Reaction mechanism, rate constants, and product yields for the oxidation of Cyclopentadienyl and embedded five-member ring radicals with hydroxyl

Combustion and Flame 187 (2018) 147–164

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Reaction mechanism, rate constants, and product yields for the oxidation of Cyclopentadienyl and embedded five-member ring radicals with hydroxyl G.R. Galimova a, V.N. Azyazov a,b,∗, A.M. Mebel a,c,∗∗ a b c

Samara National Research University, Samara, 443086, Russia Lebedev Physical Institute, Samara, 443011, Russia Department of Chemistry and Biochemistry, Florida International University, Miami, FL 33199, USA

a r t i c l e

i n f o

Article history: Received 13 June 2017 Revised 14 August 2017 Accepted 5 September 2017

Keywords: Cyclopentadienyl Hydroxyl Potential energy surface RRKM–master equation Rate constants

a b s t r a c t Potential energy surfaces for the C5 H5 + OH and C15 H9 + OH reactions have been studied by ab initio calculations at the CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311G(d,p) and G3(MP2,CC)//B3LYP/6-311G(d,p) levels of theory, respectively, in order to unravel the mechanism of oxidation of the cyclopentadienyl radical and five-member-ring radicals embedded in a sheet of six-member rings with OH. The VRC-TST approach has been employed to compute high-pressure-limit rate constants for barrierless entrance and exit reaction steps and multichannel/multiwell RRKM-ME calculations have been utilized to produce phenomenological pressure- and temperature-dependent absolute and individual-channel reaction rate constants. The calculations allowed us to quantify relative yields of various products in a broad range of conditions relevant to combustion and to generate rate expressions applicable for kinetic models of oxidation of aromatics. The C5 H5 + OH reaction is shown to proceed either by well-skipping pathways without stabilization of C5 H6 O intermediates leading to the bimolecular products ortho-C5 H5 O + H, C5 H4 OH (hydroxycyclopentadienyl) + H, and C4 H6 (1,3-butadiene) + CO, or via stabilization of the C5 H6 O intermediates, which then undergo unimolecular thermal decomposition to ortho-C5 H5 O + H and C4 H6 + CO. The well-skipping and stabilization/dissociation pathways compete depending on the reaction conditions; higher pressures favor the stabilization/dissociation and higher temperature favor the well-skipping channels. For the C15 H9 + OH reactions, the results demonstrate that embedding decreases the oxidation rate constants and hinder the decarbonylation process; the removal of CO grows less likely as the number of common edges of the five-member ring with the surrounding six-member rings increases. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction The oxidation of aromatic radicals plays an important role in combustion chemistry because their parent aromatic molecules are present in substantial amounts in all practical hydrocarbon fuels [1,2]. Therefore, reliable data on the oxidation mechanism and kinetics of the aromatics are critical for developing accurate and trustworthy kinetic models of combustion flames. The cyclopentadienyl radical, C5 H5 , has been established as a key transition species while considering the oxidation mechanisms of aromatic and acyclic molecules [3–7]. This is so because an initial step in

oxidation of a six-member aromatic ring normally results in its contraction to a five-member ring and a subsequent oxidation step produces an acyclic hydrocarbon molecule or a radical. For instance, oxidation of benzene involves formation of the phenyl radical, C6 H5 , via H abstraction by others radicals present in flames (H, OH, CH3 , etc.) [8–10] and then, C6 H5 reacts with molecular oxygen producing C5 H5 as one of the major products [11–24]:

C6 H6 + R → C6 H5 + RH C6 H5 + O2 → C6 H5 OO → C6 H5 O + O → C5 H5 + CO + O → C5 H5 + CO2

∗

Corresponding author at: Samara National Research University, Samara, 443086, Russia. ∗∗ Corresponding author at: Department of Chemistry and Biochemistry, Florida International University, Miami, FL 33199, USA. E-mail addresses: [email protected] (V.N. Azyazov), mebela@fiu.edu (A.M. Mebel).

The next oxidation step, the reactions of cyclopentadienyl with a variety of oxidizers (O2 , O, OH, and HO2 ) were first studied in detail theoretically by Zhong and Bozzelli [25], who utilized thermodynamic parameters from group additivity and semi-empirical

http://dx.doi.org/10.1016/j.combustflame.2017.09.005 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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PM3 and ab initio MP4 and G2 calculations and empirical estimates for activation energies to compute reaction rate constants using QRRK theory. More recently, Robinson and Lindstedt [26] revisited the same reactions employing more advanced G4MP2 and G3B3 calculations of pertinent potential energy surfaces (PES) and generated temperature- and pressure-dependent rate constants using a simplified Rice–Ramsperger–Kassel–Marcus Master Equation (RRKM–ME) treatment. However, the RRKM-ME calculations by Robinson and Lindstedt with the ChemRate code [27] have not taken into account multiwell/multichannel effects in the master equation set-up and treated rather approximately barrierless channels, such as the entrance C5 H5 + O and C5 H5 + OH channels and the exit C5 H6 O → C5 H5 O + H channels. To our knowledge, no direct experimental measurements of rate constants for the oxidation reactions of C5 H5 are available. The current kinetic models for oxidation of aromatics mostly rely upon evaluations of rate constants for the C5 H5 reactions based on hypothetical mechanisms derived from fitting experimental flame results on concentration profiles for the key species [28-33] or use rate expressions proposed by Robinson and Lindstedt [26]. Among the experimental/modeling studies, Butler and Glassman [34] presented the cyclopentadienyl oxidation data sets measured in a flow reactor, which provided a foundation for further investigation of the major oxidation and mass growth channels of C5 H5 . One of the most important findings by Butler and Glassman is the key role of the 2,4-cyclopentadienoxy C5 H5 O radical, which can be formed, in particular, via the C5 H5 + O reaction and further decompose by ring opening producing n-butadienyl, C4 H5 , + CO as the major products. On the contrary, 2,4-cyclopentadienone C5 H4 O was not detected. Ji et al. [32] have studied propagation and extinction of cyclopentadiene flames and modeled their experimental data using recent kinetic models. Their results indicated that both flame propagation and extinction are controlled by the fuel kinetics and the formation and consumption of such intermediates as cyclopentadienyl, cyclopentadienone, and cyclopentadienoxy. For instance, the authors concluded that among the potential consumption pathways of cyclopentadienyl radicals, two relevant reactions could improve the high temperature oxidation kinetic model of cyclopentadiene – unimolecular decomposition, C5 H5 → C3 H3 + C2 H2 , and oxidation of cyclopentadienyl with hydroxyl, C5 H5 + OH → C4 H6 + CO. In view of the importance of the C5 H5 oxidation reactions, we began systematic theoretical studies of their mechanism and kinetics employing up-to-date methods of the electronic structure to unravel their PESs and using modern kinetic theories to generate more reliable rate constants and product branching ratios for kinetic models of oxidation of the aromatics and five-member rings. In our previous paper [35], we discussed the C5 H5 + O reaction along with unimolecular and H-atom assisted decomposition of cyclopentadienone occurring on the C5 H4 O and C5 H5 O surfaces. The goal of the present study is to map out in detail the C5 H6 O PES and to utilize its features for RRKM-ME calculations of temperatureand pressure-dependent rate constants for the C5 H5 + OH reaction. The development of the non-empirical RRKM–ME theoretical scheme implemented in the MESMER package [36] and more recently in the MESS program [37,38] greatly facilitated theoretical evaluations of rate constants for complex reactions and opened an opportunity to compute them close to ‘kinetic accuracy’, i.e., with accuracies comparable to that of experiment [39], providing that the energies of the relevant species on the PES and their densities and numbers of states or partition functions are calculated with sufficient accuracy. After considering the C5 H5 + OH reaction, we extend our study to the reactions of hydroxyl radicals with PAH radicals containing a five-member ring embedded in a sheet of six-member rings, emulating oxidation of the five-member ring at the edges of a graphene

sheet, a large PAH molecule, or a soot particle. Soot and PAHs are known to be the major pollutants from combustion of fossil fuels and hence their growth and decay in flames occurring via the addition and removal of carbon, respectively, remain an active area of both experimental and theoretical research [10,40]. Previously, we simulated the oxidation at the edges of PAH with molecular oxygen using the pyrene molecule (more precisely, the pyrenyl radical produced by H abstraction from pyrene) as a model system for the PAH surface [41]. Earlier, similar studies of the O2 reaction with pyrenyl and corannulenyl radicals were reported by Raj et al. [42,43]. The results showed that, similarly to the phenyl and naphthyl [23,44] reactions with O2 , oxidation of a six-member ring in pyrenyl predominantly contracts it into a five-member ring giving a C15 H9 radical. We have also investigated the subsequent reactions of C15 H9 with O2 and O and used our results to generate rate constants for oxidation of the embedded five-member ring with molecular and atomic oxygen at the edges of PAHs and soot. The derived oxidation mechanisms and the calculated rate constants for six- and five-member rings were then utilized in kinetic Monte Carlo simulations of oxidation of a graphene “molecule” evolving in flame-like environments [41]. Along with O2 and O, the hydroxyl radical has been experimentally identified as one of the major soot oxidizers [45]. Theoretically, Edwards et al. have studied the reaction of OH with phenanthryl radicals and showed that the conversion of a six-member ring to a five-member ring is the prevailing reaction outcome [46]. However, the consequent reaction of the embedded five-member ring radical with OH has not been investigated so far. In the present work, we fill this gap and generate the PES and rate constants for the C15 H9 + OH reactions, thus simulating the oxidation of five-member rings with OH at the PAH and soot edges. In addition, we compare the mechanisms and kinetics of the reactions of a five-member ring with hydroxyl radicals when such a ring is isolated as in C5 H5 or is embedded in a sheet of sixmember rings as in different isomers of our model C15 H9 radical containing three six- and one five-member rings.

2. Theoretical methods Geometries of the reactants, various intermediates, transition states, and products participating in the C5 H5 + OH reaction on the C5 H6 O PES and in the C15 H9 + OH reactions on the C15 H10 O surface were optimized at the hybrid density functional B3LYP/6311G(d,p) level of theory [47,48]. Vibrational frequencies were computed at the same theoretical level and were utilized in calculations of zero-point vibrational energy corrections (ZPE) and rate constants. Energies of various C5 H6 O species were refined by single-point calculations using the explicitly-correlated coupled clusters CCSD(T)-F12 method [49,50] with Dunning’s correlationconsistent cc-pVTZ-f12 basis set [51,52]. The CCSD(T)-F12/cc-pVTZf12 approach closely approximates CCSD(T)/CBS energies, i.e. the energies within the coupled clusters theory with single and double excitations with perturbative treatment of triple excitations in the complete basis set limit. We expect that the accuracy of the CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311G(d,p) + ZPE(B3LYP/6311G(d,p)) relative energies should be within 1 kcal/mol based upon the assessment by Zhang and Valeev [53], who reported the mean unsigned errors in reaction energies and barrier heights for a broad range of reactions calculated at the CCSD(T)-F12/ccpVTZ-f12 level to be 0.55 and 0.28 kcal/mol, with the maximal unsigned errors being 1.53 and 0.78 kcal/mol, respectively. For C15 H10 O species, the refinement of single-point energies was carried out employing the modified G3(MP2,CC)//B3LYP [54,55] composite scheme where the energies were computed as

E0 [G3(MP2, CC )] = E[CCSD(T )/6 − 311G∗∗ ] + EMP2 + E(ZPE ),

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where EMP2 = E[MP2/G3Large] – E[MP2/6-311G∗∗ ] is a basis set correction and E(ZPE) is the zero-point energy. In the CCSD(T) and MP2 calculations for open-shell species, the energies were computed from restricted RHF-RCCSD(T) and unrestricted UMP2 energies, respectively, where RHF-RCCSD(T) here denotes partially spin- adapted open-shell coupled cluster singles and doubles theory augmented with a perturbation correction for triple excitations starting from molecular orbitals obtained from restricted open shell Hartree−Fock (ROHF) calculations. T1 diagnostics were checked during coupled cluster calculations to ensure that wave functions do not possess any multireference character. Relative energies computed within this scheme are normally accurate within 1-2 kcal/mol. All the ab initio calculations were performed using the GAUSSIAN 09 [56] and MOLPRO 2010 [52] program packages. The MESS program package [37,38] was utilized to compute temperature- and pressure-dependent phenomenological rate constants by solving the one-dimensional master equation. For the C5 H5 + OH system, we used the collision parameters generated by Jasper and Hansen for the C5 H5 + CH3 reaction with Kr as the bath gas [57], which is representative of the system considered here; earlier, these parameters were also employed by us to study the kinetics of the C5 H5 + O and C5 H4 O + H reactions. Specifically, the Lennard–Jones parameters were taken as (ε /cm−1 , ˚ = (230, 4.01) and the temperature dependence of the range σ /A) parameter α for the deactivating wing of the energy transfer function was described as α (T) = α 300 (T/300 K)n , with n = 0.7 and α 300 = 333 cm−1 , within the “exponential down” model [58] for the collisional energy transfer in the master equation. Jasper and Miller [59] have demonstrated that results for other heavy atomic and diatomic baths are rather similar to those for Kr, with differences within the accuracy of the approach for predicting collisional energy transfer parameters for master equation calculations. For the C15 H9 + OH system, the Lennard–Jones parameters ˚ (834.9, 7.24) for pyrene, C16 H10 , and (101.5, 3.615) (ε /cm−1 , σ /A), for nitrogen were taken from the works by Wang and Frenklach [60] and Vishnyakov et al. [61,62], respectively, and the pairwise C15 H9 OH/N2 values of ε and σ were calculated as the geometric and arithmetic means, respectively. For the energy transfer function parameters, we adopted the “universal” values of n = 0.85 and α 300 = 247 cm−1 for hydrocarbons proposed by Jasper et al. [63]. The Rigid–Rotor, Harmonic–Oscillator (RRHO) model was generally utilized in the calculations of the densities of states and partition functions for the local minima and the number of states for the transition states. Low-frequency normal modes were visually examined and, if they corresponded to internal rotations, were treated as one- or two-dimensional hindered rotors in partition function calculations, rather than as harmonic oscillators. Respective one- and two-dimensional torsional potentials were evaluated by scanning PESs at the B3LYP/6-311G(d,p) level of theory. For the structures involving hindered rotors, only the most favorable conformers were explicitly included in RRKM-ME calculations as potential wells or barriers, whereas all other conformations were included implicitly, within the torsional potentials. Input files used for MESS calculations are given in Supplemental Material. To evaluate the high-pressure limit (HP) rate constant for the barrierless addition of the hydroxyl radical to C5 H5 , for barrierless H addition reactions to C5 H5 O isomers, and for the C4 H5 + HCO association, we employed variable reaction coordinate transition state theory VRC-TST [64,65], which allows us to compute the (E,J)resolved reactive flux. The reactive flux was then converted to macrocanonical temperature-dependent HP rate constants, which in turn were utilized in ME calculations of pressure dependence. In these calculations, energies of various structures were probed at the CASPT2(2,2)/cc-pVDZ level of theory [66,67], where the active space included two electrons corresponding to the forming sin-

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gle bond distributed on two orbitals. The following ad hoc onedimensional corrections depending only on the RCO , RCH , or RCC distances corresponding to the forming bonds were included:

Erel [Method] = Erel [CASPT2(2, 2 )/cc − pVDZ] + E[geom] + E[CBS] where Erel is a relative energy for a particular C5 H6 O configuration with respect to the separated C5 H5 + OH, C5 H5 O + H, or C4 H5 + HCO fragments. E[geom] is a correction for geometry relaxation computed as a difference of energies of an optimized structure along the minimal energy reaction path (MEP) for the approaching fragments corresponding to a particular value of RCO , RCH , or RCC and the structure at the same distance between the fragments but with the geometry of the fragments frozen (the same as in isolated fragments). The calculations of E[geom] were carried out at the CASPT2(2,2)/cc-pVDZ level. In some cases, the geometry optimization was not complete, as we had a bond angle and a dihedral angle for the approaching OH radical or H atom frozen to ensure that they follow the MEP for the addition to a particular C or O atom in the second C5 H5 or C5 H4 O fragment. This approach underestimates E[geom] but since the correction ˚ where bottlenecks of the reappears insignificant at R > 2.4 A, active flux were normally found, we expect that the underestimation should not significantly affect the results. E[CBS] is a correction for extrapolation of the energies to the complete basis set limit, which was computed for frozen-fragment structures along the MEPs corresponding to particular values of RCO , RCH , or RCC using a two-point extrapolation [68]:

E[CBS] = Erel [CASPT2(2, 2 )/cc − pVQZ] + {Erel [CASPT2(2, 2 )/cc − pVQZ] − Erel [CASPT2(2, 2 )/cc − pVTZ]} × 0.69377 − Erel [CASPT2(2, 2 )/cc − pVDZ] The corrections were computed at finite values of RCO , RCH , or RCC between 1.6 and 8 A˚ and then an interpolation by splines was employed to evaluate the corrections at arbitrary R values within the given range. On the course of VRC-TST calculations, the corrections were added to the explicitly computed energy of a configuration based on the R value in this configuration. Additional details of the VRC-TST calculations for each particular case are provided in the Results and Discussion section. Since the HP limit rate constants for barrierless channels of the C15 H9 + OH reactions, including the initial OH addition step and various H and HCO eliminations from C15 H10 O isomers, should be close to those for the analogous reaction steps in the C5 H5 + OH system, we used phase space theory [69] for their calculations. In particular, we fitted the potential power exponents and prefactors to match the C15 H9 + OH, C15 H9 O + H, and C14 H9 + HCO rate constants with the VRC-TST calculated rate constants for the most similar C5 H5 + OH, C5 H5 O + H, and C4 H5 + HCO reactions. We were able to achieve a close match within few percent for all considered cases and within the entire 50 0-250 0 K temperature range. The phase space HP limit rate constants were then used in MESS calculations for C15 H9 + OH. 3. Results and discussion 3.1. PES for the C5 H5 + OH reaction The reaction begins with barrierless addition of the hydroxyl radical to cyclopentadienyl producing the intermediate W1 with the energy gain of 72.0 kcal/mol (Fig. 1). Next, W1 can eliminate a hydrogen atom either from the attacked carbon or from the oxygen atom respectively forming hydroxycyclopentadienyl (P3) or the

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Fig. 1. Potential energy diagram for the C5 H5 + OH reaction calculated at the CCSD(T)-F12/cc-pVTZ-f12//B3LYP/6-311G(d,p) + ZPE level of theory. All relative energies are given in kcal/mol with respect to the initial reactants. Red curves show the decarbonylation pathways and blue curves indicate the most favorable pathways to the C5 H5 O + H products.

ipso-C5 H5 O isomer (P6). Both H elimination steps occur without exit barriers and the resulting C5 H4 OH + H and ipso-C5 H5 O + H products reside 2.9 kcal/mol below and 33.4 kcal/mol above the initial products, respectively. The alternative reaction pathways initiating from W1 involve migrations of hydrogen atoms. For instance, a 1,3-H shift from O to a C atom in ortho position with respect to the OH group occurs via a transition state (TS) denoted B1, which lies 5.8 kcal/mol lower in energy than C5 H5 + OH, and leads to the intermediate W2 (60.7 kcal/mol below the reactants). In W2, the oxygen atom occupies a bridging position between two C atoms. In the subsequent reaction step, W2 undergoes a ring opening via B2 (21.3 kcal/mol below the reactants) forming an open-chain isomer W3, CH2 CHCHCHCH(O), with a relative energy of −71.1 kcal/mol. The intermediate W3 can decompose by a single C–C bond cleavage forming the C4 H5 radical, trans-CH2 CHCHCH, and HCO (P4) without an exit barrier, with the C4 H5 + HCO products residing 24.5 kcal/mol higher in energy than C5 H5 + OH. The C–C bond cleavage can be accompanied by a 1,2-H shift occurring via B4 lying 3.7 kcal/mol above the reactants and then the products are C4 H6 (1,3-butadiene) + CO (P1). C4 H6 + CO are found to be the most exothermic reaction products as they reside 71.9 kcal/mol below the initial reactants. There exists a more energetically favorable pathway from W3 to P1. Instead of the C–C bond cleavage, the H shift from the HCO group to the neighboring carbon atom can pro-

ceed in concert with a re-closure of the five-member ring, which leads to the most stable C5 H6 O intermediate W6 (88.8 kcal/mol below the reactants) via TS B7 lying 20.5 kcal/mol lower in energy than C5 H5 + OH. Next, W6 eliminates the CO group producing 1,3butadiene via B8, 38.3 kcal/mol below the reactants. An alternative, more favorable pathway also exists from W1 to C4 H6 + CO via W6, but bypassing ring opening to W3. This reaction channel begins with a 1,2-H shift from ipso to ortho position forming W4 via a barrier at B5, which lies as deep as 46.8 kcal/mol under the initial reactants. W4 then features another 1,3-H shift from the oxygen to the other ortho C atom resulting in the formation of W6 via B9 (18.4 kcal/mol below the reactants). The intermediate W4 can also lose an H atom from two different positions. H elimination from the CH2 group gives the hydroxycyclopentadienyl product P3, whereas the H loss from the oxygen atom produces a more stable ortho-C5 H5 O isomer (P2), which lies 9.6 kcal/mol below C5 H5 + OH. The last option for W4 is to undergo a second 1,2-H shift from the ortho to meta position giving rise to the intermediate W5. In turn, W5 can lose a hydrogen from the CH2 group producing P3 or from the O atom forming meta-C5 H5 O (P5) residing 0.5 kcal/mol below the reactants. Whereas the C5 H5 + OH → W1 → B5 → W4 → B9 → W6 → B8 → P1 reaction channel is clearly favorable in terms of the energies of the TSs involved, this pathway is rather demand-

G.R. Galimova et al. / Combustion and Flame 187 (2018) 147–164 Table 1 Relative energies of various species in the C5 H5 + OH reaction with respect to the reactants (in kcal/mol) calculated at the CCSD(T)-F12/cc-pVTZf12//B3LYP/6-311G(d,p) + ZPE level in comparison with the literature data. Species

CCSD(T)-F12/cc-pVTZ-f12

G4MP2a

G3B3a

C4 H6 + CO (P1) C5 H4 OH + H (P3) ipso-C5 H5 O + H (P6) W1 B1 W2 B2 W3 B4 B5 W4

−71.9 −2.9 33.4 −72.0 −5.8 −60.7 −21.3 −71.1 (−67.7)b 3.7 −46.8 −79.2

−72.6 −3.9 32.1 −72.6 −6.8 −61.2 −23.0 −68.0 0.9 −48.2 −78.4

−71.4 −2.7 33.4 −72.8 −4.4 −61.8 −20.6 −68.6 2.0 −47.8 −78.7

a

From [26]. The relative energy given in parentheses corresponds to the less favorable cis conformation of W3 considered by Robinson and Lindstedt. b

ing entropically. Hence, we can expect that the formation of the 1,3-butadiene + CO products in the C5 H5 + OH reaction would compete with the more entropically favorable H loss pathways forming various C5 H5 O isomers, such as C5 H5 + OH → W1 → P3, C5 H5 + OH → W1 → B5 → W4 → P2 (or P3), and C5 H5 + OH → W1 → B5 → W4 → B6 → W5 → P3 (or P5). Our rate constant calculations below will address the outcome of this competition. It is informative to compare our present results on the PES for the C5 H5 + OH reaction with those by Robinson and Lindstedt [26], who carried out their calculations at the G4MP2 and G3B3 levels of theory (Table 1). One can see that our results normally agree with the values from the model chemistry calculations within 1-2 kcal/mol; the largest deviation of 2.8 kcal/mol is found between the CCSD(T)-F12/cc-pVTZ-f12 and G4MP2 energies of B4. G4MP2 and G3B3 are composite schemes where larger basis set corrections rely upon their assumed additivity at different theoretical levels (HF, MP2, and MP4), whereas the CCSD(T)-F12 calculations directly approach the CBS limit at the CCSD(T) level and hence, the present calculations are expected to provide more accurate energetics. Also, the most energetically favorable channels to form the C4 H6 + CO and C5 H5 O + H products (via the intermediates W6 and W4, respectively) were not considered by Robinson and Lindstedt. Robinson and Lindstedt have studied an additional pathway involving ring opening in W4 followed by CO elimination from the chain HOCCHCHCHCH2 intermediate accompanied by a 1,3-H shift from the O atom. However, since the transition state for the last step in this channel lies 30-31 kcal/mol above C5 H5 + OH, this pathway is not expected to compete with those presented here and hence is not included in our rate constant calculations. 3.2. Rate constants for barrierless C5 H5 + OH, C5 H5 O + H, and C4 H5 + HCO reaction steps In this section, we consider high-pressure-limit rate constants for barrierless association reactions computed using VRC-TST, which are essential for determining phenomenological rate constants for the overall C5 H5 + OH reaction and its product branching ratio. For the addition of OH to C5 H5 we used a similar strategy to that we employed recently in the study of C5 H5 + O [35]. The cyclopentadienyl radical is a subject to a D5h → C2v Jahn–Teller distortion [70–72] and consequently has two nearly isoergic C2v symmetric stationary structures with 2 B1 and 2 A2 electronic states. Due to symmetry, there exist five identical 2 B1 local minima, which isomerize to one another via five identical 2 A2 TSs via pseudorotation, the partition function for which can be reasonably well described by a free rotor with the rotational constant of 230 cm−1 [73]. In the present study, the partition function treatment of C5 H5

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itself is not critical since within VRC-TST the rate constant depends only on transitional modes and partition functions of vibrational modes of the reacting fragments vanish. The potential for the OH approach to the C1 atom, which bears the highest spin density in the 2 B1 state, is the most attractive and, assuming that pseudorotation of cyclopentadienyl very rapidly turns any closest to the O atom carbon into C1 , we carried out VRC-TST calculations on OH addition to C1 . The C5 H5 fragment’s pivot points were chosen on five carbon atoms and spheres of equal radii were drawn around these pivot points creating a five-faceted dividing surface for each particular separation between the C atom and the oxygen atom, which itself served as the only pivot point on the second fragment. The reactive flux was counted only through one face of the dividing surface, a segment of the sphere surrounding C1 . The five-fold symmetry due to pseudorotation was taken into account posteriori. Such calculations were performed at shorter separations, from 3.25 to 8 bohr, whereas at long separations, between 9 and 19 bohr, pivot points were taken at the centers of mass of each fragment. To ensure that the CASPT2(2,2)/cc-pVDZ calculations for each configuration probed converge to the lowest electronic state, they began with state-averaged sa-CASSCF calculations for two states with a larger (10,8) active space involving the π system in C5 H5 and all valence electrons on the oxygen atom except the one participating in the O–H bond. The ensuing CASPT2(2,2) calculations were also performed for two electronic states and the lowest energy was selected for the computation of the reactive flux. Two different H additions were considered to ortho-C5 H5 O (P2), to the oxygen atom producing the intermediate W4 and to the C atom of the CH group in the ortho position with respect to the CO group forming W6. At shorter separations (3-8 bohr), the pivot points were placed at the O atom and three C atoms of the CH groups in ortho and meta positions, which bear some spin density and where the H atom can in principle add without barriers. As for C5 H5 + OH, the dividing surfaces in the VRC-TST calculations made from spheres centered at the pivot points were multifaceted. For the P2 + H → W4 and P2 + H → W6 reactions, we took into account the reactive fluxes only through one face, a segment surrounding the O atom or the C atom of the ortho CH group, respectively. Alternatively, at long separations (9-19 bohr), pivot points were taken at the centers of mass of each fragment and the spherical dividing surfaces were single-faceted. Similar strategies were employed for the other H additions. An H atom can add to hydroxycyclopentadienyl P3 in three distinct positions, ipso, ortho, and meta, forming W1, W4, and W5, if we do not distinguish between different conformations of W4 and W5 considering the rotation around the CO bond to be fast. Five pivot points were placed on each carbon atom and corresponding multifaceted dividing surfaces were constructed at shorter separations, with the reactive fluxes being counted only through the segments surrounding the ipso, ortho, or meta carbon atoms for the formation of W1, W4, or W5, respectively. For H addition to meta-C5 H5 O (P5) producing W5, four pivot points were located at O, two ortho carbons and one meta carbon belonging to a CH group, and the reactive flux was counted only through the segment of the multifaceted dividing surface centered at the oxygen atom. Finally, for H addition to ipso-C5 H5 O producing W1 we used five pivot points at O and four C atoms not linked to O and the flux was considered only through the segment around O. All energy calculations for the C5 H5 O + H configurations were carried out in the same way as for C5 H5 + OH, i.e. considering two lowest electronic states at the CASPT2(2,2)/saCASSCF(10,8)/cc-pVDZ level. For the C4 H5 + HCO reaction leading to W3, the pivot points were located at the carbon atoms of each fragment containing an unpaired electron (at shorter separations) and at the centers of mass of the fragments (at longer separations). The dividing surfaces were spherical and single-faceted and the to-

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Fig. 2. Calculated HP limit rate constants for barrierless reactions on the C5 H6 O PES: (a) C5 H5 + OH, literature values calculated by Zhong and Bozzelli [25] and Robinson and Lindstedt [26] are shown for comparison; (b) C5 H5 O + H reactions involving H additions to a C atom, literature values for allyl + H (divided by 2) and C5 H5 + H calculated by Harding et al. [74] are shown for comparison; (c) C5 H5 O + H reactions involving H additions to the O atom; (d) C4 H5 + HCO.

tal flux through these surfaces was counted. The energy were probed only for the ground electronic state via state-specific CASPT2(2,2)/CASSCF(10,9)/cc-pVDZ calculations. Figure 2(a) shows the computed HP limit (capture) rate constants for the entrance C5 H5 + OH reaction channel. The values slightly increase from 7.32 × 10−11 to 7.68 × 10−11 cm3 molecule−1 s−1 in the 50 0–10 0 0 K but then somewhat decrease at higher temperatures, to 5.36 × 10−11 cm3 molecule−1 s−1 at 2500 K. Overall, the computed rate constant deviates from its average value of 6.52 × 10−11 cm3 molecule−1 s−1 no more than by 18%. Earlier QRRK calculations by Zhong and Bozzelli [25] gave approximately a factor of 3 lower rate constant value of 2.5 × 10−11 cm3 molecule−1 s−1 . Robinson and Lindstedt [26] predicted the C5 H5 + OH rate constants monotonously increasing from 5.4 × 10−11 cm3 molecule−1 s−1 at 833 K to 4.0 × 10−10 cm3 molecule−1 s−1 at 2500 K using an approximate treatment of the variational addition TS with estimation of its characteristics from the properties of the reactants and products, the external rotors of the active components, and Benson correction parameters. Since VRC-TST is more rigorous than QRRK and the approach employed by Robinson and Lindstedt, which shows a rather large apparent activation energy untypical for a barrierless reaction, we expect the present results to be more reliable. In the

meantime, experimental measurements of the C5 H5 + OH association rate constants are highly desirable for validation of our calculations. The accuracy of the rate constants calculated here relies upon the assumption of VRC-TST that only transitional modes need to be taken into account and partition functions of vibrational modes of the reacting fragments vanish. This assumption is only valid to the point where the variable transition state structures (i.e., the bottlenecks of the reactive flux) do not exhibit a significant change in the vibrational partition function incorporating the non-transitional modes as compared to the separated fragments. This may not necessarily be the case for C5 H5 reactions where, as the two reactive fragments approach, the Jahn-Teller distortion in C5 H5 will be progressively lifted and hence the pseudorotation mode will be turning into a harmonic oscillator. To roughly evaluate inaccuracy, which may be introduced in such a way, we examined the structures of variable transition states obtained in our VRC-TST calculations at different temperatures. It appears that at T < 1900 K the reactive flux bottlenecks are found at large separation, ∼4 A˚ between the fragments (an outer TS). At this separation, the interaction between C5 H5 and OH is weak and the method used in our calculations is not expected to give a significant error. Alternatively, in the 190 0–250 0 K range, the variable transition state structure shifts to a shorter separation of ∼2.1 A˚ (an inner

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TS). We ran UB3LYP/6-311G(d,p) vibrational frequency calculations for this structure and identified the former pseudorotation mode with a frequency of 718 cm−1 . The ratio of the partition functions for harmonic oscillator with such frequency and a free rotor with the rotational constant of 230 cm−1 (for pseudorotation) is ∼0.4 at 190 0–250 0 K, meaning that the VRC-TST rate constant may be overestimated by a factor of 2.5 in this temperature range. This assessment is rather crude because we did not take into account changes in other vibrational modes, geometric relaxation of the fragments beyond the one-dimensional correction described above, and a possible shift of the reactive flux bottleneck due to these factors. Improving VRC-TST calculations to the higher level is beyond the scope of the present work but the consideration above allows us to put a high trust in the present rate constant values below 1900 K and to assign an error bar as a factor of 2-3 for the values at higher temperatures. Figure 2(b) illustrates rate constants for various H additions to a carbon atom in C5 H5 O in comparison with the literature data in analogous systems. First, consider H addition to the ortho carbon of the CH group in o-C5 H5 O (P2) forming W6. The computed rate constants slightly but steadily increase from 1.27 × 10−11 to 1.67 × 10−11 cm3 molecule−1 s−1 in the considered 50 0–250 0 K temperature range. The o-C5 H5 O radical has its unpaired electron delocalized between the O and the CH ortho carbon atoms and hence is analogous to the allyl radical. The o-C5 H5 O + H (P2) → W6 rate constants agree within 15-22% with those calculated by Harding et al. [74] for allyl + H (divided by 2, since allyl has two identical C atoms to accept an H). Among H additions to C5 H4 OH (P3), the overall rate constant for P3 → W4 for the two additions to ortho carbons is the highest, 1.23-2.02 × 10−10 cm3 molecule−1 s−1 , followed by that for P3 → W5, 8.72 × 10−11 1.79 × 10−10 cm3 molecule−1 s−1 , both increasing with temperature. Alternatively, the P3 → W1 rate constant decreases with temperature, from 1.20 × 10−10 to 6.69 × 10−11 cm3 molecule−1 s−1 in the 50 0-250 0 K interval. Hydroxycyclopentadienyl C5 H4 OH is an analog of cyclopentadienyl and therefore it is sensible to compare the sum of the three rate constants, i.e., the total rate constant for the C5 H4 OH + H reaction with that for C5 H5 + H. The total C5 H4 OH + H rate constant increases from 3.30 × 10−10 cm3 molecule−1 s−1 at 500 K to 4.48 × 10−10 cm3 molecule−1 s−1 at 2500 K. These results agree with the rate constants computed by Harding et al. [74] for H addition to C5 H5 in the 2 B1 electronic state within 10% and with those for C5 H5 (2 A2 ) within 15%. A slightly better agreement with the C5 H5 (2 B1 ) + H reaction can be attributed to the fact that the geometric and electronic structure of C5 H4 OH is closer to that of cyclopentadienyl in the 2 B1 state. Rate constants computed for H additions to the oxygen atom in the C5 H5 O isomers are presented in Fig. 2(c). Here, all values vary in a rather narrow range; those for P2 → W4 decrease from 2.22 × 10−10 to 1.85 × 10−10 cm3 molecule−1 s−1 , whereas the rate constants for P6 → W1 and P5 → W5 increase from 1.14 × 10−10 to 2.58 × 10−10 cm3 molecule−1 s−1 and from 1.92 × 10−10 to 2.45 × 10−10 cm3 molecule−1 s−1 , respectively, in the 50 0–250 0 K temperature range. Finally, Fig. 2(d) shows rate constants calculated for the C4 H5 + HCO association. The rate constants exhibit a decreasing trend with temperature, from 2.25 × 10−10 to 9.88 × 10−11 cm3 molecule−1 s−1 in the considered 50 0–250 0 K range. Similar behavior was found previously for the rate constants for recombination of two alkyl radicals in VRC-TST calculations by Klippenstein et al. [75]. For example, for CH3 + C2 H5 the computed rate constants varied from ∼1 × 10−10 to 3 × 10−11 cm3 molecule−1 s−1 , being a factor of 2–3 lower than our values. Two closer analogs of the C4 H5 + HCO reaction are CH3 + HCO and C2 H3 + HCO. For CH3 + HCO, the recommended value of the association rate constant is 5 × 10−11 cm3 molecule−1 s−1 in the 373-473 K

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range [76]. VRC-TST calculations by Harding et al. [77] closely reproduce this value and show a decrease with temperature, which is similar to that observed here for C4 H5 + HCO. Since both Harding et al.’s and the present calculations used comparable CASPT2 potentials, one could expect analogous accuracy from our results. Also, the C2 H3 + HCO and C4 H5 + HCO reactions can be anticipated to be faster than CH3 + HCO because the vinylic C–C bonds formed, 95.6 and 95.2 [78] kcal/mol, respectively, are significantly stronger than the alkylic C–C bond in CH3 CHO, 82.7 kcal/mol, and hence, the reactions of the vinylic radicals with HCO would follow more attractive potentials. However, Tsang and Hampson [79] recommend 3 × 10−11 cm3 molecule−1 s−1 for the C2 H3 + HCO → CH2 CHCHO reaction in the 30 0–250 0 K range, seemingly in significant disagreement with the present results and in contradiction with the above argument. The contradiction can be resolved if we consider another reaction in Tsang and Hampson’s review, C2 H3 + HCO → C2 H4 + CO, for which the recommended value is 1.5 × 10−10 cm3 molecule−1 s−1 . This reaction channels can go either via barrierless direct H abstraction or via the association process followed by isomerization of the C2 H3 CHO complex and its dissociation to the C2 H4 + CO products. Harding et al. [77] have shown that the direct abstraction reactions by HCO are slower than its association reactions with hydrocarbon radicals and hence, according to the recommended rate constants, the reaction flux to C2 H4 + CO would predominantly proceed via the association/dissociation channel. Indeed, ab initio calculations of the C3 H4 O PES by Gimondi et al. [80] showed the following pathway to the C2 H4 + CO products: C2 H3 + HCO → CH2 CHCHO (−95.2 kcal/mol) → TS (−25.4) → CH3 CHCO (−94.7) → TS (−20.0) → C2 H4 + CO (−94.9), where all intermediates and TSs lie significantly lower in energy than the reactants. This type of PES should exhibit noticeable pressure dependence of the C2 H3 + HCO → CH2 CHCHO vs. C2 H3 + HCO → C2 H4 + CO rates; Tsang and Hampson predicted the yield of C2 H4 + CO to increase at higher temperatures in the fall-off region. If we combine the two recommended rate constants (and subtract the rate constant for the direct H abstraction), the total high-pressure limit value for the C2 H3 + HCO association would be somewhat above 1.5 × 10−10 cm3 molecule−1 s−1 , i.e., in the range of the rate constants calculated here for C4 H5 + HCO. While the association and H abstraction kinetics of HCO with various hydrocarbon radicals warrants further careful consideration, the C4 H5 + HCO reaction has very little significance for the present work, since the formation of this product pair is highly unfavorable thermodynamically and C4 H5 + HCO will be shown as only a trace channel in the C5 H5 + OH reaction. 3.3. Temperature- and pressure-dependent rate constants and product branching ratios for the C5 H5 + OH reaction We now move to phenomenological rate constants for the C5 H5 + OH reaction computed at finite pressures. The total rate constant depends on pressure only slightly (Fig. 3(a)). For instance, at 1500 K, the computed values at 30 Torr, 1 10, and 100 atm, are, respectively, only 12%, 8%, 4%, and 1% lower than the HP limit rate constant. The difference slightly increases to 17–14% at 2500 K. At low temperatures, the reaction products predominantly are collisionally stabilized C5 H6 O isomers, mostly W5, followed by W4 and W1 (see Fig. 3(b) and (c) and Table 2). It should be noted that the kinks seen on the plots of the rate constants for the formation of W4 and W5 originate from “merging” of C5 H6 O intermediates, i.e., due to their rapid equilibration at higher temperatures. For instance, for T > 1125 K and 1 atm, intermediate W1 merges with W4. The reactive flux going to W1 is then incorporated into the reactive flux going to W4, which is a more thermodynamically favorable isomer under these conditions. So, the calculated rate con-

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Fig. 3. Pressure-dependent total and product channel specific rate constants for various reactions of the C5 H6 O PES: (a) total C5 H5 + OH rate constants; (b) formation of various bimolecular products in the C5 H5 + OH reaction, literature values calculated by Robinson and Lindstedt [26] are given for comparison; (c) stabilization of the C5 H6 O intermediates W4 and W5 in the C5 H5 + OH reaction, and (d) unimolecular thermal decomposition of W5. Dotted, solid, dashed, and dash-dotted lines show rate constants calculated for pressures of 30 Torr, 1, 10, and 100 atm, respectively.

stant for C5 H5 + OH → W4 in fact becomes the rate constant for C5 H5 + OH → (W1 + W4), which causes the non-monotonic behavior seen on the plot. At 10 and 100 atm, the merging of W1 and W4 takes place above 1250 and 1500 K, respectively. With temperature increasing further, W4, or rather (W1 + W4), merge (equilibrate) with the even more thermodynamically stable isomer W5. This merging occurs at temperatures above 10 0 0, 1250, 150 0, and 1650 K at the pressures of 30 Torr, 1, 10, and 100 atm, respectively. At these temperatures, the C5 H5 + OH → W5 reactive flux begins to reflect the combined C5 H5 + OH → (W1 + W4 + W5) reactive flux, resulting in the apparent kinks on the rate constant plots. As the temperature rises, ortho-C5 H5 O + H (P2) and C5 H4 OH + H (P3) become the main reaction products. The calculated yield of the most exothermic C4 H6 + CO products is rather small. It maximizes at ∼25% at 1375 K and 30 Torr. At 1, 10, and 100 atm, the branching ratio of C4 H6 + CO does not exceed 15% (1800 K), 10% (2250 K), and 7% (2500 K). The pathway to C4 H6 + CO is favored by the enthalpy factor (lower barrier heights) but H losses are entropically preferable and hence take over at higher temperatures. In the meantime, at low temperatures, the C4 H6 + CO channel is overcompeted by collisional stabilization of the C5 H6 O intermediates. This is why we find the highest yield of C4 H6 + CO at the lowest pressure considered and in the intermediate temperature range. At 1500 K and 1 atm, the computed product branching ratios are 43% (W5), 13% (C4 H6 + CO), 31% (P2), 11% (P3), and 3% (P5). At higher pressures and the same temperature, the yield of the stabilized intermediate(s) increases, while those of the bimolecular products drop. The bimolecular C5 H5 O + H products then become preferential only above 1800 K (10 atm) and 2250 K (100 atm).

Considering rate constants for unimolecular decomposition of thermalized C5 H6 O intermediates, we find that at low temperatures they prefer to isomerize to one another eventually merging to the most thermodynamically stable W5 species. Dissociation of W5 to various bimolecular products takes over at higher temperatures, in particular, at 1125, 1375, 1500, and 1800 K at the pressures of 30 Torr, 1, 10, and 100 atm, respectively. The prevailing dissociation products are C4 H6 + CO (P1) and ortho-C5 H5 O + H (P2), for which branching ratios at T = 1500 K are computed as, respectively, 52% and 39% (30 Torr), 37% and 45% (1 atm), and 26% and 46% (10 atm). At 100 atm and 1500 K, isomerization within the C5 H6 O manifold is still predominant, but at 1800 K the branching ratios of P1 and P2 are 14% and 26%. Among the other minor dissociation products of W5, in the relevant temperature range of 150 0–180 0 K, C5 H4 OH + H (P3) contribute 4–5% (30 Torr), 8–10% (1 atm), 10–14% (10 atm), and 16% (100 atm), meta-C5 H5 O + H (P5) give ∼1% (30 Torr), ∼2% (1 atm), 2–3% (10 atm), and 4% (100 atm), whereas the branching ratios for the dissociation of W5 back to the C5 H5 + OH reactants are 4-5% (30 Torr), 7-9% (1 atm), 9-12% (10 atm), and 13% (100 atm). The lifetime of C5 H6 O (W5) with respect to its dissociation channels at 1500 K is evaluated as 45, 14, and 9 μs at the pressures of 30 Torr, 1 and 10 atm, respectively, and 0.2 μs at 1800 K and 100 atm. Considering the calculated rate constants and product branching ratios, we deduce the following mechanism for the C5 H5 + OH reaction: (1) Well-skipping pathways (without stabilization of the C5 H6 O intermediates):

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Table 2 Calculated branching ratios for various products of the C5 H5 + OH reaction and unimolecular decomposition of C5 H6 O (W5). T(K) 30 Torr 500 600 700 800 900 10 0 0 1125 1250 1375 1500 1650 1800 20 0 0 2250 2500 1 atm 500 600 700 800 900 10 0 0 1125 1250 1375 1500 1650 1800 20 0 0 2250 2500 10 atm 500 600 700 800 900 10 0 0 1125 1250 1375 1500 1650 1800 20 0 0 2250 2500 100 atm 500 600 700 800 900 10 0 0 1125 1250 1375 1500 1650 1800 20 0 0 2250 2500

R→W1

R→W4

R→W5

R→P1

R→P2

R→P3

R→P5

W5→R

W5→P1

W5→P2

W5→P3

3.00% 2.92% 2.83% 2.87% 3.33% 5.15%

37.67% 37.12% 35.33% 31.80% 26.33% 19.06%

58.46% 57.24% 54.55% 49.47% 41.96% 32.63% 38.65% 23.84% 13.54% 7.22% 3.23% 1.42% 0.48%

0.62% 1.70% 3.99% 7.75% 12.54% 17.39% 22.12% 24.58% 24.88% 23.70% 21.36% 18.80% 15.74% 12.79% 10.55%

0.23% 0.95% 2.98% 7.14% 13.60% 21.58% 31.79% 40.36% 46.36% 49.90% 51.67% 51.78% 50.59% 48.35% 45.80%

0.01% 0.06% 0.26% 0.80% 1.83% 3.41% 6.03% 9.06% 12.23% 15.35% 18.92% 22.23% 26.26% 30.70% 34.52%

0.00% 0.01% 0.05% 0.16% 0.37% 0.72% 1.33% 2.07% 2.87% 3.70% 4.67% 5.59% 6.71% 7.88% 8.79%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 1.69% 2.49% 3.22% 3.86% 4.53% 5.11% 5.78%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 67.10% 60.93% 56.02% 52.21% 48.68% 45.99% 43.09%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 27.94% 33.12% 36.70% 39.20% 41.30% 42.79% 44.20%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 1.74% 2.50% 3.20% 3.81% 4.46% 5.03% 5.71%

4.24% 4.16% 4.08% 4.05% 4.25% 4.93% 7.40%

37.25% 37.28% 37.22% 36.90% 35.93% 33.78% 28.45% 29.49%

58.48% 58.44% 58.30% 57.87% 56.77% 54.48% 49.10% 43.27% 58.05% 43.06% 27.55% 16.36% 7.64% 2.83%

0.02% 0.06% 0.19% 0.50% 1.14% 2.27% 4.46% 7.26% 10.16% 12.58% 14.32% 14.74% 13.93% 12.11% 10.56%

0.01% 0.04% 0.17% 0.56% 1.55% 3.58% 8.09% 14.75% 22.72% 30.66% 38.53% 43.67% 46.72% 46.83% 45.80%

0.00% 0.00% 0.02% 0.08% 0.27% 0.75% 1.99% 4.17% 7.23% 10.90% 15.55% 19.97% 25.06% 30.19% 34.50%

0.00% 0.00% 0.00% 0.02% 0.06% 0.17% 0.46% 0.99% 1.75% 2.68% 3.89% 5.05% 6.42% 7.76% 8.78%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 6.12% 7.39% 8.57% 9.46% 10.36% 11.18%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 40.59% 36.78% 33.07% 30.26% 27.84% 25.33%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 42.72% 45.03% 46.53% 47.30% 47.77% 47.92%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 6.23% 7.62% 9.00% 10.11% 11.32% 12.53%

6.50% 5.89% 5.56% 5.37% 5.30% 5.47% 6.23% 8.15%

38.06% 37.27% 36.91% 36.75% 36.55% 36.04% 34.55% 31.34% 36.46%

55.43% 56.83% 57.48% 57.75% 57.78% 57.51% 56.45% 53.96% 50.42% 77.32% 62.88% 47.46% 29.54% 14.71% 6.93%

0.00% 0.00% 0.01% 0.03% 0.10% 0.26% 0.68% 1.47% 2.68% 4.26% 6.34% 8.17% 9.65% 9.96% 9.31%

0.00% 0.00% 0.02% 0.06% 0.19% 0.52% 1.49% 3.54% 7.04% 12.03% 19.38% 26.91% 35.03% 40.57% 42.19%

0.00% 0.00% 0.00% 0.01% 0.04% 0.12% 0.43% 1.18% 2.65% 5.02% 8.99% 13.77% 20.34% 27.41% 32.86%

0.00% 0.00% 0.00% 0.00% 0.01% 0.03% 0.10% 0.28% 0.65% 1.25% 2.27% 3.51% 5.23% 7.05% 8.36%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 9.04% 10.56% 11.63% 12.59% 13.35% 13.83%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 26.19% 24.24% 22.21% 19.96% 18.65% 17.04%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 45.96% 46.96% 47.17% 46.97% 46.46% 45.91%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 9.90% 12.03% 13.73% 15.51% 17.19% 18.49%

45.28% 35.09% 26.48% 19.81% 15.02% 11.83% 9.63% 8.87% 9.24% 10.88%

41.64% 44.42% 44.84% 43.70% 41.89% 40.02% 37.92% 36.02% 33.88% 30.70% 39.86%

13.07% 20.49% 28.68% 36.48% 43.04% 48.03% 52.10% 54.15% 54.56% 53.47% 49.61% 80.87% 65.61% 45.07% 28.19%

0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.05% 0.14% 0.34% 0.72% 1.44% 2.45% 4.01% 5.65% 6.51%

0.00% 0.00% 0.00% 0.01% 0.02% 0.06% 0.19% 0.51% 1.23% 2.58% 5.35% 9.49% 16.54% 25.36% 31.76%

0.00% 0.00% 0.00% 0.00% 0.00% 0.02% 0.06% 0.19% 0.53% 1.24% 2.87% 5.58% 10.85% 18.84% 26.50%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.04% 0.12% 0.29% 0.70% 1.39% 2.74% 4.78% 6.68%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 12.70% 13.68% 14.30% 14.58%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 14.18% 13.61% 12.50% 13.00%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.05% 46.21% 45.33% 44.15% 43.13%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 16.42% 19.01% 21.41% 23.20%

C5 H5 + OH → ortho-C5 H5 O + H (P2) → C5 H4 OH + H (P3) → C4 H6 + CO (P1)

(2) Pathways involving stabilization of C5 H6 O followed by its unimolecular decomposition:

C5 H5 + OH → C5 H6 O C5 H6 O (W5) → ortho-C5 H5 O + H (P2)

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→ C4 H6 + CO (P1) → C5 H5 + OH → C5 H4 OH + H (P3) The well-skipping and C5 H6 O stabilization pathways will compete depending on the reaction conditions; clearly, higher pressures favor the stabilization/dissociation channels. Rate expressions in the modified Arrhenius form are presented in Table 3, while more detailed fitting results including more accurate fits to a sum of two modified Arrhenius expressions are provided in the Supplemental Material. The existence of the stabilization/dissociation channels operational only up to a certain temperature, which in turn depends on pressure, complicates kinetic modeling, but this represents a rather common situation for many bimolecular reactions proceeding via deep potential wells. Therefore, this reaction scenario cannot be simply ignored; rather, the kinetic simulation software may need to be adapted to allow for this behavior. Alternatively, the stabilization/dissociation pathways can be taken into account at all temperatures of interest, but then a careful extrapolation procedure needs to be developed to extrapolate their formal rate constants, like those, for example, for the formation and decomposition of W5 here, beyond the temperature range of existence of this intermediate. This remains a challenging theoretical task. The C5 H5 O radicals formed in the C5 H5 + OH reaction would further dissociate under conditions relevant to combustion, via the following prevailing channels:

ortho-C5 H5 O → C4 H5 + CO C5 H4 OH

→ C5 H4 O (2,4-cyclopentadienone) + H

We generated temperature- and pressure-dependent rate constants for these reactions in our previous study on the cyclopentadienone + H and C5 H5 + O reactions [35]. 3.4. PES for the C15 H9 + OH reactions We now consider the reaction mechanism of the OH radical with a five-member ring radical embedded in a sheet of sixmember rings, like at the edge of a graphene sheet or a large PAH molecule. We emulate this process by the OH reactions with C15 H9 radicals made from three six-member and one five-member rings (see Figs. 4 and 5). In turn, such radicals can be produced by oxidation of pyrenyl radicals, C16 H9 , with O2 proceeding by molecular oxygen addition to the radical site and elimination by an oxygen atom followed by decarbonylation of the oxy-type radical leading to a contraction of one of the six-member rings to a fivemember ring. Depending on the position of the unpaired electron in pyrenyl, this process leads to two different isomers of C15 H9 , (A) and (B). In (A), the embedded five-member ring shares two edges (C–C bonds) with other six-member rings, whereas in (B) the embedding is deeper and three C–C bonds in the five-member ring are shared with the six-member rings. The computed potential energy diagrams for the reactions of these isomers with hydroxyl are illustrated in Figs. 4 and 5. While the general features of the mechanism of the C5 H5 + OH and C15 H9 (A)/(B) + OH reactions are similar, the details and the energetics differ substantially. In the C15 H9 (A) + OH reaction (Fig. 4), OH addition in the entrance channel is 64.5 kcal/mol exothermic and forms the intermediate A-W1, an analog of the C5 H6 O isomer W1 formed initially in the C5 H5 + OH reaction. A-W1 can lose an H atom from two different positions, from the attacked C atom producing C15 H8 OH (A-P3), which is akin to hydroxycyclopentadienyl and lies 2.8 kcal/mol below the initial reactants, and from O forming A-P6, 40.5 kcal/mol

above the reactants. The formation of this product would be unfeasible. Besides the H loss, A-W1 can evolve to 1-methylenephenalene + CO (A-P1) by isomerization and decarbonylation via the following pathways: A-W1 → A-B3 (A-B5 → A-W4 → A-B2) → AW3 → A-B7 → A-W6 → AB8 → A-P1. This channels involves either direct formation of A-W3 by 1,3-H migration from O accompanied by the five-member ring opening or via a two-step process with 1,2-H shift from ipso to meta carbon (relative to O) forming AW4 followed by a second 1,2-H shift from O to ipso-C also occurring concurrently with the ring opening. A-W3 then features one more 1,2-H migration accompanied by re-closure of the ring and formation of A-W6; the latter eliminates the CO group and produces 1-methylene-phenalene. The critical barriers on these pathways are found A-B3 or A-B2, both residing ∼11 kcal/mol below the initial reactants. Noteworthy, in relative terms these TSs are lie ∼7 kcal/mol higher than the critical TS B9 for the production of C4 H6 + CO in the C5 H5 + OH reaction and hence, the yield of CO is likely to be inhibited due to embedding of the five-member ring radical. The intermediate A-W6 can be also produced via the AW1 → A-B6 → A-W5 → A-B4 → A-W6, i.e., 1,2-H shift from ipso to the ortho carbon located in the edge between the five-member and six-member rings followed by 1,3-H shift from O to the other ortho C atom. However, here the critical TS A-B4 resides significantly higher in energy, 0.7 kcal/mol above the reactants. There also exists a more direct channel to the A-P1 product, A-W1 → AB1 → A-W2 (1,3-H shift from O to the ortho C in the edge between two rings with O moving to a bridging position between two CH groups) → A-B9 → A-W7 (1,2-H shift between the two CH groups and insertion of the oxygen atom into the five-member ring) → AB10 → A-P1 (CO elimination). This pathway has its highest in energy TS A-B9 28.2 kcal/mol above the reactants and is likely unfeasible. Along the course to the formation of A-P1, A-W4 can alternatively eliminate a hydrogen atom to form either A-P3 or A-P2 (an analog of ortho-C5 H5 O P2 residing 14.7 kcal/mol lower in energy than the reactants). A-W5 can decompose to A-P3 but also to A-P5, 10.8 kcal/mol above the reactants, which is the other analog of ortho-C5 H5 O with the extra hydrogen linked to the ortho carbon in the edge between two rings. The A-W6 structure can lose H atom from two ortho positions producing A-P2 or A-P5. Finally, A-W3 can split the HCO group forming 1-methylene-phenalen-1-yl radical (A-P4), but this product is too high in energy, 35.1 kcal/mol above the reactants. Our calculations of rate constants and product branching ratios in the subsequent section will quantify the competition between decarbonylation and various H elimination processes. In the C15 H9 (B) + OH reaction, the initial association step forming B-W1 is 76.0 kcal/mol exothermic. H eliminations from the initial intermediate form either B-P3, an analog of hydroxycyclopentadienyl P3 residing 1.7 kcal/mol lower in energy than the reactants, or B-P6, an analog of ipso-C5 H5 O P6, which lies 24.1 kcal/mol above the reactants. The decarbonylation process of B-W1 producing phenanthrene proceeds via the B-W3 and B-W6 intermediates. B-W3 can be formed from B-W1 either in one step via B-B3, by 1,3H migration from O to an ortho carbon accompanied with the fivemember ring opening, or via a two-step mechanism B-W1 → BB5 → B-W4 → B-B2 → B-W3 involving 1,2-H migration from ipso to ortho position followed by another 1,2-H shift from O to the ipso C atom with the ring opening. Here, the one-step process is clearly preferable since the TS B-B3, 0.9 kcal/mol above the reactants, lies 23.6 kcal/mol lower in energy than B-B2. B-W3 can decompose to the phenanthrene + CO products directly via the TS B-B4, by 1,2-H migration from ipso to ortho C, which prompts a concurrent cleavage of the C–C bond over which this migration takes place. Alternatively, the 1,2-H migration in B-W3 can be accompanied by re-closure of the five-member ring producing B-W6 and the latter eliminates the CO moiety via B-B8 forming phenanthrene.

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157

Table 3 Rate constants calculated in the present work in the form ATα exp(-Ea /RT) and the temperature range where they are applicable. Units are s−1 (unimolecular reactions), cm3 mol−1 s−1 (bimolecular reactions), and kcal/mol for Ea . Reaction C5 H5 + OH → C5 H6 O (W1) k30 Torr k1 atm k10 atm k100 atm C5 H5 + OH → C5 H6 O (W4) k30 Torr k1 atm k10 atm k100 atm C5 H5 + OH → C5 H6 O (W5) k30 Torr k1 atm k10 atm k100 atm C5 H5 + OH → C4 H6 + CO (P1) k30 Torr k1 atm k10 atm k100 atm C5 H5 + OH → ortho-C5 H5 O + H (P2) k30 Torr k1 atm k10 atm k100 atm C5 H5 + OH → C5 H4 OH + H (P3) k30 Torr k1 atm k10 atm k100 atm C5 H5 + OH → meta-C5 H5 O + H (P5) k30 Torr k1 atm k10 atm k100 atm C5 H5 + OH → total k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W1) → C5 H6 O (W4) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W1) → C5 H6 O (W5) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W4) → C5 H6 O (W1) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W4) → C5 H6 O (W5) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W5) → C5 H6 O (W1) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W5) → C5 H6 O (W4) k30 Torr k1 atm k10 atm k100 atm

A

α

Ea

k(1500 K)a

T range, K

7.16E-06 1.32E+00 7.45E+04 5.56E+13

5.34 3.75 2.28 −0.47

−6.56 −4.71 −3.33 −1.98

n/a n/a n/a 4.39E+12

50 0–10 0 0 500–1125 500–1250 50 0–150 0

2.49E+33 7.32E+20 2.93E+16 1.46E+18

−6.27 −2.34 −0.99 −1.49

7.47 3.08 1.31 1.99

n/a n/a n/a 1.24E+13

50 0–10 0 0 500–1250 500–1375 500–1650

3.50E+54 7.78E+38 6.43E+30 2.81E+24

−12.51 −7.63 −5.15 −3.16

17.30 11.61 8.42 7.36

2.60E+12 1.61E+13 3.03E+13 2.15E+13

50 0–20 0 0 500–2250 50 0–250 0 50 0–250 0

2.69E+34 7.55E+27 1.16E+20 1.59E+08

−6.07 −4.07 −1.75 1.68

15.34 16.61 16.78 15.56

8.55E+12 4.71E+12 1.67E+12 2.88E+11

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

2.55E+31 3.48E+25 6.73E+13 3.31E+01

−4.98 −3.18 0.20 3.69

16.09 17.32 13.69 9.42

1.80E+13 1.15E+13 4.72E+12 1.04E+12

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

1.75E+26 1.76E+23 1.06E+12 6.56E-04

−3.49 −2.49 0.76 5.05

16.63 19.38 15.96 9.26

5.54E+12 4.08E+12 1.97E+12 4.98E+11

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

9.47E+25 6.37E+23 4.12E+14 3.60E+04

−3.56 −2.80 −0.11 2.80

17.49 20.74 18.98 17.50

1.33E+12 1.00E+12 4.89E+11 1.17E+11

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

1.19E+17 2.79E+17 3.29E+17 1.73E+17

−1.04 −1.14 −1.16 −1.07

1.42 1.65 1.74 1.63

3.60E+13 3.74E+13 3.92E+13 4.03E+13

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

2.94E+55 1.45E+48 1.18E+37 7.99E+26

−13.80 −11.03 −7.39 −4.15

36.58 36.64 3.77 30.54

n/a n/a n/a 1.70E+09

50 0–10 0 0 500–1125 500–1250 50 0–150 0

3.07E+58 1.73E+54 2.20E+41 1.15E+25

−14.47 −12.53 −8.27 −3.22

41.60 45.68 44.52 40.83

n/a n/a n/a 6.13E+08

50 0–10 0 0 500–1125 500–1250 50 0–150 0

1.81E+55 9.78E+47 9.32E+36 6.90E+26

−13.71 −10.96 −7.34 −4.11

43.66 43.73 40.89 37.67

n/a n/a n/a 1.81E+08

50 0–10 0 0 500–1125 500–1250 50 0–150 0

3.70E+54 4.06E+42 6.25E+31 5.96E+23

−13.21 −9.14 −5.67 −3.14

42.27 39.96 36.68 34.00

n/a n/a n/a 6.91E+08

50 0–10 0 0 500–1250 500–1375 500–1650

7.39E+58 4.69E+54 5.60E+41 2.77E+25

−14.65 −12.72 −8.45 −3.39

48.58 52.68 51.52 47.82

n/a n/a n/a 3.97E+07

50 0–10 0 0 500–1125 500–1250 50 0–150 0

3.62E+54 3.63E+41 5.70E+30 5.25E+22

−13.29 −8.90 −5.43 −2.90

41.95 39.21 35.92 33.21

n/a n/a n/a 4.40E+08

50 0–10 0 0 500–1250 500–1375 500–1650

(continued on next page)

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Table 3 (continued) Reaction C5 H6 O (W5) → C4 H6 + CO (P1) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W5) → ortho-C5 H5 O + H (P2) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W5) → C5 H4 OH + H (P3) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W5) → meta-C5 H5 O + H (P5) k30 Torr k1 atm k10 atm k100 atm C5 H6 O (W5) → C5 H5 + OH k30 Torr k1 atm k10 atm k100 atm C15 H9 (A) + OH → C15 H10 O (A-W1) k30 Torr k1 atm k10 atm k100 atm C15 H9 (A) + OH → C15 H10 O (A-W5) k30 Torr k1 atm k10 atm k100 atm C15 H9 (A) + OH → C15 H10 O (A-W4) k30 Torr k1 atm k10 atm k100 atm C15 H9 (A) + OH → C15 H9 O + H (A-P2) k30 Torr k1 atm k10 atm k100 atm C15 H9 (A) + OH → C15 H8 OH + H (A-P3) k30 Torr k1 atm k10 atm k100 atm C15 H9 (A) + OH → total k30 Torr k1 atm k10 atm k100 atm C15 H10 O (A-W1) → C15 H10 O (A-W5) k30 Torr k1 atm k10 atm k100 atm C15 H10 O (A-W1) → C15 H10 O (A-W4) k30 Torr k1 atm k10 atm k100 atm C15 H10 O (A-W5) → C15 H10 O (A-W1) k30 Torr k1 atm k10 atm k100 atm

A

α

Ea

k(1500 K)a

T range, K

3.90E+43 6.81E+39 2.51E+34 2.65E+22

−9.08 −7.65 −5.88 −2.24

74.09 77.23 78.68 77.57

1.15E+04 2.62E+04 2.87E+04 1.56E+04

50 0–20 0 0 500–2250 50 0–250 0 50 0–250 0

2.32E+52 5.71E+39 2.85E+33 8.90E+27

−11.35 −7.43 −5.48 −3.75

85.68 81.06 78.79 78.03

8.65E+03 3.21E+04 5.04E+04 5.66E+04

50 0–20 0 0 500–2250 50 0–250 0 50 0–250 0

1.89E+59 5.05E+44 1.56E+36 1.11E+27

−13.38 −8.80 −6.18 −3.40

95.23 90.36 87.13 83.67

8.42E+02 5.43E+03 1.08E+04 1.38E+04

50 0–20 0 0 500–2250 50 0–250 0 50 0–250 0

6.16E+61 1.30E+47 8.85E+37 2.41E+26

−14.27 −9.62 −6.80 −3.36

98.50 93.72 90.15 84.41

1.60E+02 1.18E+03 2.48E+03 3.27E+03

50 0–20 0 0 500–2250 50 0–250 0 50 0–250 0

2.53E+64 5.24E+50 5.71E+42 4.70E+37

−14.82 −10.49 −8.04 −6.40

99.32 94.80 91.77 91.56

8.53E+02 5.27E+03 9.91E+03 1.20E+04

50 0–20 0 0 500–2250 50 0–250 0 50 0–250 0

1.62E-04 7.55E+29 3.59E+28 2.10E+25

4.78 −5.30 −4.70 −3.62

−9.91 4.25 4.94 4.26

n/a n/a n/a 1.44E+13

50 0–90 0 500–1125 500–1375 500–1650

5.25E-20 1.95E+39 4.40E+29 6.46E+12

9.15 −8.27 −4.91 0.29

−14.28 12.81 13.58 9.52

n/a n/a n/a 1.83E+12

50 0–80 0 50 0–10 0 0 500–1125 50 0–150 0

2.35E+55 1.62E+50 9.41E+41 1.20E+32

−12.73 −10.78 −8.15 −5.20

17.69 20.44 20.31 18.40

n/a 1.01E+13 2.25E+13 1.10E+13

500–1375 500–1650 50 0–20 0 0 50 0–250 0

2.03E+61 6.40E+56 5.61E+44 1.64E+31

−13.37 −11.87 −8.31 −4.55

38.21 42.63 41.62 38.56

2.39E+13 1.49E+13 4.29E+12 3.50E+11

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

8.01E+52 8.13E+42 7.38E+30 3.53E+20

−11.08 −8.10 −4.62 −1.81

39.64 38.33 34.72 30.85

1.14E+12 8.23E+11 2.80E+11 4.11E+10

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

8.11E+28 1.29E+29 1.42E+29 1.28E+28

−4.61 −4.67 −4.68 −4.37

6.55 6.68 6.74 6.26

2.52E+13 2.59E+13 2.71E+13 2.76E+13

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

2.89E+69 7.65E+41 3.61E+25 6.18E+19

−17.99 −9.05 −3.89 −2.06

48.92 41.05 35.54 33.69

n/a n/a n/a 1.92E+08

50 0–80 0 50 0–10 0 0 500–1125 50 0–150 0

4.09E+47 3.84E+29 3.74E+22 1.46E+17

−10.88 −5.13 −2.91 −1.23

39.65 33.95 31.62 29.63

n/a n/a n/a 8.86E+08

50 0–90 0 500–1125 500–1375 500–1650

6.17E+70 8.57E+42 1.26E+26 2.57E+20

−18.39 −9.36 −4.04 −2.23

41.32 33.38 27.67 25.87

n/a n/a n/a 3.11E+09

50 0–80 0 50 0–10 0 0 500–1125 50 0–150 0

(continued on next page)

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159

Table 3 (continued) Reaction C15 H10 O (A-W5) → C15 H10 O (A-W4) k30 Torr k1 atm k10 atm k100 atm C15 H10 O (A-W4) → C15 H10 O (A-W1) k30 Torr k1 atm k10 atm k100 atm C15 H10 O (A-W4) → C15 H10 O (A-W5) k30 Torr k1 atm k10 atm k100 atm C15 H10 O (A-W4) → C15 H9 O + H (A-P2) k30 Torr k1 atm k10 atm k100 atm C15 H10 O (A-W4) → C15 H8 OH + H (A-P3) k30 Torr k1 atm k10 atm k100 atm C15 H10 O (A-W4) → C15 H9 (A) + OH k30 Torr k1 atm k10 atm k100 atm C15 H9 (B) + OH → C15 H10 O (B-W1) k30 Torr k1 atm k10 atm k100 atm C15 H9 (B) + OH → C15 H8 OH + H (B-P3) k30 Torr k1 atm k10 atm k100 atm C15 H9 (B) + OH → total k30 Torr k1 atm k10 atm k100 atm C15 H10 O (B-W1) → C15 H8 OH + H (B-P3) k30 Torr k1 atm k10 atm k100 atm C15 H10 O (B-W1) → C15 H9 (B) + OH k30 Torr k1 atm k10 atm k100 atm

A

α

Ea

k(1500 K)a

T range, K

3.28E+78 1.45E+48 3.99E+21 4.70E+14

−19.97 −10.13 −1.95 0.05

54.84 49.20 41.30 40.23

n/a n/a n/a 6.69E+08

50 0–80 0 50 0–10 0 0 500–1125 50 0–150 0

2.24E+47 1.65E+29 9.48E+21 5.17E+16

−10.72 −4.94 −2.65 −1.02

45.14 39.39 36.95 35.00

n/a n/a n/a 2.36E+08

50 0–90 0 500–1125 500–1375 500–1650

7.96E+81 1.31E+51 2.13E+23 3.46E+16

−20.98 −10.97 −2.42 −0.46

69.68 63.94 55.63 54.61

n/a n/a n/a 9.17E+06

50 0–80 0 50 0–10 0 0 500–1125 50 0–150 0

3.51E+40 7.27E+32 5.01E+31 2.00E+33

−7.74 −5.34 −4.95 −5.37

66.35 63.54 63.40 64.58

n/a 4.26E+06 7.45E+06 9.21E+06

500–1375 500–1650 50 0–20 0 0 50 0–250 0

3.77E+57 2.84E+40 4.23E+31 1.91E+30

−12.75 −7.42 −4.77 −4.39

86.55 80.90 77.11 76.40

n/a 1.21E+05 2.75E+05 2.23E+05

500–1375 500–1650 50 0–20 0 0 500–250

3.49E+65 1.37E+61 1.39E+53 3.75E+44

−14.94 −13.22 −10.65 −8.09

90.84 93.99 94.03 92.83

n/a 2.79E+05 6.06E+05 3.65E+05

500–1375 500–1650 50 0–20 0 0 50 0–250 0

9.95E+44 1.47E+37 3.63E+39 6.82E+38

−9.58 −7.17 −7.87 −7.65

12.72 9.62 10.92 10.57

5.33E+12 1.18E+13 1.24E+13 1.24E+13

500–1650 50 0–20 0 0 50 0–250 0 50 0–250 0

4.54E+58 1.14E+34 3.29E+33 2.54E+33

−12.84 −5.87 −6.01 −6.26

37.49 27.08 27.35 27.83

5.10E+12 4.48E+11 4.68E+10 4.70E+09

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

1.44E+45 5.32E+44 1.69E+39 6.40E+38

−9.55 −9.39 −7.77 −7.64

13.43 13.44 10.76 10.55

1.04E+13 1.23E+13 1.24E+13 1.24E+13

50 0–250 0 50 0–250 0 50 0–250 0 50 0–250 0

2.29E+86 3.47E+72 1.49E+67 4.04E+66

−20.95 −16.78 −15.19 −15.03

100.30 94.23 91.64 91.34

1.70E+05 2.94E+05 3.05E+05 3.06E+05

500–1650 50 0–20 0 0 50 0–250 0 50 0–250 0

1.55E+52 3.34E+45 3.83E+48 8.88E+47

−10.82 −8.76 −9.65 −9.46

90.68 88.10 89.72 89.41

4.10E+04 8.83E+04 9.25E+04 9.30E+04

500–1650 50 0–20 0 0 50 0–250 0 50 0–250 0

a Rate constants are not available (n/a) if an intermediate involved in the reaction is not stable at given conditions.

The critical TSs for the decarbonylation process are B-B4 and BB7 respectively lying 14.8 and 12.6 kcal/mol above the reactants; clearly, this reaction channel is expected to be further suppressed in the C15 H9 (B) + OH reaction as compared to C15 H9 (A) + OH and C5 H5 + OH. The B-W4 intermediate can lose an H from two different positions forming either B-P3 or B-P2. The latter is an analog of ortho-C5 H5 O (P2) lying 11.2 kcal/mol above the reactants. Interestingly, B-P2 is substantially destabilized with respect to the reactants as compared to P2 and A-P2, apparently because the extra H atom to be linked to the C atom in the edge between the five-member and six-member rings. B-W4 can also isomerize to B-W5 via B-B6 by 1,4-H shift from O to a C atom in the neighboring six-member ring. Next, B-W5 can split a hydrogen atom producing either B-P2 or B-P5, which resides 7.0 kcal/mol above the reactants and has the extra hydrogen in meta position rela-

tive to the CO group but in the adjacent six-member ring. At last, a C–C bond cleavage in B-W3 gives phenanthryl radical + HCO, 18.5 kcal/mol above the reactants. From the PES itself one can expect B-P3 to be the predominant reaction product, but there is also a high probability of re-dissociation of various intermediates back to the initial reactants since the energy difference between C15 H9 (B) + OH and B-P3 is only 1.7 kcal/mol. The kinetics calculations in the next section will shed light on this and other competitions. 3.5. Temperature- and pressure-dependent rate constants and product branching ratios for the C15 H9 + OH reactions Calculated rate constants for the C15 H9 (A) + OH reaction are illustrated in Fig. 6. Here, we can see a stronger dependence of the

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Fig. 4. Potential energy diagram for the C15 H9 (A) + OH reaction calculated at the G3(MP2,CC)//B3LYP/6-311G(d,p) level of theory. All relative energies are given in kcal/mol with respect to the initial reactants. Red curves show the decarbonylation pathways and blue curves indicate the most favorable pathways to the C15 H9 O + H products.

total rate constants (and hence, the rate constants for the formation of individual products) than in the case of the C5 H5 + OH reaction. At 1500 K, the fall-off of the total rate constants computed at 30 Torr, 1 10, and 100 atm from the HP limit values constitutes 22%, 20%, 16%, and 15%, respectively, and increases to 48– 42% at 1800 K and 89-87% at 2500 K (Fig. 6(a)). This behavior is attributed to the fact that the decarbonylation reaction channel, i.e., the formation of A-P1 from C15 H10 O intermediates is much less favorable than the formation of C4 H6 + CO (P1) from C5 H6 O; in relative terms, the energy of the critical TS along the decarbonylation pathway increases by ∼7 kcal/mol. This makes the re-dissociation of C15 H10 O much more competitive, especially at higher temperatures, and results in the observed fall-off behavior. At low temperatures, the C15 H9 (A) + OH reaction mostly produces collisionally stabilized C15 H10 O isomers A-W1 and A-W4, with the relative yield of A-W4 increasing with temperature and that of A-W1 decreasing (see Fig. 6(b) and (c) and Table S2 in Supplemental Material). The predominance of the A-W1 and A-W4 products is sustained up to 1125, 1375, 180 0, and 250 0 K at the pressures of 30 Torr, 1, 10, and 100 atm, respectively, and at higher temperatures, the formation of bimolecular products becomes more significant. Not surprisingly, the main bimolecular product is C15 H9 O + H (A-P2), which has the calculated branching ratio rising in the 10 0 0-250 0 K temperature range from 0-21% to 84% at 30 Torr, 1 and 10 atm (Table S4). At 150 0-180 0 K and 1 atm, the branching ratio of A-P2 is computed to be 57-92%; it slightly drops at the higher temperatures due to an increase of the yield of C15 H8 OH + H (A-P3). A-P3 is the sec-

ond noticeable bimolecular product but its branching ratio is significant only at very high temperatures of 1800 K and above and can reach ∼15% at 2500 K. The relative yield of the decarbonylation product A-P1 does not exceed 1% at all conditions considered. As mentioned above, at 100 atm, the stabilized A-W4 intermediate remains the dominant reaction product even at the highest temperature of 2500 K. At this pressure, the calculated branching ratio of A-P2 is as low as 1% at 1500 K, 5% at 1800 K, and increases to 20% at 2500 K. The stabilized (thermalized) C15 H10 O intermediates A-W1 and A-W4 can undergo further unimolecular decomposition, which becomes prevalent above 10 0 0 K (30 Torr), 1250 K (1 atm), 1500 K (10 atm), and 1800 K (100 atm). At the lower temperatures A-W1 isomerizes to A-W4 and A-W4 to A-W1 just establishing an equilibrium and then merging into A-W4 as the temperature increases. Upon the temperature rise above the values mentioned above, AW4 mostly decomposes to A-P2, with small (few percent) yields of the A-P3 channel and re-dissociation back to the reactants. The branching ratio of the re-dissociation increases above 10% at 10 and 100 atm at temperatures higher than 1800 K. Based on the calculated rate constants and product branching ratios, the mechanism of the C15 H9 (A) + OH reaction can be summarized as follows: (1) Well-skipping pathways:

C15 H9 (A) + OH → C15 H9 O + H (A-P2) → C15 H8 OH + H (A-P3) (a minor channel)

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Fig. 5. Potential energy diagram for the C15 H9 (B) + OH reaction calculated at the G3(MP2,CC)//B3LYP/6-311G(d,p) level of theory. All relative energies are given in kcal/mol with respect to the initial reactants. Red curves show the decarbonylation pathways and blue curves indicate the most favorable pathways to the C15 H9 O + H products.

(2) C15 H10 O stabilization/unimolecular decomposition pathways:

C15 H9 (A) + OH → C15 H10 O (A-W1) C15 H9 (A) + OH → C15 H10 O (A-W4) C15 H10 O (A-W1)  C15 H10 O (A-W4) C15 H10 O (A-W4) → C15 H9 O + H (A-P2) → C15 H8 OH + H (A-P3) (a minor channel) The competition between the well-skipping and C15 H9 O stabilization/dissociation pathways will be controlled by the reaction conditions, where higher pressures favor the latter and higher temperatures favor the former. We included rate expressions for the relevant reactions in Table 3. It is likely that the main reaction product, the C15 H9 O A-P2 radical can undergo further decarbonylation producing 1-methylene-phenalen-1-yl and then the process of oxidation/CO removal from C15 H9 (A) by OH can be mechanistically formulated in terms of two (the well-skipping pathway) or three (the stabilization/dissociation pathway) consecutive reactions. Calculated total rate constants for the C15 H9 (B) + OH reaction exhibit even stronger fall-off behavior at finite pressures than those for C15 H9 (A) + OH (Fig. 7(a)). The deviation from the HP limit values becomes apparent at ∼10 0 0 K and at 1500 K the finite

pressure rate constants are 68% and 62% lower than kHP at 30 Torr and 1-100 atm, respectively. At 1800 K, this difference increases to 89% and 83–84%, and at 2500 K the finite pressure rate constants drop to only 1-2% of kHP . The differences between rate constants computed at different finite pressures are rather small and the values computed for 1 atm can be used for higher pressure applications. The reaction outcome is controlled by the competition between stabilization of the B-W1 intermediate and formation of the C15 H8 OH + H (B-P3) product (Fig. 7(a)), whereas all other bimolecular products can be formed only in insignificant quantities. The stabilization of B-W1 prevails at lower temperatures, up to 1500 and 20 0 0 K at 30 Torr and 1 atm, respectively, and at these pressure and higher temperature B-P3 is the dominant product (see Table S3 in Supplemental Material). At the higher pressures of 10 and 100 atm, the stabilization process persists up to the highest considered temperature and the relative yield of B-P3 does not exceed 5% and 0.4%, respectively. Thus, the stabilization process is the most important reaction channel under conditions most relevant to combustion. The stabilized (thermalized) B-W1 intermediate can dissociate to B-P3 or back to the C15 H9 + OH reactants (Fig. 7(b) and Table S3). The relative yield of B-P3 decreases from 97% to ∼76% in the 10 0 0-1650 K temperature range at 30 Torr, from 97% to 56% at 10 0 0-20 0 0 K and 1 atm, from 97% to 41% at 10 0 0-250 0 at 10 and 100 atm, whereas the yield of C15 H9 + OH grows accordingly. Thus, the mechanism of the C15 H9 (B) + OH reaction can be formulated as follows:

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Fig. 6. Pressure-dependent total and product channel specific rate constants for various reactions related to C15 H9 (A) + OH: (a) total C15 H9 (A) + OH rate constants; (b) formation of various bimolecular products in the C15 H9 (A) + OH reaction; (c) stabilization of the C5 H10 O intermediates A-W1 and A-W4 in the C15 H9 (A) + OH reaction, and (d) unimolecular thermal decomposition of A-W1 and A-W4. Dotted, solid, dashed, and dash-dotted lines show rate constants calculated for pressures of 30 Torr, 1, 10, and 100 atm, respectively.

C15 H9 (B) + OH → C15 H10 O (B-W1) → C15 H8 OH + H (B-P3) (a minor channel) C15 H10 O (B-W1) → C15 H8 OH + H (B-P3) C15 H10 O (B-W1) → C15 H9 (B) + OH By analogy with hydroxycyclopentadienyl C5 H4 OH [35], the C15 H8 OH product is likely to further dissociate to a C15 H8 O analog of 2,4-cyclopentadienone C5 H4 O, which would then undergo the five-member ring opening and decarbonylation either unimolecularly or via an H-assisted reaction. Nevertheless, we can conclude that the “deep” embedding of the five-member ring like in the case of C15 H9 (B) strongly inhibits its oxidation by OH and the removal of CO, which can be realized only through a four-step reaction mechanism involving stabilization of intermediates followed by their relatively slow unimolecular decompositions. 4. Conclusions

Fig. 7. Pressure-dependent total and product channel specific rate constants for various reactions related to C15 H9 (B) + OH: (a) total and product channel specific C15 H9 (B) + OH rate constants; (b) unimolecular thermal decomposition of B-W1. Dotted, solid, dashed, and dash-dotted lines show rate constants calculated for pressures of 30 Torr, 1, 10, and 100 atm, respectively.

Ab initio calculations of the PES for the C5 H5 + OH reaction combined with VRC-TST and RRKM-ME calculations of the pressure- and temperature-dependent absolute reaction rate constants and those for individual unimolecular and bimolecular reaction channels allowed us to unravel the oxidation mechanism of cyclopentadienyl radical with OH and to quantify relative yields of various products under various conditions relevant to combustion. The results show that the reaction proceeds either by the well-skipping pathways without stabilization of the C5 H6 O intermediates leading to the bimolecular products ortho-C5 H5 O + H (P2), C5 H4 OH + H (P3), and C4 H6 + CO (P1), or via stabilization

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of the C5 H6 O intermediates W4 and W5 (preferred under the combustion conditions), which then undergo unimolecular decomposition to P2 and P1 or, to a lesser extent, back to the C5 H5 + OH reactants or to P3. The most energetically favorable pathway for the removal of CO, C5 H5 + OH → W1 → W4 → W6 → C4 H6 + CO, involves OH addition to cyclopentadienyl, 1,2-H shift from ipso to ortho position, 1,3-H shift from O to the other ortho position, and elimination of CO. Alternatively, the most favorable ortho-C5 H5 O product P2 is formed by H losses from W4 or W6 and the hydroxycyclopentadienyl product C5 H4 OH P3 is formed from W1 or W4. The ortho-C5 H5 O product can further decompose to C4 H5 + CO, whereas hydroxycyclopentadienyl is more likely to dissociate to 2,4-cyclopentadienone, which only then can undergo unimolecular or H-assisted decomposition with a removal of CO. The wellskipping and stabilization/dissociation pathways will compete depending on the reaction conditions, where higher pressures favor the stabilization/dissociation and higher temperature favor the well-skipping channels. At typical flame conditions of 1500 K and 1 atm, the computed relative yields of the P2, P3, and P1 products are 31%, 11%, and 13% (well-skipping channels), whereas 43% of the reactants are consumed with the formation of the stabilized C5 H6 O (W5) molecule. At the same conditions, W5 decomposes unimolecularly to form 37% of P1, 45% of P2 and 7% each of the initial reactants C5 H5 + OH and P3. The 1500 K/1 atm rate constants for C5 H5 + OH reaction and for the decomposition W5 are 6.2 × 10−11 cm3 molecule−1 s−1 and 7.1 × 103 s−1 , respectively, indicating that the lifetime of C5 H6 O would be on the order of a hundred μs. Similar calculations for the C15 H9 + OH reactions addressed the oxidation mechanism with OH of a five-member radical embedded in a sheet of six-member aromatic rings, as typical for an edge of a graphene sheet, a large PAH molecule, or a soot particle. The results demonstrate that embedding decreases the oxidation rate constants and hinder the decarbonylation process. For instance, for the C15 H9 (A) radical in which the five-member ring has two common edges with six-member rings, the reaction with hydroxyl is shown to proceed by well-skipping pathways forming mostly C15 H9 O + H (A-P2) and C15 H8 OH + H (A-P3) in a minor channel and C15 H10 O stabilization/decomposition pathways producing first C15 H10 O (A-W1/A-W4), which then decompose to A-P2 and A-P3. At 1500 K and 1 atm, the calculated relative yields are 39% for A-W4, 57% for A-P2, and 3% for A-P3, and A-W4 further dissociates producing 91% of A-P2, 6% of the initial C15 H9 (A) + OH reactants, and 3% of A-P3. The 1500 K/1 atm rate constant for the C15 H9 (A) + OH reaction decreases to 4.3 × 10−11 cm3 molecule−1 s−1 , by ∼30% as compared to that for C5 H5 + OH, whereas the lifetime of the most kinetically stable C15 H10 O isomer A-W4 drops to ∼0.2 μs. The removal of CO via the reaction with OH does not occur directly and the decarbonylation process can be completed only via subsequent unimolecular decomposition of the main reaction product C15 H9 O (A-P2). The removal of CO by OH becomes even less likely when the degree of embedding increases as in the C15 H9 (B) radical, where the five-member ring has three common edges with the surrounding six-member rings. The C15 H9 (B) + OH reaction is found to predominantly proceed by the stabilization/dissociation channel forming C15 H10 O (BW1), which the further dissociates to C15 H8 OH + H (B-P3) or back to the C15 H9 (B) + OH reactants, whereas the well-skipping pathway producing B-P3 directly is only minor. At 1500 K and 1 atm, the computed branching ratios are 96% and 4% for B-W1 and BP3, respectively, in the C15 H9 (B) + OH reaction and 77% and 23% for B-P3 and C15 H9 (B) + OH, respectively, in the decomposition of the reactants. The 1500 K/1 atm rate constant for C15 H9 (B) + OH drops to only a third of that for C5 H5 + OH, whereas the lifetime of the B-W1 intermediate is in the range of ∼3 μs. For the decarbonylation to take place, two more reaction are likely required to occur, first, dissociation of the C15 H8 OH product to a C15 H8 O

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analog of 2,4-cyclopentadienone C5 H4 O, and second, a removal of CO from C15 H8 O either unimolecularly or via an H-assisted mechanism. Since this is a four-step reaction mechanism involving stabilization of intermediates followed by their relatively slow unimolecular decompositions, the oxidation of a deeply embedded five-member ring by OH is not likely to be efficient. Acknowledgments This work was supported by Ministry of Education and Science of the Russian Federation under the Grant No. 14.Y26.31.0020 to Samara University and by the US Department of Energy, Basic Energy Sciences Grant DE-FG02-04ER15570 to Florida International University. A.M.M. would like to acknowledge the Instructional & Research Computing Center (IRCC, web: http://ircc.fiu.edu) at Florida International University for providing HPC computing resources that have contributed to the research results reported within this paper. We thank Yuri Georgievskii and Stephen Klippenstein for helpful discussions on VRC-TST calculations and for their Rotd computer code used to run VRC-TST calculations. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.combustflame.2017.09. 005. References [1] A. Roubaud, R. Minetti, L.R. Sochet, Oxidation and combustion of low alkylbenzenes at high pressure: comparative reactivity and auto- ignition, Combust. Flame 121 (20 0 0) 535–541. [2] N. Grumman, Northrop grumman petroleum product survey reports, Updated Annually, available at http://pps.ms.northropgrumman.com/. [3] T. Edwards, L.Q. Maurice, Surrogate mixtures to represent complex aviation and rocket fuels, J. Propul. Power 17 (2001) 461–466. [4] A.S. Violi, S. Yan, E.G. Eddings, A.F. Sarofim, S. Granata, T. Faravelli, E. Ranzi, Experimental formulation and kinetic model for JP- 8 surrogate mixtures, Combust. Sci. Technol 174 (2002) 399–417. [5] E.G. Eddings, S. Yan, W. Ciro, A.F. Sarofim, Formulation of a surrogate for the simulation of jet fuel pool fires, Combust. Sci. Technol 117 (2005) 715–739. [6] J.A. Cooke, M. Bellucci, M.D. Smooke, A. Gomez, A. Violi, T. Faravelli, E. Ranzi, Computational and experimental study of JP-8, a surrogate, and its components in counterflow diffusion flames, Proc. Combust. Inst 30 (2005) 439–446. [7] S. Humer, A. Frassoldati, S. Granata, T. Faravelli, E. Ranzi, R. Seiser, K. Seshadri, Experimental and kinetic modeling study of combustion of JP-8, its surrogates and reference components in laminar nonpremixed flows, Proc. Combust. Inst 31 (2007) 393–400. [8] T. Seta, M. Nakajima, A. Miyoshi, High-temperature reactions of OH radicals with benzene and toluene, J. Phys. Chem. A 110 (2006) 5081–5090. [9] H.X. Zhang, S.I. Ahonkhai, M.H. Back, Rate constants for abstraction of hydrogen from benzene, toluene, and cyclopentane by methyl and ethyl radicals over the temperature range 650-770 K, Can. J. Chem 67 (1989) 1541–1549. [10] M. Frenklach, Reaction mechanism of soot formation in flames, Phys. Chem. Chem. Phys. 4 (2002) 2028–2037. [11] T. Yu, M.C. Lin, Kinetics of phenyl radical reactions studied by the cavity-ring– down method, J. Am. Chem. Soc 115 (1993) 4371–4372. [12] T. Yu, M.C. Lin, Kinetics of the C6 H5 + O2 reaction at low temperatures, J. Am. Chem. Soc. 116 (1994) 9571–9576. [13] P.M. Sommeling, P. Mulder, R. Louw, D.V. Avila, J. Lusztyk, K.U. Ingold, Rate of reaction of phenyl radicals with oxygen in solution and in the gas phase, J. Phys. Chem. 97 (1993) 8361–8364. [14] P. Frank, J. Herzler, T. Just, C. Wahl, High-temperature reactions of phenyl oxidation, Symp. (Int.) Combust. 25 (1994) 833–840. [15] J. Schaugg, R.S. Tranter, H.-H. Grotheer, Transport phenomena in combustion, 8th International Symposium on Transport Phenomena in Combustion, Taylor & Francis, Washington, D. C. (1995), p. 130. CODEN: 63UGAB. [16] C. Barckholtz, M.J. Fadden, C.M. Hadad, Computational study of the mechanisms for the reaction of O2 with aromatic radicals, J. Phys. Chem. A 103 (1999) 8108–8117. [17] M.J. Fadden, C.M. Hadad, Unimolecular decomposition of the 2-oxepinoxy radical: A key seven-membered ring intermediate in the thermal oxidation of benzene, J. Phys. Chem. A 104 (20 0 0) 8121–8130. [18] P. Lindstedt, L. Maurice, M. Meyer, Thermodynamic and kinetic issues in the formation and oxidation of aromatic species, Faraday Discuss. 119 (2001) 409–432.

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