures in measured cross sections. Such structures were recently reported in a cold chemistry experiment of ground-state hydrogen isotopologues (H₂/HD) colliding with helium atoms in the excited triplet P-state (He(2³P)) [Shagam et al. Nature Chem. 2015, 7, 921], but a theoretical explanation of their appearance was not given. This work presents a quantum explanation and simulation of this experiment, which are strictly based on ab initio calculations. We incorporate complex potential energy surfaces into adiabatic variational theory, thereby reducing the multidimensional scattering process to a series of uncoupled 1D scattering "gedanken experiments". Our theoretical result, which is in remarkable agreement with the experimental data, manifests that the structures in the observed reaction rate coefficient are due to the spatial arrangement of the excited He p-orbitals with respect to the interaction axis, consequently changing the system from a normal two-rotor model to a three-rotor one. This theoretical scheme can be applied to explain and predict cross sections or reaction rate coefficients for any resonance-related phenomenon.

High-resolution collision energy control through ion position modulation in atom-ion hybrid systems

We demonstrate an ion shuttling technique for high-resolution control of atom-ion collision energy by translating an ion held within a radio-frequency trap through a magneto-optical atom trap. The technique is demonstrated both experimentally and through numerical simulations, with the experimental results indicating control of ion kinetic energies from 0.05 to 1 K with a fractional resolution of ∼10 and the simulations demonstrating that kinetic energy control up to 120 K with a maximum predicted resolution of ∼100 is possible, offering order-of-magnitude improvements over most alternative techniques. Finally, we perform a proof-of-principle chemistry experiment using this technique and outline how the method may be refined in the future and applied to the study of molecular ion chemistry.

Observation of different reactivities of para and ortho-water towards trapped diazenylium ions

Water is one of the most fundamental molecules in chemistry, biology and astrophysics. It exists as two distinct nuclear-spin isomers, para- and ortho-water, which do not interconvert in isolated molecules. The experimental challenges in preparing pure samples of the two isomers have thus far precluded a characterization of their individual chemical behavior. Capitalizing on recent advances in the electrostatic deflection of polar molecules, we separate the ground states of para- and ortho-water in a molecular beam to show that the two isomers exhibit different reactivities in a prototypical reaction with trapped diazenylium ions. Based on ab initio calculations and a modelling of the reaction kinetics using rotationally adiabatic capture theory, we rationalize this finding in terms of different rotational averaging of ion-dipole interactions during the reaction.

Water molecules exist as two distinct nuclear-spin isomers denoted ortho and para. Here, the authors separate these two isomers in the gas phase to show that they exhibit different reactivities in a prototypical proton-transfer reaction.

Enhancing radical molecular beams by skimmer cooling

A high-intensity supersonic beam source has been a key component in studies of molecular collisions, molecule-surface interaction, chemical reactions, and precision spectroscopy. However, the molecular density available for experiments in a downstream science chamber is limited by skimmer clogging, which constrains the separation between a valve and a skimmer to at least several hundred nozzle diameters. A recent experiment (Sci. Adv., 2017, 3, e1602258) has introduced a new strategy to address this challenge: when a skimmer is cooled to a temperature below the freezing point of the carrier gas, skimmer clogging can be effectively suppressed. We go beyond this proof-of-principle work in several key ways. Firstly, we apply the skimmer cooling approach to discharge-produced radical and metastable beams entrained in a carrier gas. We also identify two different processes for skimmer clogging mitigation-shockwave suppression at temperatures around the carrier gas freezing point and diffusive clogging at even lower temperatures. With the carrier clogging removed, we now fully optimize the production of entrained species such as hydroxyl radicals, resulting in a gain of 30 in density over the best commercial devices. The gain arises from both clogging mitigation and favorable geometry with a much shorter valve-skimmer distance.

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.

Simple Closed-Form Expression for Penning Reaction Rate Coefficients for Cold Molecular Collisions by Non-Hermitian Time-Independent Adiabatic Scattering Theory

We present a simple expression and its derivation for reaction rate coefficients for cold anisotropic collision experiments based on adiabatic variational theory and time-independent non-Hermitian scattering theory. We demonstrate that only the eigenenergies of the resulting one-dimensional Schrödinger equation for different complex adiabats are required. The expression is applied to calculate the Penning ionization rate coefficients of an excited metastable helium atom with molecular hydrogen in an energy range spanning from hundreds of kelvins down to the millikelvin regime. Except for trivial quantities like the masses of the nuclei and the bond length of the diatomic molecule participating in the collision, one needs as input data only the complex potential energy surface (CPES). In calculations, we used recently obtained ab initio CPES by D. Bhattacharya et al. ( J. Chem. Theory Comput. 2017 , 13 , 1682 - 1690 ) without fitting parameters. The results show good accord with current measurements ( Nat. Phys. 2017 , 13 , 35 - 38 ).

Intrabeam Scattering for Ultracold Collisions

We demonstrate a method to probe cold and ultracold chemistry in a single molecular beam. The approach exploits beam slippage, the velocity difference of different species in the same beam, to establish the relative velocity. Average collision energies of 2.5 mK are achieved but with a spread of 100% or more. However, by implementing a dual-slit chopper that can separately fix the velocities of the two species at the interaction region, we achieve precise control over the relative velocity and narrow its spread. Relative velocities of 7-10 ± 1.1 m/s are achieved with an angular divergence less than 0.25°. In the present study, we observe l-changing collisions occurring between Xe Rydberg atoms and Xe ground state atoms at subKelvin temperatures. We show that in this case the collision energies are tunable between 200 to 450 mK with a root-mean-square deviation of ∼18%. Application of the method to other species and access to much lower energies is straightforward.