Low-temperature behavior of capture rate constants for inverse power potentials

State selective preparation and nondestructive detection of trapped O2

The ability to prepare molecular ions in selected quantum states enables studies in areas such as chemistry, metrology, spectroscopy, quantum information, and precision measurements. Here, we demonstrate (2 + 1) resonance-enhanced multiphoton ionization (REMPI) of oxygen, both in a molecular beam and in an ion trap. The two-photon transition in the REMPI spectrum is rotationally resolved, allowing ionization from a selected rovibrational state of O2. Fits to this spectrum determine spectroscopic parameters of the O2d1Πg state and resolve a discrepancy in the literature regarding its band origin. The trapped molecular ions are cooled by co-trapped atomic ions. Fluorescence mass spectrometry nondestructively demonstrates the presence of the photoionized O2+. We discuss strategies for maximizing the fraction of ions produced in the ground rovibrational state. For (2 + 1) REMPI through the d1Πg state, we show that the Q(1) transition is preferred for neutral O2 at rotational temperatures below 50 K, while the O(3) transition is more suitable at higher temperatures. The combination of state-selective loading and nondestructive detection of trapped molecular ions has applications in optical clocks, tests of fundamental physics, and control of chemical reactions.

Thermionic Emission of Negative Ions of Molecules and Small Clusters as a Probe of Low-Energy Attachment

We have been studying the thermionic emission of negatively charged molecules and small clusters for more than a decade. The kinetic energy released distribution (KERD) of mass-selected negative ions has been measured with a velocity map imaging spectrometer. A comparison of the experimental KERD to detailed balance models provided information on the reverse process, namely, the electron attachment to the parent. The electron attachment to neutral systems (reverse process of the electron emission from anions) is usually described in a simplified way as a single electron capture in the framework of the classical Langevin model. Our measurements show that this approach is insufficient and that, in addition to the capture step, an intramolecular vibrational redistribution (IVR) step should be included. As far as multiply charged anions are concerned, the electron attachment to anions (reverse process of the electron emission from dianions) is strongly affected by the repulsive Coulomb barrier (RCB). Previous studies assumed a pure over-the-barrier process, which is in disagreement with our study. Indeed, electron emission is measured below the RCB, revealing significant thermal tunneling. In the present review, we summarize these works on singly and doubly charged anions in an attempt to present a unified view of the involved processes. It is worth noting that the detailed measurements of KERDs in the very low kinetic energy region (typically around 0.1 eV) have been made possible thanks to electron imaging methods, without which all of this work could never have been done, with time-resolution capabilities allowing the disentangling of direct and delayed electron emission.

Capture Theory Models: An overview of their development, experimental verification, and applications to ion-molecule reactions

Since Arrhenius first proposed an equation to account for the behaviour of thermally activated reactions in 1889, significant progress has been made in our understanding of chemical reactivity. A number of capture theory models have been developed over the past several decades to predict the rate coefficients for reactions between ions and molecules-ranging from the Langevin equation (for reactions between ions and non-polar molecules) to more recent fully quantum theories (for reactions at ultra-cold temperatures). A number of different capture theory methods are discussed, with the key assumptions underpinning each approach clearly set out. The strengths and limitations of these capture theory methods are examined through detailed comparisons between low-temperature experimental measurements and capture theory predictions. Guidance is provided on the selection of an appropriate capture theory method for a given class of ion-molecule reaction and set of experimental conditions-identifying when a capture-based model is likely to provide an accurate prediction. Finally, the impact of capture theories on fields such as astrochemical modelling is noted, with some potential future directions of capture-based approaches outlined.

Proton leap: shuttling of protons onto benzonitrile

The detailed description of chemical transformations in the interstellar medium allows deciphering the origin of a number of small and medium - sized organic molecules. We present density functional theory analysis of proton transfer from the trihydrogen cation and the ethenium cation to benzonitrile, a recently discovered species in the Taurus Molecular Cloud 1. Detailed energy transformations along the reaction paths were analyzed using the interacting quantum atoms methodology, which elucidated how the proton carrier influences the lightness to deliver the proton to benzonitrile's nitrogen atom. The proton carriers' deformation energy represents the largest destabilizing effect, whereas a proton's promotion energy, the benzonitrile-proton Coulomb attraction, as well as non-classical benzonitrile-proton and carrier-proton interaction are the dominant stabilizing energy components. As two ion-molecule reactions proceed without energy barriers, rate constants were estimated using the classical capture theory and were found to be an order of magnitude larger for the reaction with the trihydrogen cation compared to that with the ethenium cation (∼10^-8 and 10^-9 cm³ s^-1, respectively). These results were obtained both with quantum chemical and ab initio molecular dynamics simulations (the latter performed at 10 K and 100 K), confirming that up to 100 K both systems choose energetically undemanding routes by tracking the corresponding minimum energy paths. A concept of a turning point is introduced, which is an equivalent to the transition state in barrierless reactions.

Benchmarking an improved statistical adiabatic channel model for competing inelastic and reactive processes

Inelastic collisions and elementary chemical reactions proceeding through the formation and subsequent decay of an intermediate collision complex, with an associated deep well on the potential energy surface, pose a challenge for accurate fully quantum mechanical approaches, such as the close-coupling method. In this study, we report on the theoretical prediction of temperature-dependent state-to-state rate coefficients for these complex-mode processes, using a statistical quantum method. This statistical adiabatic channel model is benchmarked by a direct comparison using accurate rate coefficients from the literature for a number of systems (H₂ + H⁺, HD + H⁺, SH⁺ + H, and CH⁺ + H) of interest in astrochemistry and astrophysics. For all of the systems considered, an error of less than factor 2 was found, at least for the dominant transitions and at low temperatures, which is sufficiently accurate for applications in the above mentioned disciplines.

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.

Toward a quantitative analysis of the temperature dependence of electron attachment to SF6

New flowing afterglow/Langmuir probe investigations of electronic attachment to SF₆ are described. Thermal attachment rate constants are found to increase from 1.5 × 10^-7 cm³ s^-1 at 200 K to 2.3 × 10^-7 cm³ s^-1 at 300 K. Attachment rate constants over the range of 200-700 K (from the present work and the literature), together with earlier measurements of attachment cross sections, are analyzed with respect to electronic and nuclear contributions. The latter suggest that only a small nuclear barrier (of the order of 20 meV) on the way from SF₆ to SF₆ ^- has to be overcome. The analysis shows that not only s-waves but also higher partial waves have to be taken into account. Likewise, finite-size effects of the neutral target contribute in a non-negligible manner.

Communication: Adiabatic quantum trajectory capture for cold and ultra-cold chemical reactions

The Langevin capture model is often used to describe barrierless reactive collisions. At very low temperatures, quantum effects may alter this simple capture image and dramatically affect the reaction probability. In this paper, we use the trajectory-ensemble reformulation of quantum mechanics, as recently proposed by one of the authors (Poirier) to compute adiabatic-channel capture probabilities and cross-sections for the highly exothermic reaction Li + CaH(v = 0, j = 0) → LiH + Ca, at low and ultra-low temperatures. Each captured quantum trajectory takes full account of tunneling and quantum reflection along the radial collision coordinate. Our approach is found to be very fast and accurate, down to extremely low temperatures. Moreover, it provides an intuitive and practical procedure for determining the capture distance (i.e., where the capture probability is evaluated), which would otherwise be arbitrary.

Quantum theory of reactive collisions for 1/r(n) potentials

We develop a general quantum theory for reactive collisions involving power-law potentials (-1/r(n)) valid from the ultracold up to the high-temperature limit. Our quantum defect framework extends the conventional capture models to include the nonuniversal case when the short-range reaction probability P(re)<1. We present explicit analytical formulas as well as numerical studies for the van der Waals (n=6) and polarization (n=4) potentials. Our model agrees well with recent merged beam experiments on Penning ionization, spanning collision energies from 10 mK to 30 K [Henson et al., Science 338, 234 (2012)].

Millikelvin reactive collisions between sympathetically cooled molecular ions and laser-cooled atoms in an ion-atom hybrid trap

We report on a study of cold reactive collisions between sympathetically cooled molecular ions and laser-cooled atoms in an ion-atom hybrid trap. Chemical reactions were studied at average collision energies <E(coll)>/k(B)>/~20 mK, about 2 orders of magnitude lower than has been achieved in previous experiments with molecular ions. Choosing N(2)(+)+Rb as a prototypical system, we find that the reaction rate is independent of the collision energy within the range studied, but strongly dependent on the internal state of Rb. Highly efficient charge exchange four times faster than the Langevin rate was observed with Rb in the excited (5p) (2)P(3/2) state. This observation is rationalized by a capture process dominated by the charge-quadrupole interaction and a near resonance between the entrance and exit channels of the system. Our results provide a test of classical models for reactions of molecular ions at the lowest energies reached thus far.

Threshold behavior and analytical fitting of partial wave capture probabilities for attractive R(-n) potentials

Numerically accurate analytical fittings for partial wave capture probabilities in the field of R(-n) potentials (n = 4 and 6) are presented across practically interesting ranges of probabilities. The results demonstrate the performance of the Bethe and Wigner threshold laws at low collision energies and should be useful for practical applications.

Classical Trajectory and Statistical Adiabatic Channel Study of the Dynamics of Capture and Unimolecular Bond Fission. VII. Thermal Capture and Specific Rate Constants k(E,J) for the Dissociation of Molecular Ions

Specific rate constants, k(E,J), and thermal capture rate constants, k cap(T), are determined by statistical adiabatic channel model/classical trajectory (SACM/CT) calculations for unimolecular dissociation and the reverse association reactions of representative polyatomic molecular ions. Simple short-range valence/long-range ion-induced dipole model potentials without reverse barriers have been employed, using the reactions C8H10 + ⇔ C7H7 + + CH3 and C9H12 + ⇔ C7H7 + + C2H5 as illustrative examples. Simplified representations of k(E) and k cap(T) from rigid activated complex Rice–Ramsperger–Kassel–Marcus (RRKM) theory are compared with the SACM/CT treatment and with experimental results. The Massey parameters of the transitional mode dynamics, for the systems considered, are smaller than unity such that their dynamics is nonadiabatic while the dynamics of the conserved modes is adiabatic. Because of the long-range/short-range switching character of the potential, simple rigid activated complex RRKM theory cannot be used without modifications. The effects of a shifting of the effective bottle-neck of the dynamics with increasing energy towards smaller interfragment distances in the present cases are amplified by a shift into a range of increasing anisotropy of the potential. As a consequence, the thermal capture rate constants markedly decrease with increasing temperature.

Chemical applications of laser- and sympathetically-cooled ions in ion traps

Ensembles of cold atomic and molecular ions in ion traps prepared at millikelvin temperatures by laser and sympathetic cooling have recently found considerable interest in both physics and chemistry. At very low temperatures the ions form ordered structures in the trap also known as "Coulomb crystals". Ion Coulomb crystals exhibit a range of intriguing properties which render them attractive systems for novel experiments in chemical dynamics, ultrahigh-resolution spectroscopy and quantum-information processing. In this article we review the methods used to prepare atomic and molecular ion Coulomb crystals and discuss some recent studies in mass spectrometry, low-temperature chemistry and precision spectroscopy to illustrate their scientific potential for chemical applications. Finally, we conclude with an outlook on outstanding challenges and prospective further developments in the field.

Nonadiabatic transitions between lambda-doubling states in the capture of a diatomic molecule by an ion

The low-energy capture of a dipolar diatomic molecule in an adiabatically isolated electronic state with a good quantum number Omega (Hund's coupling case a) by an ion occurs adiabatically with respect to rotational transitions of the diatom. However, the capture dynamics may be nonadiabatic with respect to transitions between the pair of the Lambda-doubling states belonging to the same value of the intrinsic angular momentum j. In this work, nonadiabatic transition probabilities are calculated which define the Lambda-doubling j-specific capture rate coefficients. It is shown that the transition from linear to quadratic Stark effect in the ion-dipole interaction, which damps the T(-1/2) divergence of the capture rate coefficient calculated with vanishing Lambda-doubling splitting, occurs in the adiabatic regime with respect to transitions between Lambda-doubling adiabatic channel potentials. This allows one to suggest simple analytical expressions for the rate coefficients in the temperature range which covers the region between the sudden and the adiabatic limits with respect to the Lambda-doubling states.

Low temperature capture of open shell dipolar molecules by ions: the capture of rotationally selected NO((2)Pi(1/2), j) by C(+)

The low-energy capture of dipolar diatomic molecules in an open electronic state by ions is usually considered to be induced by the first-order charge-permanent dipole interaction with other terms of the long-range potential playing a minor role. If the molecular dipole moment is anomalously small (as is the case for slightly asymmetrical molecules), however, the situation changes, and the capture dynamics is strongly affected by higher orders of the charge-permanent dipole, charge-permanent quadrupole, and charge-induced dipole interactions. The interplay of different terms in the interaction potential manifests itself in complicated temperature dependence of the rotationally state-specific capture rate coefficients. These features of the capture are studied by way of example for NO(X (2)Pi(1/2), j) + C(+) collisions in the temperature range 10(-2)-20 K where the dynamics is adiabatic with respect to rotational and fine-structure transitions and sudden with respect to transitions between Lambda doubling and hyperfine states. The theoretical rate coefficient, which depends on the translational and rotational temperature, agrees with the experimental one measured at T(tr) = 0.6 K and T(rot) = 20 K.

Rates of complex formation in collisions of rotationally excited homonuclear diatoms with ions at very low temperatures: Application to hydrogen isotopes and hydrogen-containing ions

State-selected rate coefficients for the capture of ground and rotationally excited homonuclear molecules by ions are calculated, for low temperatures, within the adiabatic channel classical (ACCl) approximation, and, for zero temperature, via an approximate calculation of the Bethe limit. In the intermediate temperature range, the accurate quantal rate coefficients are calculated for j = 0 and j = 1 states of hydrogen isotopes (H2, HD, and D2) colliding with hydrogen-containing ions, and simple analytical expressions are suggested to approximate the rate coefficients. For the ground rotational state of diatoms, the accurate quantal rate coefficients are higher compared to their ACCl counterparts, while for the first excited rotational state the reverse is true. The physical significance of quantum effects for low-temperature capture and the applicability of the statistical description of capture are considered. Particular emphasis is given to the role of Coriolis interaction. The relevance of the present capture calculations for rates of ortho-para conversion of H2 in collisions with hydrogen-containing ions at low temperatures is discussed.

The effect of spin–orbit coupling on fast neutral chemical reaction O(3P)+CH3→CH3O

The effect of nonadiabatic transitions through the spin-orbit couplings has been investigated on the fast neutral reaction, O((3)P)+CH(3)-->CH(3)O. Adiabatic potential energies and the spin-orbit coupling terms have been evaluated for the four electronic states of CH(3)O ((2)E, (2)A(2), (4)E, and (4)A(2)) that correlate with the O((3)P)+CH(3) asymptote, as a function of CO distance and OCH angle under the C(3v) symmetry, by ab initio electronic structure calculations using multireference internally contracted single and double excitation configuration interaction method with the 6-311G(2df,2pd) basis sets. Multistate quantum reactive scattering calculations have been carried out with the use of thus obtained potential energies and spin-orbit coupling matrices, based on the generalized R-matrix propagation method. The calculated thermal rate constants show a slight positive dependence on temperature in a range between 50 and 2000 K, supporting the previous experimental results. It is shown that the spin-orbit coupled excited states give rise to reflections over the centrifugal barrier due to the quantum interference. Classical capture calculations yield larger rate constants due to the neglect of quantum reflections. It is concluded that the effect of nonadiabatic transitions is of minor importance on the overall reactivity in this reaction.

Quantum scattering and adiabatic channel treatment of the low-energy and low-temperature capture of a rotating quadrupolar molecule by an ion

The capture rate coefficients of homonuclear diatomic molecules (H(2) and N(2)) in the rotational state j=1 interacting with ions (Ar+ and He+) are calculated for low collision energies assuming a long-range anisotropic ion-induced dipole and ion-quadrupole interaction. A comparison of accurate quantum rates with quantum and state-specific classical adiabatic channel approximations shows that the former becomes inappropriate in the case when the cross section is dominated by few partial contributions, while the latter performs better. This unexpected result is related to the fact that the classical adiabatic channel approximation artificially simulates the quantum effects of tunneling and overbarrier reflection as well as the Coriolis coupling and it suppresses too high values of the centrifugal barriers predicted by a quantum adiabatic channel approach. For H2(j=1)+Ar+ and N(2)(j=1)+He+ capture, the rate constants at T-->0 K are about 3 and 6 times higher than the corresponding values for H2(j=0)+Ar+ and N(2)(j=0)+He+ capture.