Ion-dip and laser photoexcitation spectroscopy of high Rydberg states in N2

N2 molecules in pulsed supersonic beams have been laser photoexcited from their X Σg+1 ground electronic state to selected singlet np and nf Rydberg states using a (2 + 1') two-color three-photon excitation scheme. This required the competition between (2 + 1) resonance-enhanced multiphoton ionization and (2 + 1') Rydberg state photoexcitation to be carefully balanced. This was achieved by performing ion-dip spectroscopy in which the signal from the N2+ cations generated by direct photoionization was selectively detected and seen to reduce under conditions in which the predissociative np Rydberg states, or long-lived nf Rydberg states, were populated. The predissocation rates of the np Rydberg states were determined from the n-dependence of the spectral widths of the transitions to them. The long-lived Rydberg states populated by excitation on nf resonances are suitable for deceleration and electrostatically trapping cold samples of N2 using inhomogeneous electric fields.

Energy Landscapes in Chemical Reactions and Transport

Both, molecular chemical reactions and transport of atoms in solid media are determined by the energy landscape in which the seemingly different processes take place. Chemical reactions can be described as cooperative translocation of two chemical entities on a common potential energy surface. Transport of atoms in a solid can be envisaged as the translocation of a single particle in the potential energy landscape of all other particles constituting the solid. The goal of this manuscript is to demonstrate common grounds but also distinct differences in the physico-chemical processes, their experimental quantification and their theoretical modelling. This work will span the range from the historical foundations all the way to the current challenges. While scientists at the beginning of the 20th century where commonly active in both fields, e. g., Wilhelm Jost has pioneered and shaped the field of transport in solids and reaction kinetics in Germany, the fields have drifted apart for the last 50 decades. It is now time to bring the fields together again. Ultimately, it is suggested that knowledge gained in the field of transport may in fact stimulate advancement in the field of molecular reactivity and vice versa. Here, the energy landscapes are pivotal for knowledge-based advancement.

Low temperature dynamics of H + HeH+→ H2+ + He reaction: On the importance of long-range interaction

While the growing realization of the importance of long-range interactions is being demonstrated in cold and ultracold bimolecular collision experiments, their influence on one of the most critical ion-neutral reactions has been overlooked. Here, we address the non-Langevin abrupt decrease observed earlier in the low-energy integral cross-sections and rate coefficients of the astrochemically important H + HeH+→ H2+ + He reaction. We attribute this to the presence of artificial barriers on existing potential energy surfaces (PESs). By incorporating precise long-range interaction terms, we introduce a new refined barrierless PES for the electronic ground state of HeH2+ reactive system, aligning closely with high-level ab initio electronic energies. Our findings, supported by various classical, quantum, and statistical methods, underscore the significance of long-range terms in accurately modeling reactive PESs. The low-temperature rate coefficient on this new PES shows a substantial enhancement as compared to the previous results and aligns with the Langevin behavior. This enhancement could noticeably affect the prediction of HeH+ abundance in early Universe condition.

Cold reactions of He+ with OCS and CO2: competitive kinetics and the effects of the molecular multipole moments

The reactions of He+ with OCS and CO2 have been studied at collision energies between ∼kB ⋅ 200 mK and ∼kB ⋅ 30 K by merging a beam of Rydberg He atoms with rotationally cold (∼3.5 K) seeded supersonic expansions containing either OCS or 13CO2 or a mixture of OCS (mole fraction 23.2%) and 13CO2 (76.8%). The observed product ions of the He+ + 13CO2 and He+ + OCS reactions are 13CO+, and CS+ and CO+, respectively. The He+ + OCS capture rate coefficient increases by ∼75% with decreasing collision energy over the investigated range, whereas that of He+ + 13CO2 decreases by ∼40%. The analysis of the experimental results using an adiabatic-channel capture model indicates that these opposite collision-energy dependences of the rate coefficients arise from the interaction between the charge of the ion and the electric multipole moments of OCS and 13CO2. From the relative product-ion yields observed when using the mixture of OCS and 13CO2, the He+ + OCS collisions are inferred to be ∼20% more reactive than those between He+ and 13CO2. The comparison of the calculated thermal rate coefficients with earlier experiments suggests that about half of the He+ + 13CO2 collisions are reactive.

Electrostatic Trapping of N_{2} Molecules in High Rydberg States

N_{2} molecules traveling in pulsed supersonic beams have been excited from their X ^{1}Σ_{g}^{+} ground electronic state to long-lived Rydberg states with principal quantum numbers between 39 and 48 using a resonance-enhanced two-color three-photon excitation scheme. The Rydberg states populated had static electric dipole moments exceeding 5000 D which allowed deceleration of the molecules to rest in the laboratory-fixed frame of reference and three-dimensional trapping using inhomogeneous electric fields. The trapped molecules were confined for up to 10 ms, with effective trap decay time constants increasing with principal quantum number, and ranging from 450 to 700  μs. These observations, and comparison with the results of similar measurements with He atoms, indicate that the decay dynamics of the trapped Rydberg N_{2} molecules are dominated by spontaneous emission and do not exhibit significant contributions from effects of intramolecular interactions that lead to non-radiative decay.

Cold Ion-Molecule Reactions in the Extreme Environment of a Coulomb Crystal

Coulomb crystals provide a unique environment in which to study ion-neutral gas-phase reactions. In these cold, trapped ensembles, we are able to study the kinetics and dynamics of small molecular systems. These measurements have connections to chemistry in the Interstellar Medium (ISM) and planetary atmospheres. This Feature Article will describe recent work in our laboratory that uses Coulomb crystals to study translationally cold, ion-neutral reactions. We provide a description of how the various affordances of our experimental system allow for detailed studies of the reaction mechanisms and the corresponding products. In particular, we will describe quantum-state resolved reactions, isomer-dependent reactions, and reactions with a rarely studied, astrophysically relevant ion, CCl+.

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 ∼ kB·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 ∼kB·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 2Π1/2 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.

Ion-molecule reactions in the HBr+ + HCl (DCl) system: a combined experimental and theoretical study

Reactions in the system HBr⁺ + HCl (DCl) were investigated inside a guided ion-beam apparatus under single-collision conditions. In the HBr⁺ + HCl system, the proton transfer (PT_HCl) and charge transfer (CT) are observable. In the HBr⁺ + DCl system, proton transfer (PT_DCl) and deuterium abstraction (DA) are accessible. The cross sections for all reaction channels were measured as a function of the collision energy E_cm and of the rotational energy E_rot of the ion. The rotationally state-selective formation of the ionic species was realized by resonance-enhanced multiphoton ionization (REMPI). As expected, the PT-channels are exothermic, and the cross section decreases with increasing collision energy for both PT_HCl and PT_DCl. The cross section for DA also decreases with an increasing E_c.m.. In the case of a considerably endothermic CT-channel, the reaction efficiency increases with increasing collision energy but has an overall much smaller cross sections compared to PT and DA reactions. Both PT-reactions are hindered by ion rotation, whereas DA is independent of E_rot. The CT-channel shows a rotational enhancement near the thermochemical threshold. The experiment is complemented by theory, using ab initio molecular dynamics (AIMD, also known as direct dynamics) simulations and taking the rotational enhancement of HBr⁺ into account. The simulations show good agreement with the experimental results. The cross section of PT_HCl decreases with an increase of the rotational energy. Furthermore, the absolute cross sections are in the same order of magnitude. The CT channel shows no reactions in the simulation.

Multipole-moment effects in ion-molecule reactions at low temperatures: part III - the He+ + CH4 and He+ + CD4 reactions at low collision energies and the effect of the charge-octupole interaction

We present experimental and theoretical studies of the He+ + CH4 and He+ + CD4 reactions at collision energies in the kB·(0-10) K range. Helium atoms in a supersonic beam are excited to a low-field-seeking Rydberg-Stark state and merged with a supersonic beam of CH4 or CD4 using a curved surface-electrode deflector. The ion-molecule reactions are studied within the orbit of the helium Rydberg [He(n)] electron, which suppresses stray-electric-fields-induced heating and makes it possible to reach very low collision energies. The collision energy is varied by adjusting the velocity of the He(n) atoms with the surface deflector, keeping the velocity of the methane beam constant. The reaction product ions (C(H/D)p+ with p∈ {1,2,3}) are collected in a time-of-flight mass spectrometer and monitored as a function of the collision energy. No significant energy-dependence of the total reaction yields of either reactions is observed. The measured relative reaction rate coefficient for the He+ + CH4 reaction is approximately twice higher than the one for the He+ + CD4 reaction. The CH+, CH2+ and CH3+ (CD+, CD2+ and CD3+) ions were detected in ratios 0.28(±0.04) : 1.00(±0.11) : 0.11(±0.04) [0.35(±0.07) : 1.00(±0.16):0.04+0.09-0.04]. We also present calculations of the capture rate coefficients for the two reactions, in which the interaction between the charge of the helium ion and the octupole moment of the methane molecule is included. The rotational-state-specific capture rate coefficients are calculated for states with J = (0-3) at collision energies below kB·15 K. After averaging over the rotational states of methane populated at the rotational temperature of the supersonic beam, the calculations only predict extremely weak enhancements (in the order of ∼0.4%) of the rate coefficients compared to the Langevin rate constant kL over the collision-energy range considered.

A variable time step self-consistent mean field DSMC model for three-dimensional environments

A self-consistent mean field direct simulation Monte Carlo (SCMFD) algorithm was recently proposed for simulating collision environments for a range of one-dimensional model systems. This work extends the one-dimensional SCMFD approach to three dimensions and introduces a variable time step (3D-vt-SCMFD), enabling the modeling of a considerably wider range of different collision environments. We demonstrate the performance of the augmented method by modeling a varied set of test systems: ideal gas mixtures, Poiseuille flow of argon, and expansion of gas into high vacuum. For the gas mixtures, the 3D-vt-SCMFD method reproduces the properties (mean free path, mean free time, collision frequency, and temperature) in excellent agreement with theoretical predictions. From the Poiseuille flow simulations, we extract flow profiles that agree with the solution to the Navier-Stokes equations in the high-density limit and resemble free molecular flow at low densities, as expected. The measured viscosity from 3D-vt-SCMF is ∼15% lower than the theoretical prediction from Chapman-Enskog theory. The expansion of gas into vacuum is examined in the effusive regime and at the hydrodynamic limit. In both cases, 3D-vt-SCMDF simulations produce gas beam density, velocity, and temperature profiles in excellent agreement with analytical models. In summary, our tests show that 3D-vt-SCMFD is robust and computationally efficient, while also illustrating the diversity of systems the SCMFD model can be successfully applied to.

Reactions of H2, HD, and D2 with H2+, HD+, and D2+: Product-Channel Branching Ratios and Simple Models

We present measurements of the product-channel branching ratios of the reactions (i) HD+ + HD forming H2D+ + D (38.1(30)%) and HD2+ + H (61.9(30)%), (ii) HD+ + D2 forming HD2+ + D (61.4(35)%) and D3+ + H (38.6(35)%), and (iii) D2+ + HD forming HD2++ D (60.5(20)%) and D3+ + H (39.5(20)%) at collision energies Ecoll near zero, i.e., below kB × 1 K. These branching ratios are compared with branching ratios predicted using three simple models: a combinatorial model (M1), a model (M2) describing the reactions as H-, H+-, D-, and D+-transfer processes, and a statistical model (M3) that relates the reaction rate coefficients to the translational and rovibrational state densities of the HnD3-n+ + H/D (n = 0, 1, 2 or 3) product channels. The experimental data are incompatible with the predictions of models M1 and M2 and reveal that the branching ratios exhibit clear correlations with the product state densities.

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.

Quantum-state-dependent decay rates of electrostatically trapped Rydberg NO molecules

Nitric oxide (NO) molecules travelling in pulsed supersonic beams have been prepared in long-lived Rydberg-Stark states by resonance-enhanced two-colour two-photon excitation from the X 2Π1/2 (v'' = 0, J'' = 3/2) ground state, through the A 2Σ+ (v' = 0, N' = 0, J' = 1/2) intermediate state. These excited molecules were decelerated from 795 ms-1 to rest in the laboratory-fixed frame of reference, in the travelling electric traps of a transmission-line Rydberg-Stark decelerator. The decelerator was operated at 30 K to minimise effects of blackbody radiation on the molecules during deceleration and trapping. The molecules were electrostatically trapped for times of up to 1 ms, and detected in situ by pulsed electric field ionisation. Measurements of the rate of decay from the trap were performed for states with principal quantum numbers between n = 32 and 50, in Rydberg series converging to the N+= 0, 1, and 2 rotational states of NO+. For the range of Rydberg states studied, the measured decay times of between 200 μs and 400 μs were generally observed to reduce as the value of n was increased. For some particular values of n deviations from this trend were seen. These observations are interpreted, with the aid of numerical calculations, to arise as a result of contributions to the decay rates, on the order of 1 kHz, from rotational and vibrational channel interactions. These results shed new light on the role of weak intramolecular interactions on the slow decay of long-lived Rydberg states in NO.

Dynamics of the isotope exchange reaction of D with H3 +, H2D+, and D2H. J Chem Phys 2021;154:084307. [PMID: 33639774 DOI: 10.1063/5.0038434]

We have measured the merged-beams rate coefficient for the titular isotope exchange reactions as a function of the relative collision energy in the range of ∼3 meV-10 eV. The results appear to scale with the number of available sites for deuteration. We have performed extensive theoretical calculations to characterize the zero-point energy corrected reaction path. Vibrationally adiabatic minimum energy paths were obtained using a combination of unrestricted quadratic configuration interaction of single and double excitations and internally contracted multireference configuration interaction calculations. The resulting barrier height, ranging from 68 meV to 89 meV, together with the various asymptotes that may be reached in the collision, was used in a classical over-the-barrier model. All competing endoergic reaction channels were taken into account using a flux reduction factor. This model reproduces all three experimental sets quite satisfactorily. In order to generate thermal rate coefficients down to 10 K, the internal excitation energy distribution of each H₃ ⁺ isotopologue is evaluated level by level using available line lists and accurate spectroscopic parameters. Tunneling is accounted for by a direct inclusion of the exact quantum tunneling probability in the evaluation of the cross section. We derive a thermal rate coefficient of <1×10^-12 cm³ s^-1 for temperatures below 44 K, 86 K, and 139 K for the reaction of D with H₃ ⁺, H₂D⁺, and D₂H⁺, respectively, with tunneling effects included. The derived thermal rate coefficients exceed the ring polymer molecular dynamics prediction of Bulut et al. [J. Phys. Chem. A 123, 8766 (2019)] at all temperatures.

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.

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.

Self-Reactions in the HBr+ (DBr+) + HBr System: A State-Selective Investigation of the Role of Rotation

Self-reactions observed in the HBr⁺ (DBr⁺) + HBr system have been investigated using a guided ion-beam experiment under single-collision conditions. The reaction channels observed are proton transfer/hydrogen abstraction (PT/HA) in the case of HBr⁺ and deuteron transfer/hydrogen abstraction (DT/HA) and charge transfer (CT) in the case of DBr⁺. HBr⁺/DBr⁺ ions have been formed with rotational energies selected using the resonance-enhanced multiphoton ionization (REMPI) formation process. Cross sections have been measured as a function of the rotational energy of the ion, E_rot, and of the center-of-mass collision energy, E_cm. In the region of low rotational energies, the cross section for both PT/HA and DT/HA decreases with increasing ion rotation. In this region, the cross section for CT increases with increasing ion rotation. For higher rotational energies, the cross section increases with increasing ion rotation for PT/HA and less pronounced for DT/HA. The cross section for CT becomes independent of ion rotation for high rotational energies. Since all reaction channels are exothermic, all cross sections decrease with increasing E_cm.

Manipulating beams of paramagnetic atoms and molecules using inhomogeneous magnetic fields

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

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.

Formation of H3 + in Collisions of H2 + with H2 Studied in a Guided Ion Beam Instrument

In order to study collisions between ions and neutrals, a new Guided Ion Beam (GIB) apparatus, called NOVion, has been assembled and tested. The primary purpose of this instrument is to measure absolute cross sections at energies relevant for technical or inter- and circumstellar plasmas. New and improved results are presented for forming H₃ ⁺ in collisions of H₂ ⁺ with H₂ . Between 0.1 eV and 2 eV, our measured effective cross sections are in good overall agreement with most previous measurements. However, at higher energies, our results do not show the steep decline, recommended in the standard literature. After critical evaluation of all experimental and theoretical data, a new analytical function is proposed, describing properly the dependence of the title reaction on the collision energy up to 10 eV.

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.

Quantum Effects on the D + H3+ → H2D+ + H Deuteration Reaction and Isotopic Variants

The title reaction and its isotopic variants are studied using quasi-classical trajectory (QCT) (without taking into account corrections to account for the possible zero point energy breakdown) and ring polymer molecular dynamics (RPMD) methods with a full dimensional and accurate potential energy surface which presents an exchange barrier of approximately 0.144 eV. The QCT rate constant increases when the temperature decreases from 1500 to 10 K. On the contrary, the RPMD rate constant decreases with decreasing temperature, in semiquantitative agreement with recent experimental results. The present RPMD results are in between the thermal and translational experimental rate constants, extracted from the measured data to eliminate the initial vibrational excitation of H₃⁺, obtained in an arc discharge. The difference between the present RPMD results and experimental values is attributed to the possible existence of non thermal vibrational excitation of H₃⁺, not completely removed by the semiempirical model used for the analysis of the experimental results. Also, it is found that, below 200 K, the RPMD trajectories are trapped, forming long-lived collision complexes, with lifetimes longer than 1 ns. These collision complexes can fragment by either redissociating back to reactants or react to products, in the two cases tunneling through the centrifugal and reaction barriers, respectively. The contribution of the formation of the complex to the total deuteration rate should be calculated with more accurate quantum methods, as has been found recently for reactions of larger systems, and the present four atoms system is a good candidate to benchmark the adequacy of RPMD method at temperatures below 100 K.

Evolutionary Algorithm Optimization of Zeeman Deceleration: Is It Worthwhile for Longer Decelerators?

In Zeeman deceleration, only a small subset of low-field-seeking particles in the incoming beam possess initial velocities and positions that place them within the phase-space acceptance of the device. In order to maximize the number of particles that are successfully decelerated to a selected final velocity, we seek to optimize the phase-space acceptance of the decelerator. Three-dimensional particle trajectory simulations are employed to investigate the potential benefits of using a covariance matrix adaptation evolutionary strategy (CMA-ES) optimization method for decelerators longer than 12 stages and for decelerating species other than H atoms. In all scenarios considered, the evolutionary algorithm-optimized sequences yield vastly more particles within the target velocity range. This is particularly evident in scenarios where standard sequences are known to perform poorly; simulations show that CMA-ES optimization of a standard sequence decelerating H atoms from an initial velocity of 500 ms-1 down to a final velocity of 200 ms-1 in a 24-stage decelerator produces a considerable 5921% (or 60-fold) increase in the number of successfully decelerated particles. Particle losses that occur with standard pulse sequences-for example, arising from the coupling of longitudinal and transverse motion-are overcome in the CMA-ES optimization process as the passage of all particles through the decelerator is explicitly considered and focusing effects are accounted for in the optimization process.

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.

Confinement of High- and Low-Field-Seeking Rydberg Atoms Using Time-Varying Inhomogeneous Electric Fields

Helium atoms in high- and low-field-seeking Rydberg states with linear and quadratic Stark shifts have been confined in two dimensions and guided over a distance of 150 mm using time-varying inhomogeneous electric fields. This was achieved with an electrode structure composed of four parallel cylindrical rods to which voltages were applied to form oscillating and rotating saddle-point fields. These two modes of operation result in time-averaged pseudopotentials that confine samples in high- and low-field-seeking states about the axis of the device. The experimental data have been compared to the results of numerical particle trajectory calculations that include effects of blackbody radiation and electric field ionization. The results highlight important contributions from single-photon blackbody-induced transitions that cause large changes in the principal quantum number of the Rydberg atoms.

A detailed account of the measurements of cold collisions in a molecular synchrotron

We have recently demonstrated a general and sensitive method to study low energy collisions that exploits the unique properties of a molecular synchrotron (Van der Poel et al., Phys Rev Lett 120:033402, 2018). In that work, the total cross section for ND3 + Ar collisions was determined from the rate at which ammonia molecules were lost from the synchrotron due to collisions with argon atoms in supersonic beams. This paper provides further details on the experiment. In particular, we derive the model that was used to extract the relative cross section from the loss rate, and present measurements to characterize the spatial and velocity distributions of the stored ammonia molecules and the supersonic argon beams.

Cold Collisions in a Molecular Synchrotron

We study collisions between neutral, deuterated ammonia molecules (ND_{3}) stored in a 50 cm diameter synchrotron and argon atoms in copropagating supersonic beams. The advantages of using a synchrotron in collision studies are twofold: (i) By storing ammonia molecules many round-trips, the sensitivity to collisions is greatly enhanced; (ii) the collision partners move in the same direction as the stored molecules, resulting in low collision energies. We tune the collision energy in three different ways: by varying the velocity of the stored ammonia packets, by varying the temperature of the pulsed valve that releases the argon atoms, and by varying the timing between the supersonic argon beam and the stored ammonia packets. These give consistent results. We determine the relative, total, integrated cross section for ND_{3}+Ar collisions in the energy range of 40-140  cm^{-1}, with a resolution of 5-10  cm^{-1} and an uncertainty of 7%-15%. Our measurements are in good agreement with theoretical scattering calculations.

The Selective Role of Long-Range Forces in the Stereodynamics of Ion-Molecule Reactions: The He+ +Methyl Formate Case From Guided-Ion-Beam Experiments

Long-range intermolecular forces play a crucial role in controlling the outcome of ion-molecule chemical reactions, such as those determining the disappearance of organic or inorganic "complex" molecules recently detected in various regions of the interstellar medium due to collisions with abundant interstellar atomic ions (e.g. H⁺ and He⁺ ). Theoretical treatments, for example, based on simple capture models, are nowadays often adopted to evaluate the collision-energy dependence of reactive cross sections and the temperature dependent rate coefficients of many ion-molecule reactions. The obtained results are widely used for the modelling of phenomena occurring in different natural environments or technological applications such as astrophysical and laboratory plasmas. Herein it is demonstrated, through a combined experimental and theoretical investigation on a prototype ion-molecule reaction (He⁺ +methyl formate), that the dynamics, investigated in detail, shows some intriguing features that can lead to rate coefficients at odds with the expectations (e.g. Arrhenius versus anti-Arrhenius behaviour). Therefore, this study casts light on some new and general guidelines to be properly taken into account for a suitable evaluation of rate coefficients of ion-molecule reactions.

Probing resonant energy transfer in collisions of ammonia with Rydberg helium atoms by microwave spectroscopy

We present the results of experiments demonstrating the spectroscopic detection of Förster resonance energy transfer from NH₃ in the X¹A₁ ground electronic state to helium atoms in 1sns ³S₁ Rydberg levels, where n = 37 and n = 40. For these values of n, the 1sns ³S₁ → 1snp ³P_J transitions in helium lie close to resonance with the ground-state inversion transitions in NH₃ and can be tuned through resonance using electric fields of less than 10 V/cm. In the experiments, energy transfer was detected by direct state-selective electric field ionization of the ³S₁ and ³P_J Rydberg levels and by monitoring the population of the ³D_J levels following pulsed microwave transfer from the ³P_J levels. Detection by microwave spectroscopic methods represents a highly state selective, low-background approach to probing the collisional energy transfer process and the environment in which the atom-molecule interactions occur. The experimentally observed electric-field dependence of the resonant energy transfer process, probed both by direct electric field ionization and by microwave transfer, agrees well with the results of calculations performed using a simple theoretical model of the energy transfer process. For measurements performed in zero electric field with atoms prepared in the 1s40s ³S₁ level, the transition from a regime in which a single energy transfer channel can be isolated for detection to one in which multiple collision channels begin to play a role has been identified as the NH₃ density was increased.