The rate of the F + H2 reaction at very low temperatures

Hyperfine-to-rotational energy transfer in ultracold atom-molecule collisions of Rb and KRb

Energy transfer between different mechanical degrees of freedom in atom-molecule collisions has been studied and largely understood. However, systems involving spins remain less explored. In this study, we directly observed energy transfer from atomic hyperfine to molecular rotation in the 87Rb ( ∣ F a , M F a = ∣ 2 , 2 ) + 40K87Rb (X1Σ+, rotational state N = 0) ⟶ Rb ( ∣ 1 , 1 ) + KRb (N = 0, 1, 2) collision with state-to-state precision. We also performed quantum scattering calculations that rigorously included the coupling between spin and rotational degrees of freedom at short range under the assumption of rigid-rotor KRb monomers moving along a single potential energy surface. The calculated product rotational state distribution deviates from the observations even after extensive tuning of the atom-molecule potential energy surface. In addition, our ab initio calculations indicate that spin-rotation coupling is enhanced close to a conical intersection that is energetically accessible at short range. This, together with the deviation, suggests that vibrational degrees of freedom and conical intersections play an important part in the coupling. Our observations confirm that spin is coupled to mechanical rotation at short range and establish a benchmark for future theoretical studies.

A new apparatus for gas-phase low temperature kinetics study: Kinetics measurement and product detection of the CH + propene reaction at 23 K

We have developed a novel instrument to study reaction kinetics of astrochemical interest at low temperatures. This setup integrates laser-induced fluorescence (LIF) and vacuum ultraviolet (VUV) photoionization reflectron time-of-flight mass spectrometry (ReTOFMS) with a supersonic uniform low-temperature flow. A pulsed helium Laval nozzle with a Mach number of 6 was employed, achieving a temperature of 23 ± 3 K and a density of (2.0 ± 0.4) × 1016 molecule cm-3. The second-order rate coefficient for the reaction between the methylidyne radical (CH) and propene (C3H6) at 23(3) K was determined to be (3.4 ± 0.6) × 10-10 cm3 molecule-1 s-1 using LIF kinetics measurements. VUV (118.27 nm) photoionization ReTOFMS detected a dominant product channel, CH + C3H6 → C4H6 + H, without isomer identification. Another less intense mass peak at m/z 53 was also observed, which could either result from the dissociative ionization of the energized C4H6 primary products or indicate another product channel, C4H5 + H2. Given the presence of CH and C3H6 in cold molecular clouds (e.g., TMC-1, Lupus-1a, L1495B, L1521F, and Serpens South 1a), it is predicted that these products can exist in low-temperature interstellar environments.

Profiling a pulsed molecular beam with cavity-enhanced absorption spectroscopy

The molecular beam plays an important role in chemical dynamics experiments. The density in the beam is one of the critical factors influencing the reaction rate in these studies. Here we present a method based on laser-locked cavity-enhanced absorption spectroscopy to measure the molecular density in the beam. The P(1) transition in the second overtone band of CO was measured in the molecular beam, demonstrating a determination of the number density of molecules in a specific quantum state from the absorption spectrum. This non-destructive spectroscopic method allows the measurement of state-resolved properties of a molecular beam, which could be applied to various studies such as molecular collision dynamics.

Product-specific reaction kinetics in continuous uniform supersonic flows probed by chirped-pulse microwave spectroscopy

Experimental studies of the products of elementary gas-phase chemical reactions occurring at low temperatures (<50 K) are very scarce, but of importance for fundamental studies of reaction dynamics, comparisons with high-level quantum dynamical calculations, and, in particular, for providing data for the modeling of cold astrophysical environments, such as dense interstellar clouds, the atmospheres of the outer planets, and cometary comae. This study describes the construction and testing of a new apparatus designed to measure product branching fractions of elementary bimolecular gas-phase reactions at low temperatures. It combines chirped-pulse Fourier transform millimeter wave spectroscopy with continuous uniform supersonic flows and high repetition rate laser photolysis. After a comprehensive description of the apparatus, the experimental procedures and data processing protocols used for signal recovery, the capabilities of the instrument are explored by the study of the photodissociation of acrylonitrile and the detection of two of its photoproducts, HC3N and HCN. A description is then given of a study of the reactions of the CN radical with C2H2 at 30 K, detecting the HC3N product, and with C2H6 at 10 K, detecting the HCN product. A calibration of these two products is finally attempted using the photodissociation of acrylonitrile as a reference process. The limitations and possible improvements in the instrument are discussed in conclusion.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Signatures of Non-universal Quantum Dynamics of Ultracold Chemical Reactions of Polar Alkali Dimer Molecules with Alkali Metal Atoms: Li(2S) + NaLi(a3Σ+) → Na(2S) + Li2(a3Σu+)

Ultracold chemical reactions of weakly bound triplet-state alkali metal dimer molecules have recently attracted much experimental interest. We perform rigorous quantum scattering calculations with a new ab initio potential energy surface to explore the chemical reaction of spin-polarized NaLi(a³Σ⁺) and Li(²S) to form Li₂(a³Σ_u⁺) and Na(²S). The reaction is exothermic and proceeds readily at ultralow temperatures. Significantly, we observe strong sensitivity of the total reaction rate to small variations of the three-body part of the Li₂Na interaction at short range, which we attribute to a relatively small number of open Li₂(a³Σ_u⁺) product channels populated in the reaction. This provides the first signature of highly non-universal dynamics seen in rigorous quantum reactive scattering calculations of an ultracold exothermic insertion reaction involving a polar alkali dimer molecule, opening up the possibility of probing microscopic interactions in atom+molecule collision complexes via ultracold reactive scattering experiments.

Tunnelling measured in a very slow ion-molecule reaction

Quantum tunnelling reactions play an important role in chemistry when classical pathways are energetically forbidden¹, be it in gas-phase reactions, surface diffusion or liquid-phase chemistry. In general, such tunnelling reactions are challenging to calculate theoretically, given the high dimensionality of the quantum dynamics, and also very difficult to identify experimentally^2-4. Hydrogenic systems, however, allow for accurate first-principles calculations. In this way the rate of the gas-phase proton-transfer tunnelling reaction of hydrogen molecules with deuterium anions, H₂ + D^- → H^- + HD, has been calculated⁵, but has so far lacked experimental verification. Here we present high-sensitivity measurements of the reaction rate carried out in a cryogenic 22-pole ion trap. We observe an extremely low rate constant of (5.2 ± 1.6) × 10^-20 cm³ s^-1. This measured value agrees with quantum tunnelling calculations, serving as a benchmark for molecular theory and advancing the understanding of fundamental collision processes. A deviation of the reaction rate from linear scaling, which is observed at high H₂ densities, can be traced back to previously unobserved heating dynamics in radiofrequency ion traps.

Intersystem crossing in the entrance channel of the reaction of O(3P) with pyridine

Two quantum effects can enable reactions to take place at energies below the barrier separating reactants from products: tunnelling and intersystem crossing between coupled potential energy surfaces. Here we show that intersystem crossing in the region between the pre-reactive complex and the reaction barrier can control the rate of bimolecular reactions for weakly coupled potential energy surfaces, even in the absence of heavy atoms. For O(3P) plus pyridine, a reaction relevant to combustion, astrochemistry and biochemistry, crossed-beam experiments indicate that the dominant products are pyrrole and CO, obtained through a spin-forbidden ring-contraction mechanism. The experimental findings are interpreted-by high-level quantum-chemical calculations and statistical non-adiabatic computations of branching fractions-in terms of an efficient intersystem crossing occurring before the high entrance barrier for O-atom addition to the N-atom lone pair. At low to moderate temperatures, the computed reaction rates prove to be dominated by intersystem crossing.

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H₂/D₂ reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H₂ and D₂) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H₂ and F + D₂ reactions are presented along with previous theoretical and experimental results.

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.

Full-Dimensional Potential Energy Surface for Ro-vibrationally Inelastic Scattering between H2 Molecules

We report a new full-dimensional potential energy surface (PES) for the inelastic scattering between ro-vibrationally excited H₂ molecules. The new PES is based on 39,462 multi-reference configuration interaction points in dynamically relevant regions. The analytic form of the PES consists of a short-range term fit with the permutational invariant polynomial-neural network method and a long-range term with a physically correct asymptotic functional form accounting for both electrostatic and dispersion terms, which are connected smoothly with a switching function. The PES compares favorably with existing accurate PESs near the H₂ equilibrium geometries but covers a much larger configuration space for H₂ with up to 10 vibrational quanta. Full-dimensional quantum scattering calculations on the new PES reproduce the recent Stark-induced adiabatic Raman passage results for the HD(v = 1) + H₂ scattering near 1 K, validating its accuracy. These calculations also revealed significant differences with existing PESs in describing scattering of vibrationally excited molecules, underscoring the ability of the new PES in handling such dynamics.

Complete Quantum Coherent Control of Ultracold Molecular Collisions

We show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics that is free from the limitations of commonly used methods that rely on external electromagnetic fields. By varying the relative populations and phases of initial coherent superpositions of degenerate molecular states, we demonstrate complete coherent control over integral scattering cross sections in the ultracold s-wave regime of both the initial and final collision channels. The proposed control methodology is applied to ultracold O_{2}+O_{2} collisions, showing extensive control over s-wave spin-exchange cross sections and product branching ratios over many orders of magnitude.

The F + HD(v = 0, 1; j = 0, 1) reactions: stereodynamical properties of orbiting resonances

The excitation functions (reaction cross-section as a function of collision energy) of the F + HD(v = 0, 1; j = 0, 1) benchmark system have been calculated in the 0.01-6 meV collision energy interval using a time-independent hyperspherical quantum dynamics methodology. Special attention has been paid to orbiting resonances, which bring about detailed information on the three-atom interaction during the reactive encounter. The location of the resonances depends on the rovibrational state of the reactants HD(v,j), but is the same for the two product channels HF + D and DF + H, as expected for these resonances that are linked to the van der Waals well at the entrance. The resonance intensities depend both on the entrance and on the exit channels. The peak intensities for the HF + D channel are systematically larger than those for DF + H. Vibrational excitation leads to an increase of the peak intensity by more than an order of magnitude, but rotational excitation has a less drastic effect. It deceases the resonance intensity of the F + HD(v = 1) reaction, but increases somewhat that of F + HD(v = 0). Polarization of the rotational angular momentum with respect to the initial velocity reveals intrinsic directional preferences in the F + HD(v = 0, 1; j = 1) reactions that are manifested in the resonance patterns. The helicities (Ω = 0, Ω = ±1) possible for j = 1 contribute to the resonances, but that from Ω± 1 is, in general, dominant and in some cases exclusive. It corresponds to a preferential alignment of the HD internuclear axis perpendicular to the initial direction of approach and, thus, to side-on collisions. This work also shows that external preparation of the reactants, following the intrinsic preferences, would allow the enhancement or reduction of specific resonance features, and would be of great help for their eventual experimental detection.

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.

A new instrument for kinetics and branching ratio studies of gas phase collisional processes at very low temperatures

A new instrument dedicated to the kinetic study of low-temperature gas phase neutral-neutral reactions, including clustering processes, is presented. It combines a supersonic flow reactor with vacuum ultra-violet synchrotron photoionization time-of-flight mass spectrometry. A photoion-photoelectron coincidence detection scheme has been adopted to optimize the particle counting efficiency. The characteristics of the instrument are detailed along with its capabilities illustrated through a few results obtained at low temperatures (<100 K) including a photoionization spectrum of n-butane, the detection of formic acid dimer formation, and the observation of diacetylene molecules formed by the reaction between the C₂H radical and C₂H₂.

Unveiling shape resonances in H + HF collisions at cold energies

Scattering resonances are pure quantum effects that appear whenever the collision energy matches the energy of a quasi-bound state of the intermolecular complex. Here we show that rotational quenching of HF(j = 1, 2) with H is strongly influenced by the presence of two resonance peaks, leading to up to a two-fold increase in the thermal rate coefficients at the low temperatures characteristic of the interstellar medium. Our results show that each resonance peak is formed by a cluster of shape resonances, each of them characterized by the same value of the orbital angular momentum but different values of the total angular momentum. The relative intensity of these resonances depends on the relative geometry of the incoming reactants, and our results predict that by changing the alignment of the HF rotational angular momentum it is possible to decompose the resonance peaks, disentangling the underlying resonance pattern and the contribution of different total angular momenta to the resonance.

Advances and New Challenges to Bimolecular Reaction Dynamics Theory

Dynamics of bimolecular reactions in the gas phase are of foundational importance in combustion, atmospheric chemistry, interstellar chemistry, and plasma chemistry. These collision-induced chemical transformations are a sensitive probe of the underlying potential energy surface(s). Despite tremendous progress in past decades, our understanding is still not complete. In this Perspective, we survey the recent advances in theoretical characterization of bimolecular reaction dynamics, stimulated by new experimental observations, and identify key new challenges.

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.

A crossed molecular beam apparatus with multi-channel Rydberg tagging time-of-flight detection

We report a new crossed molecular beam apparatus with the H atom Rydberg tagging detection technique. The multi-channel detection scheme with 15 microchannel plate (MCP) detectors enables simultaneously accumulating time-of-flight spectra over a wide range of scattering angles (112°). The efficiency of data acquisition has been enhanced by an order of magnitude. The angular distribution of H atoms from photodissociation of CH₄ at 121.6 nm was used for calibrating the detection efficiency of different MCP detectors. The differential cross section of the reaction F + H₂ → HF + H at the collision of 6.9 meV was measured, demonstrating the feasibility and accuracy of this multi-channel detection method. This apparatus could be a powerful tool for investigating the dynamics of reactions at very low collision energy.

Quantum resonances near absolute zero

Ultralow-energy atom-molecule collisions reveal quasi-bound state quantum resonances

High-resolution imaging of molecular collisions using a Zeeman decelerator

We present the first crossed beam scattering experiment using a Zeeman decelerated molecular beam. The narrow velocity spreads of Zeeman decelerated NO (X²Π_3/2, j = 3/2) radicals result in high-resolution scattering images, thereby fully resolving quantum diffraction oscillations in the angular scattering distribution for inelastic NO-Ne collisions and product-pair correlations in the radial scattering distribution for inelastic NO-O₂ collisions. These measurements demonstrate similar resolution and sensitivity as in experiments using Stark decelerators, opening up possibilities for controlled and low-energy scattering experiments using chemically relevant species such as H and O atoms, O₂ molecules, or NH radicals.

Benchmark Quantum Kinetics at Low Temperatures toward Absolute Zero and Role of Entrance Channel Wells on Tunneling, Virtual States, and Resonances: The F + HD Reaction

This paper reports a study of the quantum reaction dynamics and kinetics of the F + HD reaction at low and ultralow temperatures, focusing on the range from the Wigner limit up to 50 K. Close coupling time-independent quantum reactive scattering calculations for the production of HF and DF molecules have been carried out on two potential energy surfaces differing in the description of the reaction entrance channel. This case is computationally more demanding than the cases of F with H₂ and D₂ ( De Fazio et al. Frontiers in Chemistry 2019 , 7 , 328 ) but offers a wider phenomenology regarding the roles of quantum mechanical effects of tunneling, of virtual states, and of resonances. The results show that at the temperatures in the cold and ultracold regimes small changes in the entrance channel long-range interaction induce surprising near threshold features. The presence of a virtual state close to the reactive threshold gives rise to a marked anti-Arrhenius behavior of the rate constants below 100 mK. This effect enhances reaction rates by about 2 orders of magnitude, making them of the same order as those at room temperature and confining the onset of the Wigner regime in the microkelvin region.

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.

Competing Dynamical Mechanisms in Inelastic Collisions of H + HF

The dynamics of inelastic collisions between HF and H has been investigated in detail by means of time-independent quantum mechanical calculations on the LWA-78 potential energy surface ( Li , G. ; et al. J. Chem. Phys. 2007 , 127 , 174302 ). Reaction probabilities, differential cross sections, and three-vector correlations have been calculated and analyzed. Our results show that there are two competing collision mechanisms that correlate with low and high impact parameters and show very different stereodynamical preferences. The mechanism promoted by high impact parameters is the only one present at low collision energies. We also observe the presence of an apparent threshold in the inelastic cross section for relatively high initial HF rotational quantum numbers, which is associated with the larger energy difference between adjacent rotational quantum states with increasing rotation.

Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures

Integral cross sections and rate constants for the prototypical chemical reactions of the fluorine atom with molecular hydrogen and deuterium have been calculated over a wide interval of collision energy and temperature ranging from the sub-thermal (50 K) down to the ultra-cold regimes (0.5 mK). Rigorous close coupling time-independent quantum reactive scattering calculations have been carried out on two potential energy surfaces, differing only at long-range in the reactants' channel. The results show that tunnel, resonance and virtual state effects enhance under-barrier reactivity giving rise to pronounced deviations from the Arrhenius law as temperature is lowered. Within the ultra-cold domain (below 1 mK), the reactivity is governed by virtual state effects and by tunneling through the reaction barrier; in the cold regime (1 mK–1 K), the shape resonances in the entrance channel of the potential energy surface make the quantum tunneling contribution larger so enhancing cross sections and rate constants by about one order of magnitude; at higher temperatures (above 10 K), the tunneling pathway enhanced by the constructive interference between two Feshbach resonances trapped in the reaction exit channel competes with the thermally activated mechanism, as the energy gets closer to the reaction barrier height. The results show that at low temperatures cross sections and rate constants are extremely sensitive to small changes in the long-range intermolecular interaction in the entrance channel of the potential energy surface, as well as to isotopic substitution.

Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a "d-TST" formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

The effect of nonadiabaticity on the C+ + HF reaction

The chemistry of fluorine in the interstellar medium is particularly simple, with only a few key species and important reactions. Of the latter, the rate of the reaction of C⁺ ions with HF is not well established but is one of the key reactions that sets the relative abundance of HF and the CF⁺ ion, the two fluorine-bearing species that have been observed in interstellar clouds. The C⁺ + HF → CF⁺ + H reaction proceeds through a deeply bound HCF⁺ well. In this work, statistical methods, namely, the statistical adiabatic channel method originally developed by Quack and Troe and the quantum statistical method of Manolopoulos and co-workers, are applied to compute the total cross section as a function of energy for this reaction. This reaction proceeds on the ground 1² A' potential energy surface (PES), and there are also two non-reactive PES's, 1² A″ and 2² A', correlating with the C⁺(² P _1/2,3/2) + HF reactants. Two sets of scattering calculations were carried out, namely, a single-surface calculation on the 1² A' PES and the one in which all three PES's and the spin-orbit splitting of C⁺ are included in the description of the entrance channel. In the latter, reactivity of the spin-orbit excited ² P _3/2 level can be computed, and not just assumed to be zero, as in the single-state adiabatic approximation.

Predicted infrared spectra in the HF stretching band of the H2-HF complex

The infrared spectra with hydrogen fluoride (HF) and deuterium fluoride (DF) (v₂ = 1 ← 0) for eight isotropic species of H₂-HF complex are predicted, based on our newly constructed high-accuracy ab initio potential energy surface [D. Yang et al., J. Chem. Phys. 148, 184301 (2018)]. The radial discrete variable representation/angular finite basis representation method and Lanczos algorithm were used to determine the ro-vibrational energy levels and wave functions for eight species of H₂-HF complex (para-H₂-HF, ortho-H₂-HF, para-D₂-HF, ortho-D₂-HF, para-H₂-DF, ortho-H₂-DF, para-D₂-DF, and ortho-D₂-DF) with separating the inter- and intra-molecular vibrations. Bound states properties including their dissociation energies and rotational constants were presented. The calculated band origins are all red shifted to the isolated HF molecule and in good agreement with available experimental values. The frequencies and line intensities of ro-vibrational transitions in the HF stretching band were further calculated, and the predicted infrared spectra are consistent with available observed spectra. Among them, the spectra for three isotopic species of H₂-HF (para-H₂-DF, para-D₂-DF, and ortho-D₂-DF) were predicted for the first time.

Low temperature rates for key steps of interstellar gas-phase water formation

The gas-phase formation of water molecules in the diffuse interstellar medium (ISM) proceeds mainly via a series of reactions involving the molecular ions OH⁺, H₂O⁺, and H₃O⁺ and molecular hydrogen. These reactions form the backbone for the chemistry leading to the formation of several complex molecular species in space. A comprehensive understanding of the mechanisms involved in these reactions in the ISM necessitates an accurate knowledge of the rate coefficients at the relevant temperatures (10 to 100 K). We present measurements of the rate coefficients for two key reactions below 100 K, which, in both cases, are significantly higher than the values used in astronomical models thus far. The experimental rate coefficients show excellent agreement with dedicated theoretical calculations using a novel ring-polymer molecular dynamics approach that offers a first-principles treatment of low-temperature barrierless gas-phase reactions, which are prevalent in interstellar chemical networks.

Cold chemistry with two atoms

Two atoms react to form a molecule in an optical “beaker”

A full-dimensional potential energy surface and quantum dynamics of inelastic collision process for H2-HF

A full-dimensional ab initio potential energy surface for the H₂-HF van der Waals complex was constructed by employing the coupled-cluster singles and doubles with noniterative inclusion of connected triples with augmented correlation-consistent polarised valence quadruple-zeta basis set plus bond functions. Using the improved coupled-states approximation including the nearest neighbor Coriolis couplings, we calculated the state-to-state scattering dynamics for pure rotational and ro-vibrational energy transfer processes. For pure rotational energy transfer, our results showed a different dynamical behavior for para-H₂ and ortho-H₂ in collision with hydrogen fluoride (HF), which is consistent with the previous study. Interestingly, some strong resonant peaks were presented in the cross sections for ro-vibrational energy transfer. In addition, the calculated vibrational-resolved rate constant is in agreement with the experimental results reported by Bott et al. These dynamics data can be further applied to the numerical simulation of HF chemical lasers.

Dynamical resonances in chemical reactions

The transition state is a key concept in the field of chemistry and is important in the study of chemical kinetics and reaction dynamics.

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super-Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Stereodynamic control of star-epoxy/anhydride crosslinking actuated by liquid-crystalline phase transitions

The epoxy/anhydride copolymerization kinetics of an original star-epoxy monomer (TriaEP) was explored in dynamic heating mode using a series of isoconversional methods. Negative values of the apparent activation energy (E_α) related to an anti-Arrhenius behavior were observed. The transition from Arrhenius to anti-Arrhenius behavior and vice versa depending on the E_α of polymerization was correlated with the dynamics of mesophasic fall-in/fall-out events, physically induced transition (PIT) and chemically induced transition (CIT). This self-assembly phenomenon induces the generation of an anisotropic crosslinked architecture exhibiting both nematic discotic (N_D) and nematic columnar (N_C) organization. Particular emphasis was placed on evaluating the juxtaposition/contribution of the liquid-crystalline transitions to crosslinking, considering both the reaction dynamics and the macromolecular vision.

Advances in spectroscopy and dynamics of small and medium sized molecules and clusters

Investigations of the spectroscopy and dynamics of small- and medium-sized molecules and clusters represent a hot topic in atmospheric chemistry, biology, physics, atto- and femto-chemistry and astrophysics.

Deformed transition-state theory: Deviation from Arrhenius behavior and application to bimolecular hydrogen transfer reaction rates in the tunneling regime

A formulation is presented for the application of tools from quantum chemistry and transition-state theory to phenomenologically cover cases where reaction rates deviate from Arrhenius law at low temperatures. A parameter d is introduced to describe the deviation for the systems from reaching the thermodynamic limit and is identified as the linearizing coefficient in the dependence of the inverse activation energy with inverse temperature. Its physical meaning is given and when deviation can be ascribed to quantum mechanical tunneling its value is calculated explicitly. Here, a new derivation is given of the previously established relationship of the parameter d with features of the barrier in the potential energy surface. The proposed variant of transition state theory permits comparison with experiments and tests against alternative formulations. Prescriptions are provided and implemented to three hydrogen transfer reactions: CH₄  + OH → CH₃  + H₂ O, CH₃ Cl + OH → CH₂ Cl + H₂ O and H₂  + CN → H + HCN, widely investigated both experimentally and theoretically. © 2016 Wiley Periodicals, Inc.

Quantum Tunneling Enhancement of the C + H2O and C + D2O Reactions at Low Temperature

Recent studies of neutral gas-phase reactions characterized by barriers show that certain complex forming processes involving light atoms are enhanced by quantum mechanical tunneling at low temperature. Here, we performed kinetic experiments on the activated C((3)P) + H2O reaction, observing a surprising reactivity increase below 100 K, an effect that is only partially reproduced when water is replaced by its deuterated analogue. Product measurements of H- and D-atom formation allowed us to quantify the contribution of complex stabilization to the total rate while confirming the lower tunneling efficiency of deuterium. This result, which is validated through statistical calculations of the intermediate complexes and transition states has important consequences for simulated interstellar water abundances and suggests that tunneling mechanisms could be ubiquitous in cold dense clouds.