Temperature-Dependent, Site-Specific Rate Coefficients for the Reaction of OH (OD) with Methyl Formate Isotopologues via Experimental and Theoretical Studies.

Methyl esters are an important component of combustion and atmospheric systems. Reaction with the OH radical plays an important role in the removal of the simplest methyl ester, methyl formate (MF, CH3OCHO). In this paper, the overall rate coefficients for the reactions of OH and OD with MF isotopologues, studied under pseudo-first-order conditions, are reported using two different laser flash photolysis systems with the decay of OH monitored by laser-induced fluorescence. The room-temperature rate coefficient for OH + MF, (1.95 ± 0.34) × 10-13 cm3 molecule-1 s-1, is in good agreement with the literature. The rate coefficient exhibits curved Arrhenius behavior, and our results bridge the gap between previous low-temperature and shock tube studies. In combination with the literature, the rate coefficient for the reaction of OH with MF between 230 and 1400 K can be parametrized as kOH+MF = (3.2 × 10-13) × (T/300 K)2.3 × exp(-141.4 K/T) cm3 molecule-1 s-1 with an overall estimated uncertainty of ∼30%. The reactions of OD with MF isotopologues show a small enhancement (inverse secondary isotope effect) compared to the respective OH reactions. The reaction of OH/OD with MF shows a normal primary isotope effect, a decrease in the rate coefficient when MF is partially or fully deuterated. Experimental studies have been supported by ab initio calculations at the CCSD(T)-F12/aug-cc-pVTZ//M06-2X/6-31+G** level of theory. The calculated, zero-point-corrected, barrier heights for abstraction at the methyl and formate sites are 1.3 and 6.0 kJ mol-1, respectively, and the ab initio predictions of kinetic isotope effects are in agreement with experiment. Fitting the experimental isotopologue data refines these barriers to 0.9 ± 0.6 and 4.1 ± 0.9 kJ mol-1. The branching ratio is approximately 50:50 at 300 K. Between 300 and 500 K, abstraction via the higher-energy, higher-entropy formate transition state becomes more favored (60:40). However, experiment and calculations suggest that as the temperature increases further, with higher energy, less constrained conformers of the methyl transition state become more significant. The implications of the experimental and theoretical results for the mechanisms of MF atmospheric oxidation and low-temperature combustion are discussed.

Ozonolysis of 2-Methyl-2-pentenal: New Insights from Master Equation Modeling.

Experimental and theoretical studies were carried out to investigate the ozonolysis of trans-2-methyl-2-pentenal. The experiments were conducted in atmospheric simulation chambers coupled to a Fourier transform infrared (FTIR) spectrometer and a gas chromatograph-mass spectrometer at room temperature and atmospheric pressure in the presence of an excess of cyclohexane in dry conditions (RH < 1%). The ozonolysis reaction was investigated theoretically from the results of accurate density functional (M06-2X) and ab initio [CCSD(T)] computations, employing the AVTZ basis set. The sequence of reaction steps was established, and the system of kinetics equations was modeled using MESMER. In the first step, a primary ozonide is formed, which then decomposes along two pathways. The principal ozonolysis products are propanal, methylglyoxal, ethylformate, and a secondary ozonide. An interesting competition between sequential reaction steps and well-skipping is found, which leads to an inversion of the expected methylglyoxal/propanal product ratio at temperatures below 210 K. The mechanism of the "hot ester" reaction channel of the Criegee intermediate was revisited. The computed ozonolysis rate constant and product branching ratio are in excellent agreement with the experimental data that are also reported in the present work.

Studies on the Kinetics of the CH + H2 Reaction and Implications for the Reverse Reaction, 3CH2 + H.

The reaction of CH radicals with H2 has been studied by the use of laser flash photolysis, probing CH decays under pseudo-first-order conditions using laser-induced fluorescence (LIF) over the temperature range 298-748 K at pressures of ∼5-100 Torr. Careful data analysis was required to separate the CH LIF signal at ∼428 nm from broad background fluorescence, and this interference increased with temperature. We believe that this interference may have been the source of anomalous pressure behavior reported previously in the literature (Brownsword, R. A.; J. Chem. Phys. 1997, 106, 7662-7677). The rate coefficient k1 shows complex behavior: at low pressures, the main route for the CH3* formed from the insertion of CH into H2 is the formation of 3CH2 + H, and as the pressure is increased, CH3* is increasingly stabilized to CH3. The kinetic data on CH + H2 have been combined with experimental shock tube data on methyl decomposition and literature thermochemistry within a master equation program to precisely determine the rate coefficient of the reverse reaction, 3CH2 + H → CH + H2. The resulting parametrization is kCH2+H(T) = (1.69 ± 0.11) × 10-10 × (T/298 K)(0.05±0.010) cm3 molecule-1 s-1, where the errors are 1σ.

Master equation modelling of non-equilibrium chemistry in stellar outflows.

A current challenge in astrochemistry is to explain the formation of Fe-Mg silicate dust around evolved stars. The dust is observed to form within 2 to 3 stellar radii of oxygen-rich AGB stars, where the typical conditions are kinetic (translational) temperatures between 1200 and 1600 K, and total gas densities below 1011 cm-3. At these high temperatures, molecules with bond energies < 400 kJ mol-1 should be short-lived, and this results in kinetic bottlenecks in postulated mechanisms for converting the observed Fe, Mg, SiO and H2O into silicate. Here we show that, in the very low pressure regime of a stellar outflow, molecules can exhibit significant vibrational disequilibrium because optical transitions - both spontaneous and stimulated by the stellar radiation field - occur on a much faster timescale than collisions. As a result, relatively less stable molecules can form and survive long enough to provide building blocks to silicate formation. Here we use the molecule OSi(OH)2, formed by the recombination of SiO2 and H2O, as an example. When vibrational disequilibrium is accounted for in a master equation treatment which includes optical transitions, the quantity of metal silicates produced in a low mass loss rate evolved star (R Dor) is increased by 6 orders of magnitude.

On the determination of Lennard-Jones parameters for polyatomic molecules.

Characterizing the key length and energy scales of intermolecular interactions, Lennard-Jones parameters, i.e., collision diameter and well depth, are prerequisites for predicting transport properties and rate constants of chemical species in dilute gases. Due to anisotropy in molecular structures, Lennard-Jones parameters of many polyatomic molecules are only empirically estimated or even undetermined. This study focuses on determining the effective Lennard-Jones parameters between a polyatomic molecule and a bath gas molecule from interatomic interactions. An iterative search algorithm is developed to find orientation-dependent collision diameters and well depths on intermolecular potential energy surfaces. An orientation-averaging rule based on characteristic variables is proposed to derive the effective parameters. Cross-interaction parameters for twelve hydrocarbons with varying molecular shapes, including long-chain and planar ones, interacting with four bath gases He, Ar, N2, and O2 are predicted and reported. Three-dimensional parametric surfaces are constructed to quantitatively depict molecular anisotropy. Algorithmic complexity analysis and numerical experiments demonstrate that the iterative search algorithm is robust and efficient. By using the latest experimental diffusion data, it is found that the proposed orientation-averaging rule improves the prediction of cross-interaction Lennard-Jones parameters for polyatomic molecules, including for long-chain molecules that challenge the consistency of previous methods. By introducing characteristic variables, the present study shows a new route to determining effective Lennard-Jones parameters for polyatomic molecules.

An experimental and computational study of the reaction between 2-methylallyl radicals and oxygen molecules: optimizing master equation parameters with trace fitting.

We have investigated the reaction between 2-methylallyl radicals and oxygen molecules with experimental and computational methods. Kinetic experiments were conducted in a tubular laminar flow reactor using laser photolysis for radical production and photoionization mass spectrometry for detection. The reaction was investigated as a function of temperature (203-730 K) and pressure (0.2-9 torr) in helium and nitrogen bath gases. At low temperatures (T < 410 K), the reaction proceeds by a barrierless reaction to form 2-methylallylperoxyl. Equilibration of the peroxyl adduct and the reactants was observed between 350-410 K. Measurements were extended to even higher temperatures, up to 730 K, but no reaction could be observed. Master equation simulations of the reaction system were performed with the MESMER program. Kinetic parameters in the master equation model were optimized by direct fitting to time-resolved experimental 2-methylallyl traces. Trace fitting is a recently implemented novel feature in MESMER. The trace approach was compared with the more traditional approach where one uses experimental rate coefficients for parameter optimization. The optimized parameters yielded by the two approaches are very similar and do an excellent job at reproducing the experimental data. The optimized master equation model was then used to simulate the reaction under study over a wide temperature and pressure range, from 200 K and 0.01 bar to 1500 K and 100 bar. The simulations predict a small phenomenological rate coefficient under autoignition conditions; about 1 × 10-18 cm3 s-1 at 400 K and 5 × 10-16 cm3 s-1 at 1000 K. We provide modified Arrhenius expressions in PLOG format for the most important product channels to facilitate the use of our results in combustion models.

Global Master Equation Analysis of Rate Data for the Reaction C2H4 + H ⇄ C2H5: ΔfH0⊖C2H5.

While forward and reverse rate constants are frequently used to determine enthalpies of reaction and formation, this process is more difficult for pressure-dependent association/dissociation reactions, especially since the forward and reverse reactions are usually studied at very different temperatures. The problems can be overcome by using a data-fitting procedure based on a master equation model. This approach has been applied to existing experimental pressure-dependent forward and reverse rate coefficients for the reaction C2H4 + H ⇄ C2H5 (k1, k-1) using the MESMER code to determine ΔfH0⊖C2H5 from the enthalpy of the reaction. New measurements of k1, k-1 were included in analysis. They are based on laser flash photolysis with direct observation of H atom time profiles by vacuum ultraviolet laser-induced fluorescence under conditions where the approach to equilibrium could be observed. Measurements were made over the temperature range 798-828 K and with [He] from 2.33 to 7.21 × 1018 molecule cm-3. These data were then combined with a wide range of existing experimental data with helium as the bath gas (112 measurements of k1 and k-1, covering the temperature range 285-1094 K, and [He] = 7.1 × 1015-1.9 × 1019 molecule cm-3) and fitted using the master equation solver MESMER. The required vibrational frequencies and rotational constants of the system were obtained from ab initio calculations, and the activation threshold for association (ΔEthresh), enthalpy of reaction (ΔrH0⊖), imaginary frequency (υimag), and helium energy-transfer parameters (⟨ΔE⟩d,298(T/298)n) were optimized. The resulting parameters (errors are 2σ) are ΔEthresh = 11.43 ± 0.34 kJ mol-1, ΔrH0⊖ = -145.34 ± 0.60 kJ mol-1, υimag = 730 ± 130 cm-1, ⟨ΔE⟩d,298 = 54.2 ± 7.6 cm-1, and n = 1.17 ± 0.12. A value of ΔfH298.15⊖(C2H5) = 120.49 ± 0.57 kJ mol-1 is obtained by combining ΔrH0⊖ with standard enthalpies of formation for H and C2H4 and making the appropriate temperature corrections. The dependence of these parameters on how the internal rotor and CH2 inversion modes are treated has been explored. The experimental data for other bath gases have been analyzed, and data sets compatible with the potential energy surface parameters determined above have been identified. The parameters are virtually identical but with slightly smaller error limits. Parameterization of k1, k-1 using the Troe formalization has been used to investigate competition between ethyl decomposition and reaction with oxygen under combustion conditions.

Energy transfer in intermolecular collisions of polycyclic aromatic hydrocarbons with bath gases He and Ar.

Classical trajectory simulations of intermolecular collisions were performed for a series of polycyclic aromatic hydrocarbons interacting with the bath gases helium and argon for bath gas temperature from 300 to 2500 K. The phase-space average energy transferred per deactivating collision, ⟨∆Edown⟩, was obtained. The Buckingham pairwise intermolecular potentials were validated against high-level quantum chemistry calculations and used in the simulations. The reactive force-field was used to describe intramolecular potentials. The dependence of ⟨∆Edown⟩ on initial vibrational energy is discussed. A canonical sampling method was compared with a microcanonical sampling method for selecting initial vibrational energy at high bath gas temperatures. Uncertainties introduced by the initial angular momentum distribution were identified. The dependence of the collisional energy transfer parameters on the type of bath gas and the molecular structure of polycyclic aromatic hydrocarbons was examined.

Obtaining effective rate coefficients to describe the decomposition kinetics of the corannulene oxyradical at high temperatures.

Unimolecular reactions play an important role in combustion kinetics. An important task of reaction kinetic analysis is to obtain the phenomenological rate coefficients for unimolecular reactions based on the master equation approach. In most cases, the eigenvalues of the transition matrix describing collisional internal energy relaxation are of much larger magnitude than and well separated from the chemically significant eigenvalues, so that phenomenological rate coefficients may be unequivocally derived for incorporation in combustion mechanisms. However, when dealing with unimolecular reactions for a large molecule, especially at high temperatures, the large densities of states of the reactant cause the majority of the population distribution to lie at very high energy levels where the microcanonical reaction rate constants are large and the relaxation and chemical eigenvalues overlap, so that well-defined phenomenological rate coefficients cannot be determined. This work attempts to analyze the effect of overlapping eigenvalues on the high-temperature kinetics of a large oxyradical, based on microcanonical reaction rates and population distributions as well as the eigenvalue spectrum of the transition matrix from the master equation. The aim is to provide a pragmatic method for obtaining the most effective rate coefficients for competing elimination, dissociation, and bimolecular reactions for incorporation in combustion mechanisms. Our approach is demonstrated with a representative example, thermal decomposition and H addition reactions of the corannulene oxyradical.

Reaction and relaxation at surface hotspots: using molecular dynamics and the energy-grained master equation to describe diamond etching.

The extent to which vibrational energy transfer dynamics can impact reaction outcomes beyond the gas phase remains an active research question. Molecular dynamics (MD) simulations are the method of choice for investigating such questions; however, they can be extremely expensive, and therefore it is worth developing cheaper models that are capable of furnishing reasonable results. This paper has two primary aims. First, we investigate the competition between energy relaxation and reaction at 'hotspots' that form on the surface of diamond during the chemical vapour deposition process. To explore this, we developed an efficient reactive potential energy surface by fitting an empirical valence bond model to higher-level ab initio electronic structure theory. We then ran 160 000 NVE trajectories on a large slab of diamond, and the results are in reasonable agreement with experiment: they suggest that energy dissipation from surface hotspots is complete within a few hundred femtoseconds, but that a small fraction of CH3 does in fact undergo dissociation prior to the onset of thermal equilibrium. Second, we developed and tested a general procedure to formulate and solve the energy-grained master equation (EGME) for surface chemistry problems. The procedure we outline splits the diamond slab into system and bath components, and then evaluates microcanonical transition-state theory rate coefficients in the configuration space of the system atoms. Energy transfer from the system to the bath is estimated using linear response theory from a single long MD trajectory, and used to parametrize an energy transfer function which can be input into the EGME. Despite the number of approximations involved, the surface EGME results are in reasonable agreement with the NVE MD simulations, but considerably cheaper. The results are encouraging, because they offer a computationally tractable strategy for investigating non-equilibrium reaction dynamics at surfaces for a broader range of systems.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'.

COMPASS II: extended coverage for polymer and drug-like molecule databases.

The COMPASS II force field has been developed by extending the coverage of the COMPASS force field (J Phys Chem B 102(38):7338-7364, 1998) to polymer and drug-like molecules found in popular databases. Using a fragmentation method to systematically construct small molecules that exhibit key functional groups found in these databases, parameters applicable to database compounds were efficiently obtained. Based on the same parameterization paradigm as used in the development of the COMPASS force field, new parameters were derived by a combination of fits to quantum mechanical data for valence parameters and experimental liquid and crystal data for nonbond parameters. To preserve the quality of the original COMPASS parameters, a quality assurance suite was used and updated to ensure that additional atom-types and parameters do not interfere with the existing ones. Validation against molecular properties, liquid and crystal densities, and enthalpies, demonstrates that the quality of COMPASS is preserved and the same quality of prediction is achieved for the additional coverage.

Interception of excited vibrational quantum states by O2 in atmospheric association reactions.

Bimolecular reactions in Earth's atmosphere are generally assumed to proceed between reactants whose internal quantum states are fully thermally relaxed. Here, we highlight a dramatic role for vibrationally excited bimolecular reactants in the oxidation of acetylene. The reaction proceeds by preliminary adduct formation between the alkyne and OH radical, with subsequent O(2) addition. Using a detailed theoretical model, we show that the product-branching ratio is determined by the excited vibrational quantum-state distribution of the adduct at the moment it reacts with O(2). Experimentally, we found that under the simulated atmospheric conditions O(2) intercepts ~25% of the excited adducts before their vibrational quantum states have fully relaxed. Analogous interception of excited-state radicals by O(2) is likely common to a range of atmospheric reactions that proceed through peroxy complexes.

MESMER: an open-source master equation solver for multi-energy well reactions.

The most commonly used theoretical models for describing chemical kinetics are accurate in two limits. When relaxation is fast with respect to reaction time scales, thermal transition state theory (TST) is the theoretical tool of choice. In the limit of slow relaxation, an energy resolved description like RRKM theory is more appropriate. For intermediate relaxation regimes, where much of the chemistry in nature occurs, theoretical approaches are somewhat less well established. However, in recent years master equation approaches have been successfully used to analyze and predict nonequilibrium chemical kinetics across a range of intermediate relaxation regimes spanning atmospheric, combustion, and (very recently) solution phase organic chemistry. In this article, we describe a Master Equation Solver for Multi-Energy Well Reactions (MESMER), a user-friendly, object-oriented, open-source code designed to facilitate kinetic simulations over multi-well molecular energy topologies where energy transfer with an external bath impacts phenomenological kinetics. MESMER offers users a range of user options specified via keywords and also includes some unique statistical mechanics approaches like contracted basis set methods and nonadiabatic RRKM theory for modeling spin-hopping. It is our hope that the design principles implemented in MESMER will facilitate its development and usage by workers across a range of fields concerned with chemical kinetics. As accurate thermodynamics data become more widely available, electronic structure theory is increasingly reliable, and as our fundamental understanding of energy transfer improves, we envision that tools like MESMER will eventually enable routine and reliable prediction of nonequilibrium kinetics in arbitrary systems.

Detailed balance in multiple-well chemical reactions.

Chemical reactions that involve multiple, interconnected potential wells are of paramount importance in applications of chemical kinetics, particularly combustion and atmospheric chemistry. The only accurate way of determining phenomenological rate constants theoretically for this type of reaction is from the solution of a time-dependent, multiple-well master equation. In this Perspective we address the issue of whether or not (and to what extent) detailed balance is satisfied by rate constants obtained from such solutions. In addressing this issue we discuss a number of related topics, including necessary and sufficient conditions for a system of first-order rate equations to evolve to chemical equilibrium and the relationship between detailed balance and Wegscheider conditions. The assumption of a "near-Boltzmann" distribution in the wells sheds considerable light on the issue at hand. We discuss this approximation in some detail and suggest a quantitative measure of "near-Boltzmann". It is extremely unlikely that the rate constants of interest satisfy detailed balance exactly (there is no reason to believe that they do). However, the discrepancies are expected to be vanishingly small, as observed in practice.

Master equation methods for multiple well systems: application to the 1-,2-pentyl system.

The master equation (ME) provides a powerful technique for modeling reactions that involve at least one potential energy well. It can be widely applied to reactions with several connected energy wells and multiple product channels. The application of the technique is reviewed by reference to the H + SO(2) reaction, where phenomenological rate constants for use, for example, in a combustion model can be extracted through an analysis of the eigenvalues and eigenvectors of the collision matrix, M, that describes formation of the adducts HSO(2) and HOSO from the source H + SO(2), collisional energy transfer in the adduct wells and reaction via the product channel (sink) OH + SO. The approach is extended to systems with more than one sink and it is demonstrated that macroscopic (phenomenological) rate coefficients derived from a ME obey detailed balance if the original ME is appropriately constructed. The method has been applied to the 1-, 2-pentyl radical system, that includes isomerisation and dissociation via two channels to form C(3)H(6) + C(2)H(5) and C(2)H(4) + C(3)H(7). The calculations clearly demonstrate the importance of indirect dissociation channels, in which an isomer can dissociate to form the product set to which it is not directly connected, e.g. formation of C(3)H(6) + C(2)H(5) from 1-pentyl, via the energized states of 2-pentyl. As in previous studies of pentyl dissociation, there is a convergence of the chemically significant eigenvalues and the internal energy relaxation eigenvalues above approximately 1000 K; the consequences of this convergence are discussed.

Combined experimental and master equation investigation of the multiwell reaction H + SO2.

The temperature and pressure dependence of the rate coefficient for the reaction H + SO2 has been measured using a laser flash photolysis/laser-induced fluorescence technique, for 295 10(3) atm, the latter proceeds directly from H + SO2, via the energized states of HOSO. The derived rate coefficients rely heavily on measurements of the reverse reaction, OH + SO, which has only been determined at temperatures up to 700 K.

Master equation models for chemical reactions of importance in combustion.

The master equation provides a quantitative description of the interaction between collisional energy transfer and chemical reaction for dissociation, isomerization, and association processes. The approach is outlined for both irreversible and reversible dissociation, isomerization, and association reactions. There is increasing interest, especially in combustion, in association reactions that involve several linked potential wells, with the possibility of isomerization, collisional stabilization, and dissociation along several product channels. A major aim of the application of the master equation to such systems is the linking of the eigenvalues obtained by its solution to the rate coefficients for the phenomenological chemical reactions that describe the system and that are used in combustion models. The approach is illustrated by reference to the reactions C2H5 + O2, H + SO2, and the dissociation and isomerization of alkyl radicals.