Pressure-Dependent Rate Rules for Intramolecular H-Migration

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Pressure-Dependent Rate Rules for Intramolecular H-Migration Reactions of Hydroperoxyalkylperoxy Radicals in Low-Temperature Qian Yao, Xiao-Hui Sun, Ze-Rong Li, Fang-Fang Chen, and Xiang-Yuan Li J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b10818 • Publication Date (Web): 06 Apr 2017 Downloaded from http://pubs.acs.org on April 10, 2017

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The Journal of Physical Chemistry

Pressure-dependent Rate Rules for Intramolecular H-Migration Reactions of Hydroperoxyalkylperoxy Radicals in Low-Temperature Qian Yao,† Xiao-Hui Sun,† Ze-Rong Li,*,† Fang-Fang Chen† and Xiang-Yuan Li‡ College of Chemistry and ‡College of Chemical Engineering, Sichuan University, Chengdu 610064, China

†

ABSTRACT: Intramolecular H-migration reaction of hydroperoxyalkylperoxy radicals (•O2QOOH) is one of the most important reaction families in the low-temperature oxidation of hydrocarbon fuels. This reaction family is first divided into classes depending upon H-atom transfer from –OOH bonded carbon or non– OOH bonded carbon and then the two classes are further divided depending upon the ring size of the transition states and the types of the carbons from which the H atom is transferred. High-pressure limit rate rules and pressure-dependent rate rules for each class are derived from the rate constants of a representative set of reactions within each class using electronic structure calculations performed at the CBS-QB3 level of theory. For the intramolecular H-migration reactions of •O2QOOH radicals for abstraction from an –OOH substituted carbon atom (–OOH bonded case), the result shows that it is acceptable to derive the rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. For the abstraction from a non–OOH substituted carbon atom (non–OOH bonded case), rate rules for each class are also derived and it is shown that the difference between the rate constants calculated by CBS-QB3 method and rate constants estimated from the rate rules may be large, therefore, to get more reliable results for the low-temperature combustion modeling of alkanes, it is better to assign each reaction its CBS-QB3 calculated rate constants, instead of assigning same vales for the same reaction class according to rate rules. The intramolecular H-migration reactions of •O2QOOH radicals (a thermally equilibrated system) are pressure-dependent and the pressure-dependent rate constants of these reactions are calculated by using the Rice-Ramsberger-Kassel-Marcus/Master Equation theory at pressures varying from 0.01 to 100 atm. The impact of molecular size on the pressure-dependent rate constants of the intramolecular H-migration reactions of •O2QOOH radicals has been studied and it is shown that the pressure dependence of the rate constants of intramolecular H-migration reactions of •O2QOOH radicals decreases with the molecular size at low temperatures and the impact of molecular size on the pressure-dependent rate constants decreases as temperature increases. It is shown that it is acceptable to derive the pressure-dependent rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. The barrier heights follow the Evans-Polanyi relationship for each

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type of intramolecular hydrogen migration reaction are studied. All calculated rate constants are fitted by a nonlinear least-squares method to the form of a modified Arrhenius rate expression at pressures varying from 0.01 to 100 atm and at high-pressure limit. Furthermore, thermodynamic parameters for all species involved in these reactions are calculated by the composite CBS-QB3 method and are given in NASA format. 1. INTRODUCTION To improve the efficiency and the performance of current engines, a better understanding of the combustion mechanisms of large hydrocarbons can improve the fuel economy, and satisfy the mandatory constraint of reducing pollutants emission.1 A combustion mechanism is the starting point for the modeling of the macroscopic process of the combustion of hydrocarbons, which can provide information on the rate of heat release, the species time histories, the ignition characteristics, the rates of pollutants production. The reliability of a modeling depends on the accuracy of the completeness of the elementary reactions that comprise the combustion process and the accuracy of the associated thermodynamical parameters and rate coefficients.2 Nowadays, due to the increase of the numbers of species and elementary reactions with the size of hydrocarbons, detailed mechanisms for the combustion of hydrocarbons are usually automatically generated by computer softwares. An automatically generated detailed mechanism usually contains two parts: the reaction base or sub-mechanism or seed mechanism part, in which all species contains less than three carbon atoms (C0-C2 reaction base) or less than five carbon atoms (C0-C4 reaction base) or less than seven carbon atoms (C0-C6 reaction base), and the larger-molecules part, which is automatically generated either starting from the seed mechanism or starting from scratch.3 A reaction base is usually developed in a hierarchical manner with hydrogen–oxygen–carbon monoxide and small hydrocarbon chemistry and are extensively validated and optimized at a wide range of experimental conditions.4 For the larger-molecules part, the reactions are usually divided into reaction classes and a reaction rule for each reaction class is used to automatically generate all the possible reactions in the class, because reactions in the same class are expected to have similarities in their potential energy surfaces along their reaction coordinates.5 Automatically mechanism generated softwares are usually based on reaction classes and rate rules, which make these mechanisms relatively easy to maintain and extend.6 The kinetic mechanisms of the oxidative reactions of hydrocarbon fuels are developed to be suitable for a wide range of temperature. The oxidative regions of hydrocarbon fuels can be divided into low-, intermediate-, and high-temperature regions. Currently most combustion mechanisms of hydrocarbon fuels just contain the high-temperature oxidative region.7-9 Construction of detailed mechanisms for low-temperature combustion is more difficult than for high-temperature combustion due to the large number of chemical species and reaction classes involved. Because of its significant importance, low-temperature combustion mechanisms have been the subject of intense studies for many years. Although a lot of detailed mechanisms have


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been developed for the low-temperature combustion of many hydrocarbon fuels, it is far from complete for the understanding of low-temperature ignition chemistry. For example, simple changes of the fuel composition may have significant impact on ignition delay, which are not well reproduced in these models.10 It is widely accepted that alkanes are the simplest types of hydrocarbons and are mostly studied hydrocarbons. At low-temperatures, alkane consumption is initiated by H-atom abstraction from the alkane, which produces alkyl radicals (•R). These alkyl radicals can form alkylperoxy radicals (ROO•) by adding to molecular oxygen and this reaction can produce either stabilized alkylperoxy radicals and their hydroperoxyalkyl isomers, or bimolecular products such as hydroperoxy radicals together with olefins or cyclic alkanes, or hydroxyl radicals with aldehydes, ketones, or cyclic ethers. This reaction is a key reaction in the low-temperature oxidation of alkanes, which determines the transition between low- and high-temperature mechanisms.11 Since the C–O bond in alkylperoxy radicals is rather weak, ROO• radicals can easily re-dissociate at high temperatures and these reactions can be ignored at high-temperature region because of its small equilibrium constant. The reversibility of this reaction is also the main cause of the observed negative temperature coefficient region in ignition experiments.6,12 At low temperatures, alkylperoxyl radicals as the product of this reaction can isomerize into •QOOH radicals. Thereafter, these •QOOH radicals can again add to molecular oxygen (i.e. the second addition to O2) to produce •O2QOOH radicals. The internal transfer of a hydrogen atom in •O2QOOH radical, which is a reversible reaction, can form a di-hydroperoxyl radical and the subsequent decomposition of this radical into keto-hydroperoxides occurs simultaneously. The formation and decomposition of keto-hydroperoxides is a chain branching process because it produces three radicals (two •OH radicals and one alkoxyl radical). Therefore, at low-temperature region, the combustion of alkanes involves a large number of oxygen-containing reaction classes4,13 that can be ignored at high-temperature region and this is the reason why the low-temperature combustion mechanism of hydrocarbons is more complicated. The fundamentals of this complex reaction network are illustrated in Scheme 1. In the pioneering work of Curran et al.14 and Westbrook et al.,15 the low-temperature oxidation mechanism of alkanes contains 16 reaction classes for low-temperature region and 9 reaction classes that are common for low-temperature and high-temperature region. Recently, Ranzi et al.16 have proposed three new oxygen-containing reaction classes for the kinetic modeling of low temperature oxidation of alkanes, which include H-abstraction reactions on alkyl and carbonylhydroperoxides, molecular reactions of carbonylhydroperoxides to form organic acids and recombination/disproportionation reactions of peroxy radicals. These three reaction classes are impactive at very low temperatures (550–650 K) in reducing the overall reactivity of the system and in explaining the formation of organic acids and minor oxygenated species. Recently, apart from the above-mentioned isomerization path way to produce keto-hydroperoxides for the •O2QOOH radicals, Zhang et al.17 also proposed new reaction pathways for •O2QOOH radicals, which allow •O2QOOH radicals undergo internal H-atom transfer



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from non–OOH bonded carbon, forming a •P(OOH)2 radical and this isomerization pathway could be very important for branched alkanes due to the existence of tertiary carbons bearing hydroperoxyl groups which have no hydrogen to be abstracted. It is one of the most challenging tasks to provide accurate thermodynamic parameters and kinetic parameters for a detailed mechanism. For most of the elementary reactions in the combustion of hydrocarbons, there are no reported experimental rate constants and group additivity approximate method18 or rate rule estimation method15,19 are convenient ways to solve this problem.20 From above introduction, we may see that ROO• radicals and •O2QOOH radicals are important intermediates in the low temperature (below 900K) oxidation of hydrocarbon fuels.21 Recently, Savee et al.22 has firstly observed •QOOH radicals directly by experimental detection. The intramolecular isomerization reactions of •O2QOOH radicals with production of two •OH radicals is regarded as the most important radical chain-branching step in low temperature oxidation of hydrocarbon fuels.23 However, the unstable intermediates •O2QOOH radicals have not been detected by experimental approaches so far and the intramolecular H-migration reactions of •O2QOOH are difficult to explore experimentally.24 The purpose of this study is to provide rate rules at high-pressure limit and study the pressure dependence of the rate constants of the intramolecular H-migration reactions of •O2QOOH radicals through accurate quantum chemical calculations. In recent years, many researches about the addition reaction of O2 and R• radicals, isomerization reaction of ROO• radicals and the reaction of •QOOH radials with O2 have been published.24-34 Pfaendtner et al.32 have developed the structure-reactivity relationships to correlate the activation energy with the heat of intramolecular hydrogen transfer reactions involving peroxy radicals at B3LYP/6-311+G(d, p) level. Also, there are a lot of studies on specific reactions in the reaction class of intramolecular H-migration reactions of •O2QOOH radicals. Bozzelli et al.35 have calculated the high-pressure limit rate constants and pressure-dependent rate constants for 1,3-H shift reactions and 1,4-H shift reactions involved in •O2CH2CH2OOH radical at CBS-Q level. Goldsmith et al.27 have calculated the high-pressure limit rate constants and pressure-dependent rate constants for the reactions related to the hydroperoxylpropyl radicals + O2 using QCISD(T) method. In the studies of Bozzelli et al. and Goldsmith et al., both the isomerization in the context of a thermally equilibrated system and a chemically-activated system are considered. Villano et al.36 estimate the rate coefficient for the intramolecular H-migration reaction CC(O2•)CCOOH→[CC(OOH)CC•OOH] from that for RO2 isomerization to the γ-QOOH radical. Buda et al.37 have calculated the rate constants for 1,4-H shift reactions, 1,5-H shift reactions and 1,6-H shift reactions involved in •O2CH2CH2CH(CH3)OOH radical using a computer package (EXGAS).38 Sun et al.30 have calculated the high-pressure limit rate constant and pressure-dependent rate constants for C2C(COOH)COO• (a thermally equilibrated system)→C2•C(COOH)2 at CBS-Q level. Jiao et al.31 have calculated the high-pressure limit rate constants for the H-migration reactions of •O2QOOH radicals derived from Methyl butanoate at CBS-QB3 level. Sharma et al.39 have systematically investigated the H-migration


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reactions of •O2QOOH radicals theoretically at the CBS-QB3 level of theory and high-pressure limit rate constants for some reactions from 1,4-hydrogen shift to 1,7-hydrogen shift have been given. Miyoshi21 has also systematically performed the theoretical studies of intramolecular H-migration reactions of •O2QOOH radicals by using composite CBS-QB3 method. Miyoshi divided the reaction class in to classes according to the types of the two carbons: the carbon bonded to –OO• and the carbon that H atom is abstracted from. Rate rules for each class are derived from the minimum-sized representative reaction. However, in the work of Miyoshi, only rate rules for –OOH bonded carbon that H-atom is abstracted from were given and rate rules for abstraction from an non–OOH substituted carbon atom (non–OOH bonded case) that H-atom is abstracted from were not given because he thought that the rate constants in this case can be estimated from the corresponding values of ROO• radicals. The 1,n- hydrogen shift reactions that n is larger than 7 haven’t been studied both in the works of Miyoshi and Sharma. It is well-known that the rate constants for isomerization reactions are dependent on both temperature and pressure,40 however, no studies about the pressure-dependent rate rules for intramolecular H-migration reactions of •O2QOOH radicals have been reported. In kinetic models, gas-phase reactions involving large molecules are often assumed to be in the high-pressure limit, that is, to not exhibit significant falloff or chemical activation effects.19,41 However, Wong et al.42 has systematically studied the molecular size dependence of falloff and chemical activation and their analysis of the molecular size dependence of falloff and chemical activation indicates that many types of reactions are pressure-dependent even for very large molecules and even under relatively high-pressure conditions. The purpose of this study is to get more accurate rate rules for the intra-molecular H-shift reactions of •O2QOOH radicals: (1) The reactions are divided into classes according to the ring size of the transition states and the types of the carbons from which the H atom is transferred. Meanwhile, rate rules are given not only for –OOH bonded carbon, but also for non–OOH bonded carbon; (2) Rate rules are obtained by the average of some representative reactions, instead of from the minimum-sized representative reaction; (3) Evans-Polanyi relationships for each class of the intramolecular H-migration reactions of •O2QOOH radicals are studied; (4) Influence of the molecular sizes on the pressure-dependent rate constants and rate rules for the pressure-dependent rate constants of the unimolecular isomerization are studied. 2. COMPUTATIONAL METHODS All the electronic structure calculations are performed by using the Gaussian 09 program.43 It should be noted that the α-dihydroperoxyalkyl radicals (α-HOO•QOOH) are unstable or metastable.35,39 Due to the instability of α-HOO•QOOH radicals, carbon-centered radicals produced in abstraction from an –OOH substituted carbon atom (–OOH bonded case) will fall apart to keto-hydroperoxide and OH. In this study, no local minimum for the geometry optimization of α-HOO•QOOH radicals at the B3LYP/CBSB7 level is found. However, Sharma et al.39 have obtained a minimum for this radical using MP2/CBSB7 method,44 but they don’t use this method for the kinetic studies of this radical. So the geometries of all reactants, products and tight transition states (TS) are optimized at the level of MP2/CBSB7 in this study. The vibrational frequencies are calculated at the same level and scaled by a factor of 0.97



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for the calculation of zero point energy (ZPE).45 The local minima and saddle points are identified through the number of imaginary frequencies( 0 for local minima and 1 for saddle points). Intrinsic reaction coordinate (IRC)46 calculations are used to conform the transition states that connect the desired reactants and products. The single point energies for all stationary points are calculated by composite CBS-QB3 method, which has been shown to predict enthalpies of formation for a large test set of molecules with a standard deviation of about 1 kcal mol-1 and has been successfully applied in numerous kinetic studies.47-49 However, it is reported that CBS-QB3 method is prone to occasional lapses on predict accurate reaction barrier heights of oxygen reactions,50 therefore the suitability of this method for the studied systems in this work will be validated by comparison with the benchmark CCSD(T) method extrapolated to complete basis set (CBS). It should be notied that the CBS-QB3 method using MP2 geometries used in this work is the non-standard method. Standard enthalpies of formation ( ∆ f H θ (298K ) , kcal mol-1) are calculated using the atomization method and the experimental values of ∆ f H θ (0K) for C (169.98 kcal mol-1), H (51.63 kcal mol-1) and O (58.99 kcal mol-1) are used.51 The extrapolation schemes of the basis sets are given below.46,52-54 The HF energy approaches its CBS limit by power laws:

EXHF = E∞HF + Be−αX

(1)

where B and α are constants and X = 2, 3, 4 for D, T, Q extrapolation with the basis sets cc-pVXZ. The correlation energy approaches its CBS limit through following the extrapolation formula

E∞corr = EXcorr + A/(X + 1/ 2)3

(2)

where A is a constant and X=2, 3 for D, T extrapolation with the basis sets cc-pVXZ. Then the basis-set limit for the total single point energy is obtained by

E∞tot = E∞HF + E∞corr

(3)

Generally, using harmonic approximation to treat low-frequency vibrations can cause significant errors in the partition function.55 Thus in this study, for the reactants, products and transition states, one-dimensional (1-D) hindered internal rotors is used to treat the low-frequency vibrations corresponding to the torsions of a single bond.56 The potentials of each internal rotation for reactants and products are calculated at the MP2/CBSB7 level of theory by using a relaxed energy scan of the dihedral angle with an interval of 10° and for transition states, the internal rotor scans are performed by freezing the atoms involved in the reaction centers and by taking into account the remaining torsions. Due to the large number of species, the scan calculations are only performed for a set of reference molecules containing the reactants, transition states and products, representative of all the species considered in this work. Since the studied system is a reaction family, there will be many similar internal rotors, e.g. C-O-O-H is contained in all the species, so the scan calculations for the reactant, transition state and product of the reference molecules, and the other specials use the same parameters with the reference molecule. For torsions with energetic barriers


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greater than 10 kcal mol-1, the torsional motions are approximated treated as harmonic vibrations.57 H-bonded structures mainly exist in the reaction center of the transition states and the reaction center is a ring-like structure. The energy barriers of these torsions on the ring are high and the torsions can be treated as harmonic vibrations. All the rate constant calculations are performed by using ChemRate software.58 High-pressure limit rate constants for intramolecular H-migration reactions of •O2QOOH radicals with tight transition state are calculated with canonical transition state theory (TST). For reactions with high barriers, the tunneling correction are often necessary, especially at lower temperatures. In this study, asymmetric Eckart method is used for the tunneling corrections,59 which involves an input parameter called barrier width L. The barrier width L are calculated from three parameters, namely, E1, E-1 and F*, where E1 and E-1 are the forward and reverse barrier heights for the reactions at 0 K and F* is the second derivative of the potential energy function (i.e., force constant) evaluated at its maximum, respectively. The calculated barrier width L, E1 and E-1 for all reactions are given in the supporting information. One-dimensional asymmetric Eckart model neglects multi-dimensional tunneling. However Eckart approximation is a reasonable approach to use, at least above room temperature, to compute tunneling corrections of rate constants for intramolecular H-migration reactions of •O2QOOH radicals.60 Pressure-dependent rate constants are calculated with the RRKM/ME theory at the pressure varying from 0.01 to 100 atm. A master-equation method is used to calculate pressure-dependent rate constants. The master equation can be written in the matrix form:

dρ = Bρ + R dt

(4)

All the eigenvalues of the matrix B are negative and the overall pressure-dependent thermal rate constant kuni(T, P) can be derived as the negative of the largest eigenvalue of the matrix B61 for single-reaction channel case. This eigenvalue is the chemically significant eigenvalue, which corresponds to the slow mode describing the “chemical reaction”, and for multi-reaction channels case, there is one chemically significant eigenvalue for each reaction channel. All calculations are carried out with a series of energy grain sizes and variations in the maximum system energy to ensure that the results have converged. An exponential down model62,63 with down =0.8 T K-1cm-1 is used for the energy transfer per downward collision. The collision frequency between the bath gas (Ar) and reactant is estimated by using the Lennard-Jones (L-J) potential, where the L-J parameters σ and ε for species are taken from the JetSurF 2.0 database.64 Both Ar and N2 can be used as bath gas. Although using N2 as the bas gas is more approximate to real gas mode, Ar is usually chosen as the bath gas in the experimental conditions of shock tube as it is more stable than N2. Finally, in order to be useful in the practical modeling software like Chemkin-PRO, the modified Arrhenius form is used to describe the temperature-dependent rate



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constants and the PLOG format is used to describe the pressure dependent rate constants and the rate parameters at any pressure P are given as: k(T, P) = A( P )T n ( P ) exp[ − Ea ( P ) / RT ]

(5)

In this study, the intramolecular H-migration reactions of •O2QOOH radicals reactions are classified according to the distance between the carbon that H-atom is abstracted from and the oxygen atom that H-atom is shifted, which determines the size of the ring in the transition states, and according to the types of carbons that H is shifted from. For a 1, n-H shift reaction, n refers to the location of the carbon from which the hydrogen is abstracted relative to the oxygen of the original radical site. Thus the 1, n-H atom shift reactions undergo (n+1)-membered-ring transition states (TS). Carbon atom connects with three hydrogen atoms is defined as p section and carbon atom connects with two hydrogen atoms and one hydrogen atom is defined as s and t section, respectively. In this study the carbons that H-atom is abstracted from are classified as -OOH bonded carbon and non-OOH bonded carbon. In the text and tables, figures, we employ a chemical notation that hydrogen atoms are omitted. A radical site is indicated by a bullet. Therefore, in this study the H-shift reactions are divided into (1,n)s, (1,n)t (n=3,4,5,6,7,8,9) for –OOH bonded carbon case and divided into (1,n)p, (1,n)s, (1,n)t (n=4,5,6,7) for non–OOH bonded carbon case. In the work of Miyoshi, the classification for carbons that connects to –OO•, to which H is shifted, is also considered, however, it can be seen form their results that this classification has slight influence and can be ignored. For all of the reactions investigated, the rate constants were calculated for the temperature range from 500 to 1200 K with an interval of 100 K and are fitted to the modified Arrhenius expression, which can be used in low temperature oxidative mechanism of hydrocarbon fuels directly. 3. RESULTS AND DISCUSSION 3.1. Barrier heights Comparisons for some representative forward and reverse reactions using CBS-QB3 method and CCSD(T)/CBS method are given in Table 1. It can be seen from Table 1, the maximum absolute deviation of the energy barriers of the CBS-QB3 method from the values of the benchmark CCSD(T)/CBS method is 1.5 kcal mol-1. Therefore the CBS-QB3 method is suitable for calculating energies and barrier heights of the intramolecular isomerization reactions of •O2QOOH radicals. The main source of error in rate constants is the barrier heights and the partition functions. The accuracy of barrier heights depends on the ab initio level. The maximum absolute deviation of 1.5 kcal mol-1 of the electronic energy will give an expected uncertainty factor value of 4.53, 2.13 and 1.88 in the rate constant at 500 K, 1000 K and 1200 K, respectively. The error from the vibrational contribution mainly comes from the anharmonic correction to the low-frequency vibrations, which are usually treated using 1D-hindered internal rotors model. The effect of the correction on the rate constants can be seen from Table S5 in the Supporting Information. 3.1.1. Barrier heights for –OOH bonded case. The forward and reverse barrier heights and the reaction enthalpies for all the 1,


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n-H atom shift reactions for –OOH bonded case are given in Table 2. Energy barriers for the reverse reactions are from α-HOO•QOOH radicals, not for reverse reactions from the keto-hydroperoxide + OH. It can be seen from Table 2 that the barrier heights of the abstraction from p sites are slightly higher than those of the abstraction from t sites with the same ring-size of the transition states. Other workers have reached similar conslusions.21,28,34,39 It is indicating that the substituent groups connected to the carbon neighbor to –OOH can stabilize the transition states. However reaction enthalpies don’t vary with structure (abstraction from s vs t sites). 3.1.2. Barrier heights for non–OOH bonded case. The forward and reverse barrier heights and the reaction enthalpies for all the 1, n-H atom shift reactions for non–OOH bonded case are given in Table 3. It can be seen form Table 3 that the barrier heights and reaction enthalpies of the abstraction from p sites are slightly higher than those of the abstraction from s sites and the barrier heights of the abstraction from s sites are slightly higher than those of the abstraction from t sites with the same ring-size of the transition states. Other workers have reached similar conslusions.21,28,34,39 The barrier heights of the 1, n-H atom shift reactions of •O2QOOH calculated in this study and the barrier heights of the corresponding ROO• isomerization reactions calculated by Sharma et al.39 at CBS-QB3 level are compared as follows. The barrier height for R44 of (1,4)p reaction class calculated in this study is 38.9 kcal mol-1 and the barrier height for the corresponding ROO• isomerization reactions CCOO•→C•COO by Sharma et al. is 35.9 kcal mol-1. The barrier height for R53 of (1,5)p reaction class in this study is 23.8 kcal mol-1 and the barrier heights for the corresponding ROO• isomerization reactions CCCOO•→C•CCOOH by Sharma et al. is 23.4 kcal mol-1. It can been seen that the barrier heights for the 1, n-H atom shift reactions of •O2QOOH are slightly higher than the corresponding ROO• isomerization reactions. From Table 2 and Table 3, it also can be seen that the barrier heights and reaction enthalpies for –OOH bonded case are lower than that for non–OOH bonded case in the same ring-size transition states and the barrier heights of the H-migration reactions will decrease with the expansion of the transition state ring for the 1,3 through 1,5 H-migration reactions after which the barrier heights should begin to increase. This trend is similar to H-migration reactions of other types of radicals, such as ROO• radicals28 and R• radicals65. 3.2. High-pressure limit rate constants 3.2.1. High-pressure limit rate rules of the 1, n-H atom shift reactions for –OOH bonded case. In the work of Miyoshi, for each class of reactions, only the smallest reaction system, i.e., the reaction with the smallest molecular size, in the same class is used to derive the rate rules, however, in this work, a representative set of reactions with different sizes of the substitutes are used to derive the rate rules by taking the average of the rate constants at each temperature. For most of the reaction classes, we have chosen four or five representative reactions for each class to derive rate rule. For some classes of reaction with the larger-sized species, only three reactions are chosen. For 1,8- and 1,9-H shift reactions, only the smallest reaction in the same ring size of the



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transition state is chosen to derive the rate rules. The fitted (A, n, E) parameters for high-pressure limit rate constants of all reactions in each class of intramolecular H-migration reactions of •O2QOOH radicals for –OOH bonded case at 500-1200 K are given in Table 4. The ratios of the rate constants of all reactions and the rate constants calculated according to the rate rules to the rate constants of the smallest reaction at 500 K and 1200 K for each reaction class are also given in Table 4. These ratios can be used to reflect the differences of the rate constants between the reactions in a class and see the suitability of the rate rules. We here compare our calculated rate constants and barrier heights with results published in literatures. Miyoshi21 obtained the rate constant of 1,4-H-shift in •O2CH(CH3)CH(CH3)OOH at 700 K as 3.1 × 104 s-1 , and Sharma et al.39 obtained a rate constant of 9.1 × 104 s-1, which are close to our value of 9.8 × 104 s-1. The barrier height for 1,4-hydrogen shift in the •O2CH2CH2OOH radical was calculated to be 29.7 and 31.2 kcal mol-1 by Bozzelli et al.35 using CBS-Q//B3LYP/6-31G(d,p) and G3(MP2) methods, respectively and the corresponding value by Sharma et al using CBS-QB3 method is 30.7 kcal mol-1, both of which are close to our calculated barrier height of 31.5 kcal mol-1. The reason for the differnece of enrergy barriers with about 0.8 kcal mol-1 between us and Sharma is that different geometric optimization methods are used, resulting different lowest-energy conformations for the transition states and hence different electronic energies and ZPE. Detailed analysis is given in the Supporting Information. The impact of the sizes of substituent groups on the rate constants for each class of reactions can be seen from the calculated ratios of the rate constants of a reaction to the rate constants of the smallest reaction given in Table 4. The ratios of the rate constants are between 3.4-105.7 for (1,3)s, 3.3-91.9 for (1,3)t, 0.4-1.0 for (1,4)s, 0.4-2.1 for (1,4)t, 0.3-6.2 for (1,5)s, 0.5-2.6 for (1,5)t, 0.1-2.4 for (1,6)s, 0.5-1.7 for (1,6)t, 0.9-1.4 for (1,7)s and 0.3-1.0 for (1,7)t. The largest deviations in this study are found for the (1,3) isomerization reactions and the largest deviations in the work of Villano et al.34 for the RO2 isomerization reactions are found for (1,4) isomerization reactions. For illustration, Figure 1 and 2 show the impact of the sizes of substituent groups on the rate constants for 1,4-H and 1,5-H migration reactions. It can be seen that the ratios for 1,3-H shift reactions can be high up to a factor of 105.7, while the ratios for other reactions are less than a factor 10, indicating that the influence of the size of substituent groups on the rate constants for 1,3-H shift reactions cannot be ignored. In literatures, a rate rule is usually derived from the smallest reaction in a reaction class, however, our works has shown that it is more accurate to derive the rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes in a reaction class. While the influence of the size of substituent groups on the rate constants for 1,4-H to 1,7-H shift reactions can be ignored and it is acceptable to derive the rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. In fact, the 1,3-H shift reactions can be ignored in the automatic generation of combustion mechanism for alkanes because of their much lower rate constants compared with those of 1,4-H to 1,7-H shift reactions.


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The impact of the types of carbons connected to –OOH group on the rate constants for reactions with the same ring size of the transition states can be seen from Table 4. The ratios of the rate constants of (1,3)t, (1,4)t, (1,5)t, (1,6)t and (1,7)t reactions to the rate constants of (1,3)s, (14)s, (1,5)s, (1,6)s and (1,7)s reactions are between 0.8-769.3, 0.8-22.4, 1.0-11.4, 1.2-163.6, 0.8-8.1, respectively. In the work of Villano et al.,34 the ratios of the rate constants of (1,3)t, (1,4)t, (1,5)t, (1,6)t and (1,7)t reactions for the RO2 isomerization reactions to the rate constants of (1,3)s, (14)s, (1,5)s, (1,6)s and (1,7)s reactions are between 1.5-29.5, 1.0-67.5, 1.0-38.3, 0.9-27.3, 1.1-4.4, respectively. The ratios for •O2QOOH isomerization reactions are much larger than those for RO2 isomerization reactions. For illustration of the impact of the types of the carbons connected to –OOH group on the rate constants for reactions with the same ring size of the transition states, i.e., the H shift distance, Figure 3 plots the ratios of the rate constants between the smallest reactions from 500K to 1200K. For 1,4-, 1,5-, 1,6- and 1,7-H shift reactions ,as shown in Figure 3a, Figure 3b, Figure 3c and Figure 3d, the ratios of the rate constants of (1,4)t, (1,5)t, (1,6)t and (1,7)t reactions to (1,4)s, (1,5)s, (1,6)s and (1,7)s reactions are within 3.9, 3.0, 9.6 and 7.2, respectively. Therefore, the impact of the types of the carbons connected to –OOH group on the rate constants is relatively large and for each H shift reaction with same shift distance, it is more accurate to divide the –OOH bonded carbon atoms into a secondary (s) and tertiary (t) carbon. For reactions with the same types of carbons bonded to –OOH group, the energy barriers can be varied from 1,3-H shift to 1,7-H shift reactions. The comparison of the energy barriers is given in Figure 4. A comparison of the barrier heights for three representative reactions calculated in this study with that obtained by Miyoshi21 are given in Table S4 and the values obtained by Miyoshi are close to our calculated barrier heights. From 1,3-H shift to 1,7-H shift reactions, their transition states involve 4-member-ring to 8-member-ring and it can be seen that the energy barriers deceases from 1,3-H to 1,5-H shift reactions, which involve 4-member-ring to 6-member-ring transition states. For 1,5-H to 1,7-H shift reactions, which involve 6-member-ring to 8-member-ring transition states, the energy barriers differ less than 2 kcal mol-1. Rate constants for all reaction classes according to rate rules are shown in Figure 5. It can be seen that the curves for (1,n)t always lie above the curves for (1,n)s for the same n, indicating that the rate constants increase with the numbers of the substitution groups for reactions with same ring size of the transition state. This is generally because that the substituent groups connected to the carbon neighbor to –OOH group can stabilize the transition state and lower energy barriers. 3.2.2. High-pressure limit rate rules of the 1, n-H atom shift reactions for non– OOH bonded case. No calculated rate constants of the intramolecular H-migration reactions of •O2QOOH radicals for non–OOH bonded case have been reported17,20. In the construction of low-temperature combustion mechanism, these rate constants are usually assigned approximate values by making analogies to the corresponding intramolecular H-migration reactions of ROO• radicals17 and Curran et al.20 pointed out that this approximation may cause that the mechanism including these reaction



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paths cannot improve the modeling of the low-temperature combustion of alkanes. Therefore, it is significant to provide accurate rate constants for the intramolecular H-migration reactions of •O2QOOH radicals for non–OOH bonded case. The fitted (A, n, E) parameters for high-pressure limit rate constants of all reactions in each class of intramolecular H-migration reactions of •O2QOOH radicals for non– OOH bonded case at 500-1200 K are given in Table 5. The ratios of the rate constants of all reactions to the rate constants of the smallest reaction at 500K and 1200K for each reaction class are also given in Table 5. For most of the reaction classes, we have chosen three representative reactions for each class. For some classes of reaction with the larger-sized species, only one or two reactions are chosen. Comparison of the rate constants of the 1, n-H shift reactions of •O2QOOH radicals for non-OOH bonded case calculated in this study with rate constants of the intramolecular H-migration reactions of ROO• radicals calculated by Sharma and Miyoshi is shown in Figure 6. The ratios of our calculated rate constants to the values based on those for ROO• radicals can be three orders of magnitude, indicating that the rate constant of the 1, n-H shift reactions of •O2QOOH radicals taken from analogized reactions of ROO• radicals would cause remarkable errors. Thus, the rate constants for 1, n-H shift reactions of •O2QOOH radicals for non-OOH bonded case are assigned to calculated directly instead of using the value based on those for ROO• radicals. The impact of the sizes of substituent groups on the rate constants for each class of reactions can be seen from the calculated ratios of the rate constants of a reaction to the rate constants of the smallest reaction given in Table 5. The ratios of the rate constants are between 6.4-88.2 for (1,4)p, 1.4-10.6 for (1,4)s, 1.5-7.5 for (1,4)t, 1.1-5.2 for (1,5)p, 2.5-99.8 for (1,5)s, 5.2-101.8 for (1,5)t, 6.2-72.7 for (1,6)p, 5.9-331.8 for (1,6)s, 19.2-31.6 for (1,6)t, 5.2-5.7 for (1,7)p and 3.3-5.2 for (1,7)s. It is indicating that the influence of the size of substituent groups on the rate constants are very large and it is more accurate to derive the rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes than from the smallest reaction. The difference between the calculated rate constants by CBS-QB3 method and rate constants estimated from rate rules may be large, therefore, to get more reliable results for the low-temperature combustion modeling of alkanes, it is better to assign each reaction its CBS-QB3 calculated rate constants, instead of assigning same vales for the same reaction class according to rate rules. However, rate rules are necessary in automatic generation of combustion mechanism by softwares, therefore, approximate rate rules are provided in this study. 3.3. Pressure-Dependent Rate Constants. 3.3.1. Molecular size dependence of the rate constant in the fall-off regime. In kinetic models, gas-phase reactions involving large molecules are often assumed to be in the high-pressure limit. Molecular size dependence of the rate constants of the intramolecular H shift reactions of •O2QOOH radicals for –OOH bonded case in the fall-off regime are studies in this work. The ratios k(T,P)/k∞(T), while k(T,P) is the temperature and pressure-dependent rate constant and k∞(T) is high-pressure limit rate constant, for molecular size from C2 to C7 at temperatures 500K, 700K, 1000K and


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1200K, are given in Table 6 to Table 9, respectively, where the molecular size are characterized by the number of carbons in the •O2QOOH radicals (a thermally equilibrated system). The pressure dependent rate constants for calculating the ratios k(T,P)/k∞(T) are given in Table S6 and Table S8. It is clear from Table 6 that molecular size does not change the value of the ratio k(T,P)/k∞(T) for 1,3 H-shifts by more than 6% and for 1,4 H-shifts there are only on 2 of 30 cases that change this ratio by more than 20%. The effect of size on the ratio k(T,P)/k∞(T) is to enlarge the range of rate constants for 1,5 to 1,7 H-shifts and reduce the reliability of the rate rule for k(P,T) for these types of 1,n H-shifts. As temperature increases, the effect of pressure on 1,3 to 1,7 H-shifts grows, but k(T,P)/k∞(T) always has the most variation for the 1,5 to 1,7 H-shifts. For illustration of the impact of molecular size on the pressure dependent rate constants, Figure 7 plots the ratios k(T,P)/k∞(T) for the smallest reactions and the largest reactions considered in this study in each ring-size class. It can be seen that the pressure dependence of the rate constants of intramolecular H-migration reactions of •O2QOOH radicals decreases with the molecular size and barrier height at low temperatures and the impact of molecular size on the pressure-dependent rate constants decrease as temperature increases. The pressure dependence for these reactions cannot be ignored and the influence of pressure on the rate constant is increasing as temperature increases and it becomes significant at the temperature larger than 700K. While temperature larger than 700K, rate constants for the intramolecular H-migration reactions are less than one-half of the high-pressure limiting value in most cases. The ratios k(T,P)/k∞(T) of the intramolecular H-migration reactions of •O2QOOH radicals for non–OOH bonded case has also been calculated and the results are listed in Figure 8. It can be seen that these reactions show the same trend as reactions for – OOH bonded case. 3.3.2. Pressure-dependent rate rules for intramolecular H-migration reactions of hydroperoxyalkylperoxy radicals. As described above, the H-migration reactions of •O2QOOH radicals (a thermally equilibrated system) are pressure-dependent and there is a need to provide rate rules for these reactions for automatic mechanism generations of alkanes. In this study, pressure-dependent rate rules for the H-migration reactions of •O2QOOH radicals for –OOH bonded case are calculated by averaging the pressure-dependent rate constants of a representative set of reactions with different sizes of the substitutes for each class and then fitted to modified Arrhenius expressions and the ratios of the rate constants of all reactions and the rate constants calculated according to the rate rules to the rate constants of the smallest reaction at 500K and 1200K for each reaction class are given in Table S7. Comparison of the pressure dependent rate constants for1,4-H migration reaction O2CC(C)OO• (a thermally equilibrated system) → O2CC(C•)OO and 1,5-H migration reaction O2C(C)COO• (a thermally equilibrated system) → O2C(C•)COO calculated in this study with the results calculated by Goldsmith et al.27 are shown in Figure 9. It can be seen that the pressure dependence in the two results in Figure 9a shows opposite trends: our results show that the rate constants for 1,4-H migration



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reaction increase with pressure, while the results of Goldsmith et al. show that the rate constants decrease with pressure. However the pressure dependence in the two results in Figure 9b shows same trend: the rate constants for 1,5-H migration reaction increase with pressure. In the study of Zhang et al.,33 they concluded that the rate constants of 1,n H-shift reactions for n-alkenyl-1-peroxy radicals (a thermally equilibrated system) increase with pressure. These reactions are unimolecular isomerization reactions and the rate constants should increase with pressure, indicating our results are reasonable. The impact of the sizes of substituent groups on the pressure-dependent rate constants for each class of reactions can be seen from the calculated ratios of the rate constants of a reaction to the rate constants of the smallest reaction given in Table S7. The ratios of the pressure-dependent rate constants are between 3.1-96.3 for (1,3)s, 2.5-90.1 for (1,3)t, 0.3-1.6 for (1,4)s, 0.4-1.2 for (1,4)t, 0.2-5.8 for (1,5)s, 0.5-2.1 for (1,5)t, 0.1-2.4 for (1,6)s, 0.5-2.0 for (1,6)t, 0.8-1.3 for (1,7)s and 0.3-0.9 for (1,7)t. As in the high-pressure limit case, the ratios for 1,3-H shift reactions are large and the ratios for 1,4-H shift reactions to 1,7-H shift reactions are small, indicating deriving the pressure-dependent rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes at the same pressure is accepted for 1,4-H shift reactions to 1,7-H shift reactions. Pressure-dependent rate rules for non–OOH bonded case are calculated by averaging the pressure-dependent rate constants of a representative set of reactions with different sizes of the substitutes for each class and then fitted to modified Arrhenius expressions and the ratios of the rate constants of all reactions and the rate constants calculated according to the rate rules to the rate constants of the smallest reaction at 500K and 1200K for each reaction class are given in Table S8. 3.4. Evans-Polanyi Plots The Evans-Polanyi plots for the intramolecular H-migrations reactions of •O2QOOH radicals are shown in Figure 10. The intramolecular H-migration reactions in •O2QOOH radicals are highly exothermic by Sharma et al.39 But in our study, these reactions are all endothermic as shown in Figure 10. Because Sharma et al. set the product as HOOQO+OH, the breaking of the O-OH bond from the •P(OOH)2 releases a lot of energy. All the reactions of the intramolecular H-migrations reactions of •O2QOOH radicals to product HOOQO+OH are exothermic. In Sharma’s work, the fits for 1,4-, 1,5-, and 1,6-H migrations reactions are E=0.63∆H + 46.74, E=0.31∆H + 26.29, and E= 0.82∆H + 41.06, respectively. In this work the Evans-Polanyi plots for element reactions intramolecular H-migrations reactions of •O2QOOH radicals for –OOH bonded case are given in Figure 10(a). The Evans-Polanyi plots for element reactions of the reactions for non-OOH bonded case have also been studied systematic and the result is shown in Figure 10(b). The fits for the 1,3-, 1,4-, 1,5-, 1,6- and 1,7-H migration reactions for – OOH bonded case are E=0.84∆H + 33.17, E=1.57∆H + 11.67, E=0.78∆H + 9.76, E=1.04∆H + 6.63 and E= 0.56∆H + 11.90, respectively. The fits of the 1,4-, 1,5-, 1,6and 1,7-H migration reactions for non–OOH bonded case are E=1.15∆H + 16.87, E=0.84∆H + 9.61, E=1.02∆H + 7.54 and E= 1.18∆H + 4.96, respectively. The slopes


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of these graphs are ≈1 for all of the ring sizes. The intramolecular H-migrations reactions of •O2QOOH radicals consist of the simultaneous breaking of a C-H bond and formation of an O-H bond, and the heat of reaction really depends on the total energy gained or lost in the chemical process of bond breaking and bond forming. The slope of 1 indicates that for the forward reaction the C-H bond is almost fully broken and O-H bond is almost fully formed in the transition state. 4. SUMMARY In this work, the rate constants of the important reaction class of the intramolecular H-migration reactions of •O2QOOH radicals at 500-1200 K have been investigated. The CBS-QB3 method is suitable for predicting the energies and barrier heights as the maximum absolute deviation of the energy barriers of the CBS-QB3 method from the values of the benchmark CCSD(T)/CBS method is 1.5 kcal mol-1. The high pressure limit rate rules for –OOH bonded case which cover the 1,3- up to the 1,7-H shift reactions are derived by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. The impact of the sizes of substituent groups and the types of the carbons connected to –OOH in •O2QOOH radicals on the rate constants are discussed and the result shows that it is acceptable to derive the rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. The intramolecular H shift reactions for non–OOH bonded case of •O2QOOH radicals have also been studied. The results show that the distance between the carbon and the –OOH group has great influence on the rate constants with the same ring-size class and the same types of carbons. Rate rules are derived by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes and it is shown that the difference between the calculated rate constants by CBS-QB3 method and rate constants estimated from rate rules may be large, therefore, to get more reliable results for the low-temperature combustion modeling of alkanes, it is better to assign each reaction its CBS-QB3 calculated rate constants, instead of assigning same vales for the same reaction class according to rate rules. The intramolecular H-migration reactions of •O2QOOH radicals (a thermally equilibrated system) are pressure dependent and the influence of pressure on the rate constants increases as temperature increases. It is shown that the pressure dependence of the rate constants of intramolecular H-migration reactions decreases with the molecular size and barrier height at low temperatures and the impact of molecular size on the pressure-dependent rate constants decreases as temperature increases. The pressure-dependent rate rules are derived by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes at the same pressure. Finally, we have tabulated the rate constants and thermochemistry parameters calculated for easy reference and use in automatic generation of low-temperature combustion mechanisms for alkanes.

ASSOCIATED CONTENT Supporting Information



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The high pressure limit rate constants of the reverse rate constants for the non-OOH bonded case and pressure dependent rate constants of studied reactions are given in the Supplemental Material-Ⅰ. The optimized geometries of reactant, products and transition states, harmonic vibrational frequencies, absolute energies and ZPEs are also given in the Supplemental Material- Ⅰ . Thermodynamic parameters for all species involving in this study are given in the Supplemental Material-Ⅱ.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected](Z.R.Li) Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS We would like to express our gratitude to the reviewers for many helpful suggestions. We are also grateful for the great help of Dr. Hong-Bo Ning at The Chinese University of Hong Kong. This work is supported by the National Natural Science Foundation of China (Nos. 91441114).

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High

Temperatures,

JetSurF

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September

19,

2010.

. (65) Davis, A. C.; Francisco, J. S. Ab Initio Study of Hydrogen Migration across n-Alkyl Radicals. J. Phys. Chem. A 2011, 115, 14, 2966-2977.

Scheme 1. Reaction network for alkyl radical + O2. Table 1. Comparison of energy barriers at 0 K (kcal mol-1) by CBS-QB3 method and CCSD(T)/CBS method. E1 a Reactions

a

E-1b

CCSD(T)/CBS

CBS-QB3

CCSD(T)/CBS

CBS-QB3

(1,3)-H R1

O2CCOO• → O2CC•OO

47.21

47.20

35.76

35.50

(1,4)-H R9

O2CCOO• → O2C•COO

32.01

31.53

20.56

19.83

(1,5)-H R18

O2CCCOO• → O2C•CCOO

21.36

19.96

10.05

8.62

(1,4)-H R47

O2CCCOO•→O2CC•COO

35.23

34.58

19.65

19.01

(1,5)-H R56

O2CCCCOO•→O2CC•CCOO

25.41

23.96

9.11

7.59

b

E1 is the forward energy barrier. E-1 is the reverse energy barrier.

Table 2. The forward and reverse barrier heights for abstraction from an –OOH substituted carbon atom. Reactions 1,3-H(s) R1

E1 O2CCOO• → O2CC•OO O2CCCOO• → O2CCC•OO O2CCCCOO• → O2CCCC•OO

R2 R3 R4

O2CCCCCOO• → O2CCCCC•OO

1,3-H(t) R5 R6 R7 R8

O2CC(C)OO• → O2CC•(C)OO O2CCC(C)OO• → O2CCC•(C)OO O2CCCC(C)OO• → O2CCCC•(C)OO O2CCCCC(C)OO• → O2CCCCC•(C)OO

1,4-H(s)


E-1

∆H

47.20 35.50 11.71 42.54 31.20 11.34 46.22 33.20 13.02 44.89 32.63 12.27 44.72 40.98 42.01 43.44

32.33 28.99 30.78 30.19

12.39 11.98 11.07 13.25

Page 21 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


R9 R10 R11 R12 1,4-H(t) R13 R14 R15 R16 R17 1,5-H(s) R18 R19 R20 R21 R22 1,5-H(t) R23 R24 R25 R26 R27 1,6-H(s) R28 R29 R30 R31 1,6-H(t) R32 R33 R34 R35 1,7-H(s) R36 R37 R38 1,7-H(t) R39 R40 R41 1,8-H R42

O2CCOO• → O2C•COO O2CC(C)OO• → O2C•C(C)OO O2CC(CC)OO• → O2C•C(CC)OO O2CC(CCC)OO• → O2C•C(CCC)OO O2C(C)COO• → O2C•(C)COO O2C(C)C(C)OO• → O2C•(C)C(C)OO O2C(CC)COO• → O2C•(CC)COO O2C(C)C(CC)OO• → O2C•(C)C(CC)OO O2C(CCC)COO• → O2C•(CCC)COO O2CCCOO• → O2C•CCOO O2CCC(C)OO• → O2C•CC(C)OO O2CC(C)COO• → O2C•C(C)COO O2CC(C)C(C)OO• → O2C•C(C)C(C)OO O2CCC(C)(C)OO• → O2C•CC(C)(C)OO O2C(C)CCOO• → O2C•(C)CCOO O2C(C)CC(C)OO• → O2C•(C)CC(C)OO O2C(C)C(C)COO• → O2C•(C)C(C)COO O2C(CC)CCOO• → O2C•(CC)CCOO O2C(C)C(C)C(C)OO• → O2C•(C)C(C)C(C)OO

31.53 32.02 31.76 31.77

19.83 19.56 19.08 19.02

11.71 12.46 12.69 12.76

29.48 17.63 11.84 28.65 15.83 12.82 29.60 17.42 12.18 30.45 18.64 11.81 29.43 17.40 12.04 19.96

8.62

11.34

19.89 19.84 19.82 18.69

7.70 8.19 6.81 7.93

12.20 11.65 13.02 10.76

18.47 18.41 18.57

7.02 6.43 6.04

11.45 11.98 12.53

18.19 17.84

6.33 7.24

11.86 10.60

O2CCCCOO• → O2C•CCCOO O2CCC(C)COO• → O2C•CC(C)COO O2CCC(C)C(C)OO• → O2C•CC(C)C(C)OO O2CC(C)C(C)C(C)OO• → O2C•C(C)C(C)C(C)OO

21.34

8.31

13.02

20.37 21.55 22.58

7.20 8.75 7.26

13.17 12.80 15.31

O2C(C)CCCOO• → O2C•(C)CCCOO

18.47

5.93

12.54

O2C(CC)CCCOO• → O2C•(CC)CCCOO O2C(C)C(C)CCOO• → O2C•(C)C(C)CCOO

18.37 18.78

5.41 5.04

12.96 13.74

O2C(C)C(C)C(C)COO• → O2C•(C)C(C)C(C)COO 17.88

7.21

10.67

O2CCCCCOO• → O2C•CCCCOO

20.66

8.39

12.27

O2CC(C)CCCOO• → O2C•C(C)CCCOO O2CCCCC(C)OO• → O2C•CCCC(C)OO

19.35 20.26

6.28 6.92

13.07 13.34

O2C(C)CCCCOO• → O2C•(C)CCCCOO O2C(CC)CCCCOO• → O2C•(CC)CCCCOO

17.53 18.18

5.49 5.83

12.04 12.36

O2C(C)CCC(C)COO• → O2C•(C)CCC(C)COO

18.57

5.05

13.51

O2CCCCCCOO• → O2C•CCCCCOO


22.33 10.73 11.60


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1,9-H R43

O2CCCCCCCOO• → O2C•CCCCCCOO

Page 22 of 38

19.25 10.67

8.58

Table 3. The forward and reverse barrier heights for abstraction from a non– OOH substituted carbon atom. Reactions 1,4-H(p) R44 R45 R46 1,4-H(s) R47 R48 R49 1,4-H(t) R50 R51 R52 1,5-H(p) R53 R54 R55 1,5-H(s) R56 R57 R58 1,5-H(t) R59 R60 R61 1,6-H(p) R62 R63 R64 1,6-H(s) R65 R66 R67 1,6-H(t) R68 R69

E1

E-1

∆H

O2CC(C)OO• → O2CC(C•)OO O2CCC(C)OO• → O2CCC(C•)OO O2CCCC(C)OO• → O2CCCC(C•)OO

38.86 20.13 18.73 36.94 19.44 17.50 35.80 19.14 16.67

O2CCCOO• → O2CC•COO O2CCCCOO• → O2CCC•COO O2CCCCCOO• → O2CCCC•COO

34.58 19.01 15.57 35.27 19.17 16.10 34.16 19.23 14.92

O2CC(C)COO• → O2CC•(C)COO O2CCC(C)COO• → O2CCC•(C)COO O2CCCC(C)COO• → O2CCCC•(C)COO

30.67 18.36 12.31 31.56 19.25 12.32 31.75 18.64 13.11

O2CC(C)COO• → O2CC(C•)COO O2CCC(C)COO• → O2CCC(C•)COO O2CCCC(C)COO• → O2CCCC(C•)COO

23.76

5.31

25.60 25.93

7.01 6.42

O2CCCCOO• → O2CC•CCOO O2CCCCCOO• → O2CCC•CCOO O2CCCCCCOO• → O2CCCC•CCOO

23.96

7.59

22.14 21.59

7.99 7.79

O2CC(C)CCOO• → O2CC•(C)CCOO O2CCC(C)CCOO• → O2CCC•(C)CCOO

21.49

8.33

19.84 O2CCCC(C)CCOO• → O2CCCC•(C)CCOO 18.74

6.89 6.23

O2CC(C)CCOO• → O2CC(C•)CCOO 26.62 O2CCC(C)CCOO• → O2CCC(C•)CCOO 25.38 O2CCCC(C)CCOO• → O2CCCC(C•)CCOO 24.39

7.80

O2CCCCCOO• → O2CC•CCCOO O2CCCCCCOO• → O2CCC•CCCOO O2CCCCCCCOO• → O2CCCC•CCCOO

7.85 7.81

23.84

8.92

22.03 18.94

8.43 8.25

O2CC(C)CCCOO• → O2CC•(C)CCCOO 20.44 O2CCC(C)CCCOO• → O2CCC•(C)CCCOO 19.34

7.41

1,7-H(p)


6.72

18.45 18.60 19.51 16.37 14.15 13.79 13.16 12.95 12.51 18.82 17.53 16.58 14.92 13.11 10.69 13.04 12.63

Page 23 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


R70 R71 1,7-H(s) R72 R73

O2CC(C)CCCOO• → O2CC(C•)CCCOO 25.16 O2CCC(C)CCCOO• → O2CCC(C•)CCCOO 25.05

7.48 8.57

17.68 16.48

22.72 17.96

8.26 7.26

14.46 10.69

O2CC(C)CCCCOO• → O2CC•(C)CCCCOO 18.36

6.15

12.21

O2CCCCCCOO• → O2CC•CCCCOO O2CCCCCCCOO• → O2CCC•CCCCOO

1,7-H(t) R74

Table 4. Calculated rate constants, rate rules and ratios of rate constants of reactions to the value of the smallest reaction in each class for abstraction from an –OOH substituted carbon atom. Modified Arrhenius parameters -1

Reactions 1,3-H(s)

1,3-H(t)

1,4-H(s)

1,4-H(t)

1,5-H(s)

1,5-H(t)

A(s ) rate rule

n

-1

500K

1200K

E(kcal mol )

k

k/ksma

k

k/ksmaa

8.21E-02

4.6

34.4

1.46E-04

41.2

8.02E+06

10.9

R1

4.29E-04

5.16

36.8

3.53E-06

1.0

7.35E+05

1.0

R2

9.32E-04

4.97

32.6

1.68E-04

47.6

2.52E+06

3.4

R3

2.89E-03

5.09

36.1

3.79E-05

10.7

4.90E+06

6.7

R4

1.57E-02

4.99

35.0

3.73E-04

105.7

2.39E+07

32.6

2.69E+00

4.19

33.2

1.35E-03

45.6

2.69E+07

15.3

R5

rate rule

2.91E-02

4.42

32.1

2.95E-05

1.0

1.76E+06

1.0

R6

7.06E-02

4.42

32.1

7.72E-04

26.1

5.75E+06

3.3

R7

3.47E-01

4.49

33.0

2.72E-03

91.9

3.68E+07

20.9

R8

1.29E+00

4.45

34.6

1.88E-03

63.5

6.33E+07

36.1

1.47E-11

6.95

14.8

1.62E+01

0.7

1.02E+08

0.8

rate rule R9

5.17E-12

7.2

15.7

2.39E+01

1.0

1.22E+08

1.0

R10

7.54E-12

7.1

16.4

8.82E+00

0.4

6.35E+07

0.5

R11

3.58E-11

6.92

16.5

1.44E+01

0.6

9.89E+07

0.8

R12

4.46E-11

6.91

16.6

1.78E+01

0.7

1.24E+08

1.0

9.77E-06

5.26

16.6

8.51E+01

0.9

2.19E+08

0.9

R13

rate rule

2.80E-08

6.09

16.1

9.34E+01

1.0

2.36E+08

1.0

R14

4.93E-06

5.45

16.6

1.97E+02

2.1

4.07E+08

1.7

R15

2.28E-08

6.02

16.3

3.63E+01

0.4

9.93E+07

0.4

R16

1.07E-08

6.25

16.8

4.80E+01

0.5

2.23E+08

0.9

R17

3.31E-08

5.96

16.2

5.03E+01

0.5

1.29E+08

0.5

1.90E+05

2.35

13.9

5.67E+05

2.4

1.29E+10

1.5

R18

rate rule

3.15E+02

3.16

13.2

2.34E+05

1.0

8.76E+09

1.0

R19

4.51E+03

2.87

13.8

3.02E+05

1.3

1.30E+10

1.5

R20

5.94E+02

3.06

13.2

2.57E+05

1.1

9.11E+09

1.0

R21

6.30E+03

2.58

14.1

5.96E+05

2.5

2.41E+09

0.3

R22

5.75E+03

2.89

12.6

1.45E+06

6.2

3.10E+10

3.5

6.16E+05

2.2

13.4

9.71E+05

1.4

1.84E+10

1.2

R23

rate rule

1.38E+04

2.68

12.9

7.12E+05

1.0

1.51E+10

1.0

R24

8.14E+04

2.53

13.1

1.26E+06

1.8

2.71E+10

1.8



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 38

R25

6.33E+04

2.43

13.5

3.84E+05

0.5

9.32E+09

0.6

R26

3.93E+04

2.49

12.9

6.78E+05

1.0

1.29E+10

0.9

R27

1.41E+04

2.72

12.2

1.82E+06

2.6

2.74E+10

1.8

7.85E+02

2.96

14.1

5.93E+04

1.2

3.89E+09

1.1

1,6-H(s)

rate rule R28

7.66E+01

3.28

14.1

5.01E+04

1.0

3.69E+09

1.0

R29

1.17E+03

2.96

13.9

1.18E+05

2.4

5.71E+09

1.5

R30

4.39E+01

3.4

14.1

6.35E+04

1.3

5.26E+09

1.4

R31

6.39E+02

2.9

16.1

5.00E+03

0.1

8.93E+08

0.2

1.24E+05

2.31

13.1

4.95E+05

1.0

9.59E+09

0.9

R32

2.84E+04

2.53

13.1

4.84E+05

1.0

1.05E+10

1.0

R33

8.96E+04

2.37

13.3

4.54E+05

0.9

9.84E+09

0.9

R34

2.56E+05

2.21

14.1

2.27E+05

0.5

6.87E+09

0.7

R35

2.01E+03

2.84

11.9

8.17E+05

1.7

1.12E+10

1.1

1,6-H(t)

rate rule

1,7-H(s)

1.68E+03

2.93

13.3

2.48E+05

1.1

1.04E+10

0.9

R36

rate rule

7.46E+01

3.38

13.3

2.24E+05

1.0

1.12E+10

1.0

R37

7.46E+03

2.73

13.4

3.20E+05

1.4

9.66E+09

0.9

R38

2.51E+03

2.91

14.0

2.00E+05

0.9

1.02E+10

0.9

9.38E+04

2.36

12.7

9.13E+05

0.6

1.49E+10

0.7

R39

4.00E+04

2.51

12.2

1.62E+06

1.0

2.12E+10

1.0

R40

1.18E+05

2.28

13.1

5.25E+05

0.3

8.64E+09

0.4

R41

1.75E+05

2.33

13.6

5.91E+05

0.4

1.49E+10

0.7

R42

1.66E-01

4.07

13.6

2.64E+04

2.60E+09

3.60E-03

4.09

10.1

2.09E+04

3.03E+08

1,7-H(t)

rate rule

1,8-H 1,9-H R43 a

ksma is the rate constant for the smallest H-shift reaction in each class.

Table 5. Calculated rate constants, rate rules and ratios of rate constants of reactions to the value of the smallest reaction in each class for abstraction from a non–OOH substituted carbon atom. Modified Arrhenius parameters Reactions 1,4-H(p) rate rule R44

-1

-1

500K

1200K

A(s )

n

E(kcal mol )

k

k/ksma

k

k/ksmaa

2.56E-11

7.15

20.6

6.67E-01

36.1

5.91E+07

7.9

2.37E-12

7.34

22.9

1.85E-02

1.0

7.49E+06

1.0

R45

5.22E-12

7.34

21.0

3.54E-01

19.2

4.76E+07

6.4

R46

7.90E-11

7.09

20.4

1.63E+00

88.2

1.22E+08

16.3

1.67E-10

7.07

19.2

1.15E+01

4.3

4.67E+08

4.3

R47

1.61E-10

6.92

19.6

2.66E+00

1.0

1.07E+08

1.0

R48

2.99E-10

6.96

20.3

3.65E+00

1.4

2.31E+08

2.1

R49

3.11E-09

6.80

19.6

2.83E+01

10.6

1.06E+09

9.9

1,4-H(s) rate rule

1,4-H(t) rate rule

5.30E-08

6.30

18.0

1.16E+02

1.8

1.11E+09

3.8

R50

1.50E-09

6.55

16.4

6.39E+01

1.0

2.95E+08

1.0

R51

6.62E-09

6.54

17.6

9.35E+01

1.5

8.48E+08

2.9

R52

1.42E-07

6.26

18.3

1.92E+02

3.0

2.20E+09

7.5


Page 25 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1,5-H(p) rate rule

4.39E+05

2.46

20.9

2.26E+03

1.3

4.21E+09

3.0

R53

3.33E+05

2.29

19.4

1.79E+03

1.0

1.41E+09

1.0

R54

1.31E+05

2.61

20.7

2.03E+03

1.1

3.94E+09

2.8

R55

7.43E+05

2.48

21.2

2.96E+03

1.6

7.28E+09

5.2

1,5-H(s)

4.58E+05

2.61

17.0

3.12E+05

39.8

5.82E+10

10.5

R56

rate rule

7.58E+04

2.65

18.9

7.85E+03

1.0

5.53E+09

1.0

R57

1.94E+05

2.67

17.1

1.46E+05

18.6

1.36E+10

2.5

R58 1,5-H(t) rate rule R59

6.34E+05

2.66

16.7

7.83E+05

99.8

1.55E+11

28.1

2.31E+05

2.61

14.1

2.48E+06

38.4

1.09E+11

10.3

3.76E+04

2.68

16.3

6.47E+04

1.0

1.06E+10

1.0

R60

4.25E+05

2.50

15.1

8.07E+05

12.5

5.52E+10

5.2

R61

2.46E+06

2.40

14.3

6.58E+06

101.8

2.62E+11

24.8

3.38E+03

3.01

18.7

4.90E+03

28.7

4.44E+09

9.6

1,6-H(p)

rate rule

R62

2.19E+03

2.90

20.8

1.71E+02

1.0

4.63E+08

1.0

R63

4.51E+03

2.95

19.5

2.10E+03

12.3

2.86E+09

6.2

R64

1.04E+04

2.96

18.6

1.24E+04

72.7

9.99E+09

21.6

1,6-H(s) rate rule

1.23E+03

3.16

13.6

1.07E+06

116.2

4.22E+10

9.1

R65

9.26E+02

3.17

17.5

9.21E+03

1.0

4.62E+09

1.0

R66

5.39E+03

3.07

16.0

1.45E+05

15.7

2.72E+10

5.9

R67 1,6-H(t) rate rule R68 R69 1,7-H(p) rate rule R70 R71

7.67E+03

2.97

13.0

3.05E+06

331.8

9.48E+10

20.5

1.64E+05

2.65

14.3

3.03E+06

16.3

1.46E+11

10.1

1.43E+04

2.76

14.9

1.86E+05

1.0

1.45E+10

1.0

3.48E+05

2.63

14.3

5.87E+06

31.6

2.77E+11

19.2

1.44E+03

3.06

19.1

2.12E+03

3.4

2.47E+09

3.1

4.12E+03

2.83

19.6

6.34E+02

1.0

7.93E+08

1.0

1.43E+03

3.11

19.0

3.62E+03

5.7

4.15E+09

5.2

2.16E+01

3.58

11.7

1.33E+05

3.1

2.76E+10

2.2

R72

3.66E+03

3.05

16.8

4.30E+04

1.0

1.28E+10

1.0

R73

1.82E+04

2.74

12.5

2.24E+05

5.2

4.24E+10

3.3

8.90E+04

2.55

13.5

1.38E+06

1,7-H(s) rate rule

1,7-H(t) R74

7.76E+09

a

ksma is the rate constant for the smallest H-shift reaction in each class.

Table 6. Ratios k(T,P)/k∞(T) for abstraction from an –OOH substituted carbon atom for molecular size from C2 to C7a at 500K. P/atm

0.01 0.1 1 10 100

k/k(infinity) C2

C3

C4

C5

C6

C7

0.939 0.987 0.998 1.000 1.000

0.973 0.996 0.999 1.000 1.000

1,3-H shift 0.986 0.998 1.000 1.000 1.000 1,4-H shift

0.981 0.997 1.000 1.000 1.000

0.990 0.999 1.000 1.000 1.000

0.993 0.999 1.000 1.000 1.000



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.01 0.1 1 10 100

0.734 0.907 0.980 0.997 1.000

0.01 0.1 1 10 100

0.880 0.973 0.996 1.000 1.000 0.090 0.283 0.612 0.886 0.982

0.01 0.1 1 10 100

0.905 0.981 0.998 1.000 1.000 1,5-H shift 0.116 0.348 0.694 0.927 0.990 1,6-H shift 0.215 0.520 0.832 0.970 0.996 1,7-H shift

0.01 0.1 1 10 100

Page 26 of 38

0.935 0.989 0.999 1.000 1.000

0.944 0.991 0.999 1.000 1.000

0.965 0.995 1.000 1.000 1.000

0.060 0.223 0.558 0.869 0.980

0.072 0.260 0.616 0.902 0.987

0.088 0.293 0.647 0.913 0.989

0.283 0.624 0.895 0.984 0.998

0.448 0.783 0.956 0.995 0.999

0.456 0.797 0.962 0.996 1.000

0.130 0.379 0.726 0.939 0.992

0.154 0.432 0.778 0.957 0.995

0.155 0.439 0.788 0.961 0.995

a

In Cn, n represents the number of carbon atoms in the •O2QOOH radicals. bk(T,P) and k∞(T) are the fall-off rate constant and high-pressure limit rate constant, respectively.


k/k(infinity) C2

C3

0.01 0.1 1 10 100

0.409 0.686 0.895 0.980 0.997

0.509 0.785 0.944 0.991 0.999

0.01 0.1 1 10 100

0.108 0.292 0.588 0.856 0.973

0.203 0.474 0.780 0.950 0.993

0.01

0.004

C4 1,3-H shift 0.558 0.816 0.954 0.993 0.999 1,4-H shift 0.213 0.500 0.807 0.960 0.995 1,5-H shift 0.006

C5

C6

C7

0.465 0.748 0.928 0.988 0.999

0.472 0.746 0.923 0.986 0.998

0.508 0.784 0.943 0.991 0.999

0.243 0.551 0.847 0.973 0.997

0.246 0.564 0.859 0.976 0.997

0.271 0.617 0.895 0.984 0.998

0.002

0.002

0.004


Page 27 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.1 1 10 100

0.023 0.103 0.332 0.699

0.01 0.1 1 10 100

0.030 0.128 0.392 0.761 1,6-H shift 0.012 0.058 0.217 0.550 0.870 1,7-H shift

0.01 0.1 1 10 100

0.011 0.055 0.224 0.593

0.012 0.063 0.250 0.635

0.020 0.091 0.310 0.686

0.012 0.061 0.239 0.605 0.905

0.032 0.132 0.400 0.767 0.958

0.021 0.100 0.353 0.746 0.955

0.006 0.030 0.127 0.390 0.759

0.007 0.036 0.150 0.441 0.805

0.007 0.035 0.147 0.438 0.805

a



k/k(infinity) C2

C3

0.01 0.1 1 10 100

0.029 0.110 0.311 0.622 0.879

0.032 0.125 0.357 0.690 0.919

0.01 0.1 1 10 100

0.003 0.015 0.067 0.235 0.565

0.006 0.031 0.126 0.380 0.740

0.01 0.1 1 10 100 0.01 0.1

2×10-4 0.001 0.007 0.039 0.162

C4 1,3-H shift 0.028 0.110 0.323 0.649 0.898 1,4-H shift 0.006 0.029 0.124 0.379 0.743 1,5-H shift 3×10-4 0.002 0.010 0.048 0.193 1,6-H shift 5×10-4 0.003

C5

C6

C7

0.012 0.057 0.201 0.496 0.813

0.008 0.038 0.143 0.391 0.721

0.008 0.040 0.153 0.418 0.755

0.006 0.033 0.135 0.407 0.772

0.006 0.031 0.132 0.401 0.770

0.004 0.023 0.111 0.388 0.783

6×10-5 4×10-4 0.003 0.014 0.072

7×10-5 5×10-4 0.003 0.016 0.078

2×10-4 0.001 0.006 0.032 0.137

3×10-4 0.002

0.001 0.007

4×10-4 0.003



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1 10 100

0.017 0.079 0.283 1,7-H shift

0.01 0.1 1 10 100

Page 28 of 38

0.012 0.060 0.247

0.035 0.146 0.442

0.016 0.083 0.321

2×10-4 0.001 0.008 0.042 0.171

3×10-4 0.002 0.010 0.051 0.201

2×10-4 0.002 0.010 0.049 0.195

a



k/k(infinity) C2

C3

0.01 0.1 1 10 100

0.004 0.020 0.086 0.274 0.598

0.004 0.021 0.092 0.301 0.649

0.01 0.1 1 10 100

4.E-04 0.003 0.014 0.068 0.248

0.001 0.005 0.028 0.122 0.383

0.01 0.1 1 10 100 0.01 0.1 1 10 100 0.01 0.1

5×10-5 3×10-4 0.002 0.012 0.061

C4 1,3-H shift 0.003 0.014 0.066 0.233 0.558 1,4-H shift 0.001 0.005 0.026 0.115 0.370 1,5-H shift 6×10-5 4×10-4 0.003 0.015 0.073 1,6-H shift 1×10-4 0.001 0.004 0.024 0.110 1,7-H shift

C5

C6

C7

0.001 0.006 0.030 0.126 0.379

4×10-4 0.003 0.015 0.070 0.244

5×10-4 0.003 0.016 0.076 0.264

0.001 0.005 0.028 0.124 0.391

0.001 0.005 0.027 0.118 0.379

4.E-04 0.003 0.016 0.084 0.327

1×10-5 1×10-4 0.001 0.004 0.021

2×10-5 1×10-4 0.001 0.004 0.022

4×10-5 3×10-4 0.002 0.010 0.050

6×10-5 4×10-4 0.002 0.014 0.073

2×10-4 0.002 0.009 0.046 0.185

8×10-5 0.001 0.003 0.019 0.093

5×10-5 3×10-4

6×10-5 4×10-4

6×10-5 4×10-4


Page 29 of 38

1 10 100

0.002 0.012 0.061

0.003 0.015 0.074

0.003 0.015 0.070

a

In Cn, n represent the number of carbon atoms in the •O2QOOH radicals. bk(T,P) and k∞(T) are the fall-off rate constant and high-pressure limit rate constant, respectively.

(a) O2CCOO• O2CC(C)OO• O2CC(C2)OO• O2CC(C3)OO•

O2C(C)COO• O2C(C2)COO• O2C(C3)COO•

6

-1

-1

Log(k/s )

6

(b)

8

Log(k/s )

8

4

4

2

2 1.0

1.5

2.0

1.0

1000K/T

1000K/T

1.5

2.0

Figure 1. The impact of the size of substituent groups of the 1,4-H shift reactions for abstraction from an –OOH substituted carbon atom on the rate constants.

-1

-1

8

(b) O2C(C)CCOO• O2C(C)CC(C)OO• O2C(C)C(C)COO• O2C(C2)CCOO• O2C(C)C(C)C(C)OO•

10

Log(k/s )

(a) O2CCCOO• O2CCC(C)OO• O2CC(C)COO• O2CC(C)C(C)OO• O2CCC(C)(C)OO•

10

Log(k/s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8

6 6 1.0

1000K/T1.5

2.0

1.0

1.5

2.0

1000K/T

Figure 2. The impact of the size of substituent groups of the 1,5-H shift reactions for abstraction from an –OOH substituted carbon atom on the rate constants.



10

(a) O2CCOO• O2C(C)COO•

(b) O2CCCOO• O2C(C)CCOO•

-1

Log(k/s )

-1

Log(k/s )

6 8

3 6

1.0

1000K/T

1.5

2.0

1.0

1.5

2.0

1000K/T

(d) O2CCCCCOO• O2C(C)CCCCOO•

10

(c) O2CCCCOO• O2C(C)CCCOO• 8 -1

Log(k/s )

-1

Log(k/s )

8

6 6

1.0

1.5

2.0

1.0

1000K/T

1.5

2.0

1000K/T

Figure 3. The impact of the types of carbons connected to –OOH group on the rate constants. (a) 1,4-H migration reactions; (b) 1,5-H migration reactions; (c) 1,6-H migration reactions; (d) 1,7-H migration reactions.

50 (1,3)s 45 (1,3)t 40 -1

Ea(kcal mol )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 38

35 (1,4)s 30 (1,4)t 25 (1,5)s (1,6)s

(1,7)s

20 15

(1,5)t 2

3

4

5 n

(1,6)t 6

(1,7)t 7

8

Figure 4. Comparison of barrier heights (Ea) of the smallest reactions for abstraction from an –OOH substituted carbon atom in each reaction class.


Page 31 of 38

12 (1,5)t (1,7)s (1,7)t

8

(1,5)s

-1 Log(k/s )

(1,6)t (1,6)s

4

(1,4)t

(1,4)s

0

(1,3)s

(1,3)t

-4 1.0

1.5

2.0

1000K/T Figure 5. Comparison of rate rules of 1,3- to 1,7-H shift reactions for abstraction from an –OOH substituted carbon atom at 500-1200K. (a) Miyoshi[21] Sharma[39] this work

(b) Miyoshi[21] Sharma[39] this work

9

6

-1

Log(k/s )

-1

Log(k/s )

4

0 3

-4

1.0

1.5 1000K/T

2.0

1.0

(c) Miyoshi[21] Sharma[39] this work

1.5 1000K/T

2.0

(d) Miyoshi[21] Sharma[39] this work

8

-1

-1

Log(k/s )

6 Log(k/s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4

3

0 1.0

1.5 1000K/T

2.0

1.0

1.5 1000K/T

2.0

Figure 6. Comparison of rate constants for O2QOOH case calculated in this study with those of similar reactions in ROO case reported in other studies. (a) 1,4-H



migration reaction O2C(C)COO• → O2C(C•)COO with CCOO•→•CCOO; (b) 1,5-H migration reaction O2C (C)CCOO• → O2C(C•)CCOO with CCCOO•→• CCCOO; (c) 1,6-H migration reaction O2C(C)CCCOO• → O2C(C•)CCCOO with CCCCOO •→• CCCCOO; (d) 1,7-H migration reaction O2C(C)CCCCOO • → O2C(C•)CCCCOO with CCCCCOO•→•CCCCCOO

T=500K (a)

1,3H(C2) 1,3H(C7) 1,4H(C2) 1,4H(C7) 1,5H(C3) 1,5H(C7) 1,6H(C4) 1,6H(C7) 1,7H(C5) 1,7H(C7)

k/k(infinity)

1

0.1 0.01

0.1

1 P/atm

10

100

T=700K 1

k/k(infinity)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(b)


0.1

0.01

0.01

0.1

1 P/atm

10


100

Page 33 of 38

T=1000K 1 (c)

k/k(infinity)

0.1 1,3H(C2) 1,3H(C7) 1,4H(C2) 1,4H(C7) 1,5H(C3) 1,5H(C7) 1,6H(C4) 1,6H(C7) 1,7H(C5) 1,7H(C7)

0.01

1E-3

0.01

0.1

1 P/atm

10

100

T=1200K 1

(d)

0.1 k/k(infinity)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.01


1E-3

1E-4 0.01

0.1

1 P/atm

10

100

Figure 7. The ratios k(T,P)/k∞(T) for abstraction from an –OOH substituted carbon atom. ▲ represents the smallest reaction in each ring-size class, ● represents the largest reaction considered in this study in each ring-size class. The reactions in the same color belong to the same ring-size class.



T=500K

k/k(infinity)

1

1,4H(C3) R47 1,4H(C4) R48 1,5H(C4) R56 1,5H(C5) R57 1,6H(C5) R65 1,6H(C6) R66 1,7H(C6) R72 1,7H(C7) R73

0.1

0.01

0.1

1 P/atm

10

100

T=700K 1

k/k(infinity)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 38

0.1 1,4H(C3) R47 1,4H(C4) R48 1,5H(C4) R56 1,5H(C5) R57 1,6H(C5) R65 1,6H(C6) R66 1,7H(C6) R72 1,7H(C7) R73

0.01

0.01

0.1

1 P/atm

10


100

Page 35 of 38

T=1000K

1

k/k(infinity)

0.1

0.01

1,4H(C3) R47 1,4H(C4) R48 1,5H(C4) R56 1,5H(C5) R57 1,6H(C5) R65 1,6H(C6) R66 1,7H(C6) R72 1,7H(C7) R73

1E-3

1E-4 0.01

0.1

1 P/atm

10

100

T=1200K

1 0.1 k/k(infinity)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.01 1,4H(C3) R47 1,4H(C4) R48 1,5H(C4) R56 1,5H(C5) R57 1,6H(C5) R65 1,6H(C6) R66 1,7H(C6) R72 1,7H(C7) R73

1E-3 1E-4 1E-5 0.01

0.1

1

10

100

P/atm

Figure 8. The ratios k(T,P)/k∞(T) for abstraction from a non–OOH substituted carbon atom. ▲ represents the smallest reaction in each ring-size class. The reactions in the same color belong to the same ring-size class.



(a)

-1

Log(k/s )

100atm 10atm 1atm 5 0.1atm 0.01atm

0 0.01atm 0.1atm 1atm 10atm 100atm

-5 1.2

1.8 1000K/T

(b)

6 -1

Log(k/s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 38

3

0

black--0.01atm red--0.1atm green--1atm blue--10atm cyan--100atm 1.2

1.8 1000K/T

Figure 9. (a) Pressure dependent rate constants of 1,4-H migration reaction O2CC(C)OO • → O2CC(C • )OO. (b) Pressure dependent rate constants of 1,5-H migration reaction O2C(C)COO• → O2C(C•)COO. ▲ represents the rate constants calculated by Goldsmith et al.,27 ● represents the rate constants calculated in this study.


Page 37 of 38

Barrier Height(kcal/mol)

(a) 40 1,3-H 1,4-H 1,5-H 1,6-H 1,7-H

30

20 11

12 13 Heats of Reaction ∆Hrxn(kcal/mol)

(d) Barrier Height(kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1,4-H 1,5-H 1,6-H 1,7-H

30

20 12 16 Heats of Reaction ∆Hrxn(kcal/mol)

20

Figure 10. Evans-Polanyi plots for the intramolecular H-migration reactions of •O2QOOH radicals. (a) The reactions of abstraction from an –OOH substituted carbon atom. (b) The reactions of abstraction from a non–OOH substituted carbon atom.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

TOC Graphic

This study focuses on the pressure-dependent rate rules for intramolecular H-migration reactions of hydroperoxyalkylperoxy radicals in low-temperature.


Page 38 of 38

Pressure-Dependent Rate Rules for Intramolecular H-Migration

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