Kinetics of the Cyclopentadienyl + Acetylene, Fulvenallene + H, and 1

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J. Phys. Chem. A 2010, 114, 2275–2283

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Kinetics of the Cyclopentadienyl + Acetylene, Fulvenallene + H, and 1-Ethynylcyclopentadiene + H Reactions Gabriel da Silva,*,† John A. Cole,‡ and Joseph W. Bozzelli*,‡ Department of Chemical and Biomolecular Engineering, The UniVersity of Melbourne, Victoria 3010, Australia, and Department of Chemistry and EnVironmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102 ReceiVed: July 19, 2009; ReVised Manuscript ReceiVed: NoVember 24, 2009

Quantum chemical methods and statistical reaction rate theory are utilized to examine the kinetics and thermochemistry of three reactions occurring on the C7H7 potential energy surface: cyclopentadienyl (C5H5) + acetylene (C2H2), fulvenallene + H, and 1-ethynylcyclopentadiene + H. These reactions are relevant to the formation of polyaromatic hydrocarbons (PAHs) and the combustion of alkylated aromatics. Reaction of the resonantly stabilized C5H5 radical with C2H2 is an important PAH growth reaction; here we identify several new low-energy pathways connecting these reactants with fulvenallene + H, 1-ethynylcyclopentadiene + H, and the cycloheptatrienyl and benzyl radicals. The chemically activated C5H5 + C2H2 reaction is shown to form cycloheptatrienyl at low temperatures along with minor amounts of benzyl, which is the current evaluation in the literature. However, at typical combustion temperatures the C7H6 isomers 1-ethynylcyclopentadiene and fulvenallene are the main products. The fulvenallene + H reaction predominantly forms benzyl (among other C7H7 isomers), whereas the 1-ethynylcyclopentadiene reaction leads to C5H5 + C2H2 and fulvenallene + H as the major products. The resonantly stabilized vinylcyclopentadienyl radical is formed in both C7H6 + H processes and is proposed here as a significant C7H7 combustion intermediate. The reactions described here are believed to account for the C7H6 products observed in cyclopentene combustion, where we suggest they are a mixture of 1-ethynylcyclopentadiene and fulvenallene. The C7H6 + H reactions provide a mechanism for the conversion of 1-ethynylcyclopentadiene to fulvenallene and fulvenallene to benzyl. Introduction Polyaromatic hydrocarbon (PAH) molecules and coagulated soot particles formed in combustion are a significant health concern.1 The black carbon component of soot in the atmosphere is also a major contributor to anthropogenic global warming.2 A complete and fundamental understanding of the chemistry involved in PAH formation is important in minimizing sooting, but significant uncertainties remain with respect to even the initial stages of PAH formation (i.e., formation of the first and second aromatic rings).3 In soot formation, resonantly stabilized free radicals including cyclopentadienyl (C5H5) play key roles in production of the initial aromatic ring and in further PAH growth reactions. The reaction of C5H5 with acetylene (C2H2) is complex and is known to form a C7H7 species that can further react with acetylene to yield indene.4,5 Recent studies of the C7H7 potential energy surface have proposed that fulvenallene (C7H6) + H are the major products of benzyl decomposition.6,7 where benzyl is the most stable C7H7 isomer. Fulvenallene has been detected at high levels in the combustion8 and pyrolysis9 of toluene, and kinetic modeling supports benzyl decomposition as the source.10 Significant quantities of some C7H6 isomers have also been observed in cyclopentene flames,11 using photoionization mass spectrometry. Analysis of photoionization efficiencies at m/z ) 90 revealed that C7H6 was present as fulvenallene and/or 1-ethynylcyclopentadiene, presumably formed via the reaction * To whom correspondence should be addressed. E-mail: gdasilva@ unimelb.edu.au (G.d.S); [email protected] (J.W.B.). † The University of Melbourne. ‡ New Jersey Institute of Technology.

of C5H5 with C2H2. Pathways between benzyl and C5H5 + C2H2 are also known,7,12 providing a mechanism for the formation of benzyl and fulvenallene/1-ethynylcyclopentadiene + H in the C5H5 + C2H2 reaction. The C7H6 compounds fulvenallene and 1-ethynylcyclopentadiene have been proposed to play an important role in PAH formation.13 Both of these species possess weak C-H bonds (ca. 80 kcal mol-1) and will form the C7H5 fulvenallenyl radical in thermal, oxidizing systems.13 This resonantly stabilized radical shares properties of the PAH precursors cyclopentadienyl and propargyl and is thought to react with other radicals to directly form two- and three-ring PAHs.13 It has also been shown that fulvenallene can directly associate with acetylene to form an activated C9H8 hydrocarbon adduct that can rearrange to indene and dissociate to the 1-indenyl radical + H.14 Here we report the results of a thermochemical and kinetic study into the reaction of C5H5 with C2H2, with consideration of novel pathways to the C7H6 isomers fulvenallene and 1-ethynylcyclopentadiene + H. The reaction of these C7H6 species with free H atoms is also considered. The results of this study are expected to lead to an improved understanding of PAH formation and the combustion of alkylated aromatic hydrocarbons. Computational Methods Stationary points on the C7H7 potential energy surface are located at the B3LYP/6-31G(2df,p) level of theory. Enthalpies (298 K) are obtained using the composite G3SX model chemistry,15 which is broadly accurate for thermochemistry and kinetics in comparison to computational protocols of similar

10.1021/jp906835w  2010 American Chemical Society Published on Web 01/28/2010

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SCHEME 1: Key Species Related to the Present Studya

a

From left to right: cyclopentadienyl (C5H5), fulvenallene (C7H6), 1-ethynylcyclopentadiene (C7H6), benzyl (C7H7), cycloheptatrienyl (C7H7).

cost. The G3SX method reproduces enthalpies of formation in the G3/99 test set with mean absolute deviation of 0.88 kcal mol-1 (better when nonhydrogens are excluded),15 and barrier heights in the DBH24/08 database with mean unsigned error of 0.57 kcal mol-1.16 All electronic structure calculations are performed in Gaussian 03.17 Optimized geometries, vibrational frequencies, and G3SX energies are provided as Supporting Information. Standard heats of formation (∆fH°298) are calculated for minima and transition states from G3SX atomization enthalpies. Literature heats of formation (0 K) of 169.977 and 51.634 kcal mol-1 are used for the C and H atoms, respectively, with empirical H0 - H298 values of 0.251 and 1.010 kcal mol-1,18 as recently recommended.19 Entropies (S°298) and heat capacities [Cp(T), 300-2000 K] are reported for all species, calculated from standard statistical mechanical principles in ChemRate 1.5.2.20 Internal rotational modes are treated using a hindered rotor model, based on the results of relaxed B3LYP/631G(2df,p) rotor scans. Internal rotor scans in transition states were performed by freezing the breaking/forming bonds, as well as all adjacent bonds. High-pressure limit rate constants (k∞) are calculated from 300 to 2000 K for all elementary reactions, according to canonical transition state theory. Statistical factors accounting for degeneracy are incorporated into the reported pre-exponential factors (degeneracy of 2 for 3 T 4, 3 T 11, 10 T 14, 14 T 15,). Hydrogen-shift reactions are corrected for quantum mechanical tunnelling through the potential barrier according to the Eckart formalism,21 where barrier widths are approximated from the forward and reverse barrier heights (at 0 K) and the imaginary vibrational frequency of the transition state, as described previously.22 Rate constants between 300 and 2000 K are fit to a three-parameter Arrhenius expression (eq 1) in order to obtain the parameters Ea, A′, and n. All rate constants reported in this study are in units of s-1 (first order) or cm3 mol-1 s-1 (second order). Activation energies are in kcal mol-1.

k ) A'T ne-Ea/RT

(1)

Pressure and temperature dependent rate constants and branching ratios to products in chemically activated reaction mechanisms are obtained for 300 to 2000 K and 0.001 to 100 atm using master equation (ME) simulations for falloff, with qRRK theory for k(E), using the CHEMASTER program.23,24 In this study we have selected this qRRK approach for its efficiency in treating systems with many potential energy wells and reaction channels (12 wells in this system, with 15 transition states and intermediates/product sets), while providing similar results to full RRKM theory.6,23a,25 For this large system we were unable to perform time-dependent master equation simulations with full RRKM theory using the Chemrate program. Densities of states in the qRRK treatment are approximated

using a set of three reduced frequencies, with an internal rotor included where appropriate.24 We have previously shown reasonable agreement between the reduced and full frequency sets for density of state calculations using the exact count method.24 The master equation approach implemented here is described by Sheng et al.23b and for the treatment of chemically activated reactions assumes that the activated adduct is initially formed at steady-state, with continuous input flux from the activation channel balanced by output flux to product, stabilization, and reverse dissociation channels. Collisional energy transfer is described using an exponentialdown model, with 〈∆Edown〉 ) 500 cm-1. Argon is used as the third-body collider. Lennard-Jones parameters of 5.92 Å and 410 K are used for all C7H7 species (estimated to be the same as those of toluene). The qRRK/ME simulations were performed for energy levels up to 100 kcal mol-1 above the highest barrier, in 0.2 kcal mol-1 intervals. Apparent rate constants from the qRRK/ME calculations are fit to eq 1 to obtain input rate parameters for kinetic modeling. Results and Discussion Reaction Mechanism. Our proposed mechanism for reactions on the C7H7 energy surface is depicted in Scheme 2. Pathways are illustrated to the dissociated product sets/reactants C5H5 + C2H2, 1-ethynylcyclopentadiene + H, and fulvenallene + H. Additionally, benzyl, c-C7H7, and the vinylcyclopentadienyl radical (13) are formed as (relatively) stable intermediates. The mechanism for C5H5 + C2H2 forming c-C7H7 was reported by Fascella et al.,5 while those for isomerization of c-C7H7 with benzyl were discovered by Cavallotti et al.7 The reactions for decomposition of benzyl to fulvenallene + H were proposed in refs 6 and 7. In all instances numerous higher-energy pathways are available but are omitted in order to simplify the energy surface (some alternate pathways connecting C5H5 + C2H2 with the C7H6 isomers + H are depicted in the Supporting Information, while other relevant pathways for isomerization of C7H7 species are described in the literature5-7,26). Thermochemical Properties. Heats of formation are listed in Table 1 for all stationary points. Entropy and heat capacity data are provided in the Supporting Information. The calculated benzyl heat of formation, 51.00 kcal mol-1, is in good agreement with recent determinations of this value27 but is slightly larger than previously accepted values which are on the order of 49-50 kcal mol-1.28 The acetylene heat of formation is experimentally known to be 54.19 kcal mol-1,18 compared to our calculated value of 54.40 kcal mol-1. In our work fulvenallene is predicted to be more stable than 1-ethynylcyclopentadiene by 2.2 kcal mol-1 (respective heats of formation of 84.32 and 86.56 kcal mol-1), reflecting the results of Hansen et al.11 The cyclopentadienyl radical heat of formation is calculated to be 64.16 kcal mol-1, whereas numerous experimental and theoretical evaluations generally place it in the range of 62-64 kcal mol-1.29 The calculated cycloheptatrienyl radical heat of formation is

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SCHEME 2: Proposed Mechanism for Reactions on the C7H7 Energy Surface

66.66 kcal mol-1, consistent with respective experimental and theoretical values of 6530 and 67.231 kcal mol-1. To our knowledge experimental heats of formation are unavailable for the remaining species. Both the C5H5 and c-C7H7 radicals experience significant Jahn-Teller distortion, which has a large effect on their entropy. We have modeled the C5H5 radical using the 2A2 C2V structure for the electronic energy, along with the scaled D5h frequencies of Kiefer et al.,32 following their rigorous work on the thermodynamic properties of this molecule. The E′2 bending modes are described using 1053 cm-1 frequencies, with 1542 cm-1 for the E′2 stretching modes. The rotational symmetry is 10, and the electronic degeneracy 2. This analysis provides

similar S°(T) values to the detailed calculations of Kiefer et al.32 Less information is available on the thermochemical properties of c-C7H7. We have attempted to account for Jahn-Teller effects using the 2A2 C2V structure for the electronic energy and vibrational frequencies but with the low-frequency E′2 stretching mode made degenerate with the higher-frequency vibration (1537.5 cm-1). The rotational symmetry is 14, and the electronic degeneracy 2 (n.b., for all other species rotational symmetry is 1, except for benzyl and C2H2, where it is 2). Elementary Rate Constants. Rate constants in the highpressure limit have been calculated for elementary reactions according to canonical transition state theory, and the fitted rate parameters Ea, A′, and n are provided in Table 2. Values for

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TABLE 1: Standard Enthalpies of Formation (∆fH°298, kcal mol-1) for All Stationary Points in the Present Studya ∆fH°298 C5H5 (1) C2H2 (2) 3 4 c-C7H7 (5) 6 7 8 benzyl (9) 10 11 1-ethynylcyclopentadiene (12) 13 14 15 fulvenallene (16) TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 TS11 TS12 TS13 TS14 TS15 a

64.16 54.40 112.17 95.43 66.66 103.81 109.57 103.11 51.00 102.10 115.24 86.56 70.92 109.86 89.09 84.32 129.52 121.59 120.08 130.90 133.79 109.35 106.20 111.55 120.84 132.43 141.46 130.19 138.56 126.68 136.93

Minima and transition state numbering is defined in Figure 1.

the barrierless fulvenallene + H reaction (and its reverse) are taken from ref 6, where they were calculated using variational transition state theory. Knyazev and Slagle4 observed C7H7 formation as a secondary product in the C3H3 + C2H2 reaction and attributed it to the C5H5 + C2H2 reaction, with C7H7 being consumed by C2H2 (forming C9H8 + H). Fitting concentration profiles at 1000 K to this simple three-reaction mechanism, they obtained a pseudofirst-order reaction rate of 39.3 s-1, where [C2H2] was 4.53 × 1016 molecules cm-3. This corresponds to a rate constant of 5.2 × 108 cm3 mol-1 s-1 for the C5H5 + C2H2 f C7H7 reaction. Our transition state calculations result in a larger high-pressure limit rate constant of 9.6 × 109 cm3 mol-1 s-1 for this reaction. However, because of a significant reverse reaction to C5H5 + C2H2 in the chemically activated system (vide infra), the overall rate constant to stabilized C7H7 isomers is around 2 × 109 cm3 mol-1 s-1 (at similar pressures). Given the uncertainties in these theoretical and experimental rate constants, agreement between the two is relatively good. C7H7 Energy Surface. An energy diagram is depicted in Figure 1 for the C5H5 + C2H2 mechanism (for clarity, the pathway to fulvenallene via c-C7H7 and benzyl is drawn in blue). This energy surface is used to study the bimolecular C5H5 + C2H2 reaction, along with the 1-ethynylcyclopentadiene and fulvenallene + H reactions. Unimolecular isomerization and decomposition reactions of each C7H7 isomer to its direct products is also considered, with qRRK/ME rate parameters at different pressures available in the Supporting Information. In Figure 1 we observe that C2H2 addition produces a mildly activated C7H7* adduct (3), with around 18 kcal mol-1 excess vibrational energy over the reactants. The only forward reaction

path with energy below the entrance channel is for isomerization of 3 to c-C7H7 (5), via 4, where the highest barrier is around 8 kcal mol-1 below the entrance transition state. The barrier reported here for C2H2 addition to C5H5 is similar to that calculated by Fascella et al.,5 and the same applies for the further reactions leading to c-C7H7. Following the formation of c-C7H7, some fraction may isomerize further to benzyl in a process controlled by TS5 (4.3 kcal mol-1 above the entrance channel). The activated C7H7* adduct produced in the C5H5 + C2H2 association reaction is also expected to isomerize to 11 in a process controlled by TS10. This transition state is similar in energy to TS1, and around 10 kcal mol-1 above TS2, although it may still play some role in this reaction mechanism. Once formed, 11 can isomerize to the vinylcyclopentadienyl radical (13) with a barrier of 15.0 kcal mol-1, dissociate to 1-ethynylcyclopentadiene + H with a 26.2 kcal mol-1 barrier, or react back to 3 with a barrier of 17.2 kcal mol-1. The further reaction of 13 is expected to produce fulvenallene + H and benzyl (where the benzyl path is energetically favored, and the fulvenallene + H paths are entropically favored). The vinylcyclopentadienyl radical is resonantly stabilized, with a heat of formation similar to that of well-known c-C7H7. Accordingly, it may exist at significant concentrations in C5 flames and related combustion systems. Branching ratios for the formation of 4 and 11 from 3 are plotted in Figure 2, from their high-pressure limit rate constants. We find that while isomerization to 4 (and therefore probably c-C7H7) is the only important channel at low temperatures, significant quantities of 11 are formed at higher temperatures, and this actually becomes the dominant channel above around 2500 K. This can be explained by the loss of an internal rotor in TS2, resulting in a considerably smaller pre-exponential factor. For the chemically activated C5H5 + C2H2 reaction mechanism, Figure 2 indicates that isomerization to 11 should play a role at higher energies; branching ratios between the different product sets may also vary with pressure (due to changes in collisional energy transfer). The energy surface developed here is also useful in understanding the c-C7H7 and benzyl decomposition reactions. Benzyl can decompse to fulvenallene + H and to C5H5 + C2H2 with similar barriers (85.4 and 82.8 kcal mol-1, respectively), both consistent with the experimental activation energy (reported to be in the range of 72-97 kcal mol-1).33 The observation of C7H6 species as the main benzyl radical decomposition products34 suggests that this pathway is favored in terms of entropy, although the dissociation of benzyl to C5H5 + C2H2, followed by C5H5 + C2H2 f C7H6 + H, may also contribute. Decomposition of c-C7H7 is expected to produce C5H5 + C2H2, with the highest barrier being 62.9 kcal mol-1 above c-C7H7. This barrier is substantially lower than that required for isomerization to benzyl via 6 f 7 f 8 (67.1 kcal mol-1), or to benzyl or the C7H6 + H products via 11. Cyclopentadiene (C5H5) + Acetylene (C2H2). Pressuredependent rate constants have been obtained in the C5H5 + C2H2 reaction mechanism from qRRK/ME simulations. To simplify the mechanism benzyl was treated as an irreversible sink, where 6 and 10 directly produce benzyl, without the reverse reaction processes included. The isomerization of benzyl to c-C7H7 can be included as a secondary reaction in modeling the C5H5 + C2H2 process. Collisional stabilized 3 and 4 are assumed to proceed exclusively to c-C7H7, with 10 proceeding to benzyl; i.e., c-C7H7 is the sum of 3, 4, and 5, while benzyl is the sum of 9 and 10. Rate constants for important reactions in the C5H5 + C2H2 association mechanism are plotted in Figure 3, at 1

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Figure 1. Energy diagram for reactions on the C7H7 energy surface, featuring G3SX enthalpies of formation (kcal mol-1).

TABLE 2: Rate Parameters for Elementary Reactions on the C7H7 Energy Surfacea forward C5H5 (1) + C2H2 (2) f 3 [TS1] 3 f 4 [TS2] 4 f c-C7H7 (5) [TS3] c-C7H7 (5) f 6 [TS4] 6 f 7 [TS5] 7 f 8 [TS6] 8 f benzyl (9) [TS7] benzyl (9) f 10 [TS8] 10 f 14 [TS9] 3 f 11 [TS10] 11 f 1-ethynylcyclopentadiene (12) + H [TS11] 11 f 13 [TS12] 13 f 14 [TS13] 14 f 15 [TS14] 13 f fulvenallene (16) + H [TS15] 15 f fulvenallene (16) + H 6 a

reverse

A′

Ea

n

A′

Ea

n

4.08 × 105 9.25 × 1011 4.51 × 1012 5.50 × 108 2.48 × 106 2.10 × 1012 1.24 × 1012 1.98 × 1012 2.80 × 1013 1.01 × 1010 4.06 × 1010 7.42 × 104 1.17 × 104 6.21 × 108 4.16 × 1010 1.02 × 1013

10.80 9.81 25.25 62.12 26.83 0.30 3.62 61.00 19.35 19.17 26.18 10.59 62.71 15.29 65.98 46.70

2.24 0.16 0.26 1.56 1.85 0.14 0.31 0.50 0.15 0.97 1.16 2.23 2.78 1.38 1.24 0.34

2.36 × 1012 6.35 × 1012 1.72 × 1012 1.37 × 108 1.47 × 106 7.85 × 1012 3.45 × 1012 4.52 × 1012 1.69 × 1011 5.61 × 1010 4.14 × 108 2.80 × 104 1.17 × 103 1.98 × 1010 3.10 × 109 1.27 × 1011

17.86 26.73 53.73 25.06 21.05 6.88 55.69 10.05 11.21 16.28 2.76 54.81 23.50 36.35 0.60 -0.073

0.63 0.34 0.68 1.36 1.90 -0.01 0.25 0.19 0.59 0.81 1.50 2.39 3.07 0.94 1.51 0.85

Ea in kcal mol-1, A′T n in s-1 or cm3 mol-1 s-1 (with T in K). High-pressure limit values.

Figure 2. Branching ratios between isomerization of 3 to 4 and to 11, in the high-pressure limit.

atm. Only species that contribute at least 1% of the total reaction flux at a temperature in our studied range are included. Branching ratios to the product sets c-C7H7, benzyl, 1-ethynylcyclopentadiene + H, fulvenallene + H, and 13 are shown in Figure 4. Fitted rate parameters are provided in Table 3 for 1 atm and in the Supporting Information at other pressures. Rate

expressions for isomerization of each C7H7 isomer, as a function of pressure, are also found in the Supporting Information. Our results indicate that reverse reaction back to the reactants C5H5 + C2H2 is rapid, especially at higher temperatures, and the total rate constant for the reaction of C5H5 + C2H2 to new products will therefore lie somewhat below the high-pressure

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Figure 3. qRRK/ME rate constants in the C5H5 + C2H2 reaction, at 1 atm.

Figure 4. Branching ratios to important products in the C5H5 + C2H2 reaction, at 1 atm.

TABLE 3: Rate Parameters for Overall Reactions on the C7H7 Energy Surface, at 1 atma C5H5 (1) + C2H2 (2) f c-C7H7 (5) C5H5 (1) + C2H2 (2) f benzyl (9) C5H5 (1) + C2H2 (2) f fulvenallene (16) + H C5H5 (1) + C2H2 (2) f 1-ethynylcyclopentadiene (12) + H C5H5 (1) + C2H2 (2) f 13 fulvenallene (16) + H f C5H5 (1) + C2H2 (2) fulvenallene (16) + H f benzyl (9) fulvenallene (16) + H f 1-ethynylcyclopentadiene (12) + H fulvenallene (16) + H f 13 fulvenallene (16) + H f 15 1-ethynylcyclopentadiene (12) + H f C5H5 (1) + C2H2 (2) 1-ethynylcyclopentadiene (12) + H f fulvenallene (16) + H 1-ethynylcyclopentadiene (12) + H f c-C7H7 (5) 1-ethynylcyclopentadiene (12) + H f 11 1-ethynylcyclopentadiene (15) + H f 13 a

A′

Ea

n

1.27 × 1043 7.57 × 107 6.96 × 10-5 8.17 × 1011 1.08 × 1032 1.22 × 10-6 4.37 × 1012 9.40 × 10-4 3.42 × 1025 9.16 × 1063 5.81 × 1016 2.29 × 10-15 1.77 × 1060 1.71 × 10105 1.16 × 1031

21.72 34.42 30.93 27.43 27.21 11.04 8.42 16.04 5.68 16.11 7.87 9.26 18.97 24.60 11.32

-9.8 1.50 5.17 0.33 -6.19 6.15 0.67 5.34 -3.54 -15.92 -0.90 8.61 -15.06 -31.09 -5.65

Ea in kcal mol-1, A′Tn in s-1 or cm3 mol-1 s-1 (with T in K).

limit rate constant of the association reaction (particularly for T g 1000 K). At temperatures below around 1500 K, c-C7H7 is the dominant product of the C5H5 + C2H2 reaction, as is

conventionally thought. At high temperatures 1-ethynylcyclopentadiene + H becomes the major product set, accounting for around 70% of the total forward reaction flux at 2000 K.

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Figure 5. qRRK/ME rate constants in the fulvenallene + H reaction, at 1 atm.

Figure 6. Branching ratios to important products in the fulvenallene + H reaction, at 1 atm.

Similarly, the production of fulvenallene + H increases with increasing temperature, comprising around 20% of the products seen at 2000 K. Predominantly, fulvenallene is produced by C-H scission in 13, rather than 15. The above processes explain C7H6 formation in C5 hydrocarbon combustion, where we propose that both 1-ethynylcyclopentadiene and fulvenallene contribute to total C7H6. Somewhat surprisingly, benzyl is a relatively unimportant product in the C5H5 + C2H2 reaction, even at high temperatures (3% of the products at 2000 K). Benzyl can, however, be produced in further reactions of the C5H5 + C2H2 products. Most benzyl formed directly in the C5H5 + C2H2 reaction comes from isomerization of c-C7H7. Finally, at intermediate temperatures there is some collisional stabilization of the C7H7 isomer 13, the vinylcyclopentadienyl radical. At the temperatures at which this radical is formed, it is expected to predominantly dissociate to fulvenallene + H, although it may exist for long enough to participate in some bimolecular chemistry. All other reaction products are negligible. Fulvenallene + H. Fulvenallene is the most stable isomer on the C7H6 energy surface and is known to form in the decomposition of benzyl and in the reaction of C5H5 with C2H2. Further reactions of fulvenallene in thermal systems, however,

are not well understood. We have investigated the kinetics of the fulvenallene + H reaction, using the energy surface depicted in Figure 1. Two separate chemically activated reaction mechanisms are considered, where H associates with fulvenallene at either a ring site or at the allene dCd site, producing 15 and 13, respectively. Barriers for H addition at other locations in fulvenallene are larger, and these processes are not considered here. The assumptions made above for the C5H5 + C2H2 reaction are also used here in the fulvenallene + H qRRK/ME calculations. Calculated rate constants for important products in the fulvenallene + H mechanisms, at 1 atm, are plotted in Figure 5, with branching ratios shown in Figure 6. Rate constants to the different channels are the sum of the two separate chemically activated reactions. Reverse reaction to fulvenallene + H is significant here, especially at ca. 1500 K and above, but is less significant than the reverse dissociation process in the C5H5 + C2H2 reaction system. The benzyl radical is the major product in the fulvenallene + H reaction at higher temperatures, and the process C5H5 + C2H2 f fulvenallene + H f benzyl therefore provides a mechanism for benzyl as a C7H7 product in C5 hydrocarbon combustion. Benzyl can also be produced by H atom assisted

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Figure 7. qRRK/ME rate constants in the 1-ethynylcyclopentadiene + H reaction, at 1 atm.

Figure 8. Branching ratios to important products in the 1-ethynylcyclopentadiene + H reaction, at 1 atm.

isomerization of c-C7H7.12 Direct formation of 1-ethynylcyclopentadiene + H, C5H5 + C2H2, and c-C7H7 is relatively unimportant in the fulvenallene + H reaction at 1 atm and above, due to the collisional stabilization of C7H7 precursors like 13 (at intermediate temperatures) and 15 (at low temperatures). It is likely that these species will rapidly isomerize to benzyl or dissociate to fulvenallene + H, with slower reactions to other products. The broad temperature range for the production of quenched 13 supports this species as a stable C7H7 combustion intermediate. 1-Ethynylcyclopentadiene + H. This study also considers the 1-ethynylcyclopentadiene + H reaction process, again proceeding via the C7H7 energy surface depicted in Figure 1 (along with the same assumptions used when studying the above two reactions). The C7H6 isomer 1-ethynylcyclopentadiene is less stable than fulvenallene but is shown here to be a major product in the C5H5 + C2H2 reaction. Rate constants to important products are shown in Figure 7, with branching ratios in Figure 8. The 1-ethynylcyclopentadiene + H reaction predominantly leads to C5H5 + C2H2 at relevant combustion temperatures (branching ratios between 0.6 and 0.8 from ca. 800 to 2000 K).

At temperatures above around 1500 K, fulvenallene + H is also an important product set, constituting 10-20% of the total reaction products. Considering these two major product sets, 1-ethynylcyclopentadiene formed in the C5H5 + C2H2 reaction is expected to either react back to C5H5 + C2H2 or forward to fulvenallene + H. Comparatively, both processes are relatively slow in the fulvenallene + H reaction. Accordingly, fulvenallene may be present at similar or higher levels than 1-ethynylcyclopentadiene in cyclopentene flames, although further experimental work, along with kinetic modeling, is required in order to better understand the role of these two C7H6 isomers in combustion processes. The 1-ethynylcyclopentadiene + H reaction is also observed to form significant quantities of c-C7H7, particularly at low to intermediate temperatures. Other important collisional stabilized C7H7 isomers in this reaction mechanism are 11 and 13, whereas the production of benzyl is negligible. Conclusions Several new pathways are identified on the C7H7 energy surface, connecting C5H5 + C2H2, fulvenallene + H, 1-ethynylcyclopentadiene + H, and the heptatrienyl and benzyl

Kinetics of Reactions on the C7H7 Surface radicals. Kinetic simulations reveal that the C5H5 + C2H2 reaction forms the heptatrienyl radical at low temperatures, with mostly 1-ethynylcyclopentadiene and fulvenallene + H at higher temperatures. This result explains the observation of C7H6 isomers in cyclopentadiene flames. The 1-ethynylcyclopentadiene + H reaction produces mostly C5H5 + C2H2 and fulvenallene + H, whereas the fulvenallene + H reaction leads mostly to benzyl, in a relatively slow reaction. These processes provide a mechanism for the conversion of 1-ethynylcyclopentadiene to fulvenallene. Additionally, while benzyl is formed in relatively small amounts by the direct C5H5 + C2H2 reaction, it may arise from the secondary fulvenallene + H process. The C7H7 radical vinylcyclopentadienyl is also formed as a stable intermediate and may contribute to C7H7 isomers observed in flames. Acknowledgment. The authors acknowledge partial support for this work from an ExxonMobil education Award and from an STTR contract to Reaction Engineering International and NJIT from Wright Patterson Air Force Base (contract number FA8650-06-C-2658). Supporting Information Available: Optimized structures; vibrational frequencies; G3SX energies; entropy and heat capacity data; rate constant expressions from 0.0001 to 1000 atm; alternate pathways between C5H5 + C2H2 and C7H6 + H. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Dockery, D. W.; Pope, C. A.; Xu, X.; Spengler, J. D.; Ware, J. H.; Fay, M. E.; Ferris, B. G.; Speizer, F. E. New Engl. J. Med. 1993, 329, 1753. (2) Ramanathan, V.; Carmichael, G. Nat. Geosci. 2008, 1, 221. (3) (a) Richter, H.; Howard, J. B. Prog. Energy Combust. Sci. 2000, 26, 565. (b) Frenklach, M. Phys. Chem. Chem. Phys. 2002, 4, 2028. (4) Knyazev, V. D.; Slagle, I. R. J. Phys. Chem. A 2002, 106, 5613. (5) Fascella, S.; Cavallotti, C.; Rota, R.; Carra`, S. J. Phys. Chem. A 2005, 109, 7546. (6) da Silva, G.; Cole, J. A.; Bozzelli, J. W. J. Phys. Chem. A. 2009, 113, 6111. (7) Cavallotti, C.; Derudi, M.; Rota, R. Proc. Comb. Inst. 2009, 32, 115. (8) Li, Y.; Zhang, L.; Tian, Z.; Yuan, T.; Wang, J.; Yang, B.; Qi, F. Energy Fuels 2009, 23, 1473. (9) Zhang, T.; Zhang, L.; Hong, X.; Zhang, K.; Qi, F.; Law, C. K.; Ye, T.; Zhao, P.; Chen, Y. Combust. Flame 2009, 156, 2071. (10) Detilleux, V.; Vandooren, J. J. Phys. Chem. A 2009, 113, 10913. (11) Hansen, N.; Kasper, T.; Klippenstein, S. J.; Westmoreland, P. R.; Law, M. E.; Taatjes, C. A.; Kohse-Ho¨inghaus, K.; Wang, J.; Cool, T. A. J. Phys. Chem. A 2007, 111, 4081. (12) Cavallotti, C.; Mancarella, S.; Rota, R.; Carra`, S. J. Phys. Chem. A 2007, 111, 3959.

J. Phys. Chem. A, Vol. 114, No. 6, 2010 2283 (13) da Silva, G.; Bozzelli, J. W. J. Phys. Chem. A 2009, 113, 12045. (14) da Silva, G.; Bozzelli, J. W. J. Phys. Chem. A 2009, 113, 8971. (15) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 2001, 114, 108. (16) Zheng, J.; Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2009, 5, 808. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (18) Chase, M. W., Jr. J. Phys. Chem. Ref. Data, Monograph 9 1998, 1. (19) da Silva, G.; Moore, E. E.; Bozzelli, J. W. J. Phys. Chem. A 2009, 113, 10264. (20) Mokrushin, V.; Bedanov, V.; Tsang, W.; Zachariah, M.; Knyazev, V. ChemRate, version 1.5.2; National Institute of Standards and Testing: Gaithersburg, MD, 2006. (21) Eckart, C. Phys. ReV. 1930, 35, 1303. (22) (a) da Silva, G. Chem. Phys. Lett. 2009, 474, 13. (b) da Silva, G.; Bozzelli, J. W.; Asatryan, R. A. J. Phys. Chem. A 2009, 113, 8596. (23) (a) Chang, A. Y.; Bozzelli, J. W.; Dean, A. M. Z. Phys. Chem. 2000, 214, 1533. (b) Sheng, C. Y.; Bozzelli, J. W.; Dean, A. M.; Chang, A. Y. J. Phys. Chem. A 2002, 106, 7276. (24) Bozzelli, J. W.; Chang, A. Y.; Dean, A. M. Int. J. Chem. Kinet. 1997, 29, 161. (25) Lee, J.; Chen, C.-J.; Bozzelli, J. W. J. Phys. Chem. 2002, 106, 7155. (26) Jones, J.; Bacskay, G. B.; Mackie, J. C. J. Phys. Chem. A 1997, 101, 7105. (27) Sivaramakrishnan, R. S.; Tranter, R. S.; Brezinsky, K. J. Phys. Chem. A 2006, 110, 9388. (28) See discussion on page 290 of: da Silva, G.; Bozzelli, J. W. Proc. Comb. Inst. 2009, 32, 287. (29) Moskaleva, L. V.; Lin, M. C. Int. J. Chem. Kinet. 2004, 36, 139. (30) Vincow, G.; Dauben, H. J., Jr.; Hunter, F. R.; Volland, W. V. J. Am. Chem. Soc. 1969, 91, 2823. (31) Smith, B. J.; Hall, N. E. Chem. Phys. Lett. 1997, 279, 165. (32) Kiefer, J. H.; Tranter, R. S.; Wang, H.; Wagner, A. F. Int. J. Chem. Kinet. 2001, 33, 834. (33) (a) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just, T.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J. J. Phys. Chem. Ref. Data 1992, 21, 411. (b) Jones, J.; Bacskay, G. B.; Mackie, J. C. J. Phys. Chem. A 1997, 101, 7105. (c) Oehlschlaeger, M. A.; Davidson, D. F.; Hanson, R. K. J. Phys. Chem. A 2006, 110, 6649. (34) (a) Fro¨chtenicht, R.; Hippler, H.; Troe, J.; Toennies, J. P. J. Photochem. Photobiol., A. 1994, 80, 33. (b) Eng, R. A.; Gebert, A.; Goos, E.; Hippler, H.; Kachiani, C. Phys. Chem. Chem. Phys. 2002, 4, 3989.

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