Kinetics of the CH3 + C5H5 Reaction: A Theoretical Study - The

Article pubs.acs.org/JPCA

Kinetics of the CH3 + C5H5 Reaction: A Theoretical Study Vladislav S. Krasnoukhov,† Denis P. Porfiriev,†,‡ Igor P. Zavershinskiy,† Valeriy N. Azyazov,*,†,‡ and Alexander M. Mebel*,†,§ †

Samara National Research University, Samara 443086, Russia Lebedev Physical Institute, Samara 443011, Russia § Department of Chemistry and Biochemistry, Florida International University, Miami, Florida 33199, United States ‡

S Supporting Information *

ABSTRACT: Formation of fulvene and benzene through the reaction of cyclopentadienyl (C5H5) with methyl radical (CH3) and consequent dissociation of its primary C6H7 products has been studied using ab initio and theoretical kinetics calculations. The potential energies and geometries of all involved species have been computed at the CCSD(T)-F12/cc-pVTZ-f12//B2PLYPD3/ aug-cc-pVDZ level theory. Multichannel/multiwell RRKM-Master Equation calculations have been utilized to produce phenomenological pressure- and temperature-dependent absolute and individual-channel rate constants for various reactions at the C6H8 and C6H7 potential energy surfaces. The kinetic scheme combining the primary and secondary reactions has been used to generate the overall rate constants for the production of fulvene and benzene and their branching ratios. Analyses of the kinetic data revealed that at low pressures (0.01 atm) benzene formation prevails, with branching ratios exceeding 60%, whereas at the highest pressure (100 atm) fulvene formation is prevalent, with the branching ratio of benzene being lower than 40%. At intermediate pressures (1 and 10 atm) the two product channels compete and fulvene formation is preferable at temperatures above 1600 K. The results demonstrate that a five-member ring can be efficiently transformed into an aromatic six-member ring by methylation and corroborate the potentially important role of the methyl radical in the mechanism of PAH growth where CH3 additions alternate with H abstractions and acetylene additions.

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INTRODUCTION The cyclopentadienyl (C5H5) and methyl (CH3) radicals play an important role in the formation and growth of polycyclic aromatic hydrocarbons (PAHs), which serve as soot precursors, due to their reactivity and relatively large concentrations in flames.1−7 Various pathways exist for the formation of the resonantly stabilized cyclopentadienyl radical in the combustion zones. As illustrated on Figure 1, some of them are related to the oxidation of the first aromatic ring−benzene (C6H6). Taatjes et al.8 examined product branching ratios of the reaction between benzene and O(3P) over the temperature range 300−1000 K at pressures of 1−10 Torr using pulsed-laser photolysis in a slowflow reactor and the multiplexed chemical kinetics photoionization mass spectrometer. They identified the following product channels C6H6 + O → C5H5 + H + CO

pentadiene (C5H6) (1c), and phenoxy radical (C6H5O) (1d), whose branching ratios are close and vary in 21−33% and 18− 33% ranges, respectively. Reactions of benzene with OH and CH3 radicals and hydrogen atom

(1b)

→ C5H6 + CO

(1c)

→ C6H5O + H

(1d)

C6H6 + CH3 → C6H5 + CH4

(2b) (2c) 9,10

result in the formation of the phenyl radical (C6H5), which can react with an atomic oxygen, O2, and/or cyclopentadiene (C5H6) to produce the C5H5 radical:11−13 C6H5 + O → C5H5 + CO

(3a)

C6H5 + C5H6 → C5H5 + C6H6

(3b)

C6H5 + O2 → C5H5 + O + CO/c‐C5H5 + CO2

(3c)

Phenol formed in reaction 1b can decompose via the following processes C6H5OH → C6H5O + H

forming cyclopentadienyl radical (1a) with a less than 3% branching ratio for all the tested conditions (700−900 K, 4 and 10 Torr), phenol (C6H5OH) (1b), which is generally the predominant species with a 33−58% branching ratio, cyclo© 2017 American Chemical Society

(2a)

C6H6 + H → C6H5 + H 2

(1a)

→ C6H5OH

C6H6 + OH → C6H5 + H 2O

(4a)

Received: October 5, 2017 Revised: November 8, 2017 Published: November 8, 2017 9191

DOI: 10.1021/acs.jpca.7b09873 J. Phys. Chem. A 2017, 121, 9191−9200

Article

The Journal of Physical Chemistry A C5H5 + CH3 → C6H6 + 2H → C5H4CH 2 + 2H

(7a) (7b)

and second via H-assisted isomerization of fulvene (C5H4CH2) to benzene5,19,20 C5H4CH 2 + H → C6H6 + H

The reaction of cyclopentadienyl and methyl radicals was considered in a few works.2,5−7 Moskaleva at al.6 investigated the potential energy surface (PES) for the reaction (7) using the ab initio G2M(rcc,MP2) and B3LYP/6-311G(d,p) methods. They found several reaction pathways leading to the formation of fulvene. Sharma et al.2 calculated high-pressure-limit and pressure-dependent rate coefficients using RRKM−Master Equation theory and thermochemical parameters obtained using the CBS-QB3 level of quantum chemical calculations for the c-C5H5 + CH3 system. They identified product channels as C5H4CH2 + H2 and Ri + H, where Ri are various isomers of the C6H7 radical. Earlier, Melius at al.5 found reaction pathways resulting in the formation of fulvene and various C6H7 isomers using the BAC-MP4 and BAC-MP2 methods. Though it is known that the reaction C5H5 + CH3 can potentially lead to benzene and fulvene, where the latter can isomerize to benzene,21,22 secondary decomposition reactions of C6H7 radicals, the prevalent primary reaction products, have not yet been thoroughly investigated using up-to-date methods of quantum chemistry and theoretical kinetics. In the present work, we report a theoretical study aimed to refine the energies and molecular parameters of the C6H7 species at the modern level of theory, to compile the pathways for benzene and fulvene formation, and to calculate rate constants for decomposition of C6H7 in the temperature range 300−2500 K and at pressures of 0.03−100 atm. The computed rate constants for the C5H5 + CH3 → C6H7 + H reaction and for dissociation of C6H7 are then combined together to predict relative yields of benzene and fulvene under different combustion conditions.

Figure 1. Reaction pathways involved in transformations of C5 and C6 ring species. Blue and red arrows depict processes that result in C6 → C5 and C6 ← C5 transformations, respectively, whereas black arrows show processes that do not lead to a change in the number of C atoms in the ring.

C6H5OH → C5H6 + CO

to phenoxy radical and cyclopentadiene hydrogen

■

(4b) 14

C6H5OH + H → C6H6 + OH

THEORETICAL METHODS Ab initio calculations were applied to investigate possible pathways and products of the C5H5 + CH3 reaction and secondary dissociation of C6H7. Initially, geometries of the reactants, products, intermediates, and transition states were optimized using the hybrid density functional (DFT) B3LYP method23,24 with the 6-311G(d,p) basis set and vibrational frequencies and zero-point vibrational energy corrections (ZPE) were calculated at the same level of theory. The resulting stationary points were characterized as local minima or transition states on the basis of the number of imaginary frequencies. Then, the doubly hybrid DFT B2PLYPD3 method25−27 with Dunning’s correlation-consistent aug-cc-pVDZ basis set28 was used to refine the geometries and frequencies of all stationary points. Finally, the energies were refined using the explicitly correlated coupled clusters CCSD(T)-F12/cc-pVTZ-f12 method,28−31 which is aimed to closely approximate 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. The expected accuracy of the CCSD(T)-F12/cc-pVTZ-f12//B2PLYPD3/ aug-cc-pVDZ + ZPE(B2PLYPD3/aug-cc-pVDZ) relative energies should be better than 1 kcal/mol. Zhang and Valeev32 showed for a typical set of chemical reactions that the mean absolute errors in CCSD(T)-F12/cc-pVTZ-f12-calculated re-

or react with atomic (4c)

resulting in the formation of benzene. Cyclopentadiene can also produce cyclopentadienyl via thermal decomposition15,16 C5H6 ↔ C5H5 + H

or via the reaction with a hydrogen atom C5H6 + H → C5H5 + H 2

(5a) 17

(5b)

18

It is also known that decomposition of phenoxy radical produces cyclopentadienyl and CO C6H5O → C5H5 + CO

(8)

(6)

As can be seen from the reaction scheme presented in Figure 1, several routes from benzene C6H6 lead to the formation of C5H5. A number of pathways have been proposed2,5−7 for converting the resonance-stabilized cyclopentadienyl radical to the aromatics. Dimerization of C5H5 may form naphthalene (C10H8).5 Figure 1 shows two pathways for the benzene formation from the cyclopentadienyl radical, first through the reaction with methyl2,6 9192


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Figure 2. Schematic profile of the potential energy surface for the CH3 + C5H5 reaction and secondary dissociation of the primary C6H7 products.

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RESULTS AND DISCUSSION Potential Energy Surfaces. Figure 2 depicts a profile of the PES for the reaction between the cyclopentadienyl and methyl radicals and provides relative energies of local minima and transition states for only the most relevant channels. All relative energies are given with respect to the initial C5H5 + CH3 reactants. The first step is barrierless recombination of cyclopentadienyl and methyl radicals, which produces 5methyl-1,3-cyclopentadiene (C5H5CH3-5), one of three methylcyclopentadiene isomers, residing 70.4 kcal/mol lower in energy than the reactants. Transitions to other two isomers are possible by H atom migration. Following Sharma and Green,2 we found that an H atom shift from the ipso to the ortho position results in the formation of 1-methyl-1,3-cyclopentadiene (C5H5CH3-1) with a relative energy of −73.3 kcal/mol. One more hydrogen shift from the ortho to the meta position leads to the formation of yet another isomer, 2-methyl-1,3-cyclopentadiene (C5H5CH3-2) with nearly equal relative energy of −73.5 kcal/mol. The energies of the C5H5CH3 isomers calculated at the CCSD-F12/cc-pVTZ-f12 level are close to those obtained at CCSD(T)/6-31g+(d′) and MP4SDQ/CBSB4 levels of theory.2 The transitions between the three isomers require overcoming barriers of 24.5 and 27.4 kcal/mol (at TS11) and 27.8 and 28.0 kcal/mol (at TS12) in forward and backward directions, respectively. On the basis of the fact that the three isomeric structures have very similar ground-state energies and vibrational and rotational parameters, Sharma and Green2 concluded that the abundances of the three isomers formed in the reaction should be similar. The next reaction step is elimination of an H atom. A detachment of hydrogen from the five-membered carbon ring either from the ipso position in C5H5CH3-5 or from the CH2

action energies and barrier heights are 0.55 and 0.28 kcal/mol, with the maximal absolute errors being 1.53 and 0.78 kcal/mol, respectively. B3LYP and B2PLYPD3 calculations were performed using the Gaussian 0933 software package, whereas the CCSD(T)-calculations were performed using Molpro 2010.34 Using the refined geometries, vibrational frequencies, and relative energies of the reactants, products, intermediates, and transition states, we calculated rate constants of different reactions on the C6H8 and C6H7 potential energy surfaces (PES) at various temperatures and pressures using the Rice− Ramsperger−Kassel−Marcus Master Equation (RRKM-ME) theoretical approach as implemented in the MESS software package.35 Collision parameters for RRKM-ME calculations were taken from Jasper and Hansen who studied H-assisted isomerization of fulvene to benzene on the C6H7 PES in Kr bath gas.36 In particular, the Lennard-Jones parameters (ε/cm−1, σ/Å) = (230, 4.01) were used and the temperature dependence of the range parameter α for the deactivating wing of the energy transfer function was expressed as α(T) = α300(T/300 K)n, with n = 0.7 and α300 = 333 cm−1, where the collisional energy transfer in the master equation was described using the “exponential down” model.37 Jasper and Miller38 have demonstrated that results for other heavy atomic and diatomic baths are likely to be very similar to those for Kr, with differences within the accuracy of the approach for predicting collisional energy transfer parameters in ME calculations. The Rigid-Rotor, Harmonic-Oscillator (RRHO) model was generally adopted for the calculations of densities of states and partition functions for local minima and numbers of states for transition states. Input files used for MESS calculations are given in Supporting Information. 9193


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mol lower than that of TS3 for the ring expansion. The PES diagram presented in Figure 2 also includes the routes for Hassisted transformation of fulvene to benzene, for example, C5H4CH2 + H → TS1 → C5H5CH2-5 → TS2 → C5H5CH2(re) → TS3 → C6H6H → TS4 → C6H6 + H. This isomerization was considered before by Jasper and Hansen using QCISD(T)/ CBS//M06-2X/6-311++G(d,p) calculations.19 As follows from the results presented in Figure 2, the relative energies calculated using B2PLYPD3 are in most cases in much better agreement with those obtained at the highly accurate CCSD(T)-F12 level than the B3LYP values. This indicates that the doubly hybrid B2PLYPD3 is a more accurate DFT method than B3LYP, at least for this particular C5H5 + CH3 system. Table 1 displays a comparison of the enthalpy of formation of C5H5 computed on the basis of the calculated enthalpy of the

group in C5H5CH3-1 and C5H5CH3-2 results in the formation of 1-methyl-2,4-cyclopentadiene (C5H4CH3). The H loss processes are endothermic but do not have exit barriers and the relative energy of C5H4CH3 is 1.4 kcal/mol, just above the energy of the initial reactants. Note that the relative energy of C5H4CH3 calculated here is about 6 kcal/mol lower than the value obtained by Sharma and Green.2 A hydrogen atom elimination from the methyl group in C5H5CH3-1 or C5H5CH3-2 produces the C5H5CH2-1 or C5H5CH2-2 structures, respectively, also without an exit barrier. These structures have relative energies of 8.7 and 14.0 kcal/mol, respectively, that are close to the values reported by Sharma and Green.2 Moskaleva et al.6 and Sharma and Green2 showed that H elimination from the CH3 group in C5H5CH3-5 is much more endothermic than the reaction paths considered above. Therefore, we excluded this channel from further consideration. The C6H7 isomers produced after H eliminations serve as gateways for the formation of fulvene through two main mechanisms. The straightforward one is the direct H elimination from the CH3 group in C5H4CH3 or from the ortho and meta positions in C5H5CH2-1 and C5H5CH2-2, respectively. The C5H4CH3 → C5H4CH2 + H and C5H5CH2-1 → C5H4CH2 + H reactions exhibit no exit barriers at the B2PLYPD3 level of theory, and hence, variational transitional-state theory (VTST)39 was used to compute their rate coefficients. Here, we scanned the minimal energy reaction path (MEP) at the B2PLYPD3/aug-ccpVDZ level and then refined energies of the structures along the MEP at the CCSD(T)-F12/cc-pVTZ-f12 level. This approach approximates a search of a transition-state structure along the MEP at CCSD(T)-F12/cc-pVTZ-f12. The calculations showed the existence of maxima along the MEP for both C5H4CH3 → C5H4CH2 + H and C5H5CH2-1 → C5H4CH2 + H, respectively, placed 0.8 and 3.2 kcal/mol above the products. Nevertheless, all calculated structures along the MEPs were considered as VTST candidates in the RRKM-ME calculations. Alternatively, the C5H5CH2-2 → C5H4CH2 + H reaction has a barrier of 45.2 kcal/ mol (3.1 kcal/mol for H addition in reverse direction). C5H5CH2-1 and C5H5CH2-2 can interconvert to one another through TS7, with the barrier height for the H shift from the ortho to meta position being 34.1 kcal/mol (28.8 kcal/mol in reverse direction). The indirect path to fulvene goes through the C5H5CH2-5 isomer, which can be formed from C5H5CH2-1 or C5H4CH3. A barrier of 38.6 kcal/mol for hydrogen migration from the ortho to the ipso position C5H5CH2-1 → C5H5CH2-5 is 14.1 kcal/mol lower than a barrier of 52.7 kcal/mol for the H shift from CH3 group to the ipso position, C5H4CH3 → C5H5CH2-5. Those H shifts can be followed by final H elimination, C5H5CH2-5 → C5H4CH2 + H, via a barrier of 31.5 kcal/mol (5.0 kcal/mol for the reverse H addition). The C5H5CH2-5 isomer is a branching point where a path to benzene begins. The next structure on this route is a bicyclic isomer C5H5CH2(re) with a relative energy of 31.5 kcal/mol ,which is close to the energy of its precursor, C5H5CH2-5, 29.6 kcal/mol. A rather low barrier of 8.3 and 6.4 kcal/mol in forward and reverse directions, respectively, separates them. The next step, C5H5CH2(re) → C6H6H, is expansion of the bicyclic structure to a six-membered ring in cyclohexadienyl, where a barrier of 9.5 kcal/mol in the forward direction is much lower than 36.7 kcal/mol in the reverse direction. Another H elimination C6H6H → C6H6 + H leads to benzene. Here, the barrier for the reverse process (6.4 kcal/mol) is significantly lower than that for the forward reaction (26.8 kcal/mol). The relative energy of TS4 for the H loss is 9.9 kcal/

Table 1. Theoretical and Experimental Enthalpy of Formation (kcal/mol) of the Cyclopentadienyl Radical ΔHf° (0 K)

source and method Present work, CCSD(T)-F12/cc-pVTZ-f12// B2PLYPD3/6-311G(d,p) from C5H5 + CH3 → C6H6 + 2H da Silva,a G3X-K from C2H2 + C3H3 → C5H5 Nguyen et al.,b G2M(RCC,MP2) Sharma and Green,c CBS-QB3 Parker et al.,d electrochemistry Kern et al.,e gas-phase kinetics Roy et al.,f gas-phase kinetics NIST Database,g proton affinity cycle Nunes et al.,h photoacoustic calorimetry Nunes et al.,h recommended, experiment and theory (CBS-QB3, CCSD(T)/CBS, from isogyric reactions)

66.7

ΔHf° (298 K) 64.2

67.4

65.4

63.5 63.7 63.9 ± 0.6 65.3 62.5 62.9 65.2 ± 1.7 64.8 ± 2.0

a e

Reference 41. bReference 42. cReference 2. dReference 43. Reference 44. fReference 16. gReference 45. hReference 46.

overall C5H5 + CH3 → C6H6 + 2H reaction and experimental enthalpies of formation of benzene, H, and CH3 from the Active Thermochemical Tables40 with the literature data. As one can see, the present value shows the best agreement with the latest experimental results and deviates from the recommended value for ΔHf°(298 K) by only 0.6 kcal/mol. Reaction Kinetics. We first address the reactions on the C6H7 PES, C5H4CH3 → fulvene + H and C5H4CH3 → benzene + H, and product formation rate constants under combustion conditions. Rate constants for the former reaction in the temperature range 500−2500 K at pressures of 0.01, 1, 10, and 100 atm are illustrated in Figure 3A. Due to high barriers at TS5 and TS1 and relatively high energy of fulvene, which can be formed directly via variational TS6, the calculated rate constants are nearly the same at all pressures and almost negligible in the 500−1000 K temperature range. At 1000 K the constants start to diverge but they are still low until the temperature rises to 1500− 1600 K. The falloff behavior of the rate constants is predicted to be dependent on pressure, the largest deviations of the rate constant for 0.01 and 10 atm from the HP value are factors of 32.3 and 2.6, respectively. Rate constants for the C5H4CH3 → benzene reaction depicted in Figure 3B exhibit a different behavior. On the contrary to the previous reaction, the values tend to converge with an increase in temperature and only at high temperatures does benzene formation become competitive with fulvene formation. 9194


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Figure 3. Rate constants for the C5H4CH3 (A)/C5H5CH2-1 (C)/C5H5CH2-2 (E) → fulvene + H and C5H4CH3 (B)/C5H5CH2-1 (D)/C5H5CH2-2 (F) → benzene + H reactions at various pressures: 0.01 atm, blue down-pointing triangles; 1 atm, green triangles; 10 atm, red circles; 100 atm, black squares.

Table 2. Rate Constants (cm3·molecule−1·s−1) for H-Assisted Isomerization of Fulvene to Benzene at 1 atm 500 K present work ref 19

700 K −13

1.57 × 10 3.04 × 10−13

900 K −12

1.28 × 10 3.11 × 10−12

1100 K −12

−11

6.79 × 10 1.81 × 10−11

2.07 × 10 4.75 × 10−11

1300 K −11

3.83 × 10 8.10 × 10−11

1500 K −11

5.24 × 10 1.06 × 10−10

1700 K 6.11 × 10−11 1.19 × 0−10

reported by Jasper and Hansen19 using similar RRKM-ME calculations but with the QCISD(T)/CBS//M06-2X/6-311+ +G(d,p) PES. Table 2 shows the two sets of rate constants at 1 atm. As can be seen, the present values are by factors 1.9−2.7 lower than those obtained by Jasper and Hansen. Both studies took into account of significant variational effects and rather small tunneling corrections calculated using the asymmetric Eckart method for the H addition reaction steps. Besides the use of slightly different energetics and B2PLYPD3 vibrational frequencies in place of those from the M06-2X/6-311++G(d,p) calculations, the difference may also originate from the fact that Jasper and Hansen employed curvilinear coordinates to represent harmonic frequencies away from the saddle point. In their work, the curvilinear coordinate calculations gave rate coefficients 10−90% higher than those from Cartesian coordinate calculations because curvilinear coordinates are expected to better describe the low-frequency bending modes involving the reactant H atom.

For the formation of fulvene and benzene from C5H5CH2-1, as seen in Figure 3C and D, the dependence of the rate constants on pressure and temperature are qualitatively similar to those for dissociation of C5H4CH3. Nonetheless, there are substantial quantitative differences: due to the 7.3 kcal/mol higher energy of the reactant and the lower energy of the barrier at TS8 as compared to that of TS5, the C5H5CH2-1 → fulvene + H and C5H5CH2-1 → benzene + H reaction rate constants are 1−3 orders of magnitude higher. The last in the list of the C6H7 intermediates, C5H5CH2-2, has an even higher energy. But there is no direct route to benzene, only through C5H5CH2-1, and the direct H elimination process forming fulvene possesses a rather high barrier at TS10. These factors explain lower, under certain conditions, rate constants (Figure 3E and F) for the decomposition channels of C5H5CH2-2 as compared to those for the C5H5CH2-1 → fulvene/benzene + H reactions. Our calculations also provide the rate constants for H-assisted isomerization of fulvene to benzene which were previously 9195


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The Journal of Physical Chemistry A On the basis of the results by Sharma and Green2 for the C5H5 + CH3 → C5H5CH2-1/C5H5CH2-2/C5H4CH3 + H reaction, we can find overall rate constants for the formation of fulvene and benzene, C5H5 + CH3 → fulvene + 2H and C5H5 + CH3 → benzene + 2H. To that end, we used a combined kinetic scheme presented in Figure 4. It should be noted that our approach does

k4

C5H4CH3 → C5H4CH 2 + H k5

C5H4CH3 → C6H6 + H k6

C5H5CH 2‐1 → C5H4CH 2 + H k7

C5H5CH 2‐1 → C6H6 + H k8

C5H5CH 2‐2 → C5H4CH 2 + H k9

C5H5CH 2‐2 → C6H6 + H k10

C5H4CH3 XoooY C5H5CH 2‐1 k −10 k11

C5H4CH3 XoooY C5H5CH 2‐2 k −11

k12

C5H4CH 2 − 1 XoooY C5H5CH 2‐2

Figure 4. Combined kinetic scheme of the C5H5 + CH3 reaction and secondary dissociation of the primary C6H7 products.

k −12

Following the common procedure, we can write a system of differential equations for the concentrations of C5H5CH3, C5H5CH2-1, C5H5CH2-2, C5H4CH3, C5H4CH2, and C6H6:

not take into account any possible reactions of products or intermediates with hydrogen atoms or other molecules, which could be present in the reacting medium or be produced on the course of other reactions not included in our scheme. Formation of different C6H7 species (C5H5CH2-1 or C5H5CH2-2, or C5H4CH3) could be achieved through either a direct mechanism with skipping antecedent C6H8 wells or prior stabilization of one of the C5H5CH3-1/C5H5CH3-2/C5H5CH3-5 structures (unified under the common name C5H5CH3) followed by their thermal decomposition. The corresponding reactions are

⎧ d[C5H5CH3] = k S1[C5H5][CH3] ⎪ dt ⎪ ⎪ − (k S2 + k S3 + k S4 + k −S1)[C5H5CH3] ⎪ ⎪ d[C5H4CH3] = k1[C5H5][CH3] ⎪ dt ⎪ ⎪ + k S2[C5H5CH3] − (k4 + k5)[C5H4CH3] ⎪ − (k10 + k11)[C5H4CH3] + k −10 ⎪ [C H CH − 1] + k [C H CH ‐2] 5 5 2 2 −11 5 5 ⎪ ⎪ d[C H CH ‐1] 5 5 2 ⎪ = k 2[C5H5][CH3] dt ⎪ ⎪ + k S3[C5H5CH3] − (k6 + k 7)[C5H5CH 2‐1] ⎪ − (k + k )[C H CH ‐1] + k [C H CH ] ⎪ 12 5 5 2 10 5 4 3 −10 ⎨ + ‐ [C H CH 2] k 12 5 5 2 − ⎪ ⎪ d[C H CH ‐2] 5 5 2 ⎪ = k 3[C5H5][CH3] dt ⎪ ⎪ + k S4[C5H5CH3] − (k 8 + k 9)[C5H5CH 2‐2] ⎪ ⎪ − (k −11 + k −12)[C5H5CH 2‐2] ⎪ + k11[C5H4CH3] + k12[C5H5CH 2‐1] ⎪ ⎪ d[C5H4CH 2] = k4[C5H4CH3] + k6[C5H5CH 2 ⎪ dt ⎪ ⎪ ‐1] + k 8[C5H5CH 2‐2] ⎪ d[C H ] 6 6 ⎪ = k5[C5H4CH3] + k 7[C5H5CH 2‐1] ⎪ dt ⎪ + k [C H CH ‐2] ⎩ 9 5 5 2

k1

C5H5 + CH3 → C5H4CH3 + H k2

C5H5 + CH3 → C5H5CH 2‐1 + H k3

C5H3 + CH3 → C5H5CH 2‐2 + H k S1

C5H5 + CH3 XoooY C5H5CH3 k −S1

k S2

C5H5CH3 → C5H4CH3 + H k S3

C5H5CH3 → C5H4CH 2‐1 + H k S4

C5H5CH3 → C5H4CH 2‐2 + H

The rate constants were recomputed here within the RRKMME approach using the updated energetics obtained at the CCSD(T)-F12 level and B2PLYPD3 vibrational frequencies. For the barrierless reaction steps including the initial C5H5 + CH3 association and various H losses we adopted the high-pressure limit rate constants computed by Sharma and Green2 using variable reaction coordinate transition-state theory (VRC-TST). In our MESS calculations, we used phase space theory47 to fit the rate constants for these barrierless reactions to the Sharma and Green values. The secondary reactions and their rate constants in the proposed mechanism of fulvene/benzene formation are the following:

This system was solved using the standard MATLAB means. For the C6H7 intermediates which are not stable at higher temperatures, rate constants above such temperatures were extrapolated from their values at lower temperatures using modified Arrhenius expressions. Final rate constants for the formation of fulvene and benzene are shown in Figure 5A and 9196


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The Journal of Physical Chemistry A Table 3, the branching ratio for benzene computed as kbenzene/ (kbenzene + kfulvene) is depicted in Figure 5B.

There are two common features for all the pressures considered. First, for temperatures below 1100 K, time needed to reach steady-state conditions is excessive and hence rate constants for the combined primary and secondary reactions do not make physical sense. To illustrate this point, we plotted concentrations of various species as functions of time for the pressure of 100 atm and the temperature of 900 K in Figure 6 and for other conditions in Figure S1 of Supporting Information. Second, among the primary products C5H5CH2-1, C5H5CH2-2, and C5H4CH3, the last one always predominates the C5H5 + CH3 reaction, with its branching ratio exceeding 99%. At the lowest pressure of 0.01 atm, both rate constants for the formation of fulvene and benzene monotonically grow with temperature and the formation of benzene outstrips that of fulvene due to the lower critical barrier at TS5 (54.1 kcal/mol) as compared to the energy of fulvene (56.1 kcal/mol). In the meantime, the relative yield of benzene decreases at higher temperatures because the pathways to fulvene are more entropically favorable. The highest pressure case of 100 atm is completely different and is characterized by several distinct extrema. As the reaction goes overwhelmingly through the C5H4CH3 structure, it is reasonable to search the roots of such behavior in rate constants of reaction steps involving that intermediate (Figure 5C). The first turning point is 1250 K where the branching ratio of benzene begins to rapidly fall and that of fulvene accelerates its growth. At this temperature, the reaction C5H4CH3 → C5H5CH2-2 outruns the C5H4CH3 → C5H5CH2-5 step, which facilitates fulvene formation at the cost of the formation of benzene because the thermalized C5H5CH2-2 structure mostly decomposes to fulvene, on the contrary to C5H5CH2-5. At the second extremum, 1500 K, one could see a reverse trend; the fulvene rate constant begins to fall, whereas that of benzene starts to increase. This alteration stems from the loss of stability of C5H5CH2-5. As was mentioned above, this well is crucial for the reaction outcome because it lies at the crossroad of the pathways to the products. Without thermalization of this structure, the well-skipping pathway to benzene is more preferable than that from the thermalized C5H5CH2-5 isomer. Above 1700 K, the fulvene formation rate constant growth starts to surpass that of benzene again due to a broader variety of different pathways to fulvene through direct H elimination or via prior H shifts and their entropic preference, as compared to the only ring expansion pathway to benzene. The cases of moderate pressures of 1 and 10 atm are very similar and are characterized by slight deviations from the monotonic behavior. The main feature at these

Figure 5. (A) Rate constants for the formation of fulvene (solid symbols) and benzene (open symbols) through the combined kinetic scheme of the C5H5 + CH3 reaction and secondary dissociation of the primary C6H7 products at various pressures: 0.01 atm, blue; 1 atm, green; 10 atm, red; 100 atm, black. (B) Branching ratio of benzene at various pressures: 0.01 atm, blue; 1 atm, green; 10 atm, red; 100 atm, black. (C) Rates constants of reaction steps involving C5H4CH3: C5H4CH3 → fulvene + H, black squares; C5H4CH3 → benzene + H, red circles; C5H4CH3 → C6H6H, green diamonds; C5H4CH3 → C5H5CH21, blue triangles; C5H4CH3 → C5H5CH2-2, magenta down-pointing triangles; C5H4CH3 → C5H5CH2-5, cyan left-pointing triangles.

Table 3. Rate Constants (cm3·mol−1·s−1) for the Formation of Fulvene and Benzene via the Reaction Sequence Involving C5H5 + CH3 and Unimolecular Decomposition of the C6H7 Radicals product

1100 K

1300 K

fulvene benzene

1.23 × 10−12 3.40 × 10−12

1.87 × 10−12 4.19 × 10−12

fulvene benzene

1.39 × 10−12 3.25 × 10−12

2.32 × 10−12 3.75 × 10−12

fulvene benzene

1.80 × 10−12 2.88 × 10−12

2.43 × 10−12 3.66 × 10−12

fulvene benzene

2.83 × ×10−12 1.39 × 10−12

4.45 × 10−12 1.53 × 10−12

1500 K p = 0.01 atm 2.57 × 10−12 5.00 × 10−12 p = 1 atm 3.51 × 10−12 4.07 × 10−12 p = 10 atm 3.60 × 10−12 4.00 × 10−12 p = 100 atm 6.24 × 10−12 1.44 × 10−12 9197

1700 K

2000 K

3.29 × 10−12 5.76 × 10−12

4.24 × 10−12 6.71 × 10−12

4.77 × 10−12 4.28 × 10−12

6.34 × 10−12 4.60 × 10−12

5.09 × 10−12 3.99 × 10−12

6.83 × 10−12 4.14 × 10−12

5.90 × 10−12 3.27 × 10−12

7.71 × 10−12 3.36 × 10−12 DOI: 10.1021/acs.jpca.7b09873 J. Phys. Chem. A 2017, 121, 9191−9200

Article


Figure 6. Time profiles of the concentrations of various intermediates and products [(A) C5H5CH3; (B) C5H4CH3; (C) C5H5CH2-1; (D) C5H5CH2-2; (E) fulvene; (F) benzene)] in the combined kinetic scheme including the C5H5 + CH3 reaction and secondary decomposition of C6H7 (Figure 4) at 100 atm and 900 K, calculated by solving the corresponding system of differential equations.

C6H7 radicals or via intermediary rearrangements. Calculations of the total rate constants for reactions C5H5 + CH3 → fulvene/ benzene +2H were carried out using the combined kinetic scheme and demonstrated that for temperatures below 1100 K, the time needed to reach steady-state conditions is excessive and hence rate constants for the united primary and secondary reactions do not make physical sense. At higher temperatures, steady-state conditions are rapidly achieved and rate constants for the combined process can be generated. The results showed that formation of benzene is prevalent at the lowest pressure (0.01 atm), whereas formation of fulvene prevails at the highest pressure (100 atm). At 100 atm, the branching ratio of benzene falls below 30% in the 1250−1650 K temperature range. At intermediate pressures, the two product channels compete depending on temperature, with benzene being favorable at lower temperatures and fulvene taking the lead around 1600 K. Considering that fulvene can be rapidly converted to benzene via H-assisted isomerization, the C5H5 + CH3 reaction and subsequent secondary processes provide a facile route to the formation of the first aromatic six-member ring from a fivemember ring or to the restoration of the six-member ring after it

pressures is that fulvene and benzene swap their roles as the predominant product at temperatures around 1600 K; the formation of benzene and fulvene is favored at lower and higher temperatures, respectively.

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CONCLUSIONS We refined the PES for the reaction of cyclopentadienyl and methyl radicals and improved the energies and molecular parameters of the known C6H8 and C6H7 intermediates using the more advanced CCSD(T)-F12/cc-pVTZ-f12//B2PLYPD3/ aug-cc-pVDZ level theory. The first stage of the reaction is barrierless recombination of C5H5 and CH3 followed by H atom migrations and subsequent hydrogen elimination or by immediate C−H bond cleavage which results in formation of three C6H7 isomers, C5H5CH2-1, C5H5CH2-2, and C5H4CH3. Recalculated energies of the first two of them are close to those reported previously.2 However, the third value appears to be 5.8 kcal/mol lower, which shifts the reaction outcome in favor of the path through the C5H4CH3 radical, with its branching ratio exceeding 99%. The second part of the mechanism is formation of fulvene or benzene through direct H-eliminations from the 9198


The Journal of Physical Chemistry A was oxidized to the five-member ring via the C6H6 + O or C6H5 + O2 reactions. Thus, the present study corroborates the potentially important role of the methyl radical in conversion of five-member rings in PAH into six-member rings and, more generally, in the mechanism of PAH growth where CH3 additions alternate with H abstractions and acetylene additions (at temperatures relevant to combustion, generally above 1000 K):

ACKNOWLEDGMENTS

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REFERENCES

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C5H5 + CH3 → C5H4CH3 + H C5H4CH3 → C6H4CH 2 /C6H6 + H

C6H4CH 2 + H → C6H6 + H C6H6 + H → C6H5 + H 2 C6H5 + CH3 → C6H5CH3 (toluene) → C6H5CH 2 (benzyl) + H benzyl + C2H 2 → indene + H indene + H → indenyl + H 2

indenyl + CH3 → 1‐methylindenyl + H 1‐methylindenyl → benzofulvene/naphthalene + H benzofulvene + H → naphthalene + H

Because temperature- and pressure-dependent rate constants for the reactions in this sequence are now available,48,49 they can be extrapolated to an elementary step increasing a PAH molecule by an extra six-member ring via initial formation of an additional five-member ring and included in kinetic models for PAH growth.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b09873. Time profiles of the concentrations of various intermediates and products in the combined kinetic scheme including the C5H5 + CH3 reaction and secondary decomposition of C6H7 isomers at 100 and 0.01 atm, calculated by solving the corresponding system of differential equations; fitted modified Arrhenius expressions for dissociation of C6H7 isomers to fulvene + H and benzene + H; input files for RRKM-ME calculations on the C6H8 and C6H7 PESs using the MESS package (PDF)

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The work was supported by the Ministry of Education and Science of the Russian Federation: PES investigation by the grant No. 14.Y26.31.0020 and rate constants calculations by the grant No. 3.5708.2017/6.7 to Samara University.

C2H 2 + C3H3 → C5H5

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Article

AUTHOR INFORMATION

Corresponding Authors

*V. N. Azyazov. E-mail: [email protected]. *A. M. Mebel. E-mail: mebela@fiu.edu. ORCID

Alexander M. Mebel: 0000-0002-7233-3133 Notes

The authors declare no competing financial interest. 9199


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Kinetics of the CH3 + C5H5 Reaction: A Theoretical Study - The

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