Phenomenological Rate Constants Research Articles

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.

Theoretical Kinetics studies of isoprene peroxy radical chemistry: The fate of Z-δ-(4-OH, 1-OO)-ISOPOO radical

The OH radical recycling mechanism in isoprene oxidation is one of the most exciting topics in atmospheric chemistry, and the corresponding studies expand our understanding of oxidation mechanisms of volatile organic compounds in the troposphere and provide reliable evidence to improve and develop conventional atmospheric models. In this work, we performed a detailed theoretical kinetics study on the Z-δ-(4-OH, 1-OO)-ISOPOO radical chemistry, which is proposed as the heart of OH recycling in isoprene oxidation. With the full consideration of its accumulation and consumption channels, we studied and discussed the fate of Z-δ-(4-OH, 1-OO)-ISOPOO radical by solving the energy-resolved master equation over a broad range of conditions, including not only room temperatures but also high temperatures of a forest fire or low temperatures and pressures of the upper troposphere. We found non-negligible pressure dependence of its fate at combustion temperatures (up to two orders of magnitude) and demonstrated the significance of both the multi-structural torsional anharmonicity and tunneling for accurately calculating kinetics of the studied system. More interestingly, the tunneling effect on the phenomenological rate constants of the H-shift reaction channel is also found to be pressure-dependent due to the competition with the O2 loss reaction. In addition, our time evolution calculations revealed a two-stage behavior of critical species in this reaction system and estimated the shortest half-lives for the Z-δ-(4-OH, 1-OO)-ISOPOO radical at various temperatures, pressures and altitudes. This detailed kinetics study of Z-δ-(4-OH, 1-OO)-ISOPOO radical chemistry offers a typical example to deeply understand the core mechanism of OH recycling pathways in isoprene oxidation, and provides valuable insights for promoting the development of relevant atmospheric models.

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

TUMME 2023: Tsinghua University Minnesota Master Equation program. New version announcement

This is an updated version of TUMME (Tsinghua University Minnesota Master Equation program), which is a computer program for setting up and solving master equations for chemical kinetics of unimolecular and bimolecular reactions. The master equation is discretized in terms of energy bins, and rate constants are calculated from chemically significant eigenmodes. TUMME has interfaces to Gaussian 16, Polyrate 2023, and MSTor 2023 output files that allow the master equation code to obtain the microcanonical flux coefficients needed for the kernel of the master equation as calculated by conventional transition state theory (TST), variational transition state theory (VTST) with various tunneling methods, or multi-structural or multi-path VTST (MS-VTST or MP-VTST) with various tunneling methods. The tunneling methods supported include zero-curvature tunneling (ZCT), small-curvature tunneling (SCT), large-curvature tunneling (LCT), and microcanonically optimized multidimensional tunneling (μOMT). For mechanisms involving only unimolecular isomerization (no bimolecular pairs), TUMME can set up and solve a conservative master equation for both rate constants and time-dependent energy-bin populations. For mechanisms involving bimolecular pairs, TUMME 2023 can set up and solve two kinds of master equation: (i) a nonconservative master equation for calculating rate constants of bimolecular reactions and (ii) a conservative master equation that includes bimolecular association in the transition matrix and that can be used for calculating the time evolution of the concentration of a pseudo-first-order bimolecular reactant. TUMME is written in double precision with Python 3; quadruple and octuple precision are also available for some subtasks in C++. The Python code can run in serial or parallel (MP or MPI), and C++ code can run on a single processor or on multiple processors with OpenMP. The program includes a manual and a tutorial. New version program summaryProgram Title: TUMME 2023CPC Library link to program files:https://doi.org/10.17632/whcnvm2mc9.2Developer's repository link:https://doi.org/10.5281/zenodo.7943283Licensing Provisions: Apache-2.0 for the program and CC-BY-4.0 for the manualProgramming languages: Python 3 and C++Does the new version supersede the previous version?: YesJournal reference of previous version: Comput. Phys. Commun. 270 (2022) 108140 [1]External libraries: Numpy, Scipy, Numba, mpi4py (optional), modified mpack (optional), qd (optional), omp (optional)Interfaces to other programs: Gaussian 16 [2], Polyrate 2023 [3], and/or MSTor 2023 [4]Nature of problem: Characterize and calculate rate constants for a temperature-dependent and pressure-dependent complex reaction systemSolution method: Solve the energy-grained master equation based on the chemically significant eigenmodes to get phenomenological rate constants and time evolutions of the populations [1,5–7].Reason for new version: The new version increases the functionality and accuracy, and it offers an easier way to run the program. In addition, some bugs have been corrected.Summary of revisions:1.Added an option (available in high precision) to treat pseudo-first-order bimolecular reactions to obtain the time evolution of the reactants and intermediates. [8]2.Added an inverse-Laplace-transform option in the REACTION block.3.Abandoned rounding the sizes of energy bins to an integer wavenumber (ESOT).4.Changed the way to run TUMME by providing an executable bash script.5.Slightly adjusted the strategy for eigenmode mergers to deal with some unexpected cases.6.Adjusted the output for the partition functions.7.Added options for large-curvature tunneling (LCT) and microcanonically optimized multidimensional tunneling (μOMT).8.Added the keyword pyrfile to support a Polyrate 2023 [3] file that ends with a suffix .fu100.9.Fixed some bugs.10.Updated the manual and added a tutorial to the program distribution, so the distribution now has both a manual and a tutorial.

Investigation of Methylcyclopentadiene Reactivity: Abstraction Reactions and Methylcyclopentadienyl Radical Unimolecular Decomposition.

Understanding the reactivities of methylcyclopentadiene and the methylcyclopentadienyl radical is important in order to improve our comprehension of the chemical kinetics leading to the formation, decomposition, and growth of the first aromatic ring, as it has been shown that five-membered-ring species are important intermediates in the reaction kinetics of aromatic species. In this work, the rate constants of some key H-abstraction reactions from methylcyclopentadiene to produce the methylcyclopentadienyl radical and the formation of fulvene and benzene from the latter are theoretically determined. Rate constants are evaluated using the ab initio transition state theory-based master equation approach, determining structures and Hessians of all stationary points at the ωB97X-D/aug-cc-pVTZ level, energies at the CCSD(T) level extrapolated to the complete basis set limit, RRKM rate constants using conventional and variational transition state theory, and phenomenological rate constants through the solution of the one-dimensional master equation. Variational corrections are determined in both internal and Cartesian coordinates, and it is found that the choice of the coordinate system can impact the accuracy of the calculated rate constants by up to a factor of 4 for H-abstraction reactions and 2 for the unimolecular decomposition of the methylcyclopentadienyl radical. The calculated rate constants are in good agreement with the available literature data. Prompt dissociation of methylcyclopentadienyl radicals accessed following H-abstraction from methylcyclopentadiene was also investigated, and the corresponding rate constants were determined; the results show that prompt dissociation plays a key role under combustion conditions. Finally, lumping of theoretically derived rate constants to account for methylcyclopentadiene ⇄ methylcyclopentadienyl tautomerism allowed the derivation of a simplified set of rate constants suitable to be inserted into kinetic mechanisms.

Automated identification and calculation of prompt effects in kinetic mechanisms using statistical models

The kinetics of prompt dissociation involves rovibrationally excited species (generally formed by exothermic reactions) which may dissociate or isomerize prior to thermalization via collisions with the bath gas. Treating such rovibrationally excited species (so-called “hot” species) with standard kinetic phenomenology may result in incorrect macroscopic representation of their reactivity. This work presents the first fully automated methodology for the calculation of prompt effects of a chosen species in a kinetic mechanism, including (i) reaction selection; (ii) theoretical calculation of rate constants and prompt branching fractions; and (iii) final rate constant fitting. The energy partition between hot fragments is estimated using a variety of statistical models, including a new physically sound microcanonical statistical model based on the rovibrational density of states of the fragments. The methodology is validated against literature data for the prompt dissociations of HCO and C3H7 radicals. The microcanonical statistical model is in better agreement with trajectory simulations for larger species and is thus applicable for practical systems that typically involve large molecules, for which direct dynamics calculations are impractical. The automated workflow is applied to the evaluation of the effects of prompt dissociation for two isomeric radicals C4H71-3 (1-methylallyl) and C4H71-4 (3-buten-1-yl). Twelve H-atom abstraction reactions are selected and the corresponding rate constants are computed with first principles theory. The microcanonical statistical model predicts that prompt dissociations of C4H71-3 and C4H71-4 are already significant at 1000 K, resulting in differences of up to an order of magnitude at 2000 K with respect to the phenomenological thermal rate constants. To illustrate the effects of prompt dissociation on simulations of experimental data, the calculated prompt rate constants are implemented in both CRECK and C3MechV3.3 kinetic mechanisms. Simulations of experimental flame data illustrate the noticeable impact of prompt dissociation kinetics on the high-temperature combustion reactivity of C4H8-1 and C4H8-2.

Energy Dependence of Ensemble-Averaged Energy Transfer Moments and Its Effect on Competing Decomposition Reactions.

We carried out a direct dynamics study on the internal-energy dependence of the ensemble-averaged energy transfer moments of the isobutyl radical in collisions with N2 bath gas. We find a linear dependence of the downward moment ⟨ΔEd⟩ and the root-mean-square moment on the initial internal energy, but the upward moment ⟨ΔEu⟩ is found to be independent of the molecule's internal energy. We improved the exponential-down relaxation model by including a linear dependence of ⟨ΔEd⟩ on the initial energy, and we used the improved treatment in the 1D master equation for isobutyl radical decomposition reactions and for a model of competitive reactions with a larger difference in barrier heights. We calculated phenomenological rate constants and branching ratios from chemically significant eigenmodes of the master equation and showed that the energy dependence of ⟨ΔEd⟩ has a greater influence on channels with higher barriers in competitive reactions. Rate constants and branching ratios from master equation calculations indicate that for a given temperature and pressure, there is a constant ⟨ΔEd⟩ that can reproduce results obtained with an E-dependent ⟨ΔEd⟩. But a constant ⟨ΔEd⟩ cannot do this for all temperatures and pressures, with larger differences when the barriers for the competing channels differ more. We conclude that when the branching ratio of competitive reactions is sensitive to pressure, including the energy dependence of ⟨ΔEd⟩ in master equation simulations can make a significant difference in the results.

Theoretical Study of the Phenoxy Radical Recombination with the O(3P) Atom, Phenyl plus Molecular Oxygen Revisited

Quantum chemical calculations of the C6H5O2 potential energy surface (PES) were carried out to study the mechanism of the phenoxy + O(3P) and phenyl + O2 reactions. CASPT2(15e,13o)/CBS//CASSCF(15e,13o)/DZP multireference calculations were utilized to map out the minimum energy path for the entrance channels of the phenoxy + O(3P) reaction. Stationary points on the C6H5O2 PES were explored at the CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311++G** level for the species with a single-reference character of the wave function and at the CASPT2(15e,13o)/CBS//B3LYP/6-311++G** level of theory for the species with a multireference character of the wave function. Conventional, variational, and variable reaction coordinate transition-state theories were employed in Rice-Ramsperger-Kassel-Marcus master equation calculations to assess temperature- and pressure-dependent phenomenological rate constants and product branching ratios. The main bimolecular product channels of the phenoxy + O(3P) reaction are concluded to be para/ortho-benzoquinone + H, 2,4-cyclopentadienone + HCO and, at high temperatures, also phenyl + O2. The main bimolecular product channels of the phenyl + O2 reaction include 2,4-cyclopentadienone + HCO at lower temperatures and phenoxy + O(3P) at higher temperatures. For both the phenoxy + O(3P) and phenyl + O2 reactions, the collisional stabilization of peroxybenzene at low temperatures and high pressures competes with the bimolecular product channels.

Master equation lumping for multi-well potential energy surfaces: A bridge between ab initio based rate constant calculations and large kinetic mechanisms

Ab initio transition state theory-based master equation methodologies for the calculation of rate constants have gained enormous popularity in the past decades. Nevertheless, introducing these rate constants into large kinetic schemes is a non-trivial task when large potential energy surfaces (PESs) are investigated. To determine proper phenomenological rate constants it is in fact necessary to account for the formation of all the thermodynamically stable wells considered in the master equation (ME), even if most wells do not exhibit significant secondary reactivity. Moreover, reactions involving intermediates with lifetimes comparable to the rovibrational relaxation timescale can exhibit discontinuities both in the rate constants and in the number of thermodynamically stable wells across the investigated temperature and pressure ranges. In this work, we address these problems with a “master equation-based lumping” (MEL) approach specifically designed to process the output of ME calculations of multi-well PESs. Simple kinetic simulations allow identifying both intermediate wells with limited lifetime and isomers with similar reactivity. Then, equivalent rate constants for a smaller set of pseudospecies are derived so as to reproduce the kinetics of the detailed mechanism. Our methodology is independent of any experimental data or experience-based assumptions. The power of MEL is demonstrated with three case studies of increasing complexity, namely the PES for CH3COOH decomposition, and the portions of the C5H5OH and C10H10/C10H9 PESs accessed from C5H5 + OH and C5H5 + C5H5 recombination. This work constitutes the first systematic step addressing the robust integration of rate constants derived from ME simulations into global kinetic schemes and provides a useful approach for the entire chemical kinetics community filling the gap between detailed theoretical investigations of complex PESs and the development of detailed kinetic models.

Mechanistic investigation of water oxidation on hematite photoanodes using intensity-modulated photocurrent spectroscopy

Exploring the nature of photogenerated intermediates during the photoelectrochemical (PEC) oxidation of water is a crucial step to enhance the performance of PEC devices. In this work, the PEC water oxidation on different hematite photoanodes, either bare or modified with cobalt-based oxygen evolution co-catalyst, has been investigated using intensity-modulated photocurrent spectroscopy (IMPS) . The phenomenological rate constants for charge transfer and recombination have been determined at different bias potentials. Their potential dependence trends have been analyzed using a mechanistic model that combines the IMPS theory and the bulk characteristic of the semiconductor. Based on this model, the nature of the formed intermediates during water oxidation is explored. It is found that water oxidation takes place through the coupling of two mobile surface intermediates and two adjacent metal sites are involved in the process. The rate constants for the trapping of the photogenerated holes and the coupling of the mobile surface intermediates have been determined. All investigated photoanodes exhibit comparable rate constants for the trapping as well as for the coupling steps. The surface modification does not significantly influence the trapping and coupling rate constants but remarkably reduces the rate constant of recombination. These results indicate that the efficiency of hematite photoanode is limited by its intrinsic properties and the surface modification has a restricted impact on the overall performance.

Exploring the pyrolysis chemistry of prototype aromatic ester phenyl formate: Reaction pathways, thermodynamics and kinetics

We performed systematic ab initio calculations for the pyrolysis of phenyl formate (PF), the simplest aromatic ester, to establish the potential energy surfaces (PESs), thermodynamics and reaction kinetics. Reaction pathways considered in this work include direct bond fission and intramolecular H-shift, as well as subsequent radical decomposition and ipso-addition by H, O and OH radicals. The energies of reactants, transition states and products were determined at the ROCBS-QB3//M062X/cc-pVTZ level of theory. The standard enthalpy of formation of each species was determined using the atomization method, showing a good agreement with the literature results. For the PF unimolecular decomposition, the intramolecular H-shift reactions to produce phenol + CO and 2,4-cyclohexadienone + CO are the dominant decomposition pathways. Among the decomposition reactions of PF radicals, the isomerization and β-scission channels to form phenoxy + CO and C6H4OH + CO are the dominant pathways. Additionally, for the ipso-addition reactions, PF + H/O → HCOO + C6H6/C6H5O and PF + OH → HCOOH + C6H5O are the major pathways. Multi-well and multi-channel phenomenological rate constants were determined using the Rice–Ramsperger–Kassel–Marcus/master equation (RRKM/ME) method at 500−2000 K and the pressure range of 0.01 atm to the high-pressure limit. It is of interest to observe that the corresponding intermediates for PF radical decompositions with lower energy barriers are merged at higher temperatures and lower pressures. The rate constants of ipso-addition reactions are almost pressure-independence especially at higher temperatures (> 1000 K).

Mechanistic Investigations of Photoelectrochemical Water and Methanol Oxidation on Well-Defined TiO2 Anatase (101) and Rutile (110) Surfaces

The mechanisms of photoelectrochemical water and methanol oxidation on TiO2 anatase (101) and rutile (110) surfaces have been studied using the intensity modulated photocurrent spectroscopy (IMPS) technique. The phenomenological rate constants for the photogenerated charge carriers transfer and recombination have been determined at different band bending values in the presence and absence of methanol as well as at different methanol concentrations. The obtained results have been analyzed based on the IMPS theory for a bulk semiconductor surface together with a model to define the nature of the surface-bound intermediates. The results of the analysis indicated that (i) water oxidation proceeds via coupling of two >OH•br radicals on both surfaces and the coupling of >OH•br radicals is about 1 order of magnitude faster on the anatase (101) surface than that on the rutile (110) surface; (ii) the rate constant of surface recombination at the flatband potential on anatase (101) surface is much lower than that o...

Theoretical Study of the Reaction Mechanism and Kinetics of the Phenyl + Allyl and Related Benzyl + Vinyl Associations.

Potential energy surfaces for the allyl + phenyl and benzyl + vinyl barrierless radical association reactions have been studied at the CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311G** level of theory. Variable reaction coordinate transition state theory (VRC-TST) has been employed to evaluate high-pressure limit rate constants for the barrierless channels. Then, Rice-Ramsperger-Kassel-Marcus master equation (RRKM-ME) calculations have been performed to assess phenomenological rate constants and product branching ratios of various reaction channels at different temperatures and pressures. The initial step of both radical association reactions produces 3-phenylpropene which can further dissociate into a variety of bimolecular products including the indene precursor 1-phenylallyl + H. The results showed that at typical combustion conditions the collisional stabilization of 3-phenylpropene dominates both the phenyl + allyl and benzyl + vinyl reactions at temperatures below 1000 K and remains important at high pressures up to 2500 K. The main bimolecular products of the two reactions at high temperatures are predicted to be benzyl + vinyl and phenyl + allyl, respectively. The well-skipping mechanism to form 1-phenylallyl directly in the allyl + phenyl and benzyl + vinyl reactions appeared to be not significant, however, the reactions can provide some contributions into the formation of the indene precursor via the 3-phenylpropene stabilization/dissociation sequence and most of all, via the formation of 3-phenylpropene itself, which then can undergo H-abstraction by available radicals to produce 1-phenylallyl. The allyl + phenyl reaction can also contribute to the formation of two-ring PAH by producing benzyl radical at high temperatures, either by the well-skipping or stabilization/dissociation mechanisms; in turn, benzyl can readily react with acetylene or propargyl radical to form indene or naphthalene precursors, respectively. Rate expressions for all important reaction channels in a broad range of temperatures and pressures have been generated for kinetic modeling.

Theoretical Study on the Dynamics and Kinetics of the Reaction of CH2OH with OH.

The stochastic one-dimensional chemical master equation (CME) simulation method was used to investigate the dynamics of the reaction of CH2OH with OH. A multiwell multichannel potential energy surface (PES) was constructed at the CCSD(T)/Aug-cc-pVTZ//CBS-QB3 and QCISD(T)/Aug-cc-pVTZ//CBS-QB3 levels of theory. The constructed PES consisted of three chemically activated intermediates and two van der Waals complexes. The fractional population analysis unraveled the role of the energized intermediates and van der Waals complexes in the early stages of this complex reaction. The CME calculations provided the phenomenological rate constants through analysis of the eigenvalues and eigenvectors of collision matrices while Leonard-Jones potential was used to model the collisions. The CME results indicated that CH2O and H2O were the major products, in accordance with the literature. Also, the findings declared the temperature and pressure independence of the reaction over a wide range of temperature (250 to 2400 K) and pressure (0.1 to 7 atm). Furthermore, the efficiency of tunneling on the hydrogen transfer isomerization reaction of trans-HCOH to CH2O was confirmed over the temperature range of 250 to 3000 K. The rate constants for different reaction channels are reported.

Chemical kinetic modeling and shock tube study of methyl propanoate decomposition

The unimolecular decomposition kinetics of methyl propanoate (MP), including the direct C−O/C−C bond fissions and molecular reaction channels, were studied by using high-level ab initio calculations and Rice–Ramsperger–Kassel–Marcus/master equation (RRKM/ME) theory. Four homolytic bond-fission and ten hydrogen transfer reactions of the MP unimolecular decomposition were identified. The phenomenological rate constants were determined using the RRKM/ME theory over a temperature range of 1000−2000K and a pressure range of 0.01atm to the high-pressure limit. At 1atm, the branching ratios show that the dissociation reactions MP ↔ •CH2C(O)OCH3+CH3, MP ↔ CH3OC•(O)+C2H5 and MP ↔ CH3CH2C(O)O•+CH3 dominate MP pyrolysis over the temperature range of 1000−1500K. Our calculated rate constants were adopted in a detailed kinetic model to reproduce the laser-absorption measured CO and CO2 concentration time-histories during the pyrolysis of 0.2% MP/Ar in a shock tube from 1292−1551K and at 1.6atm. The updated mechanism accurately predicted the early-time CO and CO2 formation over the entire temperature range. In particular, our mechanism well reproduced the CO2 time-histories from the early-time formation to the final plateau level.

Theoretical kinetic studies for low temperature oxidation of two typical methylcyclohexyl radicals

To improve the understanding of low temperature oxidation of methyl cyclohexane, the potential energy surfaces for O2 addition to two of its radicals (tcy-C6H10(*)CH3 with a tertiary radical site and ortho-cy-C6H10(*)CH3 with a secondary radical site in the ortho position to the methyl substitution) have been investigated by high level quantum chemical calculations. The reaction kinetics was studied by the ab initio transition state theory based on master equation methodology. The relationship between low temperature oxidation reactivity and molecular structures was explored, typically in terms of the barrier heights of 1,5 H-shift for peroxy radicals. The computed phenomenological rate constants reveal that the ROO stabilization dominates the fates of two methyl cyclohexyl radicals reacting with O2 at pressures higher than 1atm over the studied temperature range. The balance between ROO stabilization, HO2 elimination, QOOH stabilization, and OH formation was further revealed by branching ratios of these four types of reactions. This study extends kinetic data for cyclic alkanes oxidation in a wide range of pressure and temperature.

Quadrupole association and dissociation of hydrogen in the early Universe

Radiative association and photodissociation rates are calculated for quadrupole transitions of H2. A complete set of bound and unbound states are included in a self-consistent master equation to obtain steady-state concentrations for a dilute system of hydrogen atoms and molecules. Phenomenological rate constants computed from the steady-state concentrations satisfy detailed balance for any combination of matter and radiation temperature. Simple formulas are derived for expressing the steady-state distributions in terms of equilibrium distributions. The rate constant for radiative association is found to be generally small for all temperature combinations. The photodissociation rate constant for quadrupole transitions is found to dominate the rate constants for other H2 photodestruction mechanisms for 3000 K. Implications for the formation and destruction of H2 in the early Universe are discussed.

A detailed combined experimental and theoretical study on dimethyl ether/propane blended oxidation

In this paper, a binary fuel model for dimethyl ether (DME) and propane is developed, with a focus on engine-relevant conditions (10–50atm and 550–2000K). New rapid compression machine (RCM) data are obtained for the purpose of further validating the binary fuel model, identifying reactions important to low-temperature propane and DME oxidation, and understanding the ignition-promoting effect of DME on propane. It is found that the simulated RCM data for DME/propane mixtures is very sensitive to the rates of C3H8+OH, which acts as a radical sink relative to DME oxidation, especially at high relative DME concentrations. New rate evaluations are conducted for the reactions of C3H8+OH=products as well as the self-reaction of methoxymethyl peroxy (in competition with RO2=QOOH isomerization) of 2CH3OCH2O2=products. Accurate phenomenological rate constants, k(T, P), are computed by RRKM/ME methods (with energies obtained at the CCSD(T)-F12a/cc-pVTZ-F12 level of theory) for several radical intermediates relevant to DME. The model developed in this paper (120 species and 711 reactions) performs well against the experimental targets tested here and is suitable for use over a wide range of conditions. In addition, the reaction mechanism generator software RMG is used to explore cross-reactions between propane and DME radical intermediates. These cross-reactions did not have a significant effect on simulations of the conditions modeled in this paper, suggesting that kinetic models for high- and low-reactivity binary fuel mixtures may be assembled from addition of their corresponding submodels and a small molecule foundation model.

Self-consistent quantum kinetic theory of diatomic molecule formation.

A quantum kinetic theory of molecule formation is presented which includes three-body recombination and radiative association for a thermodynamically closed system which may or may not exchange energy with its surrounding at a constant temperature. The theory uses a Sturmian representation of a two-body continuum to achieve a steady-state solution of a governing master equation which is self-consistent in the sense that detailed balance between all bound and unbound states is rigorously enforced. The role of quasibound states in catalyzing the molecule formation is analyzed in complete detail. The theory is used to make three predictions which differ from conventional kinetic models. These predictions suggest significant modifications may be needed to phenomenological rate constants which are currently in wide use. Implications for models of low and high density systems are discussed.

When Rate Constants Are Not Enough.

Real-world chemical systems consisting of multiple isomers and multiple reaction channels often react significantly prior to attaining a steady state energy distribution (SED). Detailed elementary reaction models, which implicitly require SED conditions, may be invalid when non-steady-state energy distributions (NSED) exist. NSED conditions may result in reaction rates and product yields that are different from those expected for SED conditions, although this problem is to some extent reduced by using phenomenological models and rate constants. The present study defines pragmatic diagnostics useful for identifying NSED conditions in stochastic master equation simulations. A representative example is presented for each of four classes of common combustion species: RO2 radicals, aliphatic hydrocarbons, alkyl radicals, and polyaromatic radicals. An example selected from the seminal work of Tsang et al. demonstrates that stochastic simulations and eigenvalue methods for solving the master equation predict the same NSED effects. NSED effects are common under relatively moderate combustion conditions, and accurate simulations may require a master equation analysis.