Reactions of Rydberg states of molecular hydrogen

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.

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.

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.

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).

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.

Excitation and characterization of long-lived hydrogenic Rydberg states of nitric oxide

High Rydberg states of nitric oxide (NO) with principal quantum numbers between 40 and 100 and lifetimes in excess of 10 µs have been prepared by resonance enhanced two-color two-photon laser excitation from the X ²Π_1/2 ground state through the A ²Σ⁺ intermediate state. Molecules in these long-lived Rydberg states were detected and characterized 126 µs after laser photoexcitation by state-selective pulsed electric field ionization. The laser excitation and electric field ionization data were combined to construct two-dimensional spectral maps. These maps were used to identify the rotational states of the NO⁺ ion core to which the observed series of long-lived hydrogenic Rydberg states converge. The results presented pave the way for Rydberg-Stark deceleration and electrostatic trapping experiments with NO, which are expected to shed further light on the decay dynamics of these long-lived excited states, and are of interest for studies of ion-molecule reactions at low temperatures.

Rydberg-State-Resolved Resonant Energy Transfer in Cold Electric-Field-Controlled Intrabeam Collisions of NH3 with Rydberg He Atoms

The resonant transfer of energy from the inversion sublevels in NH₃ to He atoms in triplet Rydberg states with principal quantum number n = 38 has been controlled using electric fields below 15 V/cm in intrabeam collisions at translational temperatures of ∼1 K. The experiments were performed in pulsed supersonic beams of NH₃ seeded in He at a ratio of 1:19. The He atoms were prepared in the metastable 1s2s ³S₁ level in a pulsed electric discharge in the trailing part of the beams. The velocity slip between the heavy NH₃ and the lighter metastable He was exploited to perform collision studies at center-of-mass collision speeds of ∼70 m/s. Resonant energy transfer in the atom-molecule collisions was identified by Rydberg-state-selective electric-field ionization. The experimental data have been compared to a theoretical model of the resonant dipole-dipole interactions between the collision partners based on the impact parameter method.

Rydberg Molecules for Ion-Atom Scattering in the Ultracold Regime

We propose a novel experimental method to extend the investigation of ion-atom collisions from the so far studied cold, essentially classical regime to the ultracold, quantum regime. The key aspect of this method is the use of Rydberg molecules to initialize the ultracold ion-atom scattering event. We exemplify the proposed method with the lithium ion-atom system, for which we present simulations of how the initial Rydberg molecule wave function, freed by photoionization, evolves in the presence of the ion-atom scattering potential. We predict bounds for the ion-atom scattering length from ab initio calculations of the interaction potential. We demonstrate that, in the predicted bounds, the scattering length can be experimentally determined from the velocity of the scattered wave packet in the case of ^{6}Li^{+}-^{6}Li and from the molecular ion fraction in the case of ^{7}Li^{+}-^{7}Li. The proposed method to utilize Rydberg molecules for ultracold ion-atom scattering, here particularized for the lithium ion-atom system, is readily applicable to other ion-atom systems as well.

State-to-state dynamics of high-n Rydberg H-atom scattering with H2: inelastic scattering and reactive scattering

The state-to-state dynamics of high-n Rydberg H-atom scattering with para-H2 at the collision energies of 0.45 and 1.07 eV have been studied using the H-atom Rydberg tagging time-of-flight technique. Both the inelastic scattering and reactive scattering are observed in the experimental time-of-flight spectra. The products H2(v', j' = odd) come only from reactive scattering and present clearly forward-backward asymmetric angular distributions, which differ from those of the corresponding ion-molecule reaction. The products H2(v', j' = even), however, come from both reactive scattering and inelastic scattering. Simulating the rotational distribution from reactive scattering, we found that most of the H2(v', j' = even) products come from inelastic scattering. The angular distributions of the product H2(v', j' = even) are consistent with what is predicted by the conventional textbook mechanism of inelastic scattering, and are a little different from those of the corresponding ion-molecule inelastic scattering. These results suggest that the effect of Rydberg electron could not be neglected in describing the differential cross sections of H* + para-H2 scattering. From the simulation, the branching ratios of the inelastic scattering channel were determined to be 66% and 79% at the collision energies of 0.45 and 1.07 eV, respectively.

Chirped-pulse millimeter-wave spectroscopy: spectrum, dynamics, and manipulation of Rydberg-Rydberg transitions

We apply the chirped-pulse millimeter-wave (CPmmW) technique to transitions between Rydberg states in calcium atoms. The unique feature of Rydberg-Rydberg transitions is that they have enormous electric dipole transition moments (~5 kiloDebye at n* ~ 40, where n* is the effective principal quantum number), so they interact strongly with the mm-wave radiation. After polarization by a mm-wave pulse in the 70-84 GHz frequency region, the excited transitions re-radiate free induction decay (FID) at their resonant frequencies, and the FID is heterodyne-detected by the CPmmW spectrometer. Data collection and averaging are performed in the time domain. The spectral resolution is ~100 kHz. Because of the large transition dipole moments, the available mm-wave power is sufficient to polarize the entire bandwidth of the spectrometer (12 GHz) in each pulse, and high-resolution survey spectra may be collected. Both absorptive and emissive transitions are observed, and they are distinguished by the phase of their FID relative to that of the excitation pulse. With the combination of the large transition dipole moments and direct monitoring of transitions, we observe dynamics, such as transient nutations from the interference of the excitation pulse with the polarization that it induces in the sample. Since the waveform produced by the mm-wave source may be precisely controlled, we can populate states with high angular momentum by a sequence of pulses while recording the results of these manipulations in the time domain. We also probe the superradiant decay of the Rydberg sample using photon echoes. The application of the CPmmW technique to transitions between Rydberg states of molecules is discussed.

Dynamics of the Rydberg electron in H*+D2→D*+HD reactive collisions

Experimental crossed-beam studies carried out previously have indicated that the dynamics of the Rydberg-atom-molecule reaction H*+D2-->D*+HD are very similar to those of the corresponding ion-molecule reaction H++D2-->D++HD. The equivalence of the cross sections for these related systems would open up a new approach to the experimental study of ion-molecule reactions. However, a recent experimental and theoretical study has brought to light some important qualitative differences between the Rydberg-atom reaction and the ion-molecule reaction; in particular, the experimental cross section for the Rydberg-atom reaction exhibits a higher degree of forward-backward scattering asymmetry than predicted by a quasiclassical trajectory study of the ion-molecule reaction. In this paper, the authors consider the dynamics of the Rydberg-electron over the course of a reactive collision and the implications of these dynamics for the Rydberg-atom-molecule crossed-beam experiment. Using an approach based on perturbation theory, they estimate the attenuation of the experimental signal due to the Rydberg-electron dynamics as a function of the scattering angle. They show that at least part of the experimental asymmetry can be ascribed to this angle dependent attenuation. Their results offer general insight into the practical aspects of the experimental study of ion-molecule reactions by means of their Rydberg-atom counterparts.

Chemical reaction dynamics of Rydberg atoms with neutral molecules: A comparison of molecular-beam and classical trajectory results for the H(n)+D2→HD+D(n′) reaction

Recent molecular-beam experiments have probed the dynamics of the Rydberg-atom reaction, H(n)+D2-->HD+D(n) at low collision energies. It was discovered that the rotationally resolved product distribution was remarkably similar to a much more limited data set obtained at a single scattering angle for the ion-molecule reaction H++D2-->D++HD. The equivalence of these two problems would be consistent with the Fermi-independent-collider model (electron acting as a spectator) and would provide an important new avenue for the study of ion-molecule reactions. In this work, we employ a classical trajectory calculation on the ion-molecule reaction to facilitate a more extensive comparison between the two systems. The trajectory simulations tend to confirm the equivalence of the ion+molecule dynamics to that for the Rydberg-atom+molecule system. The theory reproduces the close relationship of the two experimental observations made previously. However, some differences between the Rydberg-atom experiments and the trajectory simulations are seen when comparisons are made to a broader data set. In particular, the angular distribution of the differential cross section exhibits more asymmetry in the experiment than in the theory. The potential breakdown of the classical model is discussed. The role of the "spectator" Rydberg electron is addressed and several crucial issues for future theoretical work are brought out.

State-to-state dynamics of high-n Rydberg H-atom scattering with D2

Full quantum-state resolved scattering of a highly excited Rydberg H atom with D2 has been carried out using the Rydberg H-atom time-of-flight method. A detailed analysis of the experimental results shows that both inelastic and reactive scatterings are significant in the Hn-D2 collisions, and nuclear spin is conserved in the inelastic scattering process. The differential cross sections for the Hn-D2 reaction measured in this work are then compared with the results for the H+ reaction with D2 in an ion beam scattering experiment. The remarkable agreement between the two experiments suggests that the Fermi independent-collider model is valid even at the full quantum state-to-state scattering level, providing a promising tool for investigating the state-to-state dynamics of certain elementary ion-molecule reactions.

Deflection and deceleration of hydrogen Rydberg molecules in inhomogeneous electric fields

Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17-18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 micros after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.

Vibrationally inelastic scattering of high- n Rydberg H atoms from N2 and O2

The vibrationally inelastic scattering of Rydberg H atoms (n = 30-50) from N2 and O2 at E(coll) = 1.84 eV was studied as a function of laboratory deflection angle. On average, 4 times more vibrational excitation was observed in collisions with O2 than with N2. Vibrational excitation of O2 results largely from collisions in which an electron is briefly transferred from O2 to the proton core, while the Rydberg electron remains a spectator. This provides further evidence that the free electron model applies to low energy collisions involving the ionic core leading to substantial momentum transfer.

MOLECULES IN HIGH RYDBERG STATES

The unusual properties of high molecular Rydberg states with principal quantum number n>>100 have enabled the development of new research tools for the study of molecules and ions in the gas phase. These tools range from spectroscopic techniques such as zero kinetic energy (ZEKE) photoelectron spectroscopy and mass-analyzed threshold ionization (MATI) spectroscopy to techniques that are suited to the investigation of photodissociation processes, bimolecular reactions, and state-selected ion-molecule reactions. This review summarizes recent progress in the understanding of the properties of high molecular Rydberg states and gives an overview of recent chemical applications of these states.