Article pubs.acs.org/JPCA
Kinetics of Homoallylic/Homobenzylic Rearrangement Reactions under Combustion Conditions Zhaohui 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 radicals with the radical site located at the β position from the vinyl/phenyl group. These radicals are largely involved in combustion systems, such as the pyrolysis or oxidation of alkenes, cycloalkanes, and aromatics. The 1,2vinyl/phenyl migration via two steps (cyclization/fission) is a peculiar reaction type for the homoallylic/homobenzylic radicals, entitled homoallylic/homobenzylic rearrangement, which has been studied by theoretical calculations including the Hirshfeld atomic charge analysis in the present work. With the help of rate constant calculations, the competition between this reaction channel and other possible pathways under combustion temperatures (500−2000 K) were evaluated. Analogous 1,3- and 1,4-vinyl/ phenyl migration reactions for similar radicals with the radical sites located at 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 of homoallylic radicals under 1500 K; nevertheless, it still has noticeable contribution at higher temperature. For those radicals with the radical site at the γ or δ positions, the respective 1,3- or 1,4-vinyl/phenyl migration channel plays an insignificant role under combustion conditions.
1. INTRODUCTION Unimolecular rearrangement reactions of radicals such as the H atom, methyl, or hydroxy migration are typical reactions involved in combustion chemistry.1−6 Usually a vicinal migration is not competitive due to the high strain energy of the three-membered ring structure in the transition state. However, a typical reaction mechanism involving a 1,2-vinyl/ phenyl migration for entitled homoallylic or homobenzylic radicals whose structures are schematically shown in Figure 1
instance, George et al. calculated that the barrier height of the 1,2-vinyl migration in 1-buten-4-yl radical is less than 10 kcal/ mol.13 Kinetic studies on this homoallylic rearrangement mechanism started from 1980s.11,15 Effio et al. measured rate constants of the ring opening and reverse reaction of cyclopropylcarbinyl radical using kinetic electron paramagnetic resonance (EPR) spectroscopy at a temperature range from −21.0 to 3.5 °C,11 Chatgilialoglu et al. measured the rate constants for the overall rearrangement of the 2,2-dimcthyl-3buten-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 very important role under low temperature conditions.16−18 It has been recognized that the homoallylic and homobenzylic radicals also largely exist in the pyrolysis/oxidation processes of some hydrocarbons including alkenes,17,18 cycloalkanes,19,20 aromatics,21,22 biomass fuels,23,24 etc. However, in previous combustion kinetic studies, the predominant consumption channels of such homoallylic and homobenzylic radicals have been in controversy. It was suggested that the 1-penten-4-yl radical was overwhelmingly consumed by direct betadissociations in a kinetic modeling study on 1-pentene oxidation at high temperature.25 However, in a kinetic
Figure 1. Schematic structures of the homoallylic (a) and homobenzylic (b) radicals.
may make an exception. This reaction mechanism has been first proposed as the homoallylic rearrangement by Montgomery et al. in 19677−10 for allylcarbinyl radical. The 1,2-vinyl migration is regarded as taking place by a two-step sequence: (1) ring closure of an allylcarbinyl radical to form a cyclopropylcarbinyl radical and (2) ring opening of the formed radical to yield an allylcarbinyl radical of rearranged structure.8,11,12 Follow-up theoretical investigations revealed that this reaction mechanism could take place with quite low barrier heights.13,14 For © 2014 American Chemical Society
Received: April 3, 2014 Revised: August 1, 2014 Published: August 4, 2014 6741
dx.doi.org/10.1021/jp503325p | J. Phys. Chem. A 2014, 118, 6741−6748
The Journal of Physical Chemistry A
Article
chemistry of these homoallylic reactions, the Hirshfeld atomic charge analysis29 of all species was carried out at B3LYP/6311G(d,p) using the electronic density of the molecule and of a fictitious promolecule. The promolecule is defined as the sum (usually spherically averaged) over the ground-state atomic densities, and the electronic density of the real molecule at each point in space is then distributed over the atoms. The ratio of atomic densities in the real molecule is defined as the same as those in the promolecule. The Hirshfeld atomic charges are suggested to yield chemically meaningful charges and show little basis set dependence.30 All electronic structure calculations are carried out with the Gaussian 09 program package.31 The transition state theory with the Eckart tunneling correction32 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 for the reactions with loose transition states or barrierless reactions.33 In short, the temperature-dependent rate constant was minimized by that computed at each point along the reaction coordinate. The torsional modes corresponding to internal rotations for both radicals and transition states were assumed as one-dimensional (1-D) hindered rotors, while the hindrance potential was obtained by relaxed potential energy scan with the step of 10° at the B3LYP/6-311G(d,p) level. The potential is fitted by a Fourier series up to 14 terms to numerically compute the partition function of the internal rotors.34 The steady-state approximation (SSA) was used in deducing the HPL rate constants of overall reactions, which will be described in more detail in Section 3. All kinetic calculations including VTST were performed with an open-source chemical kinetics software, MESMER2.0.35
modeling study of methyl cyclohexane pyrolysis and oxidation, 1-penten-4-yl radical was regarded as an important source of 1,3-butadiene through a 1,2-H-shift route.20 An earlier study on the pyrolysis of 1-pentene at 873 K suggested that the homoallylic rearrangement reaction could be the dominant channel for the consumption of 1-penten-4-yl and 2-penten-5yl radicals.26 Recently, in a combined experimental and kinetic modeling study of n-propylbenzene flame, the 1,2-phenyl migration was believed to be the reason for 1-phenyl-2-propyl radical isomerizing into 2-phenyl-1-propyl radical.21 Analogous 1,3- or 1,4-vinyl/phenyl migration could also take place if the radical site is located at the γ or δ position from the vinyl/phenyl group. In the present work, we performed systematic studies on these vinyl/phenyl migration reactions of several typical alkenyl and aromatic radicals by theoretical calculations focusing on combustion temperatures (500−2000 K), as shown in Figure 2. The competitive reaction pathways of
3. RESULTS AND DISCUSSION 3.1. Homoallylic and Homobenzylic Rearrangements. Figure 3a,b illustrates the reaction pathways of the 1-penten-4yl (R1) and 1-phenyl-prop-2-yl (R2) radicals with relative energies computed at CBS-QB3 including the zero-point energy (ZPE) correction, respectively. The homoallylic/ homobenzylic rearrangement reactions are shown in red dash lines. The vicinal H-migration pathways are excluded from Figure 3 considering the high strain energy of the transition states and low entropies. One may expect strong multireference character for some loose structures such as the transitions states of C−C dissociation. The CCSD(T) T1 diagnostic for stationary points involved in vinyl migration of R1 is shown in Table S8 in the Supporting Information, which indicates that T1 diagnostic values for the transitions of endocyclization and C−C dissociation are around 0.03. Instead of providing extremely accurate energies and rate constants for numerous reactions studied in this work with high-cost multireference calculations, we aim to investigate the role of the homoallylic/ homobenzylic mechanism among the competing pathways under combustion condition by comparison; we believe CBSQB3 is reliable for this purpose. Generally, the homoallylic/ homobenzylic rearrangement takes place by overcoming quite a low barrier, e.g., ∼10 kcal/mol for R1 and ∼15 kcal/mol for R2. With the very similar three-membered ring structure in the transition states, the barrier heights of the 1,2-phenyl migration are slightly higher than that of 1,2-vinyl migration due to the loss of aromaticity in the migration process of 1-phenyl-prop-2yl radical. The exocyclization intermediates M1 and M2 both have a three-membered ring cyclic structure with the radical center on the side branch of the ring. Transition states and
Figure 2. Vinyl/phenyl migration reactions of several typical alkenyl and aromatic radicals. R, P, and M denote the reactant, product, and intermediate, respectively. Rxn means a reaction.
the decomposition of these selected radicals such as the beta dissociation and H-elimination were also studied to reveal the competition between the homoallylic rearrangement channels and those other pathways under combustion conditions.
2. COMPUTATIONAL METHODS The lowest energy conformer was first determined for each studied molecule (R1−R6 in Figure 2). The equilibrium geometries of reactants, products, intermediates, and transition states were computed with the CBS-QB3 method, using the B3LYP/6-311G(2d,d,p) method to optimize geometries followed by a series of MP2, MP4, and CCSD(T) calculations with Pople type basis sets to obtain the electron correlation energies.27 All of the stationary points were confirmed by vibrational analysis, while the saddle points were examined by intrinsic reaction coordinate (IRC)28 calculations showing that appropriate reactants and products were connected. The dissociation curve of the barrierless channels are constructed with a stepwise of 0.05 Å using the B3LYP/6-311G(d,p) method, which was scaled by the dissociation energy computed with the CBS-QB3 method. In order to deeply understand the 6742
dx.doi.org/10.1021/jp503325p | J. Phys. Chem. A 2014, 118, 6741−6748
The Journal of Physical Chemistry A
Article
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); ZPEcorrected energies (kcal/mol) are given at the CBS-QB3 level.
increases with temperature, the channels of beta-dissociation are expected to play more important roles at higher temperature due to the loose structure of transition states. Hence the HPL rate constants of the reactions shown in Figure 3 were computed in order to quantitatively reveal the importance of the homoallylic/homobenzylic rearrangements in the temperature range of 500 to 2000 K, which is of interest in combustion. As mentioned above, the partition functions of internal rotors were computed with the 1-D hindered rotor approximation, while the hindrance potential was numerically fitted with Fourier expression up to 14 terms. Figure 4 illustrates the computed and simulated hindrance potentials for the internal rotation around various C−C bonds in R1, showing pretty good agreement between the computed potential energies and the fitted functions. Table 1 lists the rate coefficients for each step in 1,2-vinyl/phenyl migration. In the 1,2-vinyl/phenyl migration, the rate constants of the ringopening step is at least 2 order of magnitudes higher than that of the ring-closure step according to our computation; thus, it is reasonable to deduce the rate constants of the 1,2-vinyl/phenyl migration 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 k1 is the forward rate constant for the reaction from reactant to intermediate, k−1 is the reverse rate constant from intermediate to reactant, and k2 is the forward rate constant from
intermediates in homoallylic rearrangement all have cis and trans isomers due to the cyclic structure, and the energy differences between the cis/trans isomers are less than 1 kcal/ mol, also shown in Figure 3a. The conjugated structure of the benzene ring has been broken in M2; consequently, the energy gap between M2 and R2 is much higher than that between M1 and R1. Besides this rearrangement reaction, R1 and R2 can also undergo other reactions such as beta dissociation, Helimination, and endocyclization, which are shown in Figure 3 as well. Comparing with the other possible pathways, the homoallylic/homobenzylic rearrangements have remarkable low barriers. The C−C bond beta dissociation for both 1penten-4-yl and 1-phenyl-prop-2-yl radicals shows relatively high barrier (∼35 kcal/mol) due to the effect of unstable vinyl and phenyl radicals. The endocyclization exhibits much higher barrier than the exocyclization since the “endo” cycloalkyl radical has broken the occupied π orbitals in a strained ring. In order to reveal the dramatic low barrier heights of the 1,2-vinyl/ phenyl migration, additional analysis on the electronic effect such as charge distribution could be helpful, which will be discussed in more detail later. The homoallylic/homobenzylic rearrangements could be overwhelmingly competitive comparing with other possible pathways considering the remarkable low barriers at least under low temperature, which has already been uncovered by previous kinetic studies.26,36 However, the entropy contribution 6743
dx.doi.org/10.1021/jp503325p | J. Phys. Chem. A 2014, 118, 6741−6748
The Journal of Physical Chemistry A
Article
Figure 4. Calculated (symbols) and simulated (solid line) hindrance potential as a function of dihedral angle defined by various C−C bonds for 1-penten-4-yl radical.
intermediate to product. Figure 5 illustrates the HPL rate constants of relevant reactions of R1 and R2, where the rate constants of the 1,2-vinyl/phenyl migration were deduced by the SSA. It indicates that the 1,2-vinyl/phenyl migration is the most favored reaction channel for R1/R2 compared with other competing reactions at least under 1500 K due to its low energy barrier. However, without further information on the final fates of P1 and P2, i.e., their decomposition pathways, it is risky to state that the 1,2-vinyl/phenyl migration route has a significant impact on the consumption of R1/R2 because it will possibly go back to the reactant without further decomposition channels. For instance, Tsang suggested that R1 is the major decomposition reactant due to its greater stability over P1 among 1000−2000 K at high pressures in his mechanism work of the decomposition of 1-pentenyl radicals.36 However, this prediction might be suspicious: first, the stability of R1 and P1 are comparable according to our results. Second, which is more important, the decomposition reactions of P1 shall also be considered. For this reason, the decomposition rate constants of P1 and P2 shown in Figure 3 are also computed and listed in the Supporting Information. With the help of the computed rate constants of P1 and P2 decomposition, the branching ratios of these competing
Figure 5. Deduced high pressure limit rate constants of the homoallylic/homobenzylic rearrangement and other competing pathways among the unimolecular reactions of R1 (a) and R2 (b) varying with temperature.
reaction routes of R1 and R2 are deduced, as shown in Figure 6. It is worth noting that the contribution of the homoallylic/ homobenzylic rearrangement mechanisms to the total consumption of the reactants depends on the rate of both homoallylic/homobenzylic rearrangements and the subsequent decomposition reactions, thus the branching ratio of vinyl/ phenyl migration shown in Figure 6 actually includes all decomposition paths of P1/P2. Although the contribution of this homoallylic/homobenzylic rearrangement mechanism is reduced with increasing temperature, it still approaches to ∼50% to 60% for R1 and R2 decomposition at 1500 K, which is a characteristic temperature for combustion studies. It even still
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
500 K 600 K 700 K 800 K 900 K 1000 K 1100 K 1200 K 1300 K 1400 K 1500 K 1600 K 1700 K 1800 K 1900 K 2000 K
× × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × ×
a
1.42 8.30 3.02 8.09 1.77 3.35 5.69 8.93 1.32 1.84 2.48 3.23 4.09 5.07 6.15 7.34
06
10 1006 1007 1007 1008 1008 1008 1008 1009 1009 1009 1009 1009 1009 1009 1009
3.51 1.14 2.67 5.05 8.30 1.24 1.72 2.27 2.87 3.52 4.21 4.93 5.68 6.44 7.22 8.01
09
10 1010 1010 1010 1010 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011
4.77 1.45 3.25 6.01 9.77 1.45 2.01 2.65 3.35 4.11 4.93 5.78 6.66 7.57 8.50 9.45
09
10 1010 1010 1010 1010 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011
1.83 1.01 3.50 9.10 1.94 3.59 6.01 9.30 1.35 1.88 2.50 3.24 4.07 5.01 6.04 7.18
06
10 1007 1007 1007 1008 1008 1008 1008 1009 1009 1009 1009 1009 1009 1009 1009
1.12 2.99 6.08 1.04 1.58 2.22 2.94 3.72 4.55 5.42 6.32 7.25 8.19 9.14 1.01 1.11
10
10 1010 1010 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1012 1012
4.00 1.20 2.66 4.89 7.92 1.17 1.62 2.14 2.71 3.33 3.99 4.68 5.40 6.14 6.90 7.67
09
10 1010 1010 1010 1010 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011
2.01 2.58 1.64 6.72 2.04 5.01 1.06 1.98 3.40 5.42 8.16 1.17 1.62 2.17 2.82 3.57
04
10 1005 1006 1006 1007 1007 1008 1008 1008 1008 1008 1009 1009 1009 1009 1009
6.73 1.20 1.82 2.49 3.17 3.85 4.50 5.14 5.74 6.32 6.86 7.38 7.87 8.33 8.76 9.16
11
10 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012
M2 → P2 2.80 5.71 9.58 1.42 1.94 2.50 3.07 3.66 4.24 4.82 5.38 5.93 6.46 6.98 7.47 7.94
× × × × × × × × × × × × × × × ×
1011 1011 1011 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012
Trans conformer. bCis conformer. 6744
dx.doi.org/10.1021/jp503325p | J. Phys. Chem. A 2014, 118, 6741−6748
The Journal of Physical Chemistry A
Article
decomposition products in a previous modeling study.20 Similar conclusion can be extrapolated to the decomposition of R2, as shown in Figure 7b. Styrene is suggested as a significant decomposition product of R2, while the homobenzylic rearrangement mechanism is responsible for this channel. This prediction has been validated by the experimental observation of n-propylbenzene flame.21 Table 2 lists the Table 2. Summary of Recommended Rate Expression for R1 and R2 Decompositions in the Modified Arrhenius Expression (k = ATn exp(−E/RT)) high-pressure limit rate expressions (s−1) A
reactions R1 → C3H6 + C2H3 R1 → 1,4-C5H8 + H R1 → 1,3-C5H8 + H R1 → 1,3-C4H6 + CH3 R1 → 2-CH3 − 1,3-C4H5 + H R2 → C3H6 + C6H5 R2 → 1-C6H5 − C3H5 + H R2 → 3-C6H5 − C3H5 + H R2 → C8H8 + CH3 R2 → 1-C6H5 − 1-CH3 − C2H2 + H
Figure 6. Branching ratio of the homoallylic/homobenzylic rearrangement and other competing pathways among the total consumption of R1 (a) and R2 (b) decomposition varying with temperature.
2.33 5.89 2.36 1.22 9.55 7.10 2.46 3.31 1.45 4.88
× × × × × × × × × ×
1019 1006 1011 1026 1022 1022 1008 1013 1033 1029
n
E (kcal/mol)
−1.41 1.74 0.58 −3.89 −3.37 −2.54 1.45 −0.065 −5.95 −5.42
40.10 30.34 35.78 35.52 39.17 44.52 35.20 36.27 41.44 44.92
Arrhenius parameters of the deduced HPL rate constants for the decomposition channels of R1 and R2, which might be valuable to kinetic modeling studies of such combustion systems involving homoallylic/homobenzylic radicals. As implied by the above theoretical investigation on the typical homoallylic/homobenzylic radicals, it is reasonable to state that the homoallylic/homobenzylic rearrangement mechanism is extremely required to be considered in kinetic models of combustion systems involving such homoallylic/homobenzylic radicals. Consequently, further decomposition of the products from this rearrangement mechanism probably leads to major products of the homoallylic/homobenzylic radicals decomposition 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 at the γ or δ position by analogy, as shown in Figure 2. The PESs of Rxn1, Rxn3, and Rxn5 are schematically shown in Figure 8, and those of Rxn2, Rxn4, and Rxn6 are in Figure 9. The exocyclization reaction has a three-, four-, and five-membered ring transition state for R1, R3, and R5, respectively. It is worth noting that the 1,2-vinyl/phenyl migration presents an exceptionally low barrier comparing with the 1,3-vinyl/phenyl migration, which might not be properly explained by the ring strain. As we know, the 3- and 4-mermbered rings show very similar strain energies in cycloalkyls.37 To obtain a better understanding of the unique features of the homoallylic and homobenzylic rearrangements, the Hirshfeld atomic charge population of the reaction processes was performed at the B3LYP/6-311G(d,p) level. Figure 10 shows the atomic charge for the C atom at the radical center of initial radicals during the reaction processes of Rxn1, Rxn3, and Rxn5. The atomic charges in Rxn1 show quite large deviation from those in Rxn3 and Rxn5: first, the inductive effect of the double bond is more distinct in R1 than those in R3 and R5, attracting the atomic charge of the radical center and leading to stronger charge localization. This localization indicates the loss of its
has ∼20% contribution even at 2000 K. One may assume propene and vinyl radical as the dominant decompostition products of R1 since they can be produced from both the direct beta-dissociation and homoallylic rearrangement.25 However, according to our computed rate constants of various decomposition channels, the favorable homoallylic rearrangement tends to produce 1,3-butadiene and methyl radical. Figure 7a illustrates the yields of various final decomposition products of R1. Obviously, the two pathways leading to 1,3-butadiene (plus methyl radical) and propene (plus vinyl radical) have overwelming contibution to the decomposition of R1, which disagrees with the estimation that 2-methyl-1,3-butadiene (isoprene) and H atom through 1,2 H-shift are major
Figure 7. Yields of the final decomposition products of R1 (a) and R2 (b) varying with temperature. 6745
dx.doi.org/10.1021/jp503325p | J. Phys. Chem. A 2014, 118, 6741−6748
The Journal of Physical Chemistry A
Article
ments in Figure 9, which will not be discussed in detail to avoid duplication. Other major unimolecular reaction pathways of R3−R6 were computed as well, shown in Figures 11 and 12. Comparing with
Figure 8. Potential energy diagram for 1,2- (blue dash line), 1,3(green solid line), and 1,4-vinyl migration reactions (red dash−dot line); relative energies are given in kcal/mol including the ZPE correction 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−dot line); relative energies are given in kcal/mol including the ZPE correction at CBS-QB3.
Figure 11. Potential energy diagram for the consumption reactions of R3 (a) and R4 (b); relative energies are given in kcal/mol including the ZPE correction at CBS-QB3.
the significant contribution of 1,2-vinyl/phenyl migration for the unimolecular reactions of R1 and R2 shown in Figure 3, the 1,3-vinyl/phenyl migration channels for R3 and R4 are obviously unfavored due to the low barrier heights of other competing pathways. For instance, the exo- and endocyclization channels have comparative barriers for R3, and the betadissociation shows quite a low barrier with an allylic product. Therefore, it is expected that the 1,3-vinyl migration of R3 will be unimportant both at low and high temperature considering the combined effect of barrier heights and entropies. Similar conclusion can be extrapolated for the kinetics of R4. The 1,4vinyl/phenyl migration for R5 and R6 exhibit lower barriers compared with the 1,3-migration for R3 and R4 due to the smaller strain energy of the five-membered ring structure. However, they will be largely suppressed by the endocyclization and the beta-dissociation considering their low barrier heights and high entropies. Therefore, different from the 1,2-vinyl/ phenyl migration, the reaction mechanisms of 1,3- or 1,4-vinyl/
Figure 10. Variation of the Hirshfeld atomic charges on the marked carbon in 1,2-, 1,3-, and 1,4-vinyl migration reactions (the radicalcenter carbon in the reactants) at the B3LYP/6-311G(d,p) level.
stabilization and the rise of its energy; second, the charges of TS1a, M1, and TS1b are much more negative than those corresponding structures in Rxn3 and Rxn5 due to the extra conjugative effect in the cyclopropylcarbinyl radicals. Similar conclusions can also be drawn for the homobenzylic rearrange6746
dx.doi.org/10.1021/jp503325p | J. Phys. Chem. A 2014, 118, 6741−6748
The Journal of Physical Chemistry A
Article
charge distribution in the reaction processes. With the help of the computed PES at CBS-QB3, the HPL rate constants and branching ratios of major competing reaction channels of the studied radicals were deduced. It is indicated that the homoallylic and homobenzylic rearrangements dominate the consumption of corresponding radicals at relatively low temperature (
