High-Pressure Rate Rules for Alkyl + O2 Reactions. 2. The Isomerization, Cyclic Ether Formation, and β-Scission Reactions of Hydroperoxy Alkyl Radicals

Kinetic Computation of Cyclization Reactions of Large Keto-Hydroperoxide Radicals in Low Temperature Combustion

The cyclization reactions of keto-hydroperoxide (KHP) radicals leading to the formation of keto cyclic ethers and OH radicals play an important role in low temperature combustion for hydrocarbon fuels or oxygenated hydrocarbon fuels. However, due to the lack of kinetic data of cyclization reactions of KHP radicals, researchers often derive high-pressure-limit rate constants of cyclization reactions of KHP radicals from analogous cyclization reactions of hydroperoxyl alkyl radicals during construction of the combustion mechanism. This study aims to systematically investigate the kinetics of cyclization reactions of KHP radicals involving short-to-large-sized radicals. The studied reactions are divided into 7 reaction classes, according to the size of the cyclic transition state, the conjugative effect (whether KHP radicals are resonance-stabilized or not), and the position of the carbonyl group (whether the carbonyl group is inside or outside of the reaction center). The isodesmic reaction method, in conjunction with transition state theory, is utilized for each reaction class to compute the energy barriers and high-pressure-limit rate constants at the DFT level. The study revealed that energy barriers calculated at the DFT level with correction by the isodesmic reaction method are close to the results from the benchmark CCSD(T) method. To develop more accurate rate rules, these reaction classes are further divided into subclasses based on the relative site of the OOH group with the carbonyl group, the type of carbon atoms where the OOH group is located, and the type of carbon atoms where the radical site is located. For each subclass, high-pressure-limit rate rules are derived by averaging the rate constants of reactions in the subclass, and it is found that the maximum absolute deviation of the energy barrier and the ratio of the largest rate constant to the smallest rate constant among reactions in each subclass are within chemical accuracy limits, indicating acceptable use of the developed rate rules. A comparison of the rate constants for cyclization reactions of KHP radicals with the values of analogous cyclization reactions of hydroperoxyalkyl radicals as provided in reported mechanisms is made. Additionally, a comparison is drawn between our developed rate rules for subclasses of the cyclization reactions of KHP radicals and the rate rules for analogous subclasses of cyclization reactions of hydroperoxyl alkyl radicals. These comparisons demonstrate significant differences and highlight the necessity for improved rate rules for cyclization reactions of KHP radicals to enhance the automatically generated combustion mechanisms for hydrocarbon and oxygenated hydrocarbon fuels.

Automated Generation of a Compact Chemical Kinetic Model for n-Pentane Combustion

We have employed automated mechanism generation tools to construct a detailed chemical kinetic model for combustion of n-pentane, as a step toward the generation of compact kinetic models for larger alkanes. Pentane is of particular interest as a prototype for combustion of alkanes and as the smallest paraffin employed as a hybrid rocket fuel, albeit at cryogenic conditions. A reaction mechanism for pentane combustion thus provides a foundation for modeling combustion of extra-large alkanes (paraffins) that are of more practical interest as hybrid rocket fuels, for which manual construction becomes infeasible. Here, an n-pentane combustion kinetic model is developed using the open-source software package Reaction Mechanism Generator (RMG). The model was generated and tested across a range of temperatures (650 to 1350 K) and equivalence ratios (0.5, 1.0, 2.0) at pressures of 1 and 10 atm. Available thermodynamic and kinetic databases were incorporated wherever possible. Predictions using the mechanism were validated against the published laminar burning velocities (Su) and ignition delay times (IDT) of n-pentane. To improve the model performance, a comprehensive analysis, including reaction path and sensitivity analyses of n-pentane oxidation, was performed, leading us to modify the thermochemistry and rate parameters for a few key species and reactions. These were combined as a separate data set, an RMG library, that was then used during mechanism generation. The resulting model predicted IDTs as accurately as the best manually constructed mechanisms, while remaining much more compact. It predicted flame speeds to within 10% of published experimental results. The degree of success of automated mechanism generation for this case suggests that it can be extended to construct reliable and compact models for combustion of larger n-alkanes, particularly when using this mechanism as a seed submodel.

Accurate Kinetics of Cyclization Reactions of the Large-Size Hydroperoxy Methyl-Ester Radicals Investigated by the Isodesmic Reaction Correction Method

The cyclization reactions of hydroperoxymethylester radicals are pivotal in low-temperature methyl-ester combustion but limited experimental and theoretical kinetic data pose challenges. Prior research has drawn upon analogous hydroperoxy alkyl radical cyclization reactions to approximate rate constants and might inaccurately represent ester group-specific behavior. This study systematically investigates these kinetics, accounting for ester group effects and computational complexities in large molecular systems. The reactions are categorized into 11 classes based on cyclic transition state size and -OOH/radical positions. Energy barriers and high-pressure-limit rate constants are calculated using the isodesmic reaction correction method, validated, and applied to 24 subclasses based on carbon sites connected to -OOH and radical moieties. Subclass high-pressure-limit rate rules are derived through averaging rate constants. Analysis reveals uncertainties within acceptable chemical accuracy limits, validating the reaction classification and rate rules. We conduct comparative analyses with values from analogous alkyl reactions in established mechanisms while comparing our results with the high-pressure-limit rate rules for analogous alkane reactions. These comparisons reveal notable disparities, emphasizing the ester group's influence and necessitating tailored ester-specific rate rules. These findings hold promise for improving automatic reaction mechanism generation, particularly for large methyl esters.

Investigating the kinetics of the intramolecular H-migration reaction class of methyl-ester peroxy radicals in low-temperature oxidation mechanisms of biodiesel

Biodiesel is a promising, sustainable, and carbon-neutral fuel. However, studying its combustion mechanisms comprehensively, both theoretically and experimentally, presents challenges due to the complexity and size of its molecules. One significant obstacle in determining low-temperature oxidation mechanisms for biodiesel is the lack of kinetic parameters for the reaction class of intramolecular H-migration reactions of alkyl-ester peroxy radicals, labeled as R(CO)OR'-OO˙ (where the 'dot' represents the radical). Current biodiesel combustion mechanisms often estimate these parameters from the analogous reaction class of intramolecular H-migration reactions of alkyl peroxy radicals in alkane combustion mechanisms. However, such estimations are imprecise and neglect the unique characteristics of the ester group. This research aims to explore the kinetics of the reaction class of H-migration reactions of methyl-ester peroxy radicals. The reaction class is divided into 20 subclasses based on the newly formed cycle size of the transition state, the positions of the peroxy radical and the transferred H atom, and the types of carbons from which the H atom is transferred. Energy barriers for each subclass are calculated by using the CBS-QB3//M06-2X/6-311++G(d,p) method. High-pressure-limit and pressure-dependent rate constants ranging from 0.01 to 100 atm are determined using the transition state theory and Rice-Ramsberger-Kassel-Marcus/master-equation method, respectively. It is noted that the pressure-dependent rate constants calculated for each individual isomerization channel could bring some uncertainties while neglecting the interconnected pathways. A comprehensive comparison is made between our values of selected reactions and high-level calculated values of the corresponding reactions reported in the literature. The small deviation observed between these values indicates the accuracy and reliability of the energy barriers and rate constants calculated in this study. Additionally, our calculated high-pressure-limit rate constants are compared with the corresponding values in combustion mechanisms of esters, which were estimated based on analogous reactions of alkyl peroxy radicals. These comparative analyses shed light on the significant impact of the ester group on the kinetics, particularly when the ester group is involved in the reaction center. Finally, the high-pressure-limit rate rule and pressure-dependent rate rule for each subclass are derived by averaging the rate constants of reactions in each subclass. The accurate and reasonable rate rules for methyl-ester peroxy radicals developed in this study play a crucial role in enhancing our understanding of the low-temperature oxidation mechanisms of biodiesel.

Unimolecular Reactions of 2-Methyloxetanyl and 2-Methyloxetanylperoxy Radicals

Alkyl-substituted cyclic ethers are intermediates formed in abundance during the low-temperature oxidation of hydrocarbons and biofuels via a chain-propagating step with ȮH. Subsequent reactions of cyclic ether radicals involve a competition between ring opening and reaction with O2, the latter of which enables pathways mediated by hydroperoxy-substituted carbon-centered radicals (Q̇OOH). Due to the resultant implications of competing unimolecular and bimolecular reactions on overall populations of ȮH, detailed insight into the chemical kinetics of cyclic ethers remains critical to high-fidelity numerical modeling of combustion. Cl-initiated oxidation experiments were conducted on 2-methyloxetane (an intermediate of n-butane oxidation) using multiplexed photoionization mass spectrometry (MPIMS), in tandem with calculations of stationary point energies on potential energy surfaces for unimolecular reactions of 2-methyloxetanyl and 2-methyloxetanylperoxy isomers. The potential energy surfaces were computed using the KinBot algorithm with stationary points calculated at the CCSD(T)-F12/cc-pVDZ-F12 level of theory. The experiments were conducted at 6 Torr and two temperatures (650 K and 800 K) under pseudo-first-order conditions to facilitate Ṙ + O2 reactions. Photoionization spectra were measured from 8.5 eV to 11.0 eV in 50-meV steps, and relative yields were quantified for species consistent with Ṙ → products and Q̇OOH → products. Species detected in the MPIMS experiments are linked to specific radicals of 2-methyloxetane. Species from Ṙ → products include methyl, ethene, formaldehyde, propene, ketene, 1,3-butadiene, and acrolein. Ion signals consistent with products from alkyl radical oxidation were detected, including for Q̇OOH-mediated species, which are also low-lying channels on their respective potential energy surfaces. In addition to species common to alkyl oxidation pathways, ring-opening reactions of Q̇OOH radicals derived from 2-methyloxetane produced ketohydroperoxide species (performic acid and 2-hydroperoxyacetaldehyde), which may impart additional chain-branching potential, and dicarbonyl species (3-oxobutanal and 2-methylpropanedial), which often serve as proxies for modeling reaction rates of ketohydroperoxides. The experimental and computational results underscore that reactions of cyclic ethers are inherently more complex than currently prescribed in chemical kinetic models utilized for combustion.

Comprehensive Theoretical Study on Four Typical Intramolecular Hydrogen Shift Reactions of Peroxy Radicals: Multireference Character, Recommended Model Chemistry, and Kinetics

Intramolecular hydrogen shift reactions in peroxy radicals (RO₂^• → ^•QOOH) play key roles in the low-temperature combustion and in the atmospheric chemistry. In the present study, we found that a mild-to-moderate multireference character of a potential energy surface (PES) is widely present in four typical hydrogen shift reactions of peroxy radicals (RO₂^•, R = ethyl, vinyl, formyl methyl, and acetyl) by a systematic assessment based on the T₁ diagnostic, %TAE diagnostic, M diagnostic, and contribution of the dominant configuration of the reference CASSCF wavefunction (C₀²). To assess the effects of these inherent multireference characters on electronic structure calculations, we compared the PESs of the four reactions calculated by the multireference method CASPT2 in the complete basis set (CBS) limit, single-reference method CCSD(T)-F12, and single-reference-based composite method WMS. The results showed that ignoring the multireference character will introduce a mean unsigned deviation (MUD) of 0.46-1.72 kcal/mol from CASPT2/CBS results by using the CCSD(T)-F12 method or a MUD of 0.49-1.37 kcal/mol by WMS for three RO₂^• reactions (R = vinyl, formyl methyl, and acetyl) with a stronger multireference character. Further tests by single-reference Kohn-Sham (KS) density functional theory methods showed even larger deviations. Therefore, we specifically developed a new hybrid meta-generalized gradient approximation (GGA) functional M06-HS for the four typical H-shift reactions of peroxy radicals based on the WMS results for the ethyl peroxy radical reaction and on the CASPT2/CBS results for the others. The M06-HS method has an averaged MUD of 0.34 kcal/mol over five tested basis sets against the benchmark PESs, performing best in the tested 38 KS functionals. Last, in a temperature range of 200-3000 K, with the new functional, we calculated the high-pressure-limit rate coefficients of these H-shift reactions by the multi-structural variational transition-state theory with the small-curvature tunneling approximation (MS-CVT/SCT) and the thermochemical properties of all of the involved key radicals by the multi-structural torsional (MS-T) anharmonicity approximation method.

Helium Droplet Infrared Spectroscopy of the Butyl Radicals

Butyl radicals ( n-, s-, i-,} and tert-butyl) are formed from the pyrolysis of stable precursors (1-pentyl nitrite, 2-methyl-1-butyl nitrite, isopentyl nitrite, and azo- tert-butane, respectively). The radicals are doped into a beam of liquid helium droplets and probed with infrared action spectroscopy from 2700-3125 cm-1, allowing for a low temperature measurement of the CH stretching region. The presence of anharmonic resonance polyads in the 2800-3000 cm-1 region complicates its interpretation. To facilitate spectral assignment, the anharmonic resonances are modeled with two model Hamiltonian approaches that explicitly couple CH stretch fundamentals to HCH bend overtones and combinations: a VPT2+K normal mode model based on CCSD(T) quartic force fields and a semi-empirical local mode model. Both of these computational methods provide generally good agreement with the experimental spectra.

High-Pressure-Limit Rate Coefficients for HO2 Elimination Reactions of Hydroperoxyalkenylperoxy Radicals based on the Reaction Class Transition State Theory

Thermokinetic parameters and transport parameters are of great importance to the combustion model and the reaction rate rules are of great importance to construct the combustion reaction mechanism for hydrocarbon fuels. The HO₂ elimination reaction class for hydroperoxyalkenylperoxy radicals is one of the key reaction classes for olefin, for which the rate coefficients are lacking. Therefore, the rate coefficients and rate rules of the HO₂ elimination reaction class for hydroperoxyalkenylperoxy radicals are studied in this work. The reaction class transition state theory (RC-TST) is used to calculate the rate coefficients. In addition, the HO₂ elimination reaction class of hydroperoxyalkenylperoxy radicals is divided into four subclasses depending upon the type of H-C_β bond that is broken in the reactant molecules, and the rate rules are calculated by taking the average of rate coefficients from a representative set of reactions in a subclass. The calculated kinetics data would be valuable for the construction of the combustion reaction mechanism for olefin.

Stereoisomer-dependent unimolecular kinetics of 2,4-dimethyloxetane peroxy radicals

2,4,dimethyloxetane is an important cyclic ether intermediate that is produced from hydroperoxyalkyl (QOOH) radicals in low-temperature combustion of n-pentane. However, reaction mechanisms and rates of consumption pathways remain unclear. In...

Chemistry of Simple Organic Peroxy Radicals under Atmospheric through Combustion Conditions: Role of Temperature, Pressure, and NOx Level

Organic peroxy radicals (RO₂) are key intermediates in the oxidation of organic compounds in both combustion systems and the atmosphere. While many studies have focused on reactions of RO₂ in specific applications, spanning a relatively limited range of reaction conditions, the generalized behavior of RO₂ radicals across the full range of reaction conditions (temperatures, pressures, and NO levels) has, to our knowledge, never been explored. In this work, two simple model systems, n-propyl peroxy radical and γ-isobutanol peroxy radical, are used to evaluate RO₂ fate using pressure-dependent kinetics. The fate of these radicals was modeled based on literature data over 250-1250 K, 0.01-100 bar, and 1 ppt to 100 ppm of NO, which spans the typical range of atmospheric and combustion conditions. Covering this entire range provides a broad overview of the reactivity of these species under both atmospheric and combustion conditions, as well as under conditions intermediate to the two. A particular focus is on the importance of reactions that were traditionally considered to occur in only one of the two sets of conditions: RO₂ unimolecular isomerization reactions (long known to occur in combustion systems but only recently appreciated in atmospheric systems) and RO₂ bimolecular reactions of RO₂ with NO (thought to occur mainly in atmospheric systems and rarely considered in combustion chemistry).

High-Pressure-Limit and Pressure-Dependent Rate Rules for Unimolecular Reactions Related to Hydroperoxy Alkyl Radicals in Normal-Alkyl Cyclohexane Combustion. 2. Cyclization Reaction Class

The hydroperoxy alkyl radicals are important intermediates in the low-temperature combustion for normal-alkyl cycloalkanes, and the cyclization reactions of hydroperoxy alkyl radicals to form cyclic ethers are responsible for a major fraction of the OH formation, which has the potential to promote ignition. In most of the previous modeling studies for normal-alkyl cycloalkane combustion, the kinetic data of the cyclization reactions in the detailed combustion mechanism were mainly taken from the analogous reactions in cyclohexane, methyl cyclohexane, and alkanes in published literature studies. In this work, the kinetics of the cyclization reaction class of hydroperoxy alkyl radicals in normal-alkyl cycloalkanes is studied, where the reaction class is divided into subclasses depending upon the ring size of the transition states, the types of the carbons on which the -OOH site is located and the types of the carbons on which the radical site is located, and the positions of the cyclization (on the alkyl side chain, on the cycle, or between the alkyl side chain and the cycle). Energy barriers and high-pressure-limit site rate constants and pressure-dependent rates for reactions in all subclasses are calculated, and rate rules for all subclasses are developed. The high-pressure-limit rate constants are determined from CBS-QB3 electronic structure calculations combined with canonical transition-state theory calculations, and pressure-dependent rate constants are calculated by using the Rice-Ramsberger-Kassel-Marcus/Master Equation theory at pressures varying from 0.01 to 100 atm. Comparisons of the rate constants for cyclization reactions of hydroperoxy alkyl cyclohexylperoxy radicals calculated in this work with the values of the corresponding reactions in some of the popular combustion mechanisms show that it is unreasonable to use the kinetic data of analogous reactions in alkanes, cyclohexanes, or smaller normal-alkyl cyclohexanes. Therefore, the accurate kinetic calculations and the construction of rate rules for normal-alkyl cycloalkanes are necessary and significant for the reliable modeling of the low-temperature combustion of normal-alkyl cyclohexanes.

High-Pressure-Limit and Pressure-Dependent Rate Rules for Unimolecular Reactions Related to Hydroperoxy Alkyl Radicals in Normal Alkyl Cyclohexane Combustion. 1. Concerted HO2 Elimination Reaction Class and β-Scission Reaction Class

The reactions of the concerted HO₂ elimination from alkyl peroxy radicals and the β-scission of the C-OOH bond from hydroperoxy alkyl radicals, which lead to the formation of olefins and HO₂ radicals, are two important reaction classes that compete with the second O₂ addition step of hydroperoxy alkyl radicals, which are responsible for the chain branching in the low-temperature oxidation of normal alkyl cycloalkanes. These two reaction classes are also believed to be responsible for the negative temperature coefficient behavior due to the formation of the relatively unreactive HO₂ radical, which has the potential to inhibit ignition of normal alkyl cycloalkanes. In this work, the kinetics of the above two reaction classes in normal alkyl cycloalkanes are studied, where reactions in the concerted elimination class are divided into subclasses depending upon the types of carbons from which the H atom is eliminated and the positions of the reaction center (on the alkyl side chain or on the cycle), and the reactions in the β-scission reaction class are divided into subclasses depending upon the types of the carbons on which the radical is located and the positions of the reaction center. Energy barriers by using quantum chemical methods at the CBS-QB3 level, high-pressure-limit rate constants by using canonical transition state theory, and pressure-dependent rate constants at pressures from 0.01 to 100 atm by using Rice-Ramsberger-Kassel-Marcus/Master Equation theory are calculated for a representative set of reactions from methyl cyclohexane to n-butyl cyclohexane in each subclass, from which high-pressure-limit rate rules and pressure-dependent rate rules for each subclass are derived from the average rate constants of reactions within each subclass. A comparison of the rate constants for the reactions in the two reaction classes calculated in this work is made with the rate constants of the same reactions from available mechanisms published in the literature, where most of the rate constants are approximately estimated from analogous reactions in alkanes or small alkyl cyclohexanes, and it is found that a large difference may exist between them, indicating that the present work, which provides more accurate kinetic parameters and reasonable rate rules for these reaction classes, can be helpful to construct higher-accuracy mechanism models for normal alkyl cyclohexane combustion.

Screening for New Pathways in Atmospheric Oxidation Chemistry with Automated Mechanism Generation

In the Earth's atmosphere, reactive organic carbon undergoes oxidation via a highly complex, multigeneration process, with implications for air quality and climate. Decades of experimental and theoretical studies, primarily on the reactions of hydrocarbons, have led to a canonical understanding of how gas-phase oxidation of organic compounds takes place. Recent research has brought to light a number of examples where the presence of certain functional groups opens up reaction pathways for key radical intermediates, including alkyl radicals, alkoxy radicals, and peroxy radicals, that are substantially different from traditional oxidation mechanisms. These discoveries highlight the need for methods that systematically explore the chemistry of complex, functionalized molecules without being prohibitively expensive. In this work, automated reaction network generation is used as a screening tool for new pathways in atmospheric oxidation chemistry. The reaction mechanism generator (RMG) is used to generate reaction networks for the OH-initiated oxidation of 200 mono- and bifunctionally substituted n-pentanes. The resulting networks are then filtered to highlight the reactions of key radical intermediates that are fast enough to compete with traditional atmospheric removal processes as well as "uncanonical" processes which differ from traditionally accepted oxidation mechanisms. Several recently reported, uncanonical atmospheric mechanisms appear in the RMG dataset. These "proof of concept" results provide confidence in this approach as a tool in the search for overlooked atmospheric oxidation chemistry. Several previously unreported reaction types are also encountered in the dataset. The most potentially atmospherically important of these is a radical-carbonyl ring-closure reaction that produces a highly functionalized cyclic alkoxy radical. This pathway is proposed as a promising target for further study via experiments and more detailed theoretical calculations. The approach presented herein represents a new way to efficiently explore atmospheric chemical space and unearth overlooked reaction steps in atmospheric oxidation.

Ab initio rate coefficients for reactions of 2,5-dimethylhexyl isomers with O2: temperature- and pressure-dependent branching ratios

Chemical kinetics of O2-addition to alkyl radicals (R), termed first O2-addition in the oxidation mechanism of alkanes, are of central importance to next-generation combustion strategies designed for operations in the low- to intermediate-temperature region (<1000 K). In the present work, stationary points on potential energy surfaces (PES), temperature- and pressure-dependent rate coefficients, and branching fractions of product formation from R + O2 reactions initiated by the addition of molecular oxygen (3O2) to the three alkyl radicals of a branched alkane, 2,5-dimethylhexane, are reported. The stationary points were determined utilizing ab initio/DFT methods and the reaction energies were computed using the composite CBS-QB3 method. Rice-Ramsperger-Kassel-Marcus (RRKM)/master equation (ME) calculations were employed to compute rate coefficients, from which branching fractions were determined over the pressure range of 10-3-20 atm and the temperature range of 400-900 K on three different surfaces. The quantum chemistry results reveal several distinct features. For the addition of O2 to the tertiary alkyl radical 2,5-dimethylhex-2-yl, the most energetically favorable channel leads to the formation of 2,2,5,5,-tetramethyl-tetrahydrofuran, a cyclic ether intermediate formed coincident with OH in a chain-propagating step from the decomposition of tertiary-tertiary hydroperoxyalkyl (QOOH). On the R + O2 surface of the secondary radical, 2,5-dimethylhex-3-yl, the pathways for the formation of methyl-propanal + iso-butene + OH via concerted C-C and O-O bond scission of tertiary QOOH and that of cyclic ether + OH are the most energetically favorable pathways. The R + O2 surface for the reaction of the primary radical, 2,5-dimethylhex-1-yl, reveals two competitive chain-propagation channels, leading to 2-iso-propyl-4-methyl-tetrahydrofuran + OH and 2,2,5-trimethyltetrahydropyran + OH. Below 100 Torr, the formation of the aforementioned species dominates the respective total R + O2 rate coefficient, while at pressures above 1 atm collisionally stabilized alkylperoxy (ROO) dominates at the temperatures considered here. The results of this study are in very good agreement with the experimentally measured intermediates and products of the 2,5-dimethylhexyl radical + O2 reaction.

Theoretical Study of Radical-Molecule Reactions with Negative Activation Energies in Combustion: Hydroxyl Radical Addition to Alkenes

Many of the radical-molecule reactions are nonelementary reactions with negative activation energies, which usually proceed through two steps. They exist extensively in the atmospheric chemistry and hydrocarbon fuel combustion, so they are extensively studied both theoretically and experimentally. At the same time, various models, such as a two transition state model, a steady-state model, an equilibrium-state model, and a direct elementary dynamics model are proposed to get the kinetic parameters for the overall reaction. In this paper, a conversion temperature T _C1 is defined as the temperature at which the standard molar Gibbs free energy change of the formation of the reaction complex is equal to zero, and it is found that when T ≫ T _C1, the direct elementary dynamics model with an inclusion of the tunneling correction of the second step reaction is applicable to calculate the overall reaction rate constants for this kind of reaction system. The reaction class of hydroxyl radical addition to alkenes is chosen as the objects of this study, five reactions are chosen as the representative for the reaction class, and their single-point energies are calculated using the method of CCSD(T)/CBS, and it is shown that the highest conversion temperature for the five reactions is 139.89 K, far below the usual initial low-temperature (550 K) oxidation chemistry of hydrocarbon fuels; therefore, the steady-state approximation method is applicable. All geometry optimizations are performed at the BH&HLYP/6-311+G(d,p) level, and the result shows that the geometric parameters in the reaction centers are conserved; hence, the isodesmic reaction method is applicable to this reaction class. To validate the accuracy of this scheme, a comparison of electronic energy difference at the BH&HLYP/6-311+G(d,p) level and the corrected electronic energy difference with the electronic energy difference at the CCSD(T)/CBS level is performed for the five representative reactions, and it is shown that the maximum absolute deviation of electronic energy difference can be reduced from 2.54 kcal·mol^-1 before correction to 0.58 kcal·mol^-1 after correction, indicating that the isodesmic reaction method is applicable for the accurate calculation of the kinetic parameters for large-size molecular systems with a negative activation energy reaction. The overall rate constants for 44 reactions of the reaction class of hydroxyl radical addition to alkenes are calculated using the transition-state theory in combination with the isodesmic correction scheme, and high-pressure limit rate rules for the reaction class are developed. In addition, the thermodynamic parameter is calculated and the results indicate that our dynamics model is applicable for our studied reaction class. A chemical kinetic modeling and sensitivity analysis using the calculated kinetic data is performed for the combustion of ethene, and the results indicate the studied reaction is important for the low-to-medium temperature combustion modeling of ethene.

Pressure-dependent rate rules for cycloaddition, intramolecular H-shift, and concerted elimination reactions of alkenyl peroxy radicals at low temperature

The reactions of cycloaddition, intramolecular H-shift and concerted elimination of alkenyl peroxy radicals are three kinds of important reactions in the low temperature combustion of alkenes. In this study, the cycloaddition reactions are divided into classes considering endo-cycloaddition, exo-cycloaddition and the size of the transition states; the intramolecular H-shift reactions are divided into classes depending upon the ring size of the transition states and the type of C-H bonds from which the hydrogen atom is transferred; the concerted elimination reactions are divided into classes according to the type of H-C_βC_αOO bond that is broken. All geometry optimizations are performed at the B3LYP/6-31G(2df,p) level. With the electronic structure calculations being performed using the composite Gaussian-4 (G4) method, high pressure limit rate constants and pressure-dependent rate constants at pressures varying from 0.01 to 100 atm are calculated by using canonical transition state theory and the Rice-Ramsberger-Kassel-Marcus/master equation method, respectively. All rate constants are given in the form of the modified Arrhenius expression. The high pressure limit rate rules and the pressure-dependent rate rules are derived by averaging the rate constants of a representative set of reactions in each class. The results show that the rate rules for these three classes of reactions have a large uncertainty and the impact of the pressure on the rate constants increases as temperature increases.

On-the-fly kinetics of hydrogen abstraction from polycyclic aromatic hydrocarbons by methyl/ethyl radicals

This work provides a rigorous procedure, within the framework of the Reaction Class Transition State Theory (RC-TST) and the Structure-Activity Relationship (SAR), for predicting reliable thermal rate constants on-the-fly for hydrogen abstraction reactions by methyl/ethyl radicals from Polycyclic Aromatic Hydrocarbons (PAHs) in a temperature range of 300-3000 K. All necessary RC-TST parameters were derived from ab initio calculations for a representative set of 36 reactions on which different error analyses and comparisons with available literature data were carried out. In addition to the good agreement between the RC-TST rate constants and the literature data, the detailed error analyses show that RC-TST/SAR, utilizing either the Linear Energy Relationship (LER) where only the reaction energy is needed or Barrier Height Grouping (BHG) where no additional data is needed, can predict the thermal rate constants for any reaction in the title reaction class with an average systematic error of less than 50% when compared to the explicit rate calculations. Therefore, the constructed RC-TST procedure can be confidently used to obtain reliable rate constants on the fly in an attempt to effectively construct detailed kinetic mechanisms for PAH-related fuels.

Sparsity Facilitates Chemical-Reaction Selection for Engine Simulations

Analysis of large-scale, realistic models incorporating detailed chemistry can be challenging because each simulation is computationally expensive, and a complete analysis may require many simulations. This paper addresses one such problem of this type, chemical-reaction selection in engine simulations. In this computationally challenging case, it is demonstrated how the important concept of sparsity can facilitate chemical-reaction selection, which is the process of finding the most important chemical reactions for modeling a chemical process. It is difficult to perform accurate reaction selection for engine simulations using realistic models of the chemistry, as each simulation takes processor weeks to complete. We developed a procedure to efficiently accomplish this selection process with a relatively small number of simulations using a form of global sensitivity analysis based on sparse regression. The chemical-reaction selection leads to an analysis of the ignition chemistry as it evolves within the compression-ignition engine simulations and allows for the spatial development of the selected chemical reactions to be studied in detail.

Multi-fuel surrogate chemical kinetic mechanisms for real world applications

The most important driving force for development of detailed chemical kinetic reaction mechanisms in combustion is the desire by researchers to simulate practical systems. This paper reviews the parallel evolution of kinetic reaction mechanisms and applications of those models to practical, real engines. Early, quite simple, kinetic models for small fuel molecules were extremely valuable in analyzing long-standing, poorly understood applied ignition and flame quenching problems, and later kinetic models have been applied to much more complex flame propagation, problems including autoignition in spark-ignition engines and issues related to octane numbers and knock in modern, high compression ratio and other engines. The recent emergence of very large, multi-fuel surrogate kinetic mechanisms that can address many different fuel types and real engine applications is discussed as a modern analytical tool that can be used for a wide variety of practical applications.

Assessing the Molecular Basis of the Fuel Octane Scale: A Detailed Investigation on the Rate Controlling Steps of the Autoignition of Heptane and Isooctane

N-Heptane and 2,2,4-trimethylpentane (isooctane) are the key species in the modeling of ignition of hydrocarbon-based fuel formulations. Isooctane is knock-resistant whereas n-heptane is a very knock-prone hydrocarbon. It has been suggested that interconversion of their associated alkylperoxy and hydroperoxyalkyl species via hydrogen-transfer isomerization reaction is the key step to understand their different knocking behavior. In this work, the kinetics of unimolecular hydrogen-transfer reactions of n-heptylperoxy and isooctylperoxy are determined using canonical variational transition-state theory and multidimensional small curvature tunneling. Internal rotation of involved molecules is taken explicitly into account in the molecular partition function. The rate coefficients are calculated in the temperature range 300-900 K, relevant to low-temperature autoignition. The concerted HO₂ elimination is an important reaction that competes with some H-transfer and is associated with chain termination. Thus, the branching ratio between these reaction channels is analyzed. We show that variational and multidimensional tunneling effects cannot be neglected for the H-transfer reaction. In particular, the pre-exponential Arrhenius fitting parameter derived from our rate constants shows a strong dependence on the temperature, because tunneling increases quickly at temperatures below 500 K. On the basis of our results, the existing qualitative model for the reasons for different knock behavior observed for n-heptane and isooctane is quantitatively validated at the molecular level.

Theoretical Analysis of the Effect of C═C Double Bonds on the Low-Temperature Reactivity of Alkenylperoxy Radicals

Biodiesel contains a large proportion of unsaturated fatty acid methyl esters. Its combustion characteristics, especially its ignition behavior at low temperatures, have been greatly affected by these C═C double bonds. In this work, we performed a theoretical analysis of the effect of C═C double bonds on the low-temperature reactivity of alkenylperoxy radicals, the key intermediates from the low-temperature combustion of biodiesel. To understand how double bonds affect the fate of peroxy radicals, we selected three representative peroxy radicals from heptane, heptene, and heptadiene having zero, one, and two double C═C bonds, respectively, for study. The potential energy surfaces were explored at the CBS-QB3 level, and the reaction rate constants were computed using canonical/variational transition state theories. We have found that the double bond is responsible for the very different bond dissociation energies of the various types of C-H bonds, which in turn affect significantly the reaction kinetics of alkenylperoxy radicals.

Modeling Ignition of a Heptane Isomer: Improved Thermodynamics, Reaction Pathways, Kinetics, and Rate Rule Optimizations for 2-Methylhexane

Accurate chemical kinetic combustion models of lightly branched alkanes (e.g., 2-methylalkanes) are important to investigate the combustion behavior of real fuels. Improving the fidelity of existing kinetic models is a necessity, as new experiments and advanced theories show inaccuracies in certain portions of the models. This study focuses on updating thermodynamic data and the kinetic reaction mechanism for a gasoline surrogate component, 2-methylhexane, based on recently published thermodynamic group values and rate rules derived from quantum calculations and experiments. Alternative pathways for the isomerization of peroxy-alkylhydroperoxide (OOQOOH) radicals are also investigated. The effects of these updates are compared against new high-pressure shock tube and rapid compression machine ignition delay measurements. It is shown that rate constant modifications are required to improve agreement between kinetic modeling simulations and experimental data. We further demonstrate the ability to optimize the kinetic model using both manual and automated techniques for rate parameter tunings to improve agreement with the measured ignition delay time data. Finally, additional low temperature chain branching reaction pathways are shown to improve the model's performance. The present approach to model development provides better performance across extended operating conditions while also strengthening the fundamental basis of the model.

Performance of First-Principles-Based Reaction Class Transition State Theory

Performance of the Reaction Class Transition State Theory (RC-TST) for prediction of rates constants of elementary reactions is examined using data from its previous applications to a number of different reaction classes. The RC-TST theory is taking advantage of the common structure denominator of all reactions in a given family combined with structure activity relationships to provide a rigorous theoretical framework to obtain rate expression of any reaction within a reaction class in a simple and cost-effective manner. This opens the possibility for integrating this methodology with an automated mechanism generator for "on-the-fly" generation of accurate kinetic models of complex reacting systems.

Reactions of allylic radicals that impact molecular weight growth kinetics

The reactions of allylic radicals have the potential to play a critical role in molecular weight growth (MWG) kinetics during hydrocarbon oxidation and/or pyrolysis.

Photoionization mass spectrometric measurements of initial reaction pathways in low-temperature oxidation of 2,5-dimethylhexane

Product formation from R + O2 reactions relevant to low-temperature autoignition chemistry was studied for 2,5-dimethylhexane, a symmetrically branched octane isomer, at 550 and 650 K using Cl-atom initiated oxidation and multiplexed photoionization mass spectrometry (MPIMS). Interpretation of time- and photon-energy-resolved mass spectra led to three specific results important to characterizing the initial oxidation steps: (1) quantified isomer-resolved branching ratios for HO2 + alkene channels; (2) 2,2,5,5-tetramethyltetrahydrofuran is formed in substantial yield from addition of O2 to tertiary 2,5-dimethylhex-2-yl followed by isomerization of the resulting ROO adduct to tertiary hydroperoxyalkyl (QOOH) and exhibits a positive dependence on temperature over the range covered leading to a higher flux relative to aggregate cyclic ether yield. The higher relative flux is explained by a 1,5-hydrogen atom shift reaction that converts the initial primary alkyl radical (2,5-dimethylhex-1-yl) to the tertiary alkyl radical 2,5-dimethylhex-2-yl, providing an additional source of tertiary alkyl radicals. Quantum-chemical and master-equation calculations of the unimolecular decomposition of the primary alkyl radical reveal that isomerization to the tertiary alkyl radical is the most favorable pathway, and is favored over O2-addition at 650 K under the conditions herein. The isomerization pathway to tertiary alkyl radicals therefore contributes an additional mechanism to 2,2,5,5-tetramethyltetrahydrofuran formation; (3) carbonyl species (acetone, propanal, and methylpropanal) consistent with β-scission of QOOH radicals were formed in significant yield, indicating unimolecular QOOH decomposition into carbonyl + alkene + OH.