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Ab Initio/RRKM-ME Study on the Mechanism and Kinetics of the Reaction of Phenyl Radical with 1,2-Butadiene V. V. Kislov and A. M. Mebel* Department of Chemistry and Biochemistry, Florida International UniVersity, Miami, Florida 33199, USA ReceiVed: December 7, 2009; ReVised Manuscript ReceiVed: May 11, 2010
Ab initio G3(MP2,CC)//B3LYP/6-311G** calculations have been performed to investigate the potential energy surface and mechanism of the reaction of phenyl radical with 1,2-butadiene followed by kinetic RRKM-ME calculations of the reaction rate constants and product branching ratios at various temperatures and pressures. The results show that the reaction can proceed by direct hydrogen abstraction to produce benzene and C4H5 radicals or by addition of phenyl to different carbon atoms in CH2CCHCH3 followed by isomerizations of C10H11 adducts and their dissociation by H or CH3 losses. The H abstraction channels are found to be kinetically preferable and to contribute 70-90% to the total product yield in the 300-2500 K temperature range, with the products including C6H6 + CH2CHCCH2 (∼40%), C6H6 + CH3CHCCH (5-31%), and C6H6 + CH2CCCH3 (24-20%). The phenyl addition channels are calculated to be responsible for 10-30% of the total product yield, with their contribution decreasing as the temperature increases. The products of the addition channels include collisionally stabilized C10H11 adducts, 1-phenyl-2-buten-2-yl, 3-phenyl-2-buten-2-yl, and 2-phenyl2-buten-1-yl/2-phenyl-1-buten-3-yl, which are favored under low temperatures, as well as their dissociation products, 1-phenyl-propyne + CH3, phenylallene + CH3, and 2-phenyl-1,3-butadiene + H, preferred at higher temperatures. Indene is predicted to be a very minor reaction product at the temperatures relevant to combustion, with the maximal calculated yield of only 2% at 700 K and 7.6 Torr. Our calculations showed that at typical combustion temperatures product branching ratios are practically independent of pressure, and collisional stabilization of reaction intermediates does not play a significant role. Three-parameter modified Arrhenius expressions have been generated for the total reaction rate constants and rate constants for the most important product channels, which can be utilized in future kinetic modeling of reaction networks related to the growth of hydrocarbons in combustion processes. Introduction A detailed understanding of chemical processes in combustion of hydrocarbon fuels, which can lead to the formation of major pollutants, such as soot and its polycyclic aromatic hydrocarbon (PAH) precursors, is of great importance for achieving a better design of efficient and clean combustion devices.1 A principal reactive precursor to the PAH growth and eventually to soot formation in hydrocarbon combustion is phenyl radical, C6H5. For instance, C6H5 participates in the hydrogen abstraction acetylene addition (HACA) mechanism of PAH formation,2-8 where phenyl radical is produced at the first step by H abstraction from benzene and then two consecutive C2H2 additions to C6H5 ultimately generate naphthalene after several isomerization steps and a loss of a hydrogen atom. Alternative to HACA, phenyl radical reactions with C4 hydrocarbons, such as vinylacetylene C4H4 or C4H6 isomers,9 may also lead to the smallest PAH, naphthalene, or the smallest cyclopentafused PAH (CP-PAH), indene. For instance, the C6H5 + C4H6 reactions explore the C10H11 surface, where some C10H11 intermediates can decompose to indene C9H8 by a methyl group loss or can serve as eventual precursors of azulene and naphthalene; these C10H8 molecules can be formed in secondary decomposition of the C10H10 or C10H9 primary products through H2 or H eliminations. * To whom correspondence should be addressed. E-mail: mebela@ fiu.edu.
Because of their relevance to the PAH formation pathways, the reactions of phenyl radical with C4H6 isomers have been a subject of several theoretical and experimental studies. For instance, Fascella et al.10 investigated the mechanism and kinetics of the reaction of C6H5 with 1,3-butadiene using ab initio G2MP2 calculations of the potential energy surface (PES) and determined total rate constants for the formation of different products utilizing QRRK theory. They found that the reaction is practically barrierless, and at 760 Torr and within the 500-1700 K temperature range the dominant reaction product should be the stabilized initial reaction adduct, 4-phenyl-buten3-yl C10H11, followed by the products of H elimination (C10H10), including 1,4-dihydronaphthalene and 1-phenyl-1,3-butadiene, with indene + CH3 giving only a minor contribution. The C6H5 + 1,3-butadiene reaction was later revisited in a combined theoretical and experimental kinetic study by Ismail et al.11 They used a B3LYP computed PES for microcanonical RRKM calculations and applied the weak collision master equation (ME) approach for computation of pressure and temperaturedependent reaction rate constants. The calculated thermal rate constant for disappearance of phenyl radical was found to be in good agreement with the experimental measurements employing the cavity-ringdown spectroscopic technique. The relative product yield calculations confirmed the conclusion by Fascella et al.10 that the initial 4-phenyl-buten-3-yl C10H11 adduct dominates the reaction at low temperatures. However, the 1-phenyl-1,3-butadiene C10H10 product of H elimination takes over around 1000 K, and above 1400 K bimolecular H-
10.1021/jp911604f 2010 American Chemical Society Published on Web 07/01/2010
Reaction of Phenyl Radical with 1,2-Butadiene abstraction channels leading to benzene + C4H5 become the major processes. The production of 1,4-dihydronaphthalene was computed to be much less significant. Experimentally, the reaction products were verified for the first time in crossed molecular beams experiments by Gu et al.12 Under singlecollision conditions corresponding to the zero-pressure limit, stabilization of the C10H11 adduct is not possible and Gu et al. identified 1-phenyl-1,3-butadiene + H as the only reaction products at high collision energies of 28-38 kcal/mol. Summarizing all these results, one can see that 1,4-dihydronaphthalene or indene are not likely to be produced in the reaction of phenyl radical with 1,3-butadiene. Reactions of C6H5 with the other C4H6 isomers, 1- and 2-butynes and 1,2-butadiene, have been recently examined experimentally by Kaiser’s group using the crossed molecular beams technique in combination with our ab initio calculations of the pertinent portions of PES and RRKM calculations of product branching ratios under single-collision conditions.13,14 In the reaction of phenyl with 1-butyne,14 the 1-phenyl-3methylallene and 1-phenyl-1-butyne C10H10 products, produced by H eliminations from the initial 1-phenyl-buten-2-yl C10H11 adduct, were identified in experiment. Meanwhile, according to the theoretical calculations, phenylallene (C9H8) + CH3 were predicted to contribute about 83% of the total product yield in decomposition of the C10H11 intermediate; additionally, the direct H abstraction channels giving rise to C6H6 + CH3CHCCH/ CH2CH2CCH as well as the formation of phenylacetylene (C8H6) + C2H5 via another 2-phenyl-buten-1-yl initial C10H11 complex were predicted to be competitive. Unfortunately, none of the C9H8 + CH3, C8H6 + C2H5, or C6H6 + C4H5 products were observed in crossed molecular beams experiments, apparently due to experimental difficulties in detection of product pairs containing heavier fragments. Similarly, in the C6H5 + 2-butyne reaction,14 only the 1-phenyl-1-methylallene C10H10 product was identified experimentally, whereas the theoretical calculations predicted the 1-phenyl-2-methylacetylene + CH3 products to be dominant and the C6H6 + CH2CCCH3 hydrogen abstraction channel to compete. Crossed molecular beams experiments on the reaction of phenyl with 1,2-butadiene13 showed the formation of two nonPAH C10H10 isomers, 1-phenyl-3-methylallene and 1-phenylbutyne-2. However, ab initio calculations of the PES indicated that the reaction pathways leading to the production of the smallest CP-PAH molecule indene + CH3 or methyl substituted indenes + H are more favorable energetically. In this view, it is important to investigate the PES of the C6H5 + 1,2-butadiene reaction in more detail, taking into account all possible competitive channels. The goal of the present work is such a detailed study of a region on the C10H11 surface relevant to this reaction, including C6H5 additions to different positions in CH2CCHCH3 and direct H abstractions from various sites. The results of the ab initio calculations will be then utilized in microcanonical RRKM calculations of reaction rate constants at different temperatures and pressures relevant to combustion, and product branching ratios will be subsequently evaluated by employing the weak collision master equation method. Both 1,3- and 1,2-butadienes have been monitored in combustion flames of hydrocarbon fuels,15,16 and mutual rearrangements between different C4H6 isomers were shown to be much faster than their decomposition at high temperatures.17,18 Since the C6H5 + 1,3-butadiene and C6H5 + 1-/2-butynes reactions do not directly lead to PAH formation on the C10H11 PES, the reaction with 1,2-butadiene is the only one among the C6H5 encounters with C4H6 isomers, which may synthesize a
J. Phys. Chem. A, Vol. 114, No. 29, 2010 7683 polycyclic aromatic molecule. The present theoretical study addresses the questions at what temperature/pressure conditions this may actually happen and what the relative yields of PAH species are expected to be. Computational Methods Potential Energy Surface Calculations. Geometries of all species involved in the C6H5 + CH2CCHCH3 reaction have been optimized using the hybrid density functional B3LYP19 method with the 6-311G** basis set. The same method was employed to obtain vibrational frequencies, molecular structural parameters, zero-point energy (ZPE) corrections, and to characterize the stationary points as minima or first-order saddle points. Unscaled vibrational frequencies were used to calculate ZPE corrections and reaction rate constants. To our experience, scaling of B3LYP frequencies does not affect significantly relative energies of isomers and transition states and RRKM calculated rate constants. To obtain more accurate energies, we applied the G3(MP2,CC)//B3LYP modification20 of the original Gaussian 3 (G3) scheme21 for high-level single-point energy calculations. The final energies at 0 K were obtained using the B3LYP optimized geometries and ZPE corrections according to the following formula
E0[G3(MP2,CC)] ) E[CCSD(T)/6-311G(d,p)] + ∆EMP2 + E(ZPE) where ∆EMP2) E[MP2/G3large] - E[MP2/6-311G(d,p)] is the basis set correction, and E(ZPE) is the zero-point energy. ∆E(SO), a spin-orbit correction, and ∆E(HLC), a higher level correction, from the original G3 scheme were not included in our calculations, as they are not expected to make significant contributions into relative energies. Here and below we denote this G3-type approach used in our computations as G3 for brevity. We applied the Gaussian 9822 program package to carry out B3LYP and MP2 calculations, and the Molpro 200223 program package was used to perform calculations of spinrestricted coupled cluster RCCSD(T) energies. The computed PESs are shown on Figures 1-3. Optimized Cartesian coordinates of all local minima and transition state structures are collected in Table S1 of the Supporting Information along with unscaled vibrational frequencies; moments of inertia; rotational constants; ZPE corrections; and B3LYP, CCSD(T), MP2, and G3(MP2,CC) total energies at 0 K. Calculations of Reaction Rate Constants and Branching Ratios. At the high-pressure limit, thermal rate constants were computed using the conventional RRKM24-26 and transition state theory (TST)27 methods including Wigner’s corrections for tunneling effects.24 Rate constants for direct H abstraction reactions were also obtained using TST. Partition functions were calculated using the harmonic oscillator and rigid rotor approximations for vibrational and rotational contributions, respectively. To compute partition functions for species with internal rotations, which have rotational barriers lower than or close to RT/2, we applied the hindered rotor approximation.24 In this case, rotational potentials and respective barriers were calculated using the same B3LYP/6-311G** level of theory; low-frequency vibrational modes corresponding to internal rotors were removed during the calculation of vibrational partition functions and hindered rotor partition functions were instead included for these oscillators. Accurate calculations of rate constants and product yields at finite pressures require solution of a time-dependent master
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Figure 1. Potential energy diagram for the C6H5 + 1,2-butadiene f i1/i5 f products reaction network calculated at the G3(MP2,CC)//B3LYP/ 6-311G** level of theory. All relative energies are given in kcal/mol.
Figure 2. Potential energy diagram for the C6H5 + 1,2-butadiene f i4 f products reaction network. Numbers without parentheses show relative energies calculated at the G3(MP2,CC)//B3LYP/6-311G** level of theory and numbers in parentheses are relative energies taken from the C6H5 + 1,2-butadiene f i1 f products scheme based on the analogy between the two reaction networks. All relative energies are given in kcal/mol.
equation. In the present study, we applied the weak collision master equation method using the ChemRate 1.5 program code28 for the reaction mechanisms involving different C6H5 additions to 1,2-butadiene. The C6H5 + 1,2-butadiene f i1/i5 initial reaction steps (see Figure 1) were considered as chemical activation. The exponential-down weak collision model was selected to describe the energy transfer, with argon considered as the buffer gas. The Lennard-Jones parameters σ and ε/kB were obtained by calculating the Lennard-Jones potential for a model C6H5-Ar system at the MP2/aug-cc-pVTZ level; the fitted parameters of σ ) 5.9 Å and ε/kB ) 407.8 K were used for all intermediates i1-i5. The hindered rotor model was used
for all species (both local minima and transition states) possessing internal rotations. Because rate constants obtained by solving a time-dependent master equation vary with time,29 it is important to find out the appropriate time scales where they actually converge; at shorter time scales vibrational relaxation affects the results, whereas at longer time scales thermal dissociation of the stabilized adducts may lead to variations of the rate constants. Thus, the time-dependent rate constants and corresponding branching ratios for various potential wells exhibit two steady-state regimessthe first one is achieved when vibrational relaxation is completed and the second when thermal dissociation takes oversand the values
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Figure 3. Potential energy diagram for the direct H abstraction channels C6H5 + 1,2-butadiene f C6H6 + C4H5, calculated at the G3(MP2,CC)// B3LYP/6-311G** level of theory. All relative energies are given in kcal/mol.
TABLE 1: TST Calculated High-Pressure Limit Rate Constants and Branching Ratios (In Parentheses) for Competing Reactions of C6H5 with 1,2-Butadiene Including Bimolecular Additions and Hydrogen Abstractions rate constants (cm3 mol-1 s-1) additions T (K)
i1
i4
300 350 400 450 475 500 550 600 700 800 900 1000 1100 1200 1300 1500 1700 2000 2500
5.88 × 10 (16.6) 1.26 × 109 (15.1) 2.36 × 109 (14.3) 3.88 × 109 (12.4) 4.83 × 109 (11.9) 5.4 × 109 (11.4) 8.26 × 109 (10.6) 1.07 × 1010 (9.9) 1.85 × 1010 (8.8) 2.93 × 1010 (8.0) 4.33 × 1010 (7.2) 6.09 × 1010 (6.7) 8.23 × 1010 (6.2) 1.08 × 1011 (5.8) 1.38 × 1011 (5.4) 2.12 × 1011 (4.9) 3.07 × 1011 (4.5) 4.91 × 1011 (4.0) 9.14 × 1011 (3.5) 8
abstractions i5
1.79 × 10 (5.1) 4.01 × 108 (4.8) 7.73 × 108 (4.7) 1.3 × 109 (4.2) 1.65 × 109 (4.1) 1.89 × 109 (4.0) 2.92 × 109 (3.8) 3.9 × 109 (3.6) 6.98 × 109 (3.3) 1.12 × 1010 (3.0) 1.68 × 1010 (2.8) 2.39 × 1010 (2.6) 3.26 × 1010 (2.5) 4.32 × 1010 (2.3) 5.55 × 1010 (2.2) 8.63 × 1010 (2.0) 1.26 × 1011 (1.8) 2.02 × 1011 (1.7) 3.86 × 1011 (1.5) 8
3.01 × 10 (8.5) 7.09 × 108 (8.5) 1.44 × 109 (8.7) 2.56 × 109 (8.2) 3.28 × 109 (8.1) 3.88 × 109 (8.2) 6.14 × 109 (7.9) 8.61 × 109 (8.0) 1.63 × 1010 (7.8) 2.75 × 1010 (7.5) 4.27 × 1010 (7.1) 6.24 × 1010 (6.9) 8.72 × 1010 (6.6) 1.17 × 1011 (6.3) 1.53 × 1011 (6.0) 2.43 × 1011 (5.6) 3.6 × 1011 (5.3) 5.86 × 1011 (4.8) 1.14 × 1012 (4.3) 8
found at the first steady state represent the required master equation solutions.29 These branching ratios for each potential well were then used to compute apparent rate constants for the formation of all products and stabilized intermediates, where the apparent rate constant for each product/intermediate is equal to a product of the chemical activation rate constant and the branching ratio for the corresponding potential well. Master equation calculations were performed for pressures of 7.6, 760, and 7600 Torr and within the 300-2500 K temperature range. The computed high-pressure limit and apparent rate constants at various temperatures and pressures are collected in Table 1 and Tables S2-S4 of the Supporting Information. There is one reaction considered in our study (i5 f p6 + H, see Figure 1) which proceeds without an exit barrier. In this case we applied canonical variational transition state theory (CVTST)30-32 to locate variational transition states required in RRKM-ME calculations of pressure- and temperature-dependent rate constants. We performed PES scan considering the C-H bond distance (for the C-H bond to be broken) r(CH) in the i5 adduct as a reaction coordinate. During the scan, for each r(CH) we performed partial geometry optimization with r(CH) being fixed and other geometric parameters being fully optimized at the B3LYP/6-311G** level. All geometry optimizations were followed by calculations of 3N - 7 projected vibrational frequencies (i.e., an imaginary frequency corresponding to the reaction coordinate was projected out), molecular structure parameters, and ZPE corrections. The B3LYP relative energies were further scaled to match the i5 f p6 + H dissociation
C6H6 + CH2CCCH3
C6H6 + CH3CHCCH
C6H6 + CH2CHCCH2
8.56 × 10 (24.2) 1.98 × 109 (23.8) 3.79 × 109 (23.0) 7.17 × 109 (22.9) 9.26 × 109 (22.8) 1.08 × 1010 (22.8) 1.75 × 1010 (22.5) 2.43 × 1010 (22.5) 4.65 × 1010 (22.1) 8.06 × 1010 (21.9) 1.3 × 1011 (21.7) 1.96 × 1011 (21.5) 2.83 × 1011 (21.3) 3.95 × 1011 (21.2) 5.35 × 1011 (21.1) 9.06 × 1011 (20.9) 1.42 × 1012 (20.7) 2.5 × 1012 (20.5) 5.37 × 1012 (20.3)
1.84 × 10 (5.2) 5.81 × 108 (7.0) 1.43 × 109 (8.7) 3.24 × 109 (10.4) 4.5 × 109 (11.1) 5.62 × 109 (11.9) 1.03 × 1010 (13.3) 1.55 × 1010 (14.4) 3.49 × 1010 (16.6) 6.79 × 1010 (18.4) 1.19 × 1011 (19.9) 1.93 × 1011 (21.2) 2.97 × 1011 (22.4) 4.37 × 1011 (23.4) 6.15 × 1011 (24.2) 1.12 × 1012 (25.8) 1.85 × 1012 (27.0) 3.46 × 1012 (28.4) 7.96 × 1012 (30.1)
1.43 × 109 (40.4) 3.4 × 109 (40.8) 6.7 × 109 (40.6) 1.31 × 1010 (41.9) 1.71 × 1010 (42.1) 1.97 × 1010 (41.7) 3.25 × 1010 (41.9) 4.48 × 1010 (41.6) 8.7 × 1010 (41.4) 1.52 × 1011 (41.2) 2.46 × 1011 (41.2) 3.74 × 1011 (41.1) 5.45 × 1011 (41.1) 7.65 × 1011 (41.0) 1.04 × 1012 (41.0) 1.77 × 1012 (40.8) 2.79 × 1012 (40.7) 4.96 × 1012 (40.7) 1.07 × 1013 (40.4)
8
8
energy computed at the more accurate G3(MP2,CC)//B3LYP level, and the scaled energies were then utilized in CVTST calculations. Then, for each temperature we calculated a set of conventional TST rate constants k(T) considering each structure on the scanned dissociation path as a regular transition state with its respective energy relative to i5 as the reaction barrier height and using its molecular parameters, such as projected vibrational frequencies and moments of inertia, to compute partition functions. Then, the structure with the minimal k(T) value was chosen as the variational transition state and was utilized in subsequent RRKM-ME calculation of the pressuredependent rate constant at the same temperature. The choice of the G3(MP2,CC)//B3LYP approach to generate the minimal energy reaction path (MEP) potential of the H loss for CVTST calculations is dictated by the size of the molecular system under consideration; more accurate multireference CASPT2//CASSCF calculations are considerably more expensive. Moreover, it is our experience that CVTST rate constants for H elimination reactions computed using CCSD(T)//B3LYP MEPs normally agree with those obtained with the use of MEPs from multireference calculations within a factor of 2 or less.33 Results and Discussion Potential Energy Surface and the Reaction Mechanism. 1,2-Butadiene contains two CdC double and hence three sp2 hybridized carbon atoms participating in the π-system, which can serve as sites for the phenyl radical addition at the initial
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reaction step. Let us first consider the addition of C6H5 to the terminal C1 atom of the CH2 group in CH2CCHCH3. The potential energy diagram for this reaction route is illustrated in Figure 1. The addition occurs via a barrier of 2.0 kcal/mol and results in the initial complex i1, 1-phenyl-2-buten-2-yl, residing 36.9 kcal/mol lower in energy than the reactants. The intermediate i1 can then decompose by splitting a hydrogen atom or the CH3 group or undergo further isomerization steps ultimately leading to the formation of a five-member ring of the indene core. For instance, H elimination from the C1 atom in the attacked CH2 group leads to the product p1, 1-phenyl-3methylallene, lying 7.9 kcal/mol lower in energy than the reactants. This process takes place via a barrier of 34.2 kcal/ mol relative to i1, with the corresponding transition state positioned 2.7 kcal/mol below the reactants. Alternatively, a hydrogen atom can be split from the C3 carbon giving rise to the 1-phenyl-butyne-2 product p2, 5.7 kcal/mol under the reactants zero energy level. In this case, the barrier is slightly higher, 35.4 kcal/mol with respect to i1. Elimination of the CH3 group requires a somewhat lower barrier of 33.0 kcal/mol to be overcome and generates the product p5, 1-phenyl-propyne, 12.5 kcal/mol below the reactants. One can see that all three transition states for H and CH3 eliminations lie 1.5-3.9 kcal/ mol lower in energy than C6H5 + CH2CCHCH3 and are close in energy to each other, making the three product channels potentially competitive. Alternatively to its dissociation, i1 can be subjected to the rearrangement involving a 1,3-H shift from the phenyl ring to the C2 carbon producing another intermediate i2, where the radical center is shifted to the phenyl ring. The barrier for this process is computed to be 23.4 kcal/mol, nearly 10 kcal/mol lower than that for the CH3 loss, and i2 resides 33.1 kcal/mol lower in energy than the reactants. Next, i2 can undergo a facile closure of a five-member ring overcoming a 10.8 kcal/mol barrier and leading to the formation of the 1-methyl-3H-inden2-yl intermediate i3, which possesses an indene core containing fused six- and five-member rings and lies in a deep potential energy well, 65.5 kcal/mol below C6H5 + CH2CCHCH3. This intermediate can dissociate to indene or its methyl substituted analogs by CH3 or H eliminations, respectively. For instance, the loss of the CH3 group occurs via a barrier of 28.7 kcal/mol with the corresponding transition state positioned as low as at -36.8 kcal/mol relative to the zero energy level of the reactants. Indene + CH3 are the most thermodynamically favorable reaction products exothermic by 46.5 kcal/mol. Two feasible H eliminations from i3 can produce 3-methyl-indene (p3) and 1-methyl-indene (p4) exothermic by 39.9 and 36.7 kcal/mol, respectively, via barriers of 31.9 and 33.2 kcal/mol, respectively, which are 3-4 kcal/mol higher than the barrier for the CH3 loss. As seen in Figure 1, some additional products can be formed via a mechanism involving migration of the phenyl moiety from C1 to the middle carbon atom C2. This migration over the C1-C2 bond occurs in two steps and leads to the formation of the intermediate i5, 2-phenyl-2-buten-1-yl/2-phenyl-1-buten-3-yl, residing 61.4 kcal/mol below the reactants. At the first step, C6H5 moves toward the center of the C1-C2 bond forming the bycyclic intermediate i6 via a barrier of 20.2 kcal/mol. i6 resides in a shallow potential well and rearranges to i5 overcoming a low barrier of 0.7 kcal/mol. Alternatively, i5 can be produced directly from the reactants by addition of C6H5 to the central C2 atom of 1,2-butadiene taking place via a barrier of 2.0 kcal/ mol. H elimination in i5 is only feasible from the CH3 group leading to the formation of 2-phenyl-1,3-butadiene p6, exo-
Kislov and Mebel thermic by 17.2 kcal/mol. No distinct transition state was found for the H loss, which therefore is predicted to occur without an exit barrier. Note that p6 is the most stable isomer among nonPAH C10H10 products of the C6H5 + CH2CCHCH3 reaction. The CH3 loss from i5 is not anticipated to be competitive as it would lead to a carbene or a biradical product. The two entrance channels leading to i1 and i5 are interconnected. The highest barrier on the i1 f i5 pathway is 3.2 kcal/mol lower than that for the i1 f i2 f i3 isomerization. This means that both addition channels forming i1 and i5 can lead to a common set of products, including indene + CH3 (-46.5 kcal/mol), 3-methylindene + H (p3, -39.7 kcal/mol), 1-methylindene + H (p4, -36.6 kcal/mol), 2-phenyl-1,3-butadiene + H (p6, -17.2 kcal/ mol), 1-phenyl-propyne + CH3 (p5, -12.5 kcal/mol), 1-phenyl3-methylallene + H (p1, -7.9 kcal/mol), and 1-phenyl-butyne2 + H (p2, -5.7 kcal/mol). It should be noted that other channels involving isomerizations of i1 via various H migrations are not expected to be competitive. For example, a 1,3-H shift from the CH3 group to the radical site could be feasible with the formation of 4-phenylbuten-3-yl, the initial adduct in the C6H5 + 1,3-butadiene reaction. However, a barrier for such H shift in the similar C4H7 radical (but without phenyl substitution) was calculated to be as high as 41.5 kcal/mol for the trans-2-buten-2-yl to trans-1methylallyl rearrangement;34 this is about 18 kcal/mol higher than that for i1 f i2 and at least 6 kcal/mol higher than those for H and CH3 losses from i1. By the analogy with the C4H7 system carefully studied by Miller,34 other H migrations in i1 are anticipated to exhibit even higher barriers. Next we consider C6H5 addition to the C3 carbon atom of 1,2-butadiene (Figure 2). The calculated barrier for this process is 2.1 kcal/mol, very close to the 2.0 kcal/mol barrier for the C1 addition. The initial complex i4, 3-phenyl-2-buten-2-yl, lies 36.9 kcal/mol lower in energy than the C6H5 + CH2CCHCH3 reactants and thus its energy is practically identical with that of 1-phenyl-2-buten-2-yl i1. The isomers i4 and i1 can be converted to one another by switching the position of the CH3 group with that of a hydrogen atom in the CH2 group. As evident from the comparison of the energies of i1 and i4 as well as of the transition states for the phenyl radical additions to C1 and C3, the CH3/H swap does not affect the energetics significantly. Therefore, we can extrapolate the results obtained for dissociation and isomerization of i1 to the processes involving i4 (also denoted as i1′ in Figure 2). H eliminations from the C3 and C1 atoms in i4 are expected to produce 1-phenyl-1-methylallene p1′ and 3-phenyl-butyne-1 (1-phenyl-1-methylpropyne) p2′, respectively. Alternatively, the CH3 loss should lead to the formation of phenylallene p5′. A 1,3-H shift from the phenyl ring to the radical site of i4 is expected to produce the intermediate i2′, which in turn should easily undergo a fivemember ring closure producing i3. As it was discussed above, the intermediate i3 can dissociate to indene + CH3 or 3- and 1-methyl substituted indenes + H. One can see that the reaction pathway starting with the phenyl addition to C3 and proceeding via the initial complex i4 can also contribute to the indene formation in the phenyl +1,2-butadiene reaction. Since the reaction scheme via i4 is anticipated to be similar to that via i1, we will not perform detailed kinetic RRKM-ME calculations for the i4-related pathways. Figure 3 shows direct H abstraction pathways leading to various C6H6 + C4H5 products. There are three distinct types of hydrogen atoms in the CH, CH2, and CH3 groups of 1,2butadiene and therefore three different H abstraction channels are possible. They produce benzene together with C4H5 isomers
Reaction of Phenyl Radical with 1,2-Butadiene
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Figure 4. RRKM-ME calculated branching ratios vs temperature (top panels) and corresponding Arrhenius plots (bottom panels) for the formation of various products in the C6H5 + 1,2-butadiene f i1/i5 f products reaction network at various pressures: 7.6 Torr (a), 760 Torr (b), and 7600 Torr (c).
CH2CCCH3, CH2CHCCH2, and CH3CHCCH with exothermicities of 25.1, 22.8, and 22.2 kcal/mol via barriers of 2.8, 3.2, and 4.3 kcal/mol, respectively. One can see that the H abstraction barriers are only slightly higher than the C6H5 addition barriers, therefore the H abstraction routes can compete with the addition channels. All these competitive channels were considered in calculations of the total rate constant and product branching ratios described in the next Section. Rate Constants and Product Branching Ratios. As described in the previous Section, the reaction of phenyl radical with 1,2-butadiene can proceed either by intramolecular addition forming one of the i1, i4, or i5 adducts, or by abstraction of an H-atom from 1,2-butadiene, resulting in the formation of CH2CCCH3, CH2CHCCH2, or CH3CHCCH isomers together with benzene (see Figures 1-3). We computed bimolecular rate constants for all of these six competing reactions, which are presented in Table 1 within the 300-2500 K temperature range along with their branching ratios. At all studied temperatures, the abstraction channels combined demonstrate significantly higher branching ratio (70% and more) as compared to the addition channels combined. Indeed, at 300, 1000, and 2000 K the computed branching ratios between the addition and
abstraction channels are 30.2:69.8, 16.2:83.8, and 10.5:89.5, respectively. At low reaction temperatures, the contribution of the addition processes is found to be higher than at high temperatures relevant to combustion. The results indicate that the combined relative yield of all products formed via the C6H5 + 1,2-butadiene f i1/i4/i5 additions will not exceed 30% of the total product yield and is typically within 10-15% at 1000-2000 K. Among the individual reactions, the H abstraction from the CH3 group of 1,2-butadiene is the fastest process, followed by the abstractions from the CH2 and CH groups. Noteworthy, the H abstraction from CH exhibits the lowest barrier of the three, 2.8 kcal/mol, but the H abstraction from CH3 occurring with a slightly higher barriers of 3.2 kcal/mol is favored due to a higher symmetry factor of 3. The additions leading to the formation of the i1 and i5 intermediates exhibit similar rates, except at the temperatures below 600 K, where the C6H5 + 1,2-butadiene f i1 reaction is found to be about a factor of 2 faster than the addition leading to i5. The formation of the i4 adduct is the slowest process among all six competitive reactions. Now let us discuss the C6H5 + 1,2-butadiene f i1/i5 reaction network shown in Figure 1. First, we need to justify why we
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Figure 4. Continued.
do not have to include the reaction pathways initiating from i4 into the common kinetic scheme. On one hand, one can expect that the C6H5 group in i5 can continue its migration and move over the C2-C3 bond to produce i4 via a barrier similar to that for the i5 f i1 rearrangement. On the other hand, i5 resides in a much deeper potential well than i1 and i4; and the barrier for the H loss in i5, i5 f p6 + H, is slightly lower than that for the reverse i5 f i1 reaction and hence than that for i5 f i4. Also, the H loss in i5 is favored over the phenyl group migration by the entropy factor. As a result, the calculated high-pressurelimit rate constants for i5 f p6 + H are several times higher than those for i5 f i1 (see Table S2 in Supporting Information) and therefore for i5 f i4, so that the i1 f i5 and i4 f i5 reactions can be considered practically irreversible, and the reaction flux from i5 to i4 would be minimal. In addition, the addition channels in the C6H5 + 1,2-butadiene reaction are found to be responsible for less than 30% of the total product yield (10-15% at combustion temperatures); therefore, small errors in kinetic calculations due to closing of the i5 f i4 path are not expected to affect the overall picture significantly. Nevertheless, the pathways via i1 and i5 are intervened and have to be treated together. In our RRKM-ME calculations, we first considered the C6H5 + 1,2-butadiene f i1 f intermediates/
products reaction scheme (including i1 f i5) and then the C6H5 + 1,2-butadiene f i5 f intermediates/products scheme (including i5 f i1) and the computed rate constants for the formation of each product (or stabilization of each intermediate) from the two calculations were added together, because the bimolecular reactions leading from the reactants to i1 and i5 are independent. The resulting rate constants and branching ratios are illustrated in Figure 4 , with their numerical values given in Tables S3 and S4 of Supporting Information. As follows from our calculations, at low temperatures the stabilization of the i1, i3, and i5 intermediates is the dominant outcome of the phenyl + 1,2-butadiene addition reactions. At low pressures, the major product is i5 followed by i1, whereas at p ) 760 and 7600 Torr i1 is preferable over i5 up to about 500 and 600 K, respectively. The collisional stabilization of the intermediates becomes negligible above 1000 K at 7.6 Torr and above 1200 K at the higher pressures. At 7.6 Torr, the yields of p6 + CH3 and p5 + H become significant around 700 K, and they overtake the yield of i5 just above 800 K. At higher pressures, this happens at higher temperatures around 1000 K (760 Torr) and 1100 K (7600 Torr). At temperatures above 1100 K, p5 + H and p6 + CH3 are the major products with relative yields in the ranges of 46-62% and 43-26% (7.6 Torr),
Reaction of Phenyl Radical with 1,2-Butadiene
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Figure 4. Continued.
TABLE 2: Fitted Rate Expressions k ) ATnexp(-E/RT) for the Computed Apparent Rate Constants for the Formation of Most Important Products/Intermediates in C6H5 + 1,2-Butadiene Reaction at 760 Torr reaction k(total)a C6H5 C6H5 C6H5 C6H5 C6H5 C6H5 C6H5 C6H5 C6H5 C6H5 C6H5 C6H5 C6H5
+ + + + + + + + + + + + +
300-2500 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene 1,2-butadiene
f f f f f f f f f f f f f
p1 + H p2 + H p3 + H p4 + H p5 + CH3 indene + CH3 p6 + H p6 + H i1 i2 i3 i5 i5
C6H5 + 1,2-butadiene f C6H6 + CH2CCCH3 C6H5 + 1,2-butadiene f C6H6 + CH3CHCCH C6H5 + 1,2-butadiene f C6H6 + CH2CHCCH2 a
temperature range (K) Additions 300-2500 300-2500 300-2500 300-2500 300-2500 300-2500 300-900 900-2500 300-2500 300-2500 300-2500 300-900 900-2500 Abstractionsb 300-2500 300-2500 300-2500
ln A (cm3 mol-1 s-1) 6.37 26.30 28.01 92.77 90.88 36.12 102.42 -105.69 47.66 298.44 326.92 402.84 13.62 530.77 5.04 5.57 5.73
n 3.17 0.08 -0.0011 -8.68 -8.33 -0.78 -9.62 18.52 -2.30 -38.29 -43.32 -51.87 1.87 -65.35 3.14 3.15 3.14
E (cal mol-1) 1458.22 12 274.61 12 943.45 26 581.95 26 740.23 12 582.53 26 556.13 -4330.18 15 085.13 37 007.13 40 001.68 59 550.50 2869.44 109 725.94 1424.93 2706.53 1537.51
Total rate constant for disappearance of the reactants including all six addition and abstraction channels. Reverse dissociation back to the reactants has been taken into account. b Computed at the high-pressure limit.
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Figure 5. Overall branching ratios of different products in the C6H5 + 1,2-butadiene reaction calculated at various pressures: 7.6 Torr (a), 760 Torr (b), and 7600 Torr (c).
Reaction of Phenyl Radical with 1,2-Butadiene 44-62% and 40-26% (760 Torr), and 40-62% and 38-26% (7600 Torr), respectively. The yield of indene + CH3 maximizes at 800 K at the low pressure (∼10%) and at 900 K at higher pressures, 6% and 5% at 760 and 7600 Torr, respectively, and falls down at higher temperatures. p2 + H and p1 + H are found to be noticeable minor products at high temperatures with their yields reaching ∼8% and ∼3% at 2500 K independent of pressure. Our kinetic calculations clearly demonstrate that at combustion temperatures of 1200-1300 K and above, the pressure effects on branching ratios become insignificant and the production of collisionally stabilized adducts is unimportant. Alternatively, for low-temperature conditions, such as in pyrolysis and shock tubes, the rate constants are strongly pressuredependent and stabilization of reaction intermediates is essential as they exhibit high relative yields. The results of our kinetic calculations for the C6H5 + 1,2butadiene f products reaction as a whole are summarized in Table 2 and Figure 5. Table 2 shows three-parameter modified Arrhenius expressions for the total reaction rate constants and those leading to most important products at normal atmospheric pressure. These expressions can be utilized in future for kinetic modeling of reaction networks related to the formation of indene and other PAH species. Figure 5 shows relative yields of all possible reaction products, with numerical values collected in Table S5 of Supporting Information. The products, which can be formed in the C6H5 + 1,2-butadiene f i4/i5 network (Figure 2), p1′ + H, p2′ + H, p5′ + CH3, and stabilized i4 (i1′) and i2′, are also included, assuming that i4 is connected to i5 via a barrier similar to that for i1 f i5 and that the product branching ratios within this network are the same as those computed for C6H5 + 1,2-butadiene f i1/i5. Also, we allowed for the formation of indene + CH3, p3 + H, p4 + H, and p6 + H, and stabilization of i3 and i5 both via the i1 and i4 intermediates. To obtain the branching ratios in Figure 5, we simply multiplied the temperature-dependent branching ratios of various bimolecular phenyl addition channels (Table 1) by the pressure and temperature-dependent branching ratios for each product within the particular C6H5 + 1,2-butadiene f i1/i5 and C6H5 + 1,2butadiene f i1/i4 networks. For the direct H abstraction C6H6 + C4H5 products, branching ratios are pressure independent; the values drawn in Figure 5 are the same as those presented in Table 1 for the high-pressure limit and they do not require further discussion. One can see that besides C6H6 + C4H5, noticeable reaction products include the C9H8 isomers p5 and p5′ (+ CH3) and C10H10 p6 (+ H) at higher temperatures above 900-1100 K, as well as the stabilized C10H11 intermediates i5, i1, and i4 at lower temperatures. The calculated branching ratios for p5 + CH3 and p5′ + CH3 reach the ranges of 2-4 and 1-2%, respectively, at high temperatures. The branching ratio of p6 + H grows with temperature up to ∼7% at 1000 K and 7.6 Torr, but then decreases to 5-3% at 1300-2000 K and ∼2% at 2500 K. Stabilization of i1 and i4 is maximal at 300 K (∼14 and 6%, respectively, at 760 and 7600 Torr) and remains significant up to 700 K at the high pressures. The yield of stabilized i5 has a maximal value of ∼20% at 300-500 K and 7.6 Torr and then monotonously falls down at higher temperatures. At the higher pressures, the temperature dependence of the relative yield of i5 is different; initially, it increases from 10% at 300 K to 13-14% at 700-800 K and then decreases to nearly zero at 1200-1300 K. The yield of indene is very small, with the largest value of 2% found at 700 K and 7.6 Torr. Since the intermediates i1 and i5 can be collisionally stabilized and therefore are likely to react with O2 or other radicals in a real combustion system, it is helpful to estimate their lifetimes
J. Phys. Chem. A, Vol. 114, No. 29, 2010 7691 at various temperatures, if they were only undergoing unimolecular decay. These estimates can be done using inverse values of the high-pressure limit rate constants (Table S2) for the most favorable unimolecular decomposition channels, i1 f p5 + CH3 and i5 f p6 + H. Such calculations give the lifetimes from 28 µs to 0.2 ps for i1 and from 0.9 s to 40 ps for i5 at 700 to 2500 K, respectively, indicating that i5 indeed is a long-lived intermediate at low combustion temperatures. The intermediate i3 is found to be stabilized only to a small extent, but since it might react bimolecularly providing alternative routes to indene, we estimated its lifetime as well, with respect to the i3 f indene + CH3 unimolecular decomposition. This calculation gives the values of 17 µs - 2 ps in the same 700-2500 K temperature range. Conclusions Ab initio calculations of the PES for the reaction of phenyl radical with 1,2-butadiene demonstrate that the reaction can proceed either by direct hydrogen abstraction producing benzene and C4H5 radical isomers or by addition of phenyl to three different carbon atoms C1-C3 in CH2CCHCH3 followed by isomerizations of C10H11 adducts and their dissociation by H or CH3 losses. The H abstraction channels occurring via barriers of 2.8-4.3 kcal/mol are kinetically preferable in the entire considered 300-2500 K temperature range contributing 70-90% to the total product yield. The most favorable of them is H abstraction from the methyl group producing C6H6 + CH2CHCCH2 (∼40%). The calculated branching ratio of C6H6 + CH3CHCCH (H abstraction from CH2) increases from 5% to 30% as the temperature rises from 300 to 2500 K, whereas the yield of C6H6 + CH2CCCH3 (H abstraction from CH) slightly decreases from 24 to 20%. The phenyl addition channels occur via barriers of ∼2 kcal/mol and are responsible for 30-10% of the total product yield, with their contribution decreasing with a temperature increase. The products of the addition channels include collisionally stabilized C10H11 adducts, 1-phenyl-2-buten-2-yl i1, 3-phenyl-2-buten-2-yl i4, and 2-phenyl-2-buten-1-yl/2-phenyl-1-buten-3-yl i5, which are favored under low temperature conditions, as well as their dissociation products, 1-phenyl-propyne p5 + CH3, phenylallene p5′ + CH3, and 2-phenyl-1,3-butadiene p6 + H, more preferable at higher temperatures. The calculated yield of the CP-PAH product indene is relatively small and is maximized at 2% at 700 K and 7.6 Torr, so that indene can only be a minor reaction product at the temperatures relevant to combustion. Nevertheless, CPPAH or PAH molecules can be potentially formed in secondary reactions involving the primary products of C6H5 + 1,2butadiene, such as, for example, H-assisted isomerization of C8H9 and C10H10, or via HACA-type sequences. Three-parameter modified Arrhenius expressions have been generated for the total reaction rate constants and rate constants for the most important product channels, which can be utilized in kinetic modeling of reaction networks related to PAH and CP-PAH formation. Our calculations also attest that, at typical combustion temperatures, product branching ratios are practically independent of pressure, and collisional stabilization of reaction intermediates does not play a significant role. Acknowledgment. This work is funded by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Sciences of U.S. Department of Energy (Grant No. DE-FG02-04ER15570). We thank Prof. Vadim Knyazev for helpful discussions on RRLM-ME calculations.
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Supporting Information Available: B3LYP, CCSD(T), MP2, and G3 calculated total energies, zero-point energy corrections (ZPE), B3LYP/6-311G** optimized Cartesian coordinates, vibrational frequencies, moments of inertia, and rotational constants of all species involved in the studied reaction mechanisms (Table S1); RRKM calculated high-pressure limit thermal rate constants for rearrangements/decompositions of various C10H11 intermediates in the C6H5 + 1,2-butadiene f i1/i5 f products reaction network (Table S2); computed apparent rate constants for the formation of various products at different temperatures and pressures in the C6H5 + 1,2-butadiene f i1/i5 reaction network (Table S3); computed branching ratios for the formation of various products and collisional stabilization of various C10H11 intermediates in the C6H5 + 1,2-butadiene f i1/i5 network (Table S4); and overall branching ratios of different products in the C6H5 + 1,2-butadiene reaction (Table S5). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Frenklach, M. Phys. Chem. Chem. Phys. 2002, 4, 2028. (2) Frenklach, M.; Wang, H. Proc. Combust. Inst. 1991, 23, 1559. (3) Frenklach, M.; Clary, D. W.; Gardiner, W. C.; Stein, S. E. Proc. Int. Symp. Combust. 1984, 20, 887. (4) Wang, H.; Frenklach, M. J. Phys. Chem. 1994, 98, 11465. (5) Appel, J.; Bockhorn, H.; Frenklach, M. Combust. Flame 2000, 121, 122. (6) Bittner, J. D.; Howard, J. B. Proc. Int. Symp. Combust. 1981, 18, 1105. (7) (a) Frenklach, M.; Moriarty, N. W.; Brown, N. J. Proc. Combust. Inst. 1998, 27, 1655. (b) Moriarty, N. W.; Brown, N. J.; Frenklach, M. J. Phys. Chem. A 1999, 103, 7127. (8) Kislov, V. V.; Islamova, N. I.; Kolker, A. M.; Lin, S. H.; Mebel, A. M. J. Chem. Theory Comput. 2005, 1, 908. (9) Linstedt, P.; Maurice, L.; Meyer, M. Faraday Discuss. 2001, 119, 409. (10) Fascella, S.; Cavallotti, C.; Rota, R.; Carra, S. J. Phys. Chem. A 2004, 108, 3829. (11) Ismail, H.; Park, J.; Wong, B. M.; Green, W. H., Jr.; Lin, M. C. Proc. Combust. Inst. 2005, 30, 1049. (12) Gu, X.; Zhang, F.; Kaiser, R. I. J. Phys. Chem. A 2009, 113, 998. (13) Gu, X.; Zhang, F.; Kaiser, R. I.; Kislov, V. V.; Mebel, A. M. Chem. Phys. Lett. 2009, 474, 51. (14) Kaiser, R. I.; Zhang, F.; Gu, X.; Kislov, V. V.; Mebel, A. M. Chem. Phys. Lett. 2009, 481, 46. (15) Musick, M.; Van Tiggelen, P. J.; Vandooren, J. Combust. Sci. Technol. 2000, 153, 247. (16) Marinov, N. M.; Pitz, W. J.; Westbrook, C. K.; Castaldi, M. J.; Senkan, S. M. Combust. Sci. Technol. 1996, 116-117, 211. (17) Hidaka, Y.; Higashihara, T.; Ninomiya, N.; Masaoka, H.; Nakamura, T.; Kawano, H. Int. J. Chem. Kinet. 1996, 28, 137.
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