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

Efficient quantum mechanical minimum free energy path calculation by combining path integral hybrid Monte Carlo and climbing image nudged elastic band methods, and its application to the addition reaction of hydrogen isocyanide to formaldehyde

We propose an efficient algorithm for a minimum free energy path calculation based on the path integral hybrid Monte Carlo (PIHMC) method by combining the climbing image-nudged elastic band (CI-NEB) and the thermodynamic integration (TI) methods. Here, the CI-NEB and the TI methods are used to find a transition state along the reaction path and evaluate the free energy path, respectively. Our algorithm is applied to the Walden inversion reaction of the hydronium ions (H3O+). The numerical results show that the computational effort by our algorithm is significantly reduced compared to that of the previously proposed algorithm combining PIHMC without losing accuracy. We also demonstrate the importance of temperature and isotope effects on the addition reaction of hydrogen isocyanide to formaldehyde. In this reaction, the nuclear quantum effect causes the structural change at the TS and decreases the energy barrier.

Experimental and theoretical study of the low-temperature kinetics of the reaction of CN with CH2O and implications for interstellar environments

Rate coefficients for the reaction of CN with CH2O were measured for the first time below room temperature in the range 32-103 K using a pulsed Laval nozzle apparatus together with the Pulsed Laser Photolysis-Laser-Induced Fluorescence technique. The rate coefficients exhibited a strong negative temperature dependence, reaching (4.62 ± 0.84) × 10-11 cm3 molecule-1 s-1 at 32 K, and no pressure dependence was observed at 70 K. The potential energy surface (PES) of the CN + CH2O reaction was calculated at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ level of theory, with the lowest energy channel to reaction characterized by the formation of a weakly-bound van der Waals complex, bound by 13.3 kJ mol-1, prior to two transition states with energies of -0.62 and 3.97 kJ mol-1, leading to the products HCN + HCO or HNC + HCO, respectively. For the formation of formyl cyanide, HCOCN, a large activation barrier of 32.9 kJ mol-1 was calculated. Reaction rate theory calculations were performed with the MESMER (Master Equation Solver for Multi Energy well Reactions) package on this PES to calculate rate coefficients. While this ab initio description provided good agreement with the low-temperature rate coefficients, it was not capable of describing the high-temperature experimental rate coefficients from the literature. However, increasing the energies and imaginary frequencies of both transition states allowed MESMER simulations of the rate coefficients to be in good agreement with data spanning 32-769 K. The mechanism for the reaction is the formation of a weakly-bound complex followed by quantum mechanical tunnelling through the small barrier to form HCN + HCO products. MESMER calculations showed that channel generating HNC is not important. MESMER simulated the rate coefficients from 4-1000 K which were used to recommend best-fit modified Arrhenius expressions for use in astrochemical modelling. The UMIST Rate12 (UDfa) model yielded no significant changes in the abundances of HCN, HNC, and HCO for a variety of environments upon inclusion of rate coefficients reported here. The main implication from this study is that the title reaction is not a primary formation route to the interstellar molecule formyl cyanide, HCOCN, as currently implemented in the KIDA astrochemical model.

Reaction N(2D) + CH2CCH2 (Allene): An Experimental and Theoretical Investigation and Implications for the Photochemical Models of Titan

We report on a combined experimental and theoretical investigation of the N(2D) + CH2CCH2 (allene) reaction of relevance in the atmospheric chemistry of Titan. Experimentally, the reaction was investigated (i) under single-collision conditions by the crossed molecular beams (CMB) scattering method with mass spectrometric detection and time-of-flight analysis at the collision energy (E c) of 33 kJ/mol to determine the primary products and the reaction micromechanism and (ii) in a continuous supersonic flow reactor to determine the rate constant as a function of temperature from 50 to 296 K. Theoretically, electronic structure calculations of the doublet C3H4N potential energy surface (PES) were performed to assist the interpretation of the experimental results and characterize the overall reaction mechanism. The reaction is found to proceed via barrierless addition of N(2D) to one of the two equivalent carbon-carbon double bonds of CH2CCH2, followed by the formation of several cyclic and linear isomeric C3H4N intermediates that can undergo unimolecular decomposition to bimolecular products with elimination of H, CH3, HCN, HNC, and CN. The kinetic experiments confirm the barrierless nature of the reaction through the measurement of rate constants close to the gas-kinetic rate at all temperatures. Statistical estimates of product branching fractions (BFs) on the theoretical PES were carried out under the conditions of the CMB experiments at room temperature and at temperatures (94 and 175 K) relevant for Titan. Up to 14 competing product channels were statistically predicted with the main ones at E c = 33 kJ/mol being formation of cyclic-CH2C(N)CH + H (BF = 87.0%) followed by CHCCHNH + H (BF = 10.5%) and CH2CCNH + H (BF = 1.4%) the other 11 possible channels being negligible (BFs ranging from 0 to 0.5%). BFs under the other conditions are essentially unchanged. Experimental dynamical information could only be obtained on the overall H-displacement channel, while other possible channels could not be confirmed within the sensitivity of the method. This is also in line with theoretical predictions as the other possible channels are predicted to be negligible, including the HCN/HNC + C2H3 (vinyl) channels (overall BF < 1%). The dynamics and product distributions are dramatically different with respect to those observed in the isomeric reaction N(2D) + CH3CCH (propyne), where at a similar E c the main product channels are CH2NH (methanimine) + C2H (BF = 41%), c-C(N)CH + CH3 (BF = 32%), and CH2CHCN (vinyl cyanide) + H (BF = 12%). Rate coefficients (the recommended value is 1.7 (±0.2) × 10-10 cm3 s-1 over the 50-300 K range) and BFs have been used in a photochemical model of Titan's atmosphere to simulate the effect of the title reaction on the species abundance (including any new products formed) as a function of the altitude.

Chemistry and physics of dopants embedded in helium droplets

Helium droplets represent a cold inert matrix, free of walls with outstanding properties to grow complexes and clusters at conditions that are perfect to simulate cold and dense regions of the interstellar medium. At sub-Kelvin temperatures, barrierless reactions triggered by radicals or ions have been observed and studied by optical spectroscopy and mass spectrometry. The present review summarizes developments of experimental techniques and methods and recent results they enabled.

Kinetic Study of the Gas-Phase O(1D) + CH3OH and O(1D) + CH3CN Reactions: Low-Temperature Rate Constants and Atomic Hydrogen Product Yields

Atomic oxygen in its first excited singlet state, O(¹D), is an important species in the photochemistry of several planetary atmospheres and has been predicted to be a potentially important reactive species on interstellar ices. Here, we report the results of a kinetic study of the reactions of O(¹D) with methanol, CH₃OH, and acetonitrile, CH₃CN, over the 50-296 K temperature range. A continuous supersonic flow reactor is used to attain these low temperatures coupled with pulsed laser photolysis and pulsed laser-induced fluorescence to generate and monitor O(¹D) atoms, respectively. Secondary experiments examining the atomic hydrogen product channels of these reactions are also performed, through laser-induced fluorescence measurements of H(²S) atom formation. On the kinetic side, the rate constants for these reactions are seen to be large (>2 × 10^-10 cm³ s^-1) and consistent with barrierless reactions, although they display contrasting dependences as a function of temperature. On the product formation side, both reactions are seen to yield non-negligible quantities of atomic hydrogen. For the O(¹D) + CH₃OH reaction, the derived yields are in good agreement with the conclusions of previous experimental and theoretical works. For the O(¹D) + CH₃CN reaction, whose H-atom formation channels had not previously been investigated, electronic structure calculations of several new product formation channels are performed to explain the observed H-atom yields. These calculations demonstrate the barrierless and exothermic nature of the relevant exit channels, confirming that atomic hydrogen is also an important product of the O(¹D) + CH₃CN reaction.

An Experimental and Theoretical Investigation of the Gas-Phase C(3P) + N2O Reaction. Low Temperature Rate Constants and Astrochemical Implications

The reaction between atomic carbon in its ground electronic state, C(³P), and nitrous oxide, N₂O, has been studied below room temperature due to its potential importance for astrochemistry, with both species considered to be present at high abundance levels in a range of interstellar environments. On the experimental side, we measured rate constants for this reaction over the 50-296 K range using a continuous supersonic flow reactor. C(³P) atoms were generated by the pulsed photolysis of carbon tetrabromide at 266 nm and were detected by pulsed laser-induced fluorescence at 115.8 nm. Additional measurements allowing the major product channels to be elucidated were also performed. On the theoretical side, statistical rate theory was used to calculate low temperature rate constants. These calculations employed the results of new electronic structure calculations of the ³A″ potential energy surface of CNNO and provided a basis to extrapolate the measured rate constants to lower temperatures and pressures. The rate constant was found to increase monotonically as the temperature falls (k_C(³P)+N2O (296 K) = (3.4 ± 0.3) × 10^-11 cm³ s^-1), reaching a value of k_C(³P)+N2O (50 K) = (7.9 ± 0.8) × 10^-11 cm³ s^-1 at 50 K. As current astrochemical models do not include the C + N₂O reaction, we tested the influence of this process on interstellar N₂O and other related species using a gas-grain model of dense interstellar clouds. These simulations predict that N₂O abundances decrease significantly at intermediate times (10³ - 10⁵ years) when gas-phase C(³P) abundances are high.

Experimental and theoretical studies of the gas-phase reactions of O(1D) with H2O and D2O at low temperature

Here we report the results of an experimental and theoretical study of the gas-phase reactions between O(¹D) and H₂O and O(¹D) and D₂O at room temperature and below. On the experimental side, the kinetics of these reactions have been investigated over the 50-127 K range using a continuous flow Laval nozzle apparatus, coupled with pulsed laser photolysis and pulsed laser induced fluorescence for the production and detection of O(¹D) atoms respectively. Experiments were also performed at 296 K in the absence of a Laval nozzle. On the theoretical side, the existing full-dimensional ground X ¹A potential energy surface for the H₂O₂ system involved in this process has been reinvestigated and enhanced to provide a better description of the barrierless H-atom abstraction pathway. Based on this enhanced potential energy surface, quasiclassical trajectory calculations and ring polymer molecular dynamics simulations have been performed to obtain low temperature rate constants. The measured and calculated rate constants display similar behaviour above 100 K, showing little or no variation as a function of temperature. Below 100 K, the experimental rate constants increase dramatically, in contrast to the essentially temperature independent theoretical values. The possible origins of the divergence between experiment and theory at low temperatures are discussed.

Carbon Atom Reactivity with Amorphous Solid Water: H2O-Catalyzed Formation of H2CO

We report new computational and experimental evidence of an efficient and astrochemically relevant formation route to formaldehyde (H₂CO). This simplest carbonylic compound is central to the formation of complex organics in cold interstellar clouds and is generally regarded to be formed by the hydrogenation of solid-state carbon monoxide. We demonstrate H₂CO formation via the reaction of carbon atoms with amorphous solid water. Crucial to our proposed mechanism is a concerted proton transfer catalyzed by the water hydrogen bonding network. Consequently, the reactions ³C + H₂O → ³HCOH and ¹HCOH → ¹H₂CO can take place with low or without barriers, contrary to the high-barrier traditional internal hydrogen migration. These low barriers (or the absence thereof) explain the very small kinetic isotope effect in our experiments when comparing the formation of H₂CO to D₂CO. Our results reconcile the disagreement found in the literature on the reaction route C + H₂O → H₂CO.

Anharmonic spectral features via trajectory-based quantum dynamics: A perturbative analysis of the interplay between dynamics and sampling

The performance of different approximate algorithms for computing anharmonic features in vibrational spectra is analyzed and compared on model and more realistic systems that present relevant nuclear quantum effects. The methods considered combine approximate sampling of the quantum thermal distribution with classical time propagation and include Matsubara dynamics, path integral dynamics approaches, linearized initial value representation, and the recently introduced adaptive quantum thermal bath. A perturbative analysis of these different methods enables us to account for the observed numerical performance on prototypes for overtones and combination bands and to draw qualitatively correct trends for the numerical results obtained for Fermi resonances. Our results prove that the unequal performances of these approaches often derive from the method employed to sample initial conditions and not, as usually assumed, from the lack of coherence in the time propagation. Furthermore, as confirmed by the analysis reported in Benson and Althorpe, J. Chem. Phys. 130, 194510 (2021), we demonstrate, both via the perturbative approach and numerically, that path integral dynamics methods fail to reproduce the intensities of these anharmonic features and follow purely classical trends with respect to their temperature behavior. Finally, the remarkably accurate performance of the adaptive quantum thermal bath approach is documented and motivated.

Large Anharmonic Effects on Tunneling and Kinetics: Reaction of Propane with Muonium

Calculations of kinetic isotope effects (KIEs) provide challenging tests of quantal mass effects on reaction rates, and muonium KIEs are the most challenging. Here, we show that it can be very important to include reaction-coordinate-dependent vibrational anharmonicity along the whole reaction path to calculate tunneling probabilities and KIEs. For the reaction of propane with Mu, this decreases both the height and width of the vibrationally adiabatic potential barrier, with both effects increasing the rate constants. Our results agree well with the experimental observations.

Multidimensional Tunneling Dynamics Employing Quantum-Trajectory Guided Adaptable Gaussian Bases

An efficient basis representation of time-dependent wavefunctions is essential for theoretical studies of high-dimensional molecular systems exhibiting large-amplitude motion. For fully coupled anharmonic systems, the complexity of a general wavefunction scales exponentially with the system size; therefore, for practical reasons, it is desirable to adapt the basis to the time-dependent wavefunction at hand. Often times on this quest for a minimal basis representation, time-dependent Gaussians are employed, in part because of their localization in both configuration and momentum spaces and also because of their direct connection to classical and semiclassical dynamics, guiding the evolution of the basis function parameters. In this work, the quantum-trajectory guided adaptable Gaussian (QTAG) bases method [ J. Chem. Theory Comput. 2020, 16, 18-34] is generalized to include correlated, i.e., non-factorizable, basis functions, and the performance of the QTAG dynamics is assessed on benchmark system/bath tunneling models of up to 20 dimensions. For the popular choice of initial conditions describing tunneling between the reactant/product wells, the minimal "semiclassical" description of the bath modes using essentially a single multidimensional basis function combined with the multi-Gaussian representation of the tunneling mode is shown to capture the dominant features of dynamics in a highly efficient manner.

A kinetic study of the N(2D) + C2H4 reaction at low temperature

Electronically excited nitrogen atoms N(²D) are important species in the photochemistry of N₂ based planetary atmospheres such as Titan. Despite this, few N(²D) reactions have been studied over the appropriate low temperature range. During the present work, rate constants were measured for the N(²D) + ethene (C₂H₄) reaction using a supersonic flow reactor at temperatures between 50 K and 296 K. Here, a chemical reaction was used to generate N(²D) atoms, which were detected directly by laser induced fluorescence in the vacuum ultraviolet wavelength region. The measured rate constants displayed very little variation as a function of temperature, with substantially larger values than those obtained in previous work. Indeed, considering an average temperature of 170 K for the atmosphere of Titan leads to a rate constant that is almost seven times larger than the currently recommended value. In parallel, electronic structure calculations were performed to provide insight into the reactive process. While earlier theoretical work at a lower level predicted the presence of a barrier for the N(²D) + C₂H₄ reaction, the present calculations demonstrate that two of the five doublet potential energy surfaces correlating with reagents are likely to be attractive, presenting no barriers for the perpendicular approach of the N atom to the C[double bond, length as m-dash]C bond of ethene. The measured rate constants and new product channels taken from recent dynamical investigations of this process are included in a 1D coupled ion-neutral model of Titan's atmosphere. These simulations indicate that the modeled abundances of numerous nitrogen bearing compounds are noticeably affected by these changes.

Experimental and theoretical studies of the N(2D) + H2 and D2 reactions

This study reports the first kinetic measurements of the N(²D) + H₂, D₂ reactions below 200 K.

A uniform flow-cavity ring-down spectrometer (UF-CRDS): A new setup for spectroscopy and kinetics at low temperature

The UF-CRDS (Uniform Flow-Cavity Ring Down Spectrometer) is a new setup coupling for the first time a pulsed uniform (Laval) flow with a continuous wave CRDS in the near infrared for spectroscopy and kinetics at low temperature. This high resolution and sensitive absorption spectrometer opens a new window into the phenomena occurring within UFs. The approach extends the detection range to new electronic and rovibrational transitions within Laval flows and offers the possibility to probe numerous species which have not been investigated yet. This new tool has been designed to probe radicals and reaction intermediates but also to follow the chemistry of hydrocarbon chains and PAHs which play a crucial role in the evolution of astrophysical environments. For kinetics measurements, the UF-CRDS combines the CRESU technique (French acronym meaning reaction kinetics in uniform supersonic flows) with the SKaR (Simultaneous Kinetics and Ring-Down) approach where, as indicated by its name, the entire reaction is monitored during each intensity decay within the high finesse cavity. The setup and the approach are demonstrated with the study of the reaction between CN (v = 1) and propene at low temperature. The recorded data are finally consistent with a previous study of the same reaction for CN (v = 0) relying on the CRESU technique with laser induced fluorescence detection.

Chemical Kinetics Approves the Occurrence of C (3Pj) Reaction with H2O

Although both atomic carbon and water are omnipresent in human life, there is a debate about the possibility of carbon reaction with water. Some low-temperature spectroscopic investigations have rejected the reaction, whereas some room-temperature experiments and theoretical studies have accepted the possibility of the reaction by reporting rate coefficients ranging from 10⁵ to 10⁹ L mol^-1 s^-1. This study provides new lines of evidence about the reaction through exploration of the reaction mechanism using the CCSD(T) method and solving the corresponding master equation by following two main approaches. According to the results, the rate coefficient of the reaction is significantly influenced by the tunneling and hindered rotation effects, in addition to the selected total angular momentum (J). Furthermore, the total rate coefficient of the reaction increases dramatically (from 10⁷ to 10¹¹ L mol^-1 s^-1) with the rise of temperature from 100 to 4000 K, while the total rate coefficient is insensitive to pressure (0.1-10 atm). Despite some differences between the results of the two approaches, the rate coefficients of both methods are consistent with the previously reported rate coefficients. Also, in agreement with the previous studies, the major products are ²HOC + ²H and ²HCO + ²H. In general, the findings approve the occurrence of the title reaction and indicate that the mentioned conflict is due to the sensitivity of the reaction to the investigated temperature and J level. The sensitivity does not permit low-temperature spectroscopic studies to detect any products and varies the measured and calculated rate coefficients.

Low-Temperature Rate Constants and Product-Branching Ratios for the C(1D) + H2O Reaction

The gas-phase reaction between atomic carbon in its first electronically excited ¹D state and water has been studied over the 50-296 K temperature range using a supersonic flow apparatus. C(¹D) atoms were produced by pulsed ultraviolet multiphoton dissociation of carbon tetrabromide; a process that also generates ground-state atomic carbon C(³P). The reaction was followed by detecting product H-atoms by pulsed vacuum ultraviolet laser-induced fluorescence. Two types of experiment were performed. First, temperature-dependent rate constants were derived by recording H-atom formation curves at various gas-phase water concentrations at each temperature. Secondly, temperature-dependent H-atom yields were extracted by comparing the H-atom fluorescence intensities generated by the target C(¹D) + H₂O reaction with those of a reference reaction. The second-order rate constants are large and increase to low temperature, whereas the measured H-atom yields are close to the theoretical maximum value of 2 above 100 K. At 50 K, neither rate constants nor H-atom yields could be derived because of H-atom formation by quantum tunneling in the activated C(³P) + H₂O reaction. The present results are discussed in the context of earlier work on the C(¹D)/C(³P) + H₂O reactions.

A low temperature investigation of the N(2D) + CH4, C2H6 and C3H8 reactions

Low temperature rate constants for the N(²D) + C₂H₆, C₃H₈ reactions are shown to be much smaller than previously thought.

Rate constants for the N(2D) + C2H2 reaction over the 50–296 K temperature range

The reactions of metastable atomic nitrogen N(²D) are important processes in the gas-phase chemistry of several planetary atmospheres.

A combined theoretical and experimental investigation of the kinetics and dynamics of the O(1D) + D2 reaction at low temperature

The O(¹D) + H₂ reaction is a prototype for simple atom-diatom insertion type mechanisms considered to involve deep potential wells. While exact quantum mechanical methods can be applied to describe the dynamics, such calculations are challenging given the numerous bound quantum states involved. Consequently, efforts have been made to develop alternative theoretical strategies to portray accurately the reactive process. Here we report an experimental and theoretical investigation of the O(¹D) + D₂ reaction over the 50-296 K range. The calculations employ three conceptually different approaches - mean potential phase space theory, the statistical quantum mechanical method and ring polymer molecular dynamics. The calculated rate constants are in excellent agreement over the entire temperature range, exhibiting only weak temperature dependence. The agreement between experiment and theory is also very good, with discrepancies smaller than 26%. Taken together, the present and previous theoretical results validate the hypothesis that long-lived complex formation dominates the reaction dynamics at low temperature.

A low temperature investigation of the gas-phase N(2D) + NO reaction. Towards a viable source of N(2D) atoms for kinetic studies in astrochemistry

The gas-phase reaction of metastable atomic nitrogen N(²D) with nitric oxide has been investigated over the 296–50 K temperature range using a supersonic flow reactor.

Kinetics and dynamics of the C(3P) + H2O reaction on a full-dimensional accurate triplet state potential energy surface

A full-dimensional accurate PES for the C(³P) + H₂O reaction is developed using the PIP-NN method.

An experimental and theoretical investigation of the C(1D) + D2 reaction

Rate constants derived from ring polymer molecular dynamics calculations confirm the validity of this method for studying low-temperature complex-forming reactions