Computational studies on the reactions of 3-butenyl and 3-butenylperoxy radicals

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.

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.

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

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

Hierarchical Study of the Reactions of Hydrogen Atoms with Alkenes: A Theoretical Study of the Reactions of Hydrogen Atoms with C2-C4 Alkenes

The present study complements our previous studies of the reactions of hydrogen atoms with C₅ alkene species including 1- and 2-pentene and the branched isomers (2-methyl-1-butene, 2-methyl-2-butene, and 3-methyl-1-butene), by studying the reactions of hydrogen atoms with C₂–C₄ alkenes (ethylene, propene, 1- and 2-butene, and isobutene). The aim of the current work is to develop a hierarchical set of rate constants for Ḣ atom addition reactions to C₂–C₅ alkenes, both linear and branched, which can be used in the development of chemical kinetic models. High-pressure limiting and pressure-dependent rate constants are calculated using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory and a one-dimensional master equation (ME). Rate constant recommendations for Ḣ atom addition and abstraction reactions in addition to alkyl radical decomposition reactions are also proposed and provide a useful tool for use in mechanisms of larger alkenes for which calculations do not exist. Additionally, validation of our theoretical results with single-pulse shock-tube pyrolysis experiments is carried out. An improvement in species mole fraction predictions for alkene pyrolysis is observed, showing the relevance of the present study.

Atmospheric Chemistry of Allylic Radicals from Isoprene: A Successive Cyclization-Driven Autoxidation Mechanism

The atmospheric chemistry of isoprene has broad implications for regional air quality and the global climate. Allylic radicals, taking 13-17% yield in the isoprene oxidation by ^•Cl, can contribute as much as 3.6-4.9% to all possible formed intermediates in local regions at daytime. Considering the large quantity of isoprene emission, the chemistry of the allylic radicals is therefore highly desirable. Here, we investigated the atmospheric oxidation mechanism of the allylic radicals using quantum chemical calculations and kinetics modeling. The results indicate that the allylic radicals can barrierlessly combine with O₂ to form peroxy radicals (RO₂^•). Under ≤100 ppt NO and ≤50 ppt HO₂^• conditions, the formed RO₂^• mainly undergo two times "successive cyclization and O₂ addition" to finally form the product fragments 2-alkoxy-acetaldehyde (C₂H₃O₂^•) and 3-hydroperoxy-2-oxopropanal (C₃H₄O₄). The presented reaction illustrates a novel successive cyclization-driven autoxidation mechanism. The formed 3-hydroperoxy-2-oxopropanal product is a new isomer of the atmospheric C₃H₄O₄ family and a potential aqueous-phase secondary organic aerosol precursor. Under >100 ppt NO condition, NO can mediate the cyclization-driven autoxidation process to form C₅H₇NO₃, C₅H₇NO₇, and alkoxy radical-related products. The proposed novel autoxidation mechanism advances our current understanding of the atmospheric chemistry of both isoprene and RO₂^•.

Two-Dimensional Master Equation Modeling of Some Multichannel Unimolecular Reactions

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

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.

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

A simple model based on a quantum chemical approach with polarizable continuum models (PCMs) to provide reasonable translational and rotational entropies for liquid phase molecules was developed.

Atmospheric Reaction of Cl with 4-Hydroxy-2-pentanone (4H2P): A Theoretical Study

The kinetics and the mechanism of the reaction of 4-hydroxy-2-pentanone (4H2P) with Cl atom were investigated using quantum theoretical calculations. Density functional theory, CBS-QB3, and G3B3 methods are used to explore the reaction pathways. Rice-Ramsperger-Kassel-Marcus theory is employed to obtain rate constants of the reaction at atmospheric pressure and the temperature range 278-400 K. This study provides the first theoretical and kinetic determination of Cl rate constant for reactions with 4H2P over a large temperature range. The obtained rate constant 1.47 × 10^-10 cm³ molecule^-1 s^-1 at 298 K is in reasonable agreement with those obtained for C4-C5 hydroxyketones both theoretically and experimentally. The results regarding the structure-reactivity relationship and the atmospheric implications are discussed.

Theoretical Kinetics Analysis for Ḣ Atom Addition to 1,3-Butadiene and Related Reactions on the Ċ4H7 Potential Energy Surface

The oxidation chemistry of the simplest conjugated hydrocarbon, 1,3-butadiene, can provide a first step in understanding the role of polyunsaturated hydrocarbons in combustion and, in particular, an understanding of their contribution toward soot formation. On the basis of our previous work on propene and the butene isomers (1-, 2-, and isobutene), it was found that the reaction kinetics of Ḣ-atom addition to the C═C double bond plays a significant role in fuel consumption kinetics and influences the predictions of high-temperature ignition delay times, product species concentrations, and flame speed measurements. In this study, the rate constants and thermodynamic properties for Ḣ-atom addition to 1,3-butadiene and related reactions on the Ċ₄H₇ potential energy surface have been calculated using two different series of quantum chemical methods and two different kinetic codes. Excellent agreement is obtained between the two different kinetics codes. The calculated results including zero-point energies, single-point energies, rate constants, barrier heights, and thermochemistry are systematically compared among the two quantum chemical methods. 1-Methylallyl (Ċ₄H₇1-3) and 3-buten-1-yl (Ċ₄H₇1-4) radicals and C₂H₄ + Ċ₂H₃ are found to be the most important channels and reactivity-promoting products, respectively. We calculated that terminal addition is dominant (>80%) compared to internal Ḣ-atom addition at all temperatures in the range 298-2000 K. However, this dominance decreases with increasing temperature. The calculated rate constants for the bimolecular reaction C₄H₆ + Ḣ → products and C₂H₄ + Ċ₂H₃ → products are in excellent agreement with both experimental and theoretical results from the literature. For selected C₄ species, the calculated thermochemical values are also in good agreement with literature data. In addition, the rate constants for H atom abstraction by Ḣ atoms have also been calculated, and it is found that abstraction from the central carbon atoms is the dominant channel (>70%) at temperatures in the range of 298-2000 K. Finally, by incorporating our calculated rate constants for both Ḣ atom addition and abstraction into our recently developed 1,3-butadiene model, we show that laminar flame speed predictions are significantly improved, emphasizing the value of this study.

Toward the Development of a Fundamentally Based Chemical Model for Cyclopentanone: High-Pressure-Limit Rate Constants for H Atom Abstraction and Fuel Radical Decomposition

Theoretical aspects of the development of a chemical kinetic model for the pyrolysis and combustion of a cyclic ketone, cyclopentanone, are considered. Calculated thermodynamic and kinetic data are presented for the first time for the principal species including 2- and 3-oxo-cyclopentyl radicals, which are in reasonable agreement with the literature. These radicals can be formed via H atom abstraction reactions by Ḣ and Ö atoms and ȮH, HȮ2, and ĊH3 radicals, the rate constants of which have been calculated. Abstraction from the β-hydrogen atom is the dominant process when ȮH is involved, but the reverse holds true for HȮ2 radicals. The subsequent β-scission of the radicals formed is also determined, and it is shown that recent tunable VUV photoionization mass spectrometry experiments can be interpreted in this light. The bulk of the calculations used the composite model chemistry G4, which was benchmarked in the simplest case with a coupled cluster treatment, CCSD(T), in the complete basis set limit.

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.

Computational Study of the Rate Coefficients for the Reactions of NO2 with CH3NHNH, CH3NNH2, and CH2NHNH2

The reactions of NO2 with cis-/trans-CH3NHNH, CH3NNH2 and CH2NHNH2 have been studied theoretically by quantum chemical calculations and steady-state unimolecular master equation analysis based on RRKM theory. The barrier heights for the roaming transition states between nitro (RNO2) and nitrite (RONO) isomerization reactions and those for the concerted HONO and HNO2 elimination reactions from RNO2 and RONO, affect the pressure dependences of the product-specific rate coefficients. At ambient temperature and pressure, the dominant product of the reactions of NO2 with cis-/trans-CH3NHNH and CH2NHNH2 would be expected to be HONO with trans-CH3NNH and CH2NNH2, respectively, whereas it is CH3N(NH2)NO2 for CH3NNH2 + NO2. The product-specific rate coefficients for the titled and related reactions on the same potential energy surfaces were proposed for kinetics modeling.

Evaluated kinetics of terminal and non-terminal addition of hydrogen atoms to 1-alkenes: a shock tube study of H + 1-butene

Single-pulse shock tube methods have been used to thermally generate hydrogen atoms and investigate the kinetics of their addition reactions with 1-butene at temperatures of 880 to 1120 K and pressures of 145 to 245 kPa. Rate parameters for the unimolecular decomposition of 1-butene are also reported. Addition of H atoms to the π bond of 1-butene results in displacement of either methyl or ethyl depending on whether addition occurs at the terminal or nonterminal position. Postshock monitoring of the initial alkene products has been used to determine the relative and absolute reaction rates. Absolute rate constants have been derived relative to the reference reaction of displacement of methyl from 1,3,5-trimethylbenzene (135TMB). With k(H + 135TMB → m-xylene + CH3) = 6.7 × 10(13) exp(-3255/T) cm(3) mol(-1) s(-1), we find the following: k(H + 1-butene → propene + CH3) = k10 = 3.93 × 10(13) exp(-1152 K/T) cm(3) mol(-1) s(-1), [880-1120 K; 145-245 kPa]; k(H + 1-butene → ethene + C2H5) = k11 = 3.44 × 10(13) exp(-1971 K/T) cm(3) mol(-1) s(-1), [971-1120 K; 145-245 kPa]; k10/k11 = 10((0.058±0.059)) exp [(818 ± 141) K/T), 971-1120 K. Uncertainties (2σ) in the absolute rate constants are about a factor of 1.5, while the relative rate constants should be accurate to within ±15%. The displacement rate constants are shown to be very close to the high pressure limiting rate constants for addition of H, and the present measurements are the first direct determination of the branching ratio for 1-olefins at high temperatures. At 1000 K, addition to the terminal site is favored over the nonterminal position by a factor of 2.59 ± 0.39, where the uncertainty is 2σ and includes possible systematic errors. Combining the present results with evaluated data from the literature pertaining to temperatures of <440 K leads us to recommend the following: k∞(H + 1-butene → 2-butyl) = 1.05 × 10(9)T(1.40) exp(-366/T) cm(3) mol(-1) s(-1), [220-2000 K]; k∞(H + 1-butene → 1-butyl) = 9.02 × 10(8)T(1.40) exp(-1162/T) cm(3) mol(-1) s(-1) [220-2000 K]. Analogous rate constants for other unbranched 1-olefins should be very similar. Despite this, a factor of three discrepancy in the branching ratio for terminal and nonterminal addition is noted when comparing the present values with recommendations from a recent model of the important H + propene reaction. This difference is suggested to be well outside of the possible experimental errors of the present study or the expected differences with 1-butene. There thus appear to be inconsistencies in the current model for propene. In particular the addition branching ratio from that model should not be used as a reference value in extrapolations to other systems via rate rules or automated mechanism generation techniques.