Kinetics of Homoallylic/Homobenzylic Rearrangement Reactionsunder Combustion ConditionsZhaohui Wang, Lidong Zhang, and Feng Zhang*

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, P. R. China

*S Supporting Information

ABSTRACT: Homoallylic/homobenzylic radicals refer to typical radicalswith the radical site located at the β position from the vinyl/phenyl group.These radicals are largely involved in combustion systems, such as thepyrolysis or oxidation of alkenes, cycloalkanes, and aromatics. The 1,2-vinyl/phenyl migration via two steps (cyclization/fission) is a peculiarreaction type for the homoallylic/homobenzylic radicals, entitled homo-allylic/homobenzylic rearrangement, which has been studied by theoreticalcalculations including the Hirshfeld atomic charge analysis in the presentwork. With the help of rate constant calculations, the competition betweenthis reaction channel and other possible pathways under combustiontemperatures (500−2000 K) were evaluated. Analogous 1,3- and 1,4-vinyl/phenyl migration reactions for similar radicals with the radical sites locatedat the γ and δ positions from the vinyl/phenyl group were also computed.The results indicate that the 1,2-vinyl/phenyl migration is particularly important for the kinetics of unimolecular reactions ofhomoallylic radicals under 1500 K; nevertheless, it still has noticeable contribution at higher temperature. For those radicals withthe radical site at the γ or δ positions, the respective 1,3- or 1,4-vinyl/phenyl migration channel plays an insignificant role undercombustion conditions.

1. INTRODUCTIONUnimolecular rearrangement reactions of radicals such as the Hatom, methyl, or hydroxy migration are typical reactionsinvolved in combustion chemistry.1−6 Usually a vicinalmigration is not competitive due to the high strain energy ofthe three-membered ring structure in the transition state.However, a typical reaction mechanism involving a 1,2-vinyl/phenyl migration for entitled homoallylic or homobenzylicradicals whose structures are schematically shown in Figure 1

may make an exception. This reaction mechanism has been firstproposed as the homoallylic rearrangement by Montgomery etal. in 19677−10 for allylcarbinyl radical. The 1,2-vinyl migrationis regarded as taking place by a two-step sequence: (1) ringclosure of an allylcarbinyl radical to form a cyclopropylcarbinylradical and (2) ring opening of the formed radical to yield anallylcarbinyl radical of rearranged structure.8,11,12 Follow-uptheoretical investigations revealed that this reaction mechanismcould take place with quite low barrier heights.13,14 For

instance, George et al. calculated that the barrier height of the1,2-vinyl migration in 1-buten-4-yl radical is less than 10 kcal/mol.13

Kinetic studies on this homoallylic rearrangement mecha-nism started from 1980s.11,15 Effio et al. measured rateconstants of the ring opening and reverse reaction ofcyclopropylcarbinyl radical using kinetic electron paramagneticresonance (EPR) spectroscopy at a temperature range from−21.0 to 3.5 °C,11 Chatgilialoglu et al. measured the rateconstants for the overall rearrangement of the 2,2-dimcthyl-3-buten-1-yl radical to the 1,1-dimethyl-3-buten-1-yl radical from−145 to −101 °C by the kinetic EPR spectroscopy as well.12

Previous studies indicated that this reaction plays a veryimportant role under low temperature conditions.16−18 It hasbeen recognized that the homoallylic and homobenzylicradicals also largely exist in the pyrolysis/oxidation processesof some hydrocarbons including alkenes,17,18 cycloalkanes,19,20

aromatics,21,22 biomass fuels,23,24 etc. However, in previouscombustion kinetic studies, the predominant consumptionchannels of such homoallylic and homobenzylic radicals havebeen in controversy. It was suggested that the 1-penten-4-ylradical was overwhelmingly consumed by direct beta-dissociations in a kinetic modeling study on 1-penteneoxidation at high temperature.25 However, in a kinetic

Received: April 3, 2014Revised: August 1, 2014Published: August 4, 2014

Figure 1. Schematic structures of the homoallylic (a) andhomobenzylic (b) radicals.

Article

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modeling study of methyl cyclohexane pyrolysis and oxidation,1-penten-4-yl radical was regarded as an important source of1,3-butadiene through a 1,2-H-shift route.20 An earlier study onthe pyrolysis of 1-pentene at 873 K suggested that thehomoallylic rearrangement reaction could be the dominantchannel for the consumption of 1-penten-4-yl and 2-penten-5-yl radicals.26 Recently, in a combined experimental and kineticmodeling study of n-propylbenzene flame, the 1,2-phenylmigration was believed to be the reason for 1-phenyl-2-propylradical isomerizing into 2-phenyl-1-propyl radical.21

Analogous 1,3- or 1,4-vinyl/phenyl migration could also takeplace if the radical site is located at the γ or δ position from thevinyl/phenyl group. In the present work, we performedsystematic studies on these vinyl/phenyl migration reactionsof several typical alkenyl and aromatic radicals by theoreticalcalculations focusing on combustion temperatures (500−2000K), as shown in Figure 2. The competitive reaction pathways of

the decomposition of these selected radicals such as the betadissociation and H-elimination were also studied to reveal thecompetition between the homoallylic rearrangement channelsand those other pathways under combustion conditions.

2. COMPUTATIONAL METHODSThe lowest energy conformer was first determined for eachstudied molecule (R1−R6 in Figure 2). The equilibriumgeometries of reactants, products, intermediates, and transitionstates were computed with the CBS-QB3 method, using theB3LYP/6-311G(2d,d,p) method to optimize geometriesfollowed by a series of MP2, MP4, and CCSD(T) calculationswith Pople type basis sets to obtain the electron correlationenergies.27 All of the stationary points were confirmed byvibrational analysis, while the saddle points were examined byintrinsic reaction coordinate (IRC)28 calculations showing thatappropriate reactants and products were connected. Thedissociation curve of the barrierless channels are constructedwith a stepwise of 0.05 Å using the B3LYP/6-311G(d,p)method, which was scaled by the dissociation energy computedwith the CBS-QB3 method. In order to deeply understand the

chemistry of these homoallylic reactions, the Hirshfeld atomiccharge analysis29 of all species was carried out at B3LYP/6-311G(d,p) using the electronic density of the molecule and of afictitious promolecule. The promolecule is defined as the sum(usually spherically averaged) over the ground-state atomicdensities, and the electronic density of the real molecule at eachpoint in space is then distributed over the atoms. The ratio ofatomic densities in the real molecule is defined as the same asthose in the promolecule. The Hirshfeld atomic charges aresuggested to yield chemically meaningful charges and showlittle basis set dependence.30 All electronic structure calcu-lations are carried out with the Gaussian 09 program package.31

The transition state theory with the Eckart tunnelingcorrection32 was used to compute the high pressure limit(HPL) rate constants of all the studied elementary reactions.The canonical variational transition state theory was used forthe reactions with loose transition states or barrierlessreactions.33 In short, the temperature-dependent rate constantwas minimized by that computed at each point along thereaction coordinate. The torsional modes corresponding tointernal rotations for both radicals and transition states wereassumed as one-dimensional (1-D) hindered rotors, while thehindrance potential was obtained by relaxed potential energyscan with the step of 10° at the B3LYP/6-311G(d,p) level. Thepotential is fitted by a Fourier series up to 14 terms tonumerically compute the partition function of the internalrotors.34 The steady-state approximation (SSA) was used indeducing the HPL rate constants of overall reactions, which willbe described in more detail in Section 3. All kinetic calculationsincluding VTST were performed with an open-source chemicalkinetics software, MESMER2.0.35

3. RESULTS AND DISCUSSION3.1. Homoallylic and Homobenzylic Rearrangements.

Figure 3a,b illustrates the reaction pathways of the 1-penten-4-yl (R1) and 1-phenyl-prop-2-yl (R2) radicals with relativeenergies computed at CBS-QB3 including the zero-pointenergy (ZPE) correction, respectively. The homoallylic/homobenzylic rearrangement reactions are shown in red dashlines. The vicinal H-migration pathways are excluded fromFigure 3 considering the high strain energy of the transitionstates and low entropies. One may expect strong multireferencecharacter for some loose structures such as the transitions statesof C−C dissociation. The CCSD(T) T1 diagnostic forstationary points involved in vinyl migration of R1 is shownin Table S8 in the Supporting Information, which indicates thatT1 diagnostic values for the transitions of endocyclization andC−C dissociation are around 0.03. Instead of providingextremely accurate energies and rate constants for numerousreactions studied in this work with high-cost multireferencecalculations, we aim to investigate the role of the homoallylic/homobenzylic mechanism among the competing pathwaysunder combustion condition by comparison; we believe CBS-QB3 is reliable for this purpose. Generally, the homoallylic/homobenzylic rearrangement takes place by overcoming quite alow barrier, e.g., ∼10 kcal/mol for R1 and ∼15 kcal/mol for R2.With the very similar three-membered ring structure in thetransition states, the barrier heights of the 1,2-phenyl migrationare slightly higher than that of 1,2-vinyl migration due to theloss of aromaticity in the migration process of 1-phenyl-prop-2-yl radical. The exocyclization intermediates M1 and M2 bothhave a three-membered ring cyclic structure with the radicalcenter on the side branch of the ring. Transition states and

Figure 2. Vinyl/phenyl migration reactions of several typical alkenyland aromatic radicals. R, P, and M denote the reactant, product, andintermediate, respectively. Rxn means a reaction.

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intermediates in homoallylic rearrangement all have cis andtrans isomers due to the cyclic structure, and the energydifferences between the cis/trans isomers are less than 1 kcal/mol, also shown in Figure 3a. The conjugated structure of thebenzene ring has been broken in M2; consequently, the energygap between M2 and R2 is much higher than that between M1and R1. Besides this rearrangement reaction, R1 and R2 canalso undergo other reactions such as beta dissociation, H-elimination, and endocyclization, which are shown in Figure 3as well. Comparing with the other possible pathways, thehomoallylic/homobenzylic rearrangements have remarkablelow barriers. The C−C bond beta dissociation for both 1-penten-4-yl and 1-phenyl-prop-2-yl radicals shows relativelyhigh barrier (∼35 kcal/mol) due to the effect of unstable vinyland phenyl radicals. The endocyclization exhibits much higherbarrier than the exocyclization since the “endo” cycloalkylradical has broken the occupied π orbitals in a strained ring. Inorder to reveal the dramatic low barrier heights of the 1,2-vinyl/phenyl migration, additional analysis on the electronic effectsuch as charge distribution could be helpful, which will bediscussed in more detail later.The homoallylic/homobenzylic rearrangements could be

overwhelmingly competitive comparing with other possiblepathways considering the remarkable low barriers at least underlow temperature, which has already been uncovered by previouskinetic studies.26,36 However, the entropy contribution

increases with temperature, the channels of beta-dissociationare expected to play more important roles at highertemperature due to the loose structure of transition states.Hence the HPL rate constants of the reactions shown in Figure3 were computed in order to quantitatively reveal theimportance of the homoallylic/homobenzylic rearrangementsin the temperature range of 500 to 2000 K, which is of interestin combustion. As mentioned above, the partition functions ofinternal rotors were computed with the 1-D hindered rotorapproximation, while the hindrance potential was numericallyfitted with Fourier expression up to 14 terms. Figure 4illustrates the computed and simulated hindrance potentials forthe internal rotation around various C−C bonds in R1, showingpretty good agreement between the computed potentialenergies and the fitted functions. Table 1 lists the ratecoefficients for each step in 1,2-vinyl/phenyl migration. In the1,2-vinyl/phenyl migration, the rate constants of the ring-opening step is at least 2 order of magnitudes higher than thatof the ring-closure step according to our computation; thus, it isreasonable to deduce the rate constants of the 1,2-vinyl/phenylmigration by assuming the steady-state approximation (SSA)for the intermediates. The rate constants of the 1,2-vinyl/phenyl migration can be given by k = k1k2/(k−1 + k2), where k1is the forward rate constant for the reaction from reactant tointermediate, k−1 is the reverse rate constant from intermediateto reactant, and k2 is the forward rate constant from

Figure 3. Potential energy diagram for the consumption reactions of (a) 1-penten-4-yl radical (R1) and (b) 1-phenyl-prop-2-yl radical (R2); ZPE-corrected energies (kcal/mol) are given at the CBS-QB3 level.

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intermediate to product. Figure 5 illustrates the HPL rateconstants of relevant reactions of R1 and R2, where the rateconstants of the 1,2-vinyl/phenyl migration were deduced bythe SSA. It indicates that the 1,2-vinyl/phenyl migration is themost favored reaction channel for R1/R2 compared with othercompeting reactions at least under 1500 K due to its low energybarrier. However, without further information on the final fatesof P1 and P2, i.e., their decomposition pathways, it is risky tostate that the 1,2-vinyl/phenyl migration route has a significantimpact on the consumption of R1/R2 because it will possiblygo back to the reactant without further decompositionchannels. For instance, Tsang suggested that R1 is the majordecomposition reactant due to its greater stability over P1among 1000−2000 K at high pressures in his mechanism workof the decomposition of 1-pentenyl radicals.36 However, thisprediction might be suspicious: first, the stability of R1 and P1are comparable according to our results. Second, which is moreimportant, the decomposition reactions of P1 shall also beconsidered. For this reason, the decomposition rate constantsof P1 and P2 shown in Figure 3 are also computed and listed inthe Supporting Information.With the help of the computed rate constants of P1 and P2

decomposition, the branching ratios of these competing

reaction routes of R1 and R2 are deduced, as shown in Figure6. It is worth noting that the contribution of the homoallylic/homobenzylic rearrangement mechanisms to the total con-sumption of the reactants depends on the rate of bothhomoallylic/homobenzylic rearrangements and the subsequentdecomposition reactions, thus the branching ratio of vinyl/phenyl migration shown in Figure 6 actually includes alldecomposition paths of P1/P2. Although the contribution ofthis homoallylic/homobenzylic rearrangement mechanism isreduced with increasing temperature, it still approaches to∼50% to 60% for R1 and R2 decomposition at 1500 K, which isa characteristic temperature for combustion studies. It even still

Figure 4. Calculated (symbols) and simulated (solid line) hindrancepotential as a function of dihedral angle defined by various C−C bondsfor 1-penten-4-yl radical.

Table 1. Rate Coefficients (s−1) for Each Step in 1,2-Vinyl/Phenyl Migration

reactions R1 → M1a M1a → R1 M1a → P1 R1 → M1b M1b → R1 M1b → P1 R2 → M2 M2 → R2 M2 → P2

500 K 1.42 × 1006 3.51 × 1009 4.77 × 1009 1.83 × 1006 1.12 × 1010 4.00 × 1009 2.01 × 1004 6.73 × 1011 2.80 × 1011

600 K 8.30 × 1006 1.14 × 1010 1.45 × 1010 1.01 × 1007 2.99 × 1010 1.20 × 1010 2.58 × 1005 1.20 × 1012 5.71 × 1011

700 K 3.02 × 1007 2.67 × 1010 3.25 × 1010 3.50 × 1007 6.08 × 1010 2.66 × 1010 1.64 × 1006 1.82 × 1012 9.58 × 1011

800 K 8.09 × 1007 5.05 × 1010 6.01 × 1010 9.10 × 1007 1.04 × 1011 4.89 × 1010 6.72 × 1006 2.49 × 1012 1.42 × 1012

900 K 1.77 × 1008 8.30 × 1010 9.77 × 1010 1.94 × 1008 1.58 × 1011 7.92 × 1010 2.04 × 1007 3.17 × 1012 1.94 × 1012

1000 K 3.35 × 1008 1.24 × 1011 1.45 × 1011 3.59 × 1008 2.22 × 1011 1.17 × 1011 5.01 × 1007 3.85 × 1012 2.50 × 1012

1100 K 5.69 × 1008 1.72 × 1011 2.01 × 1011 6.01 × 1008 2.94 × 1011 1.62 × 1011 1.06 × 1008 4.50 × 1012 3.07 × 1012

1200 K 8.93 × 1008 2.27 × 1011 2.65 × 1011 9.30 × 1008 3.72 × 1011 2.14 × 1011 1.98 × 1008 5.14 × 1012 3.66 × 1012

1300 K 1.32 × 1009 2.87 × 1011 3.35 × 1011 1.35 × 1009 4.55 × 1011 2.71 × 1011 3.40 × 1008 5.74 × 1012 4.24 × 1012

1400 K 1.84 × 1009 3.52 × 1011 4.11 × 1011 1.88 × 1009 5.42 × 1011 3.33 × 1011 5.42 × 1008 6.32 × 1012 4.82 × 1012

1500 K 2.48 × 1009 4.21 × 1011 4.93 × 1011 2.50 × 1009 6.32 × 1011 3.99 × 1011 8.16 × 1008 6.86 × 1012 5.38 × 1012

1600 K 3.23 × 1009 4.93 × 1011 5.78 × 1011 3.24 × 1009 7.25 × 1011 4.68 × 1011 1.17 × 1009 7.38 × 1012 5.93 × 1012

1700 K 4.09 × 1009 5.68 × 1011 6.66 × 1011 4.07 × 1009 8.19 × 1011 5.40 × 1011 1.62 × 1009 7.87 × 1012 6.46 × 1012

1800 K 5.07 × 1009 6.44 × 1011 7.57 × 1011 5.01 × 1009 9.14 × 1011 6.14 × 1011 2.17 × 1009 8.33 × 1012 6.98 × 1012

1900 K 6.15 × 1009 7.22 × 1011 8.50 × 1011 6.04 × 1009 1.01 × 1012 6.90 × 1011 2.82 × 1009 8.76 × 1012 7.47 × 1012

2000 K 7.34 × 1009 8.01 × 1011 9.45 × 1011 7.18 × 1009 1.11 × 1012 7.67 × 1011 3.57 × 1009 9.16 × 1012 7.94 × 1012

aTrans conformer. bCis conformer.

Figure 5. Deduced high pressure limit rate constants of thehomoallylic/homobenzylic rearrangement and other competing path-ways among the unimolecular reactions of R1 (a) and R2 (b) varyingwith temperature.

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has ∼20% contribution even at 2000 K. One may assumepropene and vinyl radical as the dominant decompostitionproducts of R1 since they can be produced from both the directbeta-dissociation and homoallylic rearrangement.25 However,according to our computed rate constants of variousdecomposition channels, the favorable homoallylic rearrange-ment tends to produce 1,3-butadiene and methyl radical. Figure7a illustrates the yields of various final decomposition productsof R1. Obviously, the two pathways leading to 1,3-butadiene(plus methyl radical) and propene (plus vinyl radical) haveoverwelming contibution to the decomposition of R1, whichdisagrees with the estimation that 2-methyl-1,3-butadiene(isoprene) and H atom through 1,2 H-shift are major

decomposition products in a previous modeling study.20

Similar conclusion can be extrapolated to the decompositionof R2, as shown in Figure 7b. Styrene is suggested as asignificant decomposition product of R2, while the homo-benzylic rearrangement mechanism is responsible for thischannel. This prediction has been validated by the experimentalobservation of n-propylbenzene flame.21 Table 2 lists the

Arrhenius parameters of the deduced HPL rate constants forthe decomposition channels of R1 and R2, which might bevaluable to kinetic modeling studies of such combustionsystems involving homoallylic/homobenzylic radicals.As implied by the above theoretical investigation on the

typical homoallylic/homobenzylic radicals, it is reasonable tostate that the homoallylic/homobenzylic rearrangement mech-anism is extremely required to be considered in kinetic modelsof combustion systems involving such homoallylic/homoben-zylic radicals. Consequently, further decomposition of theproducts from this rearrangement mechanism probably leads tomajor products of the homoallylic/homobenzylic radicalsdecomposition especially at relatively low temperature.

3.2. Analogous Rearrangements. The 1,3- and 1,4-vinyl/phenyl migration could also take place with the radical site atthe γ or δ position by analogy, as shown in Figure 2. The PESsof Rxn1, Rxn3, and Rxn5 are schematically shown in Figure 8,and those of Rxn2, Rxn4, and Rxn6 are in Figure 9. Theexocyclization reaction has a three-, four-, and five-memberedring transition state for R1, R3, and R5, respectively. It is worthnoting that the 1,2-vinyl/phenyl migration presents anexceptionally low barrier comparing with the 1,3-vinyl/phenylmigration, which might not be properly explained by the ringstrain. As we know, the 3- and 4-mermbered rings show verysimilar strain energies in cycloalkyls.37 To obtain a betterunderstanding of the unique features of the homoallylic andhomobenzylic rearrangements, the Hirshfeld atomic chargepopulation of the reaction processes was performed at theB3LYP/6-311G(d,p) level. Figure 10 shows the atomic chargefor the C atom at the radical center of initial radicals during thereaction processes of Rxn1, Rxn3, and Rxn5. The atomiccharges in Rxn1 show quite large deviation from those in Rxn3and Rxn5: first, the inductive effect of the double bond is moredistinct in R1 than those in R3 and R5, attracting the atomiccharge of the radical center and leading to stronger chargelocalization. This localization indicates the loss of its

Figure 6. Branching ratio of the homoallylic/homobenzylic rearrange-ment and other competing pathways among the total consumption ofR1 (a) and R2 (b) decomposition varying with temperature.

Figure 7. Yields of the final decomposition products of R1 (a) and R2(b) varying with temperature.

Table 2. Summary of Recommended Rate Expression for R1and R2 Decompositions in the Modified ArrheniusExpression (k = ATn exp(−E/RT))

high-pressure limit rate expressions(s−1)

reactions A nE

(kcal/mol)

R1 → C3H6 + C2H3 2.33 × 1019 −1.41 40.10R1 → 1,4-C5H8 + H 5.89 × 1006 1.74 30.34R1 → 1,3-C5H8 + H 2.36 × 1011 0.58 35.78R1 → 1,3-C4H6 + CH3 1.22 × 1026 −3.89 35.52R1 → 2-CH3 − 1,3-C4H5 + H 9.55 × 1022 −3.37 39.17R2 → C3H6 + C6H5 7.10 × 1022 −2.54 44.52R2 → 1-C6H5 − C3H5 + H 2.46 × 1008 1.45 35.20R2 → 3-C6H5 − C3H5 + H 3.31 × 1013 −0.065 36.27R2 → C8H8 + CH3 1.45 × 1033 −5.95 41.44R2→ 1-C6H5 − 1-CH3 − C2H2 + H 4.88 × 1029 −5.42 44.92

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stabilization and the rise of its energy; second, the charges ofTS1a, M1, and TS1b are much more negative than thosecorresponding structures in Rxn3 and Rxn5 due to the extraconjugative effect in the cyclopropylcarbinyl radicals. Similarconclusions can also be drawn for the homobenzylic rearrange-

ments in Figure 9, which will not be discussed in detail to avoidduplication.Other major unimolecular reaction pathways of R3−R6 were

computed as well, shown in Figures 11 and 12. Comparing with

the significant contribution of 1,2-vinyl/phenyl migration forthe unimolecular reactions of R1 and R2 shown in Figure 3, the1,3-vinyl/phenyl migration channels for R3 and R4 areobviously unfavored due to the low barrier heights of othercompeting pathways. For instance, the exo- and endocyclizationchannels have comparative barriers for R3, and the beta-dissociation shows quite a low barrier with an allylic product.Therefore, it is expected that the 1,3-vinyl migration of R3 willbe unimportant both at low and high temperature consideringthe combined effect of barrier heights and entropies. Similarconclusion can be extrapolated for the kinetics of R4. The 1,4-vinyl/phenyl migration for R5 and R6 exhibit lower barrierscompared with the 1,3-migration for R3 and R4 due to thesmaller strain energy of the five-membered ring structure.However, they will be largely suppressed by the endocyclizationand the beta-dissociation considering their low barrier heightsand high entropies. Therefore, different from the 1,2-vinyl/phenyl migration, the reaction mechanisms of 1,3- or 1,4-vinyl/

Figure 8. Potential energy diagram for 1,2- (blue dash line), 1,3-(green solid line), and 1,4-vinyl migration reactions (red dash−dotline); relative energies are given in kcal/mol including the ZPEcorrection at CBS-QB3.

Figure 9. Potential energy diagram for 1,2- (blue dash line), 1,3-(green solid line), and 1,4-phenyl migration reactions (red dash−dotline); relative energies are given in kcal/mol including the ZPEcorrection at CBS-QB3.

Figure 10. Variation of the Hirshfeld atomic charges on the markedcarbon in 1,2-, 1,3-, and 1,4-vinyl migration reactions (the radical-center carbon in the reactants) at the B3LYP/6-311G(d,p) level.

Figure 11. Potential energy diagram for the consumption reactions ofR3 (a) and R4 (b); relative energies are given in kcal/mol includingthe ZPE correction at CBS-QB3.

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phenyl migration for radicals with similar structures as R3−R6are not favored under combustion temperatures. The HPL rateconstants of reactions computed in Figures 9 and 10 are listedin the Supporting Information.

4. CONCLUSIONSFor an alkenyl or aromatic radical with the radical site located atthe β position to the vinyl or phenyl group, the 1,2-vinyl/phenyl migration could take place via two steps (the ringclosure by exoaddition and the ring opening by beta-dissociation). This typical unimolecular reaction mechanismwas entitled as the homoallylic/homobenzylic rearrangement.By analogy, the 1,3- or 1,4-vinyl/phenyl migration is alsopossible when the radical site is located at the γ or δ position.By choosing six typical radicals with such homoallyic/homobenzylic structures as examples, these particular reactionmechanisms and their significance under combustion temper-atures were studied theoretically in this work. The 1,2-vinyl/phenyl migration has extremely low barrier height comparedwith that of 1,3 and 1,4 migrations despite the high angle strainof the three-membered ring intermediate, which can beexplained by extra electronic effects revealed by the change of

charge distribution in the reaction processes. With the help ofthe computed PES at CBS-QB3, the HPL rate constants andbranching ratios of major competing reaction channels of thestudied radicals were deduced. It is indicated that thehomoallylic and homobenzylic rearrangements dominate theconsumption of corresponding radicals at relatively lowtemperature (<1500 K) due to the low energy barrier andthat they still have noticeable contribution at higher temper-ature although the entropy effect becomes more significant.However, the analogous 1,3- and 1,4-vinyl/phenyl migrationmay not be competitive pathways for the unimolecularreactions of corresponding radicals since the contribution ofother possible pathways such as endocyclization and beta-dissociation becomes more important. Our studies suggest thatthe homoallylic/homobenzylic rearrangements have greatinfluence on the unimolecular reaction of such radicals withhomoallylic/homobenzylic structures, which are extremelyneeded in the kinetic models of combustion systems involvingsuch homoallylic/homobenzylic radicals.

■ ASSOCIATED CONTENT

*S Supporting InformationRate constants of unimolecular reactions of R1−R6 radicals(Table S1). Cartesian coordinates (in Å) and Hirshfeld chargesof all stationary points involved in vinyl and phenyl migrationare also included (Tables S2−S7). T1 diagnostics from theCCSD(T) calculations of stationary points involved in vinylmigration of R1 was provided in Table S8. The minimumpotential energy curves of the barrierless C−H dissociationfrom R5 and R6 with the variational transition states are shownin Figures S1 and S2. An example for MESMER input was alsogiven. This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*(F.Z.) E-mail: feng2011@ustc.edu.cn. Fax: +86-551-65141078.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSAuthors are grateful for the funding support from NaturalScience Foundation of China (51376170, 21303174, andU1232127) and the Youth Foundation of the University ofScience and Technology of China (WK2310000029). Authorsare grateful to Dr. Hans Heinrich Carstensen for fruitfuldiscussions, and two anonymous referees for their extensivecontributions towards improving this work.

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Figure 12. Potential energy diagram for the consumption reactions ofR5 (a) and R6 (b); relative energies are given in kcal/mol includingthe ZPE correction at CBS-QB3.

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