Thermochemistry and Reaction Paths in the Oxidation Reaction of

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Thermochemistry and Reaction Paths in the Oxidation Reaction of Benzoyl Radical: C6H5C•(dO) Nadia Sebbar,† Joseph W. Bozzelli,*,‡ and Henning Bockhorn† † ‡

Karlsruhe Institute of Technology, Engler-Bunte-Institut, Verbrennungstechnik (VBT) 76131 Karlsruhe, Germany Department of Chemical Engineering and Chemistry—Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102, United States

bS Supporting Information ABSTRACT: Alkyl substituted aromatics are present in fuels and in the environment because they are major intermediates in the oxidation or combustion of gasoline, jet, and other engine fuels. The major reaction pathways for oxidation of this class of molecules is through loss of a benzyl hydrogen atom on the alkyl group via abstraction reactions. One of the major intermediates in the combustion and atmospheric oxidation of the benzyl radicals is benzaldehyde, which rapidly loses the weakly bound aldehydic hydrogen to form a resonance stabilized benzoyl radical (C6H5C•dO). A detailed study of the thermochemistry of intermediates and the oxidation reaction paths of the benzoyl radical with dioxygen is presented in this study. Structures and enthalpies of formation for important stable species, intermediate radicals, and transition state structures resulting from the benzoyl radical + O2 association reaction are reported along with reaction paths and barriers. Enthalpies, ΔfH2980, are calculated using ab initio (G3MP2B3) and density functional (DFT at B3LYP/6-311G(d,p)) calculations, group additivity (GA), and literature data. Bond energies on the benzoyl and benzoyl-peroxy systems are also reported and compared to hydrocarbon systems. The reaction of benzoyl with O2 has a number of low energy reaction channels that are not currently considered in either atmospheric chemistry or combustion models. The reaction paths include exothermic, chain branching reactions to a number of unsaturated oxygenated hydrocarbon intermediates along with formation of CO2. The initial reaction of the C6H5C•dO radical with O2 forms a chemically activated benzoyl peroxy radical with 37 kcal mol1 internal energy; this is significantly more energy than the 21 kcal mol1 involved in the benzyl or allyl + O2 systems. This deeper well results in a number of chemical activation reaction paths, leading to highly exothermic reactions to phenoxy radical + CO2 products.

’ INTRODUCTION Aromatic hydrocarbons such as toluene, xylene, trimethylbenzene, ethylbenzene, and other alkylbenzenes, form a significant component of petroleum-derived fuels. Reactivity of alkylated aromatics varies widely with the number, position, and length of the alkyl side chains. Yet at present, this behavior is not fully understood. A detailed fundamental understanding of fuel reactivity at low to moderate temperatures is critical to reduce emissions and improve engine efficiency, as well as to design new fuel formulations and engines. Octane rating is a widely used and important measure of low-temperature fuel reactivity (or, more precisely, nonreactivity).14 While significant effort has been directed to the development of kinetic models, which describe the reactions of these aromatic compounds in combustion systems and in the atmosphere, mechanisms for aromatics and substituted aromatics are often not as complete as those of hydrocarbons or not studied at all. For example the toluene oxidation5 starts with the abstraction of a benzylic hydrogen to form a benzyl radical which, in an oxygen environment, reacts further to form benzaldehyde via a benzylperoxy radical. The radical resulting from the abstraction of the aldehyde hydrogen will then dissociate to a phenyl radical and CO. While these reactions are included in mechanisms, there is, r 2011 American Chemical Society

for most of the mechanisms available, no inclusion of molecular oxygen in the reactions of the benzyl or benzoyl radicals. There is a need for accurate kinetic models describing the reactions of important, stable intermediates generated by combustion and oxidation of alkyl-substituted aromatic fuels. One highly important step in the initial reactions of alkyl aromatic molecules is the abstraction of a benzyl hydrogen atom CH6 (see Figure 1). Several recent studies have illustrated a number of pathways leading to phenyl radical production through reactions of benzyl and benzylic radicals.713 One of the major intermediates in this path is benzaldehyde; this is an aldehydic benzylic carbon on the aromatic ring. The CH bond on the benzaldehyde group is relatively weak due to resonance stabilization of the radical, and this H atom is easily lost through abstraction paths to the radical pool species. To our knowledge, there are no studies on the detailed reactions of benzaldehyde reaction with dioxygen. This may be a result of the low reaction energy of the benzyl radical + O2 (similar to allyl radical + O2) at only some 20 kcal mol1 and which results mostly in reverse dissociation of the peroxy radical Received: August 14, 2011 Published: September 23, 2011 11897

dx.doi.org/10.1021/jp2078067 | J. Phys. Chem. A 2011, 115, 11897–11914

The Journal of Physical Chemistry A

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Figure 1. Formation of phenyl radical through toluene oxidation (ΔH0rxn,298 in kcal mol1) goes through benzoyl radical.

Figure 2. Major Channels in the PhC•(dO) + O2 Reaction System.

formed. The reactions of the benzoyl radical with O2 provide pathways to further oxidation of the benzylic carbon group or even the aromatic ring. In addition, properties and reactions of radicals and peroxy radicals formed from the radical and the dioxygen association are difficult to study experimentally. In the benzoyl system, the resonance of the radical with the carbonyl results in a resonantly stabilized system. The CH bond energy of the benzoyl is similar to that of a CH bond on a primary allyl site in olefins or that of a benzylic on the aromatic. Typically the combustion kineticists do not consider or study simple single olefin systems, allyl or benzylic radical reactions with O2, because of the very shallow well depth which reverses the reaction is rapid. Acetyl radicals are similar in structure to the benzoyl and show resonance and weak CH bonds on the

carbonyl. However, they show significant well depth along with rapid formation of new products plus generation of OH radicals. To our knowledge, the benzoyl system has not been studied previously and can provide important oxidation paths for substituted aromatics that are important to combustion and atmospheric chemistry. Specifically it may provide oxidation paths that do not require initial generation or initial reactions to the phenyl moiety on the aromatic system. Enthalpy (ΔfH0298) and dissociation bond energies are reported for the species resulting from the benzoyl radical plus O2 reaction system. Transition state structures and important species that result from the isomerization and reactions of the benzoylperoxy radical are calculated using density functional (B3LYP/6-311 g(d,p)), ab initio (G3MP2B3), and group 11898

dx.doi.org/10.1021/jp2078067 |J. Phys. Chem. A 2011, 115, 11897–11914


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Figure 3. Pathways for the PhC•(dO) + O2 reaction system.

Figure 4. Reactions of the stable hydroperoxide phenyl radical.

Figure 5. Reaction of Y(C6H5•)Y(C3O2)dO intermediate after peroxy radical addition at ortho site.

additivity (GA) calculations. Properties and reaction paths are reported for a significant number of low barrier paths as well as further reactions of the intermediates. We find that the initial reaction of the C6H5C•dO radical with O2 forms a chemically activated benzoyl peroxy radical with 36 kcal mol1 internal energy; this is significantly higher than the 21 kcal mol1 energy involved in the benzyl or allyl + O2 systems. This deeper well results in access to a number of chemical activation reaction and unimolecular dissociation paths with highly exothermic product sets such as phenoxy radical plus CO2.

’ COMPUTATIONAL METHODS Molecular properties are calculated using the Gaussian 03 program suite.1416 The hybrid DFT method B3LYP was applied

to all species and transition state structures in the benzoyl + O2 reaction system. Additionally, the modified G3 method reported as G3MP2B3 was applied for all stable species and radicals. For two transition state structures for which other methods were not successful, PM317 was applied and B3LYP was applied to a similar reaction with a smaller (model) molecule. The PM3 model has been widely used for rapid estimation of molecular properties and has been recently extended to include many elements, including some transition metals. PM3 (Parameterized Model number 3) is a semiempirical method which is based on the NDDO (Neglect of Differential Diatomic Overlap)18 integral approximation. PM3 uses parameters derived from experimental data to simplify the computation. As a result, 11899



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Figure 6. Reaction paths for dissociation of the BY(C6H5O)C(dO)O• intermediate in the PhC•(dO) + O2 reaction system.

Figure 7. Reaction paths for dissociation of the BY(C6H5• O)C(dO)OH intermediate in the PhC•(dO) + O2 reaction system.

semiempirical methods are very fast, applicable to large molecules, and may provide accurate results and reasonable qualitative description of molecular system when applied to molecules that are similar to the molecules used for parametrization. Different parametrization and slightly different treatment of nuclear repulsion allow PM3 to treat hydrogen bonds rather well, but it amplifies nonphysical

hydrogenhydrogen attractions in other cases. The accuracy of thermochemical predictions with PM3 is slightly better than that of AM1. The B3LYP method combines the three-parameter Becke exchange Functional, B3, with the LeeYangParr nonlocal correlation Functional, LYP. We use a double polarized set, 6-311G(d,p)19,20 and for one species the 3-21G basis set. The 11900


The Journal of Physical Chemistry A G3MP2B3 method uses B3LYP geometries (G3MP2//B3LYP/ 6-31G(d,p)).2123 Transition states were identified by their single imaginary frequency and by analysis of the vibration motion. Enthalpies of formation were calculated from work reactions that were isodesmic

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wherever possible. B3LYP/6-311G(d,p) is chosen for initial structures because it is well regarded to yield accurate geometries and reasonable energies24,25 Curtiss et al.26 reported that G3(MP2) with B3LYP/6-31G(d) geometries yield overall enthalpy values for alkyl hydrocarbons showing a low overall deviation from experimental values. The overall accuracy of DFT methods is lower than that achieved with the high-level ab initio and composite calculation methods; however the accuracy of density functional theory can be improved by use of isodesmic reactions where DFT calculation errors can be reduced. This is a hypothetical reaction that has the same number and type of bonds on both sides and is used to calculate the enthalpy of the reaction (ΔH0rxn,298). Here the errors on a given type of bond on each side of the reaction will cancel, and the resulting accuracy of ΔH0rxn,298 will be improved over atomization. The enthalpy of formation of a species is determined as

∑ðtotal energies at 298 K of productsÞ ∑ðtotal energies at 298 K of reactantsÞ

0 ΔHrxn, 298 ¼

0 ΔHrxn, 298 ¼

Figure 8. Potential barriers for internal rotation of—C(dO)OH about Y(C6H5•O).

0 of productsÞ ∑ðexperimental Δf H298 0 ∑ðexperimental Δf H298 of reactantsÞ

Table 1. Nomenclature Table

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Table 2. Enthalpies of Formation for Stable and Radical Species Used in Work Reactions ΔfH0298 (kcal mol1)

source

CH4

17.89 ( 0.07

30

C6H5CHdO

8.80 ( 0.72

CH3CH3

20.24 ( 0.12

30

CH3C(dO)OH

103.5 ( 0.6

48

CH2dCH2

12.55 ( 0.1

31

CH3C(dO)CH3

51.9 ( 0.12

49

HCtCH

54.19

31

CH2dCHC(dO)OH

80.51 ( 0.55

50

C6H5CH3

11.95 ( 0.15

32

CH3CH2C(dO)OH

108.9 ( 0.48

51

C6H6

19.81 ( 0.13

32

H

52.103 ( 0.001

35

CH2dCHCHdCH2

26 ( 0.19

33

O

59.55 ( 0.024

52

Y(C6H6)dO CO2

4.88 ( 0.78 94.05 ( 0.03

34 35

HO• HOO•

8.93 ( 0.03 2.94 ( 0.06

53 53

CO

26.41 ( 0.04

35

CH3CH2•

28.4 ( 0.5

54

CH2O2 (dioxirane)

18.65 ( 0.95

36

C6H5CH2•

49.5 ( 1.

56

CH2dCdO

20.85

37

CH•dCdO

40.4

6

Y(C2H4O2)

10.26

6

CH2dCHCHdCH•

86.73

6

C2H4O (Y(C2H4O))

12.58

31

C6H5•

81.4 ( 0.16

43

species

ΔfH0298 (kcal mol1)

species

source 47

CH3CHdO

40.80 ( 0.35

38

CH3O•

4.1 ( 1.

31

HC(dO)OH CH2dCHCHdO

90.49 8.37/9.42

39 40

CH3CH2O• CH3OO•

2.03 ( 0.39 2.15 ( 1.22

43 54

CH3OH

48.08 ( 0.05

41

CH3CH2OO•

6.5 ( 2.36

55

CH3CH2OH

56.23 ( 0.12

41

C6H5OO•

31.28 ( 0.48

43

CH3OOH

31.8 ( 0.94

42

CH3C•dO

2.9 ( 0.7

31

CH3CH2OOH

39.28 ( 0.01

43

Y(C6H7•)

49.94 ( 0.74

6

CH2dCHOOH

9.63 ( 0.08

43

C•H2CHdO

3.52 ( 0.38

56

C6H5OH

23.03 ( 0.14

44

OdCHCHdCH•

41.76 ( 0.7

36

C6H5OOH C6H5CH2OH

2.68 ( 0.49 22.6 ( 0.72

43 45

CH2dCHC(dO)O• Y(C6H5•)dO

22.47 13.43 ( 0.29

36 34

C6H5CH3

11.95 ( 0.15

46

The isodesmic reactions used experimental or computed standard enthalpies of formation values for the reference species. In development of the isodesmic work reactions, efforts were made to preserve the bonding environment in the target species, including aromaticity and ring structure, so as to effectively cancel errors in the DFT calculations. We try to include the same number and type of radicals, internal rotors, and molecular fragments on each side of the reaction; but this is not always possible because accurate enthalpies of formation for the reference species are not always available. Nomenclature. The nomenclature used in this paper is as follows: Ph represents a phenyl group, Y(A) indicates a cyclic structure (Y(C5) is cyclopentadiene), D is a double bond (CDO is CdO), B(YA) is a bicyclic (B(YC6•YC2O)). For example, Y(C6)DO represents a cyclic six member carbon ring with a double bond to an oxygen on a ring carbon. Y(C6•O) or Y(C6H5•O) represents a seven-member ring with six carbons, one oxygen, and a radical in the ring structure. A• or AJ represent a radical site on the A atom, TS is a transition state structure. We note that there are often several resonance structures for a given species. Figures 27 along with Tables 15 illustrate the species structures with the abbreviated nomenclature used.

’ RESULTS AND DISCUSSION 1. Enthalpy of Formation, ΔfH0298 Calculations. Enthalpies

of formation for the stable parent species, intermediate radicals, and products and the transition state structures resulting from the benzoyl + O2 reaction system have been calculated using the B3LYP, the G3MP2B3. A set of two to four work reactions are

used for standard enthalpy of molecules and radicals. Group additivity (GA) methods are also used for these non-transitionstate structures. Enthalpies of formation needed for the reference species used in our isodesmic reactions are listed in Table 2. Enthalpy values of some reference species were also further calculated to provide additional support to our isodesmic reaction analysis. Table 3 reports the enthalpy of these values as well as their structures and the work reactions used. Comparison of the DFT and the G3MP2B3 methods shows good agreement for stable molecules and the intermediate radicals, the difference between the two calculation methods is within 1 kcal mol1, for all but two species. The GA method of Benson27 with the hydrogen bond increment method of Ritter and Bozzelli28 was also used for these species. Table 3 shows that the deviation between GA and B3LYP and/or G3MP2B3 calculated values is less than 2 kcal mol1. Table 4 illustrates the structures of stable molecules and intermediate radicals resulting from our analysis of the benzoyl + O2 reaction system. Enthalpies of formation of 25 intermediate species reported in Table 4 have been calculated using a series of two to four isodesmic or near isodesmic reactions with the B3LYP and the G3MP2B3 methods. Group additivity has also been applied for species composed by known groups. The standard enthalpies of most species calculated by the two theoretical methods are in good agreement with the exception of three species where the difference is 23 kcal mol1. The group additivity estimates are generally within several kcal mol1, but several species have up to 4 kcal mol1 deviation. We feel that the deviations provide a general concept of the accuracy in the ΔfH0(298) values. 11902



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Table 3. Calculated ΔfH0298 for Species Used as Reference Molecules in the Isodesmic Reactions

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The Journal of Physical Chemistry A Transition-state (TS) geometries are identified by the existence of only one imaginary frequency in the normal mode coordinate analysis, an evaluation of the TS geometry, and the reaction coordinate’s vibrational motion. Enthalpies at 298 K have been calculated for 34 transition state structures at the B3LYP/ 6-311G(d,p) level and listed in Table 5. These are determined as the difference to reactants and products. Several reactions

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illustrating transition state structures are illustrated in Table 5 (reactant f TS f product). 2. Entropy S0(298) and Heat Capacities, Cp(T) (300 e T/K e 1500) Calculations. Vibration frequencies and moments of inertia from the optimized B3LYP/6-311G(d,p) structures were used to calculate the contributions to entropies and heat capacities from vibration, translation, and external rotation (TVR) on

Table 4. Calculated ΔfH0298 for Intermediates in the Benzoyl + O2 Reaction System

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Table 4. Continued

*

B3LYP/3-21G calculations.

the basis of formula from statistical mechanics and by use of the SMCPS29 program. The contributions to S0f298 and Cpf298(T) from low barrier (below 3.5 kcal mol1) torsion frequencies were removed from the calculations and contributions from internal rotations (IRs) were substituted. The torsion frequencies are identified by viewing bond motions using the GaussView 3.09 program.15 3. Potential Energy (298 K) Diagramst for PhC•(dO) + O2. Figure 2 illustrates five major reaction pathways in the benzoyl + O2 reaction system. Three of the paths consist of a series of complex reactions each of them having a reaction barrier near 13 kcal mol1 below the entrance channel. A fourth channel has a

loose transition state structure and will be important at high temperatures. The association results in a chemically activated benzoylperoxy radical [PhC(dO)OO•]# with a significant, 36 kcal mol1, well depth. The deep well, some 46 kcal mol1 deeper than acetyl, is a result of the radical site coupling with the carbonyl and with the phenyl group. The benzoylperoxy radical is more strongly bound than the acetylperoxy radical, and this system may be important in reactions similar to those for acetylperoxynitrate (PAN) formation. Reactions available to the energized adduct include the following: (a) reverse reaction back to benzoyl radical + O2 11905


The Journal of Physical Chemistry A (no reaction); (b) the intramolecular hydrogen abstraction from the ortho position of the phenyl ring forming a o-carboperoxyphenyl radical (TS1); (c) the ROO bond cleavage (simple oxygen atom elimination) (TS2), which is a chain branching channel; (d) the attack of the peroxy radical on the benzene ring at the ortho position (addition reaction) forming a five-member bicyclic-peroxy ring (TS3); (e) the attack of the peroxy radical on the benzene ring at the ipso

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position (addition reaction), initially forming a dioxirane ring (TS4). A detailed description of these reaction paths is given in the following sections. The transition state structures of the continuing reactions from each of these primary paths are numbered according to the respective initial path TS1-1, TS1-2, ... for TS1, TS2-1 for TS2, etc., as illustrated in Table 5 and Figures 2, 3, 6, and 7.

Table 5. Calculated ΔfH0298 of Transition State Structures

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Table 5. Continued

3.1. Intramolecular Hydrogen Abstraction (TS1). Formation of a reactive, ortho-peroxyacid-phenyl radical occurs through TS1 via intramolecular abstraction (H-shift) from C6H5C(dO)OO• to C6H4•C(dO)OOH though a cyclic six-member

ring structure (TS1). This abstraction was found to have a barrier that is 12.8 kcal mol1 below the entrance channel and is accessible to the chemically activated benzoyl peroxy radical before it is stabilized. This intramolecular abstraction can also 11907



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Table 5. Continued

*

PM3 calculations.

occur from the stabilized benzoyl peroxy radical to form an active phenyl radical with a hydroperoxide on the benzoyl group; this is calculated to be endothermic, with a barrier of 17.9 kcal mol1. This reaction is readily accessible under combustion conditions. The newly formed, peroxyacid phenyl radical can abstract the hydroxyl group from the HOOC(dO)Ph on the peroxy acid (TS1-1) forming an ortho phenol-carboxy radical, which rapidly

cleaves the carboxy group over a 7 kcal mol1 barrier (TS1-2) and forms an ortho hydroxyl phenyl radical plus CO2. This orthohydroxyl phenyl radical can undergo a hydrogen atom shift (TS1-3) over a 32 kcal mol1 barrier to form phenoxy radical or it can further react with O2. This reaction sequence is illustrated in Figure 3. Another path for the stabilized ortho-peroxyacid phenyl radical (C6H4•C(dO)OOH) involves a hydrogen transfer from 11908


The Journal of Physical Chemistry A the hydroperoxide to the CdO oxygen forming an alcohol. Then transfer of an oxygen from the peroxy group to the phenyl radical site and hydrogen transfer from the alcohol group to the ring with elimination of CO2 as illustrated in Figure 4. The barriers here are high (∼45 kcal mol1) and the paths are not important. 3.2. Oxygen Atom Elimination from the Benzoyl Peroxide to Form Benzoyloxy Radical + O Atom (TS2). Simple dissociation of the benzoyl peroxy (C6H5C(dO)OO•) adduct to C6H5C(dO)O• + O is endothermic by 45 kcal mol1 (TS2) relative to

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the stabilized C6H5C(dO)OO• radical and proceeds with a barrier of 7 kcal mol1 above the entrance channel. This simple bond cleavage reaction has a loose transition state and is important under thermal and higher temperature combustion conditions. 3.3. Addition of the Peroxy Radical to the Aromatic Ring at the Ortho Position (TS3). The attack (addition reaction) of the peroxy oxygen radical on the benzene ring at the ortho position results in the formation a five-member carbonyl peroxide ring

Table 6. Calculated Thermochemical Properties of Radicals and Stable Speciesa

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Table 6. Continued

Calculated Thermochemical Properties of Transition State Structuresa Cp (T) cal mol1 K ΔfH0298b

species TS1 TS1-1

TS1-2 = TS4-11

TS1-3 TS2

TS2-1

TS3

c

TVR TVRc IR total TVRc IR total TVRc TVRc IR total TVRc IR total TVRc IR total

17.84 Cb—CO2• 29.14 Cb—CO2• 50.06 72.56 Cb—CO2• 38.05 Cb—CO2• 4.64 Cb—CO2• 17.36

S0298b

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

85.51 89.50 4.80 94.3 87.49 4.80 92.29 76.54 88.83 4.80 93.63 88.14 4.80 92.94 86.76 4.80 91.56

30.68 33.33 2.13 35.46 31.45 2.13 33.58 22.80 31.06 2.13 33.19 29.14 2.13 31.27 31.29 2.13 33.42

39.54 41.90 2.29 44.19 39.72 2.29 42.01 29.63 39.37 2.29 41.66 36.93 2.29 39.22 40.24 2.29 42.53

46.75 48.77 2.51 51.28 46.41 2.51 48.92 35.41 46.23 2.51 48.74 43.38 2.51 45.89 47.48 2.51 49.99

52.42 54.13 2.71 56.84 51.69 2.71 54.4 40.05 51.67 2.71 54.38 48.52 2.71 51.23 53.14 2.71 55.85

60.41 61.71 2.91 64.62 59.29 2.91 62.2 46.76 59.46 2.91 62.37 55.95 2.91 58.86 61.16 2.91 64.07

65.62 66.77 2.83 69.6 64.41 2.83 67.24 51.26 64.67 2.83 67.5 60.97 2.83 63.8 66.48 2.83 69.31

72.76 73.98 2.26 76.24 71.77 2.26 74.03 57.59 72.04 2.26 74.3 68.18 2.26 70.44 73.96 2.26 76.22

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Table 6. Continued Calculated Thermochemical Properties of Transition State Structuresa Cp (T) cal mol1 K ΔfH0298b

species TS3-1

TS3-2

TS3-3 = TS4-16

TS4 TS4-1 TS4-2

TS4-3 TS4-4

TS4-5

TS4-6 TS-7 TS4-8

TS4-9

TS4-10

TS4-10b

TS4-12

TS4-13

TS4-14

TS4-15

TS4-17

c

TVR IR total TVRc IR total TVRc IR total TVRc TVRc TVRc

TVRc TVRc IR total TVRc IR total TVRc TVRc TVRc IR total TVR IR total TVR IR total TVR IR total TVR IR total TVR IR total TVR IR total TVR IR total TVR IR total

Cb—CO2• 23.25 Cb—CO2• 12.18 Cb—CO2• 29.83 18.85 20.84 Cb—CO2• 1.98 76.87 Cb—CO2• 7.45 Cb—CO2• 4.33 97.17 84.03 CCO2H 5.98 Cb—CO2H 1.55 Cb—CO2 62.48 Cb—CO2 18.76 Cb—CO2H 8.02 Cb—CO2H 17.37 Cb—CO2H 4.55 Cb—CO2 18.84 CCO2H 2.92

S0298b

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

88.04 4.80 92.84 92.31 4.80 97.11 91.25 4.80 96.05 89.44 89.14 89.87 4.80 94.67 74.47 88.76 4.80 93.56 94.15 4.80 98.95 78.69 73.74 86.57 4.80 91.37 90.03 4.80 94.83 86.68 4.80 91.48 91.05 4.80 95.85 88.65 4.80 93.45 90.71 4.80 95.51 88.84 4.80 93.64 91.04 4.80 95.84 94.14 4.80 98.94

31.51 2.13 33.64 33.60 2.13 35.73 32.81 2.13 34.94 31.86 32.58 32.51 2.13 34.64 22.28 31.78 2.13 33.91 33.54 2.13 35.67 25.06 21.96 31.94 2.13 34.07 33.26 2.13 35.39 30.78 2.13 32.91 32.98 2.13 35.11 32.22 2.13 34.35 32.62 2.13 34.75 32.29 2.13 34.42 32.98 2.13 35.11 34.64 2.13 36.77

40.26 2.29 42.55 42.07 2.29 44.36 41.26 2.29 43.55 40.56 41.31 41.26 2.29 43.55 29.26 40.59 2.29 42.88 41.72 2.29 44.01 31.51 29.02 40.96 2.29 43.25 41.89 2.29 44.18 39.53 2.29 41.82 41.51 2.29 43.8 40.90 2.29 43.19 41.05 2.29 43.34 40.97 2.29 43.26 41.51 2.29 43.8 42.72 2.29 45.01

47.46 2.51 49.97 48.98 2.51 51.49 48.15 2.51 50.66 47.67 48.35 48.33 2.51 50.84 35.04 47.78 2.51 50.29 48.39 2.51 50.9 36.72 34.85 48.28 2.51 50.79 48.80 2.51 51.31 46.81 2.51 49.32 48.52 2.51 51.03 47.93 2.51 50.44 48.05 2.51 50.56 47.98 2.51 50.49 48.52 2.51 51.03 49.23 2.51 51.74

53.14 2.71 55.85 54.43 2.71 57.14 53.61 2.71 56.32 53.25 53.83 53.86 2.71 56.57 39.61 53.41 2.71 56.12 53.69 2.71 56.4 40.86 39.45 54.02 2.71 56.73 54.18 2.71 56.89 52.61 2.71 55.32 54.09 2.71 56.8 53.44 2.71 56.15 53.64 2.71 56.35 53.48 2.71 56.19 54.09 2.71 56.8 54.37 2.71 57.08

61.22 2.91 64.13 62.22 2.91 65.13 61.43 2.91 64.34 61.19 61.60 61.67 2.91 64.58 46.18 61.39 2.91 64.3 61.34 2.91 64.25 46.91 46.07 62.12 2.91 65.03 61.77 2.91 64.68 60.91 2.91 63.82 62.05 2.91 64.96 61.25 2.91 64.16 61.68 2.91 64.59 61.27 2.91 64.18 62.06 2.91 64.97 61.77 2.91 64.68

66.57 2.83 69.4 67.38 2.83 70.21 66.67 2.83 69.5 66.48 66.78 66.86 2.83 69.69 50.64 66.67 2.83 69.5 66.52 2.83 69.35 51.11 50.56 67.40 2.83 70.23 66.81 2.83 69.64 66.40 2.83 69.23 67.31 2.83 70.14 66.43 2.83 69.26 67.02 2.83 69.85 66.45 2.83 69.28 67.31 2.83 70.14 66.77 2.83 69.6

74.06 2.26 76.32 74.56 2.26 76.82 74.07 2.26 76.33 73.94 74.10 74.16 2.26 76.42 57.09 74.08 2.26 76.34 73.93 2.26 76.19 57.30 57.05 74.63 2.26 76.89 73.99 2.26 76.25 74.02 2.26 76.28 74.57 2.26 76.83 73.80 2.26 76.06 74.41 2.26 76.67 73.81 2.26 76.07 74.57 2.26 76.83 73.96 2.26 76.22

Thermodynamic properties are referred to a standard state of an ideal gas at 1 atm. b ΔfH0298 in kcal mol1; S0298 in cal mol1 K1. c Density Functional Theory at B3LYP/6-311G(d,p). a

attached to the benzoyl carbon and the ortho carbon of the aromatic ring forming a bicyclic intermediate (Y(C6H5•)Y(C3O2)dO).

The aromatic ring is converted to a cyclohexadienyl radical (see Figures 3 and 5 via TS3). This intermediate is the lowest-energy 11911


The Journal of Physical Chemistry A adduct in the reaction path from the initial benzoylperoxy radical, at 6.5 kcal mol1 (24 kcal mol1 below the entrance channel). The reaction proceeds with a 24 kcal mol1 barrier relative to the stabilized peroxy adduct, over (TS3); this barrier is 13.3 kcal mol1 below the entrance channel. This resonantly stabilized bicyclic has three reaction path sequences: (a) It needs 23.2 kcal mol1 over (TS3-1) to cleave the strained cyclic peroxide OO bond, then it reacts in two steps over two intermediate transition state structures before forming two low energetic products, CO2 and 2,5cyclohexadienyl-4-one (Y(C6H5•)dO). The initial intermediate resulting from the strained OO bond cleavage (after the TS3-1) is calculated to be 11.3 kcal mol1 at the B3LYP/3-21G level. This multiradical shifts a hydrogen atom to the ring atom bonded to the carbonyl (TS3-2, Figure 5) over a 12 kcal mol1 barrier forming double bond with the oxygen at the ortho site and a low energy 24-cyclohexadien-6-one carboxyloxy radical (O = Y(C6H5)CO2•) with enthalpy of 32.2 kcal mol1. This adduct is 62 kcal mol1 below the entrance channel. The CO2 elimination occurs through a barrier that is at 60 kcal mol1 relative to the entrance channel (TS3-3), leading to two products, 2,5-cyclohexadienyl-4-one (Y(C6H5•)dO) and CO2, as illustrated in Figures 3 and 5. This overall reaction is 112 kcal mol1 exothermic. (b) The bicyclic radical has a resonance structure with the radical site on the cyclohexadienyl on the carbon bonded to the carbonyl. This radical can attack the oxygen bonded to the ortho carbon, cleaving the OO peroxide bond and forming an oxirane ring (different bicyclic) over TS34. This forms a bicyclic with a cyclohexadiene ring, an oxirane (epoxide) ring, and a carboxy radical group at enthalpy of 9.5 kcal mol1 (BY(C6H5O)C(dO)O•). This intermediate is also the product of the TS4-1b reaction. To calculate a barrier for this TS3-4 at B3LYP/6-311G(d,p), we simplified the bicyclic to one ring and a double bond, Y(C3•H3O2)dO, keeping then the same active site and have calculated the transition state structure for the reaction of Y(C3•H3O2)dO to Y(CH2OCH)C(dO)O•. The barrier was found to be 6.1 kcal mol1 which supports a value from a PM3 calculation. The bicyclic cyclohexadieneepoxide carboxo radical will eliminate CO2, open the epoxide ring, and re-form the aromatic in a phenoxy radical (not shown). Our initial kinetic calculations indicate that this path is one of the three major paths for the benzoyl radical plus O2 reaction. (c) A third path for this resonantly Y(C6H5•)Y(C3O2)dO bicyclic is the ketene formation at the carbonyl site froming a peroxy radical ortho to the ketene carbon (TS3-5 and TS3-6). This path has a higher energy, due to loss of aromaticity plus formation of the ketene structure, and it also shows the very interesting further reaction: re-formation of the benzoyl radical + O2. This 6-carbonyl-2,4-cyclohexadienylperoxy radical has the peroxy group bonded to a double allylic carbon site, where the R—OO bond energy is only ∼12 kcal mol1. The peroxy group will dissociate rapidly under combustion conditions as with any allylic peroxy system and the result is formation of the resonant form of the benzoyl radical plus O2.

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3.4. Ipso Addition of the Peroxy Oxygen Radical Site to the Aromatic Ring (TS4). Two additional, low energy reaction sequences of the benzoyl peroxy [C6H5C(dO)OO•], start with the intramolecular addition of the peroxy oxygen radical site to the ring at the ipso position (see Figures 2 and 3). The peroxy radical undergoes addition at the ipso position to form a fourmember, dioxetane radical (Y(C6H5•)Y(C2O2)dO), with a barrier 12 kcal mol1 below the benzoyl radical + O2 entrance channel (TS4). The addition creates a bicyclic structure consisting of a dioxetane ring and a resonance stabilized cyclohexadienyl radical (see Figures 3 and 6). The weak peroxide bond in the strained four-membered ring cleaves forming a carboxy radical. The system undergoes elimination of CO2 with formation of 2,5-cyclohexadienyl-4-one (Y(C6H5•) dO) (phenoxy radical) via (TS4-1). This reaction provides significant energy to the reaction system as above; the products are 112 kcal mol1 below the entrance channel. A second path leading to the same set of products is more complex. The radical with a resonance structure at the ortho position attacks the peroxide oxygen (TS4-1b) forming the same oxirane cyclohexadiene carboxy (BY(C6H5O)C(dO)O•) at an enthalpy of 9.5 kcal mol1. This intermediate is also formed by TS3-4. There are a number of steps available to this intermediate (BY(C6H5O)C(dO)O•) from TS4-1b and these are illustrated in Figures 6 and 7. (a) The carboxy group on this BY(C6H5O)C(dO)O• intermediate can eliminate the CO2 via TS4-2 through a barrier of only 7 kcal mol1 forming a radical at the carbon of the epoxide group B(YC6H5•YC2O) at 20 kcal mol1 relative to the entrance channel (see Figure 6). The bicycle B(YC6H5•YC2O) (TS4-3) can then dissociate through a 3 kcal mol1 barrier, to form a phenoxy Y(C6H5•)dO radical plus CO2. This epoxide radical path forms the same products as through TS4-1. (b) A second reaction sequence from this epoxide adduct involves insertion of the epoxide oxygen into the cyclohexadienyl ring (TS4-4). This forms a carboxy group on a sevenmember ether (pinoxy) ring (Y(C6H5O)CO2•) via cleavage of the allylic CC bond in the six-member ring and electron rearrangement. The carboxy group exothermically eliminates (TS4-5) leaving the seven-member ether ring with a radical at a vinylic site. The cyclic seven-member ether (pinoxy) intermediate (Y(C6H5•O)) undergoes ring opening to form a linear unsaturated (CH•dCHCHdCHCHd CdO) over a 11.5 kcal mol1 barrier (TS4-6). This ring opened vinyl radical can form two acetylenes plus a ketenyl radical through a sequence of elimination reactions. Alternately the seven-member ether ring (Y(C6H5•O)) can undergo intramolecular addition. Here the radical site adds across the ether bridge, to a vinyl carbon adjacent to the ether; this forms a six-member ring and cleaves the ether bond (TS4-7). The six-member ring undergoes electronic rearrangement to form phenoxy radical. (c) The BY(C6H5O)C(dO)O• oxirane radical (Figure 6) can undergo intramolecular hydrogen transfer over (TS4-8) with a barrier of 15.6 kcal mol1; this forms an acid at the carboxy site and a radical on the ring BY(C6•O)C(dO)OH. We note that the initial 15.6 kcal mol1 barrier is more than 10 kcal mol1 higher than the barriers of this bicyclic structure to form the epoxide or the seven-member 11912


The Journal of Physical Chemistry A ether (pinoxy) ring intermediates described in (a) and (b) above. This bicyclic carboxylic acid, BY(C6•O)C(dO)OH, intermediate opens the oxirane ring by forming a double bond to the oxygen (beta scission of one oxirane CO bond) and results in a lower energy 2,5-cyclohexadienyl-4-one radical benzoic acid, as shown in Figure 7 via TS4-9, over a 10.8 kcal mol1 barrier. This radical is at 73 kcal mol1 (see structure in Tables 4 and 6). Further reactions of this radical involve two paths. The first path is a H-shift from the acid group to the phenoxy oxygen (TS4-10) and then CO2 elimination over ca. 19 kcal mol1 barrier (TS4-11) to form an o-hydroxyphenyl radical. The second path is an internal rotation of the carboxylic acid, then H-shift from the acid group to the ring (TS4-10b), and then elimination of CO2 over (TS3-3) to form phenoxy, Y(C6•)dO. A second reaction of BY(C6H4•O)C(O)OH is the formation of a seven-member ring (pinoxy ether), Figure 7, by opening of the oxirane oxygencarbon bond and electron rearrangement via (TS4-12) over an 8.4 kcal mol1 barrier to form (Y(C6H4•O)C(dO)OH1). The acid group (C(dO)OH) rotation barrier is 8.7 kcal mol1, which is illustrated in Figure 8, this potential is determined at the B3LYP/6-311G(d,p) calculation level from a scan at a torsion angle of 180° at 15° intervals and allowing the remaining structural parameters to be optimized. The barrier for hydrogen transfer across the acid group is ca. 29 kcal mol1 (TS4-13) which is very similar to an enolketo isomerization barrier. Figure 7 shows the possible reactions of this new formed oxipinoxy-CO2H radical Y(C6H4•O)C(dO)OH2. The sevenmember ring closes to a low energy o-carboxylphenoxy radical through a low barrier (TS4-14 = 7.3 kcal mol1) at 73 kcal mol1. This last transfers the H atom over a 50 kcal mol1 barrier (TS4-15) to the phenyl ring, then eliminates the CO2 (TS14-16) to form phenoxy radical (Y(C6H5•)dO) at 82 kcal mol1 as illustrated in Figure 7. The ring opened OdCdCCdCdC 3 CO2H in Figure 7 also reacts to low energy products CO + cyclopentadiene-1-carboxylic acid-2-yl radical (not shown). Figure 7 also shows that the seven-member ring Y(C6H4•O)C(dO)OH2 can open over 14.8 kcal mol1 barrier (TS4-17) forming a ketene (OH(CdO)C6H4•dO) at 12 kcal mol1. The radical in the open ring adds to a different site via TS4-20 forming the low energy o-carboxylphenoxy radical at 73 kcal mol1. The OH(CdO)C6H4•dO opened ring can also undergo a series of beta scission reactions forming HOC(dO)CtCH + CH•dCHCHdCdO via (TS4-18) and through a sequence of steps to form HOC(dO)CCH + CHtCH + CH•dCdO over 86 kcal mol1 (TS4-19). Important Reaction Paths. The reaction of benzoyl radical with O2 has a deep, 36 kcal mol1, well compared to other chemical bonds systems that have similar, ∼90 kcal mol1 bonds strengths, where well depths are only ∼20 kcal mol1. The reaction of the benzoyl radical with oxygen will have significant importance under atmospheric and moderate combustion conditions, where peroxy adduct resonance systems such as allyl or carbons adjacent to carbonyl groups on ketones are only of importance at atmospheric and lower temperatures. There are three reaction sequences that have similar barriers that are on the order of 10 or more kcal mol1 below the entrance channel. These are readily accessed in the chemical activated adduct and in low to moderate temperature thermal or

ARTICLE

combustion systems. These reactions involve (i) abstraction by the peroxy radical of an ortho-hydrogen on the aromatic ring forming a very active phenyl radical—hydroperoxide; (ii) addition of the peroxy radical to the aromatic ring at the ortho position, forming a bicyclic cyclohexadienyl radical-dioxolane (five-member peroxide ring) with several resonant forms in the cyclohexadienyl; (iii)ipso addition of the peroxy radical to aromatic carbon at the benzoyl group, again forming a cyclohexadienyl radicaldioxitane bicyclic. Both of the bicyclic peroxides have several resonant forms in the cyclohexadienyl group allowing for reaction from the different sites of the radical. There are a number of subsequent reactions for each of these isomers that lead to phenoxy radical plus CO2, which are some 112 kcal mol1 below the reaction entrance channel; these result in energy influx to the reaction system. The phenoxy radical and CO2 products appear to be dominant in our preliminary kinetic analysis on this system, but ring opening is also shown to have importance.

’ SUMMARY Structure and enthalpy of formation, entropy and heat capacities of important intermediates, transition state energies, and products resulting from the oxidation of the benzoyl radical (C6H5C•(dO)) were determined using computational chemistry. The benzoyl + O2 association results in a chemically activated benzoylperoxy radical [C6H5COO•(dO)]* with 36 kcal mol1 well depth. Important forward reaction channels of this chemically activated system are stabilization to benzoylperoxy radical, dissociation to phenyl carboxy radical + O, and several paths to formation of phenoxy radical (2,5-cyclohexadienyl-4-one) + CO2. These reactions of the benzoyl radical intermediate with dioxygen will be of importance in both atmospheric and combustion chemistry. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ASSOCIATED CONTENT

bS

Supporting Information. Description of the formation of the stabilized benzoyl-peroxy radical. Figure of the potential energy curve. Tables of geometry parameters, vibration frequencies, and moments of inertia. This material is available free of charge via the Internet at http://pubs.acs.org.

’ REFERENCES

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Thermochemistry and Reaction Paths in the Oxidation Reaction of

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