Ring Growth Mechanism in the Reaction between Fulvenallenyl and Cyclopentadienyl Radicals.

Recombination between resonance-stabilized hydrocarbon radicals is an important class of reactions that contribute to molecular growth chemistry in combustion. In the present study, the ring growth mechanism in the reaction between fulvenallenyl (C7H5) and cyclopentadienyl (C5H5) radicals is investigated computationally. The reaction pathways are explored by quantum chemical calculations, and the phenomenological and steady-state rate constants are determined by solving the multiple-well master equations. The primary reaction routes following the recombination between the two radicals are found to be as follows: formation of the adducts, isomerization by hydrogen shift reactions, cyclization to form tricyclic compounds, and their isomerization and dissociation reactions, leading to the formation of acenaphthylene. The overall process can be approximately represented as C7H5 + C5H5 → acenaphthylene + 2H with the bimolecular rate constant of about 4 × 10-12 cm3 molecule-1 s-1. A reaction mechanism consisting of 20 reactions, including the formation, isomerization, and dissociation processes of major intermediate species, is proposed for use in kinetic modeling.

Computation of entropy values for non-electrolyte solute molecules in solution based on semi-empirical corrections to a polarized continuum model.

A simple heuristic model was developed for estimating the entropy of a solute molecule in an ideal solution based on quantum mechanical calculations with polarizable continuum models (QM/PCMs). A translational term was incorporated that included free-volume compensation for the Sackur-Tetrode equation and a rotational term was modeled based on the restricted rotation of a dipole in an electrostatic field. The configuration term for the solute at a given concentration was calculated using a simple lattice model that considered the number of configurations of the solute within the lattice. The configurational entropy was ascertained from this number based on Boltzmann's principle. Standard entropy values were determined for 41 combinations of solutes and solvents at a set concentration of 1 mol dm-3 using the proposed model, and the computational values were compared with experimental data. QM/PCM calculations were conducted at the ωB97X-D/6-311++G(d,p)/IEF-PCM level using universal force field van der Waals radii scaled by 1.2. The proposed model accurately reproduced the entropy values reported for solutes in non-aqueous solvents within a mean absolute deviation of 9.2 J mol-1 K-1 for 33 solutions. This performance represents a considerable improvement relative to that obtained using the method based on the ideal gas treatment that is widely utilized in commercially available computation packages. In contrast, computations for aqueous molecules overestimated the entropies because hydrophobic effects that decrease the entropy of aqueous solutions were not included in the present model.

Potential Nonstatistical Effects on the Unimolecular Decomposition of H2O2.

An attempt is made to evaluate the nonstatistical effects in the thermal decomposition of hydrogen peroxide (H2O2). Previous experimental studies on this reaction reported an unusual pressure dependence of the rate constant indicating broader falloff behavior than expected from conventional theory. In this work, the possibility that the rate constant is affected by nonstatistical effects is investigated based on classical trajectory calculations on the global potential energy surfaces of H2O2 and H2O2 + Ar. The emphasis is on the intramolecular energy redistribution from the K-rotor, that is, the external rotor for rotation around the principal axis of least moment of inertia. The calculations for the H2O2 molecules excited above the dissociation threshold suggest that the energy redistribution from the torsion and K-rotor to vibrations can be competitive with dissociation. In particular, the slow redistribution of the energy associated with the K-rotor significantly affects the dissociation rate. The successive trajectory calculations for collisions of H2O2 with Ar show that the energy associated with the K-rotor can be collisionally transferred more efficiently than the vibrational energy. On the basis of these results and several assumptions, a simple model is proposed to account for the nonstatistical effects on the pressure-dependent thermal rate constants. The model predicts significant broadening of the falloff curve of the rate constants but still cannot fully explain the experimental data.

Two-Dimensional Master Equation Modeling of Some Multichannel Unimolecular Reactions.

Multichannel thermal decomposition reactions of n-propyl radicals, 1-pentyl radicals, and toluene are investigated by solving a two-dimensional master equation formulated as a function of total energy (E) and angular momentum (J). The primary aim of this study is to elucidate the role of angular momentum in the kinetics of multichannel unimolecular reactions. The collisional transition processes of the reactants colliding with argon are characterized based on the classical trajectory calculations and implemented in the master equation. The rate constants calculated by using the two-dimensional master equation are compared with those of one-dimensional master equations. The consequence of the explicit treatment of angular momentum depends on the J dependence of the microscopic rate constants and is particularly emphasized in the thermal decomposition of toluene, for which the C-H and C-C bond fission channels are considered. The centrifugal effect is insignificant in the energetically favored C-H bond fission but is substantial in the energetically higher C-C bond fission, which causes rotational channel switching of the microscopic rate constants. The proper treatment of the J-dependent channel coupling effect, weak collisional transfer of J, and initial-J-dependent collisional energy transfer are found to be essential for predicting the branching fractions at low pressures.

Modeling Collisional Transitions in Thermal Unimolecular Reactions: Successive Trajectories and Two-Dimensional Master Equation for Trifluoromethane Decomposition in an Argon Bath.

Collisional transition processes in thermal unimolecular reactions are modeled by collision frequency, Z, and probability distribution function, P(E, J; E', J'), which describes the probabilities of collisional transitions from the initial state specified by the total energy and angular momentum, (E', J'), to the final states, (E, J). The validity of the collisional transition model, consisting of Z and P(E, J; E', J'), is assessed here for the title reaction. The present model and its parameters are derived from the moments of transition probabilities calculated by classical trajectory simulations. The model explicitly accounts for coupling between the energy and angular momentum transfer and the dependence of transition probability on the initial state. The performance of the model is evaluated by comparing the rate constants calculated by solving the two-dimensional master equation with those obtained from the classical trajectory calculations of the sequence of successive collisions. The rate constants are also compared with available experimental data. The present collisional transition model is found to perform fairly well for predicting the pressure-dependent rate constants. The uncertainty in the prediction and sensitivities of the rate constants to the model parameters are discussed. A simplified version of the model is proposed, which performs as well as the full model. The simplifications and robust procedures for calculating the model parameters are described.

A high-repetition-rate shock tube for transient absorption and laser-induced fluorescence studies of high-temperature chemical kinetics.

A newly constructed high-repetition-rate shock tube designed for kinetic studies of high-temperature reactions using spectroscopic methods is described. The instrument operates at a 0.2-Hz cycle rate with a high reproducibility of reaction conditions that permits extensive signal averaging to improve the quality of kinetic trace data. The density and temperature of the gas behind the reflected shock wave are examined by probing the product formation from reference reactions. Two types of experimental techniques are implemented: transient absorption spectroscopy and time-resolved laser-induced fluorescence. Both methods are shown to be suitable for kinetic measurements of elementary reactions, as illustrated by their application in thermal decomposition reactions of the benzyl radicals and trifluoromethane.

Thermal Decomposition of Benzyl Radicals: Kinetics and Spectroscopy in a Shock Tube.

Understanding the mechanism of high-temperature reactions of aromatic hydrocarbons and radicals is essential for the modeling of hydrocarbon growth processes in combustion environments. In this study, the thermal decomposition reaction of benzyl radicals was investigated using time-resolved broadband cavity-enhanced absorption spectroscopy behind reflected shock waves at a postshock pressure of 100 kPa and temperatures of 1530, 1630, and 1740 K. The transient absorption spectra during the decomposition were recorded over the spectral range of 282-410 nm. The spectra were contributed by the absorption of benzyl radicals and some transient and residual absorbing species. The temporal behavior of the absorption was analyzed using a kinetic model to determine the rate constant for benzyl decomposition. The obtained rate constants can be represented by the Arrhenius expression k1 = 1.1 × 1012 exp(-30 500 K/T) s-1 with an estimated logarithmic uncertainty of Δlog10 k = ±0.2. Kinetic simulation of the secondary reactions indicated that fulvenallenyl radicals are potentially responsible for the transient absorption that appeared around 400 nm. This assignment is consistent with the available spectroscopic information of this radical. Possible candidates for the residual absorbing species are presented, suggesting the potential importance of ortho-benzyne as a reactive intermediate.

Gas-phase reaction mechanism in chemical dry etching using NF3 and remotely discharged NH3/N2 mixture.

Modeling of dry etching processes requires a detailed understanding of the relevant reaction mechanisms. This study aims to elucidate the gas-phase mechanism of reactions in the chemical dry etching process of SiO2 layers which is initiated by mixing NF3 gas with the discharged flow of an NH3/N2 mixture in an etching chamber. A kinetic model describing the gas-phase reactions has been constructed based on the predictions of reaction channels and rate constants by quantum chemical and statistical reaction-rate calculations. The primary reaction pathway includes the reaction of NF3 with H atoms, NF3 + H → NF2 + HF, and subsequent reactions involving NF2 and other radicals. The reaction pathways were analyzed by kinetic simulation, and a simplified kinetic model composed of 12 reactions was developed. The surface process was also investigated based on preliminary quantum chemical calculations for ammonium fluoride clusters, which are considered to contribute to etching. The results indicate the presence of negatively charged fluorine atoms in the clusters, which are suggested to serve as etchants to remove SiO2 from the surface.

Interfacial Water Mediates Oligomerization Pathways of Monoterpene Carbocations.

The air-water interface plays central roles in "on-droplet" synthesis, living systems, and the atmosphere; however, what makes reactions at the interface specific is largely unknown. Here, we examined carbocationic reactions of monoterpene (C10H16 isomer) on an acidic water microjet by using spray ionization mass spectrometry. Gaseous monoterpenes are trapped in the uppermost layers of a water surface via proton transfer and then undergo a chain-propagation reaction. The oligomerization pathway of ß-pinene (ß-P), which showed prompt chain-propagation, is examined by simultaneous exposure to camphene (CMP). (CMP)H+ is the most stable isomer formed via rearrangement of (ß-P)H+ in the gas phase; however, no co-oligomerization was observed. This indicates that the oligomerization of (ß-P)H+ proceeded via ring-opening isomerization. Quantum chemical calculations for [carbocation-(H2O)n=1,2] complexes revealed that the ring-opened isomer is stabilized by hydrogen-π bonds. We propose that partial hydration is a key factor that makes the interfacial reaction unique.

A simple heuristic approach to estimate the thermochemistry of condensed-phase molecules based on the polarizable continuum model.

A simple model based on a quantum chemical approach with polarizable continuum models (PCMs) to provide reasonable translational and rotational entropies for liquid phase molecules was developed. A translational term was evaluated with free-volume compensation for the Sackur-Tetrode equation. We assumed that the free-volume corresponds to the cavity volume in the PCM. A rotational term was modeled as restricted rotation of a dipole in the electrostatic field. Entropies were assessed for twenty species in the liquid-phase using the proposed model, and the computed values were compared with experimental values. Quantum chemistry calculations were conducted at the ωB97X-D/6-311++G(d,p) level with the conductor-like PCM method. Predicted entropies were in good agreement with the experimental entropies, and the root mean square deviation was 17.2 J mol-1 K-1. The standard enthalpy change of formation was then investigated for eleven specific species. The CBS-QB3//ωB97X-D method provides a reasonable standard enthalpy of formation for gasified species; however, improvement of the accuracy is required for liquid species. Finally, the dependence of the Gibbs energy on temperature was investigated for the eleven specific species. When the ideal gas treatment is used, the Gibbs energy trends for the gaseous and liquid phases are quasi-parallel for all of the species, although the Gibbs energy trends for liquids based on the proposed model intersected the gaseous trend (i.e. the intersection is the boiling point). However, the model significantly under or overestimated the experimental boiling points. The error of the boiling points was predominantly due to the inaccuracy of the enthalpy.

Origin of Bath Gas Dependence in Unimolecular Reaction Rates.

The bath gas dependence of thermal unimolecular reaction rates arises from different rates and efficiencies of collisions between reactant and third-body molecules. This study aims to unravel the mechanistic origin of this dependence based on the classical trajectories of methyl isocyanide (CH3NC) colliding with 15 different bath gas molecules (CH3NC, He, Ar, H2, N2, CO, CO2, HCN, NH3, CH4, CH3F, CF4, C2H2, C2H4, and C2H6). The collision frequencies, energy transfer parameters, and relative third-body efficiencies are evaluated from the trajectory calculations. The relative third-body efficiencies of the studied bath gases are found to be in good agreement with available experimental data. The results indicate that differences in collision frequencies are the primary source of the bath gas dependence of the low-pressure rate constants. The nature of the long-range intermolecular interaction, particularly, its anisotropy, is suggested to play a key role in determining the collision frequency.

Chain-propagation, chain-transfer, and hydride-abstraction by cyclic carbocations on water surfaces.

Atmospheric particles contain a wide range of oligomers, but the formation mechanism and the origin of complexity are still unclear. Here, we report the direct detection of carbocationic oligomers generated from the exposure of a series of cyclic unsaturated hydrocarbon gases to acidic water microjets through interface-sensitive mass spectrometry. By changing gas concentrations, H2O (D2O) solvent, bulk pH and comparing results from experiments on acyclic, cyclic, and aromatic compounds, we elucidated three competing reaction mechanisms: chain propagation (CP), chain transfer (CT), and hydride abstraction (HA). We found that conjugative π-electron delocalization in the carbocation is the most important factor for the interfacial oligomerization processes. Our results showed that electrophilic attack on C[double bond, length as m-dash]C double bonds (CP and CT) is limited, and that on C-H single bonds (HA) is enhanced for carbocations lacking conjugation, which is not the case in bulk organic solutions. Carbocationic oligomers generated by the encounter of gaseous unsaturated hydrocarbons and acidic water surfaces potentially contribute to the molecular complexity in atmospheric particles.

Dissociation channels, collisional energy transfer, and multichannel coupling effects in the thermal decomposition of CH3F.

The thermal unimolecular decomposition of CH3F has been studied with the aim of elucidating the multichannel character of the reaction. Experimentally, the temporal profiles of HF were recorded following the decomposition of CH3F in a shock tube. The profiles indicated that the yield of HF is close to unity at a pressure of ∼100 kPa (Ar bath) over the studied temperature range 1888-2279 K. The reaction channels were explored using quantum chemical calculations, which suggested that the decomposition of CH3F proceeds through direct C-H bond fission (CH3F → CH2F + H) or HF elimination (CH3F → 1CH2 + HF) reactions on the singlet potential energy surface. The rate constants were calculated by multichannel master equation analysis based on statistical reaction rate theory and classical trajectory calculations of the collisional energy transfer process. The analysis indicated that the two decomposition channels are competitive at the high-pressure limit but the 1CH2 + HF channel is dominant under the experimental conditions due to the multichannel coupling effect. The collision model dependency of the predicted rate constants and branching fractions has also been investigated, highlighting the importance of selecting the appropriate model for the collision frequency and energy transfer probability function.

Controlling factors of oligomerization at the water surface: why is isoprene such a unique VOC?

Recent studies have shown that atmospheric particles are sufficiently acidic to enhance the uptake of unsaturated volatile organic compounds (VOCs) by triggering acid-catalyzed oligomerization. Controlling factors of oligomerization at the aqueous surfaces, however, remain to be elucidated. Herein, isoprene (2-methyl-1,3-butadiene, ISO), 1,3-butadiene (1,3-b), 1,4-pentadiene (1,4-p), 1-pentene (1-p), and 2-pentene (2-p) vapors are exposed to an acidic water microjet (1 ≤ pH ≤ 5), where cationic products are generated on its surface within ∼10 µs and directly detected using surface-sensitive mass spectrometry. We found that carbocations form at the air-water interface in all the cases, whereas the extent of oligomerization largely depends on the structure in the following order: ISO ≫ 1,3-b > 1,4-p ≫ 1-p ≈ 2-p. Importantly, the cationic oligomerization of ISO yields a protonated decamer ((ISO)10H+, a C50 species of m/z 681.6), while the pentenes 1-p/2-p remain as protonated monomers. We suggest that ISO oligomerization is uniquely facilitated by (1) the resonance stabilization of (ISO)H+ through the formation of a tertiary carbocation with a conjugated C[double bond, length as m-dash]C bond pair, and (2) π-electron enrichment induced by the neighboring methyl group. Experiments in D2O and D2O : H2O mixtures revealed that ISO oligomerization on the acidic water surface proceeds via two competitive mechanisms: chain-propagation and proton-exchange reactions. Furthermore, we found that ISO carbocations undergo addition to relatively inert 1-p, generating hitherto uncharacterized co-oligomers.

Collision Frequency for Energy Transfer in Unimolecular Reactions.

Pressure dependence of unimolecular reaction rates is governed by the energy transfer in collisions of reactants with bath gas molecules. Pressure-dependent rate constants can be theoretically determined by solving master equations for unimolecular reactions. In general, master equation formulations describe energy transfer processes using a collision frequency and a probability distribution model of the energy transferred per collision. The present study proposes a novel method for determining the collision frequency from the results of classical trajectory calculations. Classical trajectories for collisions of several polyatomic molecules (ethane, methane, tetrafluoromethane, and cyclohexane) with monatomic colliders (Ar, Kr, and Xe) were calculated on potential energy surfaces described by the third-order density-functional tight-binding method in combination with simple pairwise interaction potentials. Low-order (including non-integer-order) moments of the energy transferred in deactivating collisions were extracted from the trajectories and compared with those derived using some probability distribution models. The comparison demonstrates the inadequacy of the conventional Lennard-Jones collision model for representing the collision frequency and suggests a robust method for evaluating the collision frequency that is consistent with a given probability distribution model, such as the exponential-down model. The resulting collision frequencies for the exponential-down model are substantially higher than the Lennard-Jones collision frequencies and are close to the (hypothetical) capture rate constants for dispersion interactions. The practical adequacy of the exponential-down model is also briefly discussed.

Thermal Decomposition of 2,3,3,3- and trans-1,3,3,3-Tetrafluoropropenes.

The thermal decomposition reactions of 2,3,3,3- and trans-1,3,3,3-tetrafluoropropenes (TFPs) have been studied both experimentally and computationally to elucidate their kinetics and mechanism. The experiments were performed by observing the temporal profiles of HF produced in the decomposition of the tetrafluoropropenes behind shock waves at temperatures of 1540-1952 K (for 2,3,3,3-TFP) or 1525-1823 K (for trans-1,3,3,3-TFP) and pressure of 100-200 kPa in Ar bath. The reaction pathways responsible for the profiles were explored based on quantum chemical calculations. The decomposition of 2,3,3,3-TFP was predicted to proceed predominantly via direct 1,2-HF elimination to yield CHCCF3, while trans-1,3,3,3-TFP was found to decompose to HF and a variety of isomeric C3HF3 products including CHCCF3, CF2CCHF, CCHCF3, and CF2CHCF. The C3HF3 isomers can subsequently decompose to either CF2 + CHCF or CF2CC + HF products. Multichannel RRKM/master equation calculations were performed for the identified decomposition channels. The observed formation rates and apparent yields of HF are shown to be consistent with the computational predictions.

Thermal Decomposition of Nitromethane and Reaction between CH3 and NO2.

The thermal decomposition of gaseous nitromethane and the subsequent bimolecular reaction between CH3 and NO2 have been experimentally studied using time-resolved cavity-enhanced absorption spectroscopy behind reflected shock waves in the temperature range 1336-1827 K and at a pressure of 100 kPa. Temporal evolution of NO2 was observed following the pyrolysis of nitromethane (diluted to 80-140 ppm in argon) by monitoring the absorption around 400 nm. The primary objectives of the current work were to evaluate the rate constant for the CH3 + NO2 reaction (k2) and to examine the contribution of the roaming isomerization pathway in nitromethane decomposition. The resultant rate constant can be expressed as k2 = (9.3 ± 1.8) × 10-10(T/K)-0.5 cm3 molecule-1 s-1, which is in reasonable agreement with available literature data. The decomposition of nitromethane was found to predominantly proceed with the C-N bond fission process with the branching fraction of 0.97 ± 0.06. Therefore, the upper limit of the branching fraction for the roaming pathway was evaluated to be 0.09.

Time-Resolved Broadband Cavity-Enhanced Absorption Spectroscopy behind Shock Waves.

A fast and sensitive broadband absorption technique for measurements of high-temperature chemical kinetics and spectroscopy has been developed by applying broadband cavity-enhanced absorption spectroscopy (BBCEAS) in a shock tube. The developed method has effective absorption path lengths of 60-200 cm, or cavity enhancement factors of 12-40, over a wavelength range of 280-420 nm, and is capable of simultaneously recording absorption time profiles over an ∼32 nm spectral bandpass in a single experiment with temporal and spectral resolutions of 5 µs and 2 nm, respectively. The accuracy of the kinetic and spectroscopic measurements was examined by investigating high-temperature reactions and absorption spectra of formaldehyde behind reflected shock waves using 1,3,5-trioxane as a precursor. The rate constants obtained for the thermal decomposition reactions of 1,3,5-trioxane (to three formaldehyde molecules) and formaldehyde (to HCO + H) agreed well with the literature data. High-temperature absorption cross sections of formaldehyde between 280 and 410 nm have been determined at the post-reflected-shock temperatures of 955, 1265, and 1708 K. The results demonstrate the applicability of the BBCEAS technique to time- and wavelength-resolved sensitive absorption measurements at high temperatures.

Dissociation of 1,1,1-trifluoroethane is an intrinsic RRKM process: classical trajectories and successful master equation modeling.

Rate constants for thermal decomposition of 1,1,1-trifluoroethane (CH3CF3) in the high-temperature falloff region were previously reported to have an unusual pressure dependence that could not be explained by Rice-Ramsperger-Kassel-Marcus (RRKM) theory in combination with unimolecular master equation analysis. This study investigates the dynamics of the CH3CF3 dissociation and the energy transfer of CH3CF3 in collisions with Ar and Kr by classical trajectory calculations on a global potential energy surface constructed from a large number of quantum chemical calculations. The simulations showed that the ensemble-averaged CH3CF3 populations decay with single exponential profiles that have rate constants close to those predicted by RRKM theory, indicating that the microcanonical ensemble is maintained during decomposition. The trajectory calculation also indicated that a significant portion of the HF product is formed in its vibrationally excited state. Such observation motivated this study to correct some of the reported rate constants for the CH3CF3 decomposition. With the correction applied, the experimental rate constants were well reproduced by the RRKM/master equation calculation using the collisional energy transfer parameters that were also obtained from trajectory calculations. Overall, the title reaction is demonstrated to be another successful example of RRKM/master equation modeling.

Thermal decomposition of 1,1,1-trifluoroethane revisited.

1,1,1-Trifluoroethane (CH3CF3) has been frequently used as a chemical thermometer or an internal standard in shock tube studies to determine relative rates of chemical reactions. The rate constants for the thermal decomposition of CH3CF3 were recently reported to have anomalous pressure dependence in the high-temperature falloff region. In the present study, the kinetics of the CH3CF3 decomposition were reinvestigated using shock tube/laser absorption (ST/LA) spectroscopy and single-pulse shock tube (SPST) methods over the temperature range 1163-1831 K at pressures from 95 to 290 kPa. The present rate constants are 2-3 times smaller than those reported in previous single-pulse experiments performed at near high-pressure limit conditions. The recommended rate constant expression, k = 5.71 × 10(46)T(-9.341) exp(-47073 K/T) s(-1), was obtained over the temperature range 1000-1600 K with uncertainties of ±40% at temperatures below 1300 K and ±32% at 1600 K. The rate constants at the high-temperature region showed clear falloff behavior and were in good agreement with recent high-temperature experiments. The falloff rate constants could not be reproduced by a standard RRKM/master-equation model; this study provides additional evidence for the unusual pressure dependence previously reported for this reaction. Additionally, the rate constants for the decomposition of 1,1-difluoroethylene (CH2CF2) were determined over the temperature range 1650-2059 K at pressures of 100 and 205 kPa, and were reproduced by the RRKM/master-equation calculation with an average downward energy transfer of 900 cm(-1).