Atmospheric Photochemical Oxidation of Benzene: Benzene+ OH and ...

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This reaction and subsequent reactions of the BOH adduct with O2 are chemically activated reactions. Rate constants of these chemically activated bimolecular ...
J. Phys. Chem. 1996, 100, 6543-6554

6543

Atmospheric Photochemical Oxidation of Benzene: Benzene + OH and the Benzene-OH Adduct (Hydroxyl-2,4-cyclohexadienyl) + O2 Tsan H. Lay and Joseph W. Bozzelli* Department of Chemical Engineering, Chemistry and EnVironmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102

John H. Seinfeld† Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125 ReceiVed: June 20, 1995; In Final Form: January 15, 1996X

The addition of hydroxyl radical to benzene leading to the formation of the hydroxyl-2,4-cyclohexadienyl radical (benzene-OH adduct, BOH) initiates the atmospheric oxidation of benzene. This reaction and subsequent reactions of the BOH adduct with O2 are chemically activated reactions. Rate constants of these chemically activated bimolecular reactions and unimolecular decompositions are analyzed using a quantum version of Rice-Ramsperger-Kassel theory (QRRK) for k(E) and a modified strong collision approach for falloff. Results of QRRK analyses show that stabilization channels of energized BOH and benzene-OHO2 (BOHO2) adducts are dominant in chemically activated reaction systems under atmospheric condition. Unimolecular reactions of stabilized adducts to products are also important. Thermodynamic parameters (∆Hf°298, S°298, and Cp(T)s) are calculated using group additivity techniques with evaluated bond energies (for ∆Hf°298) and semiempirical PM3 molecular orbital calculations (for S°298 and Cp(T)s). A limited elementary reaction mechanism that includes 29 reactions and 26 species is developed with reverse reaction rates determined from species thermodynamic parameters and microscopic reversibility for each step. Simulation results of three reaction systems indicate that pseudo-equilibrium is attained and that equilibrium levels of the important BOH and BOHO2 adducts are controlled by thermodynamic properties. The most important bicyclic intermediate leading to ring cleavage products is adduct III. Rate constants of important bimolecular reactions are (k ) A(T/K)n exp(-Ea/RT), A in cm3/(mol s), Ea in kcal/mol): k4, (4.65 × 1015)(T/K)-1.18 e-1.23/RT for C6H6 + OH w BOH; k7, (3.55 × 1036)(T/K)-8.86 e-3.79/RT for BOH + O2 w BOHO2; k8, (1.73 × 1010)(T/K)-0.26 e-8.28/RT for BOH + O2 w hexadienedial + OH; k9, (7.06 × 1014)(T/K)-1.83 e-5.36/RT for BOH + O2 w phenol + HO2; k10, (2.14 × 1015)(T/K)-2.05 e-4.69/RT for BOH + O2 w adduct III. Rate constants of important unimolecular reactions are (A in s-1): k6, (2.04 × 1025)(T/K)-4.2 e-24.5/RT for BOH w phenol + H; k15, (6.30 × 1040)(T/K)-10.86 e-19.4/RT for BOHO2 w phenol + HO2; k16, (1.43 × 1042)(T/K)-11.34 e-18.8/RT for BOHO2 w adduct III.

Introduction Photochemical oxidation of aromatic hydrocarbons, such as benzene,1,2,3 toluene,1-8 and xylenes,1,6,9,10 is an important component in the chemistry of the reactive hydrocarbons in the urban atmosphere.8,11,12 Several reaction mechanisms have been proposed for interpretation of experimental laboratory and smog chamber photooxidation data.4,8,13-17 Although model predictions on formation and decay of a few products appear to fit major experimental observances,4,8 only about one-half of the carbon mass is accounted for as products in these experiments. Most kinetic models of atmospheric chemistry use unidirectional (irreversible) rate constants,4,16,17 where the values have been derived from measurements on net reaction processes. These models often do not account for equilibrium of intermediate adducts, which can react or isomerize to form new products or dissociate (in the reverse direction) back to reactants. The adducts in these reaction systems are actually present in near steady-state (SS) concentrations. Their SS levels and reactions will reflect changes in overall chemistry at different conditions. * Author to whom correspondence should be addressed. Phone: 201596-3459. E-mail: [email protected]. † Phone: 818-395-4100. E-mail: [email protected]. X Abstract published in AdVance ACS Abstracts, March 1, 1996.

0022-3654/96/20100-6543$12.00/0

Competition between reactions of the adductsunimolecular dissociations and bimolecular reaction with other constituentss appears to control the rates of final product formation, not the rate of initial adduct formation. Interpretation of experimental results in aromatic hydrocarbon photochemical oxidations using existing mechanisms is limited, due to the lack of knowledge on elementary reaction steps involving conversion, the destruction of the aromatic ring, and formation of observed products including dicarbonyl compounds, glyoxal ((CHO)2) and methyl glyoxal (CH3COCHO). Reaction barriers to form the key intermediates, such as bicyclic peroxy adducts from benzene-OH adduct + O2, are unknown. It is, in addition, difficult to determine elementary rate constants from overall reaction studies without knowledge of the thermodynamic data (enthalpies and entropies) of reactants and products. In this study we elect to use elementary reaction paths with reverse reactions and to include the adducts (reaction intermediates) in the kinetic calculations. We begin a systematic analysis on the mechanism of atmospheric aromatic photooxidation with benzene, because it is the simplest aromatic hydrocarbon, and the analysis allows us to focus on reactions involving the aromatic ring. This benzene photooxidation model will serve © 1996 American Chemical Society

6544 J. Phys. Chem., Vol. 100, No. 16, 1996 as an important template and submodel for oxidation of other aromatics, such as toluene and phenol. Reaction path analysis, energy well depths, and absolute rate constants are studied for reactions initiated by OH radical attack and subsequent reactions with O2. The addition of the OH radical to benzene forms an energized benzene-OH adduct. This energized benzene-OH adduct can dissociate back to reactants, be stabilized (4), or react to form phenol + H atom, Via β-scission (5). The stabilized benzeneOH can also undergo β-scission (6) to form phenol + H.

The addition of molecular oxygen to the benzene-OH adduct which forms the benzene-OH-O2 adduct (II, hydroxyl-2,4cyclohexadienyl-6-peroxy) is the next reaction system. This addition reaction can occur at either position 2 or position 4 of the ring;4,16 however, we discuss only the addition at position 2 to simplify the reaction system. The energized benzeneOH-O2 adduct from the addition of benzene-OH to O2 can dissociate back to reactants, react Via hydrogen transfer and a subsequent β-scission to form 2,4-hexadiene-1,6-dial + OH (8), react to form to phenol + HO2 (9), or isomerize to one of four bicyclic peroxy adducts III, IV, V, and VI (10, 11, 12, 13). The stabilized benzene-OH-O2 adduct can also undergo unimolecular reactions 14-19 to form the above products.

Lay et al.

butenedial Via one hydrogen being abstracted by molecular oxygen (reactions 29 and 30).

The objective is to develop an elementary reaction mechanism for atmospheric photochemical oxidation of benzene, initiated by the OH reaction, including reactions leading to the formation of dicarbonyl products (e.g., glyoxal and butenedial), as well as the formation of oxygenated aromatics (phenol). Reverse rate constants (kr) for all reactions are incorporated in the mechanism Via the principle of microscopic reversibility and thermodynamic parameters. This allows thermodynamic consistency and accurate steady state species concentrations. It also allows use of elementary rate constants in the reaction mechanism. We propose to use these detailed mechanisms, after they are further developed and validated, for use in generating smaller (reduced) mechanisms in atmospheric transport modeling. Methods

The third reaction system is the bicyclic benzene-OH-O2 adducts III, IV, V, and VI reacting with O2 to form a second series of peroxy radicals. These bicyclic peroxy adducts subsequently become alkoxy radicals VII, VIII, IX, and X after the terminal oxygen atom is abstracted by NO. Ring-opening reactions of these alkoxy adducts occur Via a series of β-scission steps eventually leading to two dicarbonyl compounds, glyoxal and butene-1,4-dial, or their precursors (reactions 22, 25, and 28). The precursors form glyoxal and

Thermodynamic Parameters. Thermodynamic properties (∆Hf°298, S°298, and Cp(T)s, 300 e T/K e 1500) of stable molecules are calculated using group additivity (GA)18,19 and the THERM computer program.19 The semiempirical molecular orbital (MO) method PM320 in the MOPAC 6.021 package is used whenever groups in the GA method are not available for specific molecules. The PM3-determined enthalpies of bicyclic peroxy compounds are scaled by 0.83 for use in the thermodynamic data base. This scaling factor is obtained from the comparison between PM3-determined enthalpies and experimentally determined enthalpies on the series of monocyclic and bicyclic hydrocarbons and oxyhydrocarbons (see Appendix, section 4). No scale factor is used for entropy and heat capacity determined by the PM3 MO calculation because a number of systematic studies20,22 show that PM3 can provide correct fundamental vibrational frequencies and moments of inertia (from correct molecular structures), leading to the reliable results of entropies and heat capacities. The thermodynamic properties of free radical species (R•) are determined using those of their corresponding parent

Atmospheric Oxidation of Benzene

J. Phys. Chem., Vol. 100, No. 16, 1996 6545

TABLE 1: Input Parametersa and High-Pressure Limit Rate Constants (k∞)b for QRRK Calculations and the Results of Apparent Rate Constants: Benzene + OH (Temp ) 298 K) High-Pressure Limit Rate Constants k∞ (4) (-4) (5)

reaction

A∞ (s-1 or cm3/(mol s))

Ea,∞ (kcal/mol)

benzene + OH w benzene-OHc benzene-OH w benzene + OHd benzene-OH w phenol + He

2.29 × 1012 1.77 × 1014 1.95 × 1013

0.68 19.2 22.5

Calculated Apparent Reaction Parameters at P ) 1 atm, k ) A(T/K)n(-Ea/RT) (Temp ) 200-400 K) reaction A n Ea (kcal/mol) k298 (s-1 or cm3/(mol s)) (4) (-4) (5) (6)

benzene + OH w benzene-OH benzene-OH w benzene + OHf benzene + OH w phenol + H benzene-OH w phenol + Hg

4.65 × 10+15

-1.18

1.23

3.34 × 10-5 2.04 × 10+25

5.62 -4.2

2.59 24.54

7.03 × 1011 0.146 3.39 × 107 8.36 × 10-4

a Geometric mean frequency (from CPFIT, ref 28): 741.6 cm-1 (21.6); 1859.0 cm-1 (1.63); 2523.0 cm-1 (12.77). Lennard-Jones parameters: σLJ ) 5.50 Å, /k ) 450 K estimated from phenol (ref 29). b The units of A factors and rate constants k are s-1 for unimolecular reactions and cm3/(mol s) for bimolecular reactions. c k∞,4: Baulch et al., ref 32. d k∞,-4: MR. e k∞,5: The rate constant of reverse reaction, A-5 and Ea-5 taken from ref 33 for H + C6H6 f C6H7; A-5 ) 3.98 × 1013 cm3/(mol s); Ea-5 ) 4.00 kcal/mol. k∞,5 is from MR. f The dissociation of stabilized benzene-OH adduct to benzene + OH; rate constant is calculated from apparent k4,298 and MR. g The reaction of stabilized benzene-OH adduct to phenol + H.

molecules, RH, and the hydrogen-atom-bond-increment (HBI) method.23 The thermodynamic properties obtained either by GA or by PM3 are more reliable for stable (closed-shell) molecules than for free radicals. We choose not to use these two methods to directly determine the thermodynamic parameters of free radicals; instead, the HBI method is used. Enthalpy for each free radical, R•, is determined from enthalpy of the corresponding parent molecule, RH, along with the evaluated literature R-H bond energies. For instance, ∆Hf°298 of an alkyl peroxy radical is determined from ∆Hf°298 of the corresponding hydroperoxide, ROOH, along with the bond energy, D°(ROO-H), equal to 88.0 kcal/mol.24 Entropy and heat capacities for each free radical, R•, are determined from those of the parent molecule, RH, along with the corresponding HBI group values.23 The HBI groups are derived for the calculation of S°298 and Cp(T) on generic classes of radicals (R•) from the corresponding parent stable molecules (RH), see Appendix, section 1, for a further description of this method. For instance, S°298 and Cp(T) of alkyl peroxy radicals are calculated using a HBI group, peroxy (see Appendix, section 1) as follows (where σ indicates the symmetry number and R is the ideal gas constant).

S°298(ROO•) ) S°298(ROOH) + ∆S°298(peroxy) + R ln(σROO/σROOH) Cp(T)(ROO•) ) Cp(T)(ROOH) + ∆Cp(T)(peroxy), 300 e T e 1000 K Quantum Rice-Ramsperger-Kassel (QRRK) Analysis. Quantum Rice-Ramsperger-Kassel (QRRK) analysis25 is used to calculate energy-dependent rate constants, k(E), for chemically activated reactions 4, 5, and 7-13. The rate constants of pressure-dependent, unimolecular reactions 6 and 14-19 are also calculated using QRRK. The QRRK calculation of k(E) is combined with the “modified strong collision approach” of Gilbert et al.26 for falloff and steady-state assumption for the adduct population at each energy, to compute rate constants over a range of temperature and pressure. Results presented here are for 1 atm. A significant number of modifications have been made since the initial descriptions of the QRRK and falloff calculations were published.25a,b They are incorporated in the present calculations.25c Reduced sets of three vibrational frequencies and their degeneracies (totaling 3N - 6, where N is number of atoms in the energized adduct) plus energy levels of one external rotor

are used to yield the ratio of density of states to partition coefficient, F(E)/(Q).27 Each set of three vibrational frequencies and respective degeneracies is computed from fitting heat capacity data, as described by Ritter (CPFIT computer code).28 Lennard-Jones parameters, σLJ (in angstroms) and /k (in Kelvin), are obtained from tabulations.29 Limitations resulting from the assumptions in the QRRK and falloff calculations are often overshadowed by uncertainties in high-pressure limit rate constants and thermodynamic parameters. The addition reactions along with subsequent chemically activated reactions and unimolecular reactions are first analyzed by construction of potential energy diagrams. High-pressure limit rate constants (k∞) are taken from generic reactions in the literature (e.g., k∞,4, k∞,-6, k∞,7), estimated from the principles of microscopic reversibility, MR (e.g., k∞,6), or determined from transition state theory (TST) and principles of thermodynamic kinetics18 (e.g., k∞,14, k∞,15 k∞,16, k∞,17, k∞,18, k∞,19); see below and Tables 1 and 2 for more details. The barriers of reactions 14-19 are estimated using thermochemical kinetics.18 High-pressure limit A factors (A∞) of these unimolecular reactions are calculated using TST along with PM3 at the unrestricted Hartree-Fock (UHF) level of theory for the determination of vibrational and rotational contributions to entropies (S°298,vib and S°298,rot) of transition states (TSs). The TS geometries obtained by the PM3 method are identified by the existence of only one imaginary frequency in the normal mode coordinate analysis. Loss (or gain) of internal rotors and change of optical isomer and symmetry numbers are also incorporated into the calculation of entropy for each TS. Entropies of reactants and TSs are then used to determine the pre-exponential factor, A, Via conventional TST18 for a unimolecular reaction

A ) (ehpT/kb) exp(∆Sq) where hp is Planck’s constant, kb is the Boltzmann constant, and ∆Sq is equal to S°298,TS - S°298,reactant. A factors of unimolecular reactions 22, 25, and 28 are also determined using TST and PM3-determined entropies. The PM3-determined enthalpies of formation (scaled by 0.83) for the reactants and their TSs are used to determine the activation energies of reactions 22, 25, and 28.

Ea ) [∆Hf°298,TS - ∆Hf°298,reactant] Kinetic Modeling. A kinetic mechanism consisting of the initial reactions of atmospheric benzene oxidation is developed. In the present mechanism:

6546 J. Phys. Chem., Vol. 100, No. 16, 1996

Lay et al.

TABLE 2: Input Parametersa and High-Pressure Limit Rate Constants (k∞)b for QRRK Calculations and the Results of Apparent Rate Constants: Benzene-OH + O2 (Temp ) 298 K) High-Pressure Limit Rate Constants k∞ (7) (-7) (8) (9) (10) (11) (12) (13)

reaction

A∞ (s-1 or cm3/(mol s))

Ea,∞ (kcal/mol)

benzene-OH + O2 w benz-OH-O2c benz-OH-O2 w benzene-OH + O2d benz-OH-O2 w 2,4-hexadiene-1,6-dial + OHe benz-OH-O2 w phenol + HO2f benz-OH-O2 w adduct IIIg benz-OH-O2 w adduct IVg benz-OH-O2 w adduct Vg benz-OH-O2 w adduct VIg

1.21 × 1012 2.27 × 1014 4.77 × 1011 2.62 × 1011 1.41 × 1011 1.76 × 1011 2.49 × 1011 1.69 × 1011

0.0 11.4 19.4 15.0 14.0 14.0 15.6 39.6

Calculated Apparent Reaction Parameters at P ) 1 atm, k ) A(T/K)n(-Ea/RT) (Temp ) 200-400 K) (7) (-7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19)

reaction

A

n

Ea (kcal/mol)

k298 (s-1 or cm3/(mol s))

benz-OH + O2 w benz-OH-O2 benz-OH-O2 w benz-OH + O2h benz-OH + O2 w hexadienedial + OH benz-OH + O2 w phenol + HO2 benz-OH + O2 w adduct III benz-OH + O2 w adduct IV benz-OH + O2 w adduct V benz-OH + O2 w adduct VI benz-OH-O2 w hexadienedial + OHi benz-OH-O2 w phenol + HO2i benz-OH-O2 w adduct IIIi benz-OH-O2 w adduct IVi benz-OH-O2 w adduct Vi benz-OH-O2 w adduct VIi

3.55 × 1036

-8.86

3.79

1.73 × 1010 7.06 × 1014 2.14 × 1015 2.67 × 1015 6.07 × 109 8.68 × 106 4.43 × 1035 6.30 × 1040 1.43 × 1042 1.78 × 1032 2.46 × 1037 1.44 × 1024

-0.26 -1.83 -2.05 -2.05 -0.16 0.69 -9.27 -10.86 -11.34 -11.34 -9.81 -5.83

8.28 5.36 4.69 4.69 4.64 27.78 22.44 19.45 18.80 18.80 18.93 41.02

7.08 × 1011 5.87 × 105 3.26 × 103 2.49 × 106 6.56 × 106 8.19 × 106 9.61 × 105 1.83 × 10-12 1.75 × 10-4 0.47 2.01 2.51 0.17 4.52 × 10-21

Geometric mean frequency (from CPFIT, ref 28): 421.8 cm-1 (13.7); 1261.0 cm-1 (20.1); 3347.0 cm-1 (8.2). Lennard-Jones parameters: σLJ ) 5.50 Å, /k ) 450 K, estimated from phenol (ref 29). b The units of A factors and rate constants k are s-1 for unimolecular reactions and cm3/(mol s) for bimolecular reactions. c k∞,7: Estimated from regression plot R + O2 by assuming activation energy equal to 0 (ref 34). d k∞,-7: MR. e k∞,8: A8 is calculated using TST and entropy of transition state for H transfer step, ∆Sq298 ) -7.09 cal/(mol K) (∆Sqvib ) +2.0 eu and ∆Sqrot ) -0.33 eu obtained from the PM3/UHF method; loss of one rotor, -10.14 eu; gain of one optical isomer, +1.38 eu); Ea8 ) (Eaabstraction, 7.05) + (∆Hrxn, 16.36) - (∆Hhydrogen-bonding, 4) ) 19.41 kcal/mol. Eaabstraction estimated from 12.5 kcal/mol - ∆Hrxn × 1/3 (Evans’ Polanyi plot); 4 kcal/mol is adapted as an average value of ∆Hhydrogen-bonding. f k∞,9: A9, TST and entropy of TS for the H transfer first step (rate-determining step), ∆Sq298 ) -8.28 cal/(mol K) (∆Sqvib ) +0.84 eu and ∆Sqrot ) -0.36 eu obtained from the PM3/UHF method; loss of one rotor, -10.14 eu; gain of one optical isomer, +1.38 eu); Ea9, estimated from (Eaabstraction, 9.4 kcal/mol) + (ring strain, 5.6 kcal/mol) ) 16.6 kcal/mol. g k∞,10, k∞,11, k∞,12, and k∞,13: TST and entropies of TSs are assumed to be the same as those of products (i.e., Sq298 ≈ S°298(product)), plus one optical isomer gained at TSs. ∆Sq298 ) S°298,product - S°298,benzene-OH-O2 + R ln 2. Ea ) (Eaaddition, 5 kcal/mol) + (bicyclic ring strain) - (1,3-cyclohexadiene ring strain, 4.19 kcal/mol). For ring strain energy of bicyclic adducts, see Appendix, section 4. h The dissociation of stabilized benzene-OH-O2 adduct to benzene-OH + O2; the rate constant is calculated from apparent k7,298 and MR. i The reaction of stabilized benzene-OH-O2 adduct to products. a

(1) All reactions are elementary or treated in such a way that the elementary reaction steps are incorporated. (2) All reactions are reversible. (3) Reverse reaction rates are calculated from thermodynamic parameters and principles of microscopic reversibility (MR). Reverse rate constants (kr) are determined by kf/Keq and Keq (in concentration units) ) exp(-∆G°rxn/RT) + (RT)-∆n, where ∆G° ) ∆H°rxn + T∆S°rxn and ∆n is the mole change in the reaction. The computer code CHEMKIN-II30 is used for numerical integration. For convenience, the OH mixing ratio is held constant at 4.1 × 10-8 ppm (1.0 × 106 molecule/cm3)31 in the calculation of product profiles. Two dummy molecules, XX and YY, and two dummy reactions, 1 and 2, are used to maintain the steady-state OH mixing ratio at the prescribed constant value. Rate constants of reactions 1 and 2 are adjusted to hold [OH] concentration at 4.1 × 10-8 ppm during the model simulations. Doing so avoids the need to include an entire set of additional reactions that control tropospheric OH levels. Initial benzene and NO mixing ratios in the calculation are both chosen as 1 ppm. Initial O2 mixing ratio is 0.22, and N2 is the bath gas.

XX w YY + OH

(1)

YY + OH w XX (2) Results and Discussion First we describe the rate constants obtained using QRRK calculations and then the product profiles obtained from model

computation of each subsystem mechanism. This allows us to evaluate the importance of reaction paths and intermediate species and to analyze pseudo-steady-state level for the adducts. Evaluations of the A∞ factors and Eas for reaction paths in benzene + OH and benzene-OH + O2 reaction systems as the QRRK input parameters and results of QRRK calculations are given in Tables 1 and 2, respectively. Table 3 lists the reaction mechanism with forward rate constants at 298 K, 1 atm. The thermodynamic parameters for all species considered in this work are listed in Table 4. OH Addition to Benzene. High-Pressure Limit Rate Constants as QRRK Input Parameters. The potential energy diagram for the reaction benzene + OH is illustrated in Figure 1. The well depth for OH addition to benzene is 18.5 kcal/ mol. This addition has a high-pressure limit A∞,4 factor of 2.29 × 1012 cm3/(mol s) with a small barrier of 0.68 kcal/mol, following the recommendation of Baulch et al.32 The reverse rate constant k∞,-4 is calculated Via the principle of MR, resulting in A∞,-4 ) 1.77 × 1014 s-1 with Ea∞,-4 ) 19.2 kcal/mol. k∞,-6 is assumed to be the same as that for H atom addition to the benzene:

k∞,-6 ) k(H+C6H6wC6H7) ) (3.98 × 1013 cm3/(mol s)) exp(-4 kcal mol-1/RT)33 A∞,6 and Ea∞,6 are then determined Via MR, as 1.95 × 1013 s-1 and 22.5 kcal/mol, respectively.

Atmospheric Oxidation of Benzene

J. Phys. Chem., Vol. 100, No. 16, 1996 6547

TABLE 3: Mechanism of Benzene Photooxidation (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30)

reactionsa,b

A

n

Ea (cal/mol)

comment

XX + hv w YY+OH YY + OH w XX C6H6 + OH ) Ph + H2O C6H6 + OH ) benzene-OH C6H6 + OH ) PhOH + H benzene-OH ) PhOH + H benzene-OH + O2 ) benzene-OH-O2 benzene-OH + O2 ) HDEDA+OH benzene-OH + O2 ) PhOH+HO2 benzene-OH + O2 ) adduct III benzene-OH + O2 ) adduct IV benzene-OH + O2 ) adduct V benzene-OH + O2 ) adduct VI benzene-OH-O2 ) HDEDA+OH benzene-OH-O2 ) PhOH+HO2 benzene-OH-O2 ) adduct III benzene-OH-O2 ) adduct IV benzene-OH-O2 ) adduct V benzene-OH-O2 ) adduct VI adduct III + O2 ) adduct VIIO adduct VIIO + NO ) adduct VII + NO2 adduct VII ) BDA + GLYH adduct IV + O2 ) adduct VIIIO adduct VIIIO + NO ) adduct VIII + NO2 adduct VIII ) BDAH + GLY adduct V + O2 ) adduct IXO adduct IXO + NO ) adduct IX + NO2 adduct IX ) BDA + GLYH GLYH + O2 ) GLY+HO2 BDAH + O2 ) BDA+HO2

1.54 × 10-6 2.00 × 10+13 6.03 × 10+11 4.65 × 10+15 3.34 × 10-5 2.04 × 10+25 3.55 × 10+36 1.73 × 10+10 7.06 × 10+14 2.14 × 10+15 2.67 × 10+15 6.07 × 10+9 8.68 × 10+6 4.43 × 10+35 6.30 × 10+40 1.43 × 10+42 1.78 × 10+42 2.46 × 10+37 1.44 × 10+24 1.20 × 10+12 5.36 × 10+12 3.07 × 10+13 1.20 × 10+12 5.36 × 10+12 3.45 × 10+13 1.20 × 10+12 5.36 × 10+12 2.75 × 10+13 5.66 × 10+12 5.66 × 10+12

0 0 0 -1.18 5.62 -4.2 -8.86 -0.26 -1.83 -2.05 -2.05 -0.16 0.69 -9.27 -10.86 -11.34 -11.34 -9.81 -5.83 0 0 0 0 0 0 0 0 0 0 0

0 0 4948 1228 2588 24536 3789 8277 5356 4690 4690 4637 27780 22444 19447 18798 18798 18927 41023 0 0 8180 0 0 8020 0 0 8630 0 0

c c d e e f e e e e e e e f f f f f f g h i g h i g h i j j

k ) A(T/K)n exp(-Ea/RT); A in s-1 for unimolecular reactions and cm3/(mol s) for bimolecular reactions. All reactions in the mechanism are considered by the integrator, CHEMKIN2, in both forward and reverse directions Via principles of MR. b Symbols of species in the mechanism (also see Table 4 for detailed formula): Ph ) C6H5- (phenyl group), HDEDA ) 2,4-hexadiene-1,6-dial, BDA ) 2-butene-1,4-dial, GLYH ) CH(O)C•HOH (the precursor of glyoxal), GLY ) glyoxal, BDAH ) 4-hydroxy-1-oxo-2-buten-4-yl (the precursor of butenedial), adduct VIIO ) the peroxy radical with one more oxygen than adduct VII (alkoxy radical), as are adduct VIIIO and adduct IXO. c Rate constants of reactions 1 and 2 are adjusted to hold [OH] concentration at 4.1 × 10-8 ppm. In submodel BM1, k1 ) 3.37 × 10-6 s-1, k2 ) 2.00 × 1013 cm3/(mol s), at [XX] ) 4.1 × 10-1 ppm and [YY] ) 4.1 × 10-2 ppm. In submodel BM2 and model BM3, k1 ) 1.54 × 10-6 s-1, k2 ) 2.00 × 1013 cm3/(mol s), at [XX] ) 1.8 × 10-1 ppm and [YY] ) 4.1 × 10-2 ppm. d Reference 32. e Bimolecular QRRK calculation. f Unimolecular QRRK calculation. g Estimated as recommended in ref 34. h Adopted from k of C2H5OO + NO w C2H5O + NO2; Atkison, R.; Baulch, L. D.; Cox, R. A.; Hampson, R. F., Jr.; Kerr, J. A.; Troe, J. J. J. Phys. Chem. Ref. Data 1992, 21, 1125. i TST; see text. j Adopted from CH2OH + O2 w CH2O + HO2; the same source as in h. a

Figure 1. Potential energy diagram for benzene + OH.

Figure 2. Rate constants at different temperatures and 1 atm for chemically activated reactions: benzene + OH w products.

QRRK Analysis Results. The apparent rate constants at different temperatures (200 e T/K e 2000) and 1 atm for each reaction channel are illustrated in Figure 2. Rate constants k ) A(T/K)n exp(-Ea/RT) are obtained by fitting the rate constants in the temperature range from 200 to 400 K. The stabilization channel is dominant at room temperature and 1 atm. The apparent rate constant of benzene + OH w benzene-OH adduct at 298 K is calculated to be 7.03 × 1011 cm3/(mol s), which is identical to the value measured by flash photolysis-resonance fluorescence.1 Reaction 5, benzene + OH w phenol + H, is a relatively slow path below 500 K, although it is significantly

faster at higher temperatures. The stabilized benzene-OH adduct formed at this step can dissociate back to benzene + OH (-4), form phenol + H Via β-scission (6), or react with O2 (7; see below). The apparent rate constant of β-scission of the stabilized benzene-OH adduct to form phenol + H, k6, is calculated using unimolecular QRRK and listed in Table 1. Model Computation (BM1). The mechanism for subsystem BM1 contains reactions 1-6. The abstraction path (3), C6H6 + OH w C6H5 + H2O, is included, where its rate constant is taken from the literature.32 The calculated product profile from subsystem BM1 at 298 K, 1 atm is illustrated in Figure 3. The

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TABLE 4: Ideal Gas Phase Thermodynamic Properties ∆Hf°298 (kcal/mol), S°298 (cal/(mol K)), and Cp(T)s (cal/(mol K), 300 e T/K e 1000) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

speciesa

∆Hf°298

S°298

Cp300

Cp400

Cp500

Cp600

Cp800

Cp1000

formula

H O OH O2 H2O glyoxal (GLY) CH(O)CHOH (GLYH) CH(O)CH2OH 2-butene-1,4-dial (BDA) 4-hydroxy-1-oxo-2-buten-4-yl (BDAH) CH(O)CHCHCH2OH benzene cyclohexa-1,3-dien-5-yl cyclohexa-1,3-diene I (benzene-OH) I+H II (benzene-OH-O2) II+H III III+H IV IV+H V V+H VI VI+H VII VII+H VII+O VII+OHb VIII VIII+H VIII+O VIII+OHb IX IX+H IX+O IX+OHb Ph PhO phenol (PhOH) PhOO PhOOH 2,4-hexadiene-1,6-dial

52.10 59.55 9.49 0.00 -57.80 -50.60 -34.60 -73.50 -53.16 -32.60 -62.65 19.81 49.93 3.89 10.17 -13.73 -1.20 -37.30 -13.2 -44.93 2.10 -43.9 3.86 -42.14 12.59 -19.14 -32.11 -84.07 -32.40 -68.50 -29.84 -81.8 -30.13 -66.23 -30.35 -82.31 -30.64 -66.74 79.44 10.36 -23.03 37.04 0.94 -37.60

27.36 38.47 43.88 49.01 45.10 65.42 67.38 73.57 78.18 82.27 86.62 64.37 73.19 72.49 84.11 84.79 100.65 100.43 87.17 87.11 88.81 86.63 90.28 88.10 89.55 89.49 94.19 96.65 102.97 102.75 114.61 117.07 123.39 123.17 94.29 96.75 103.07 102.85 69.83 74.89 75.43 85.62 85.40 92.32

4.97 5.23 7.15 7.02 8.02 14.90 15.54 17.53 23.82 25.01 25.49 19.92 21.86 22.66 25.51 26.31 32.72 34.77 30.00 30.36 30.44 30.41 30.23 30.20 30.66 31.02 32.90 34.01 36.77 38.82 33.60 34.71 37.47 39.52 32.69 33.80 36.56 38.61 21.01 24.79 24.90 26.76 28.81 30.06

4.97 5.14 7.10 7.23 8.19 17.54 18.62 20.07 29.12 30.91 30.95 27.09 29.48 30.72 33.94 35.18 42.33 45.17 40.16 40.93 40.65 41.20 40.24 40.79 40.72 41.49 44.10 45.39 48.08 50.92 44.41 45.70 48.39 51.23 43.69 44.98 47.67 50.51 27.06 31.31 32.45 34.25 37.09 38.52

4.97 5.08 7.07 7.44 8.41 19.64 21.25 22.34 33.14 35.48 35.52 33.25 35.99 37.76 40.94 42.71 50.06 53.61 48.58 49.88 48.94 50.16 48.53 49.75 48.97 50.27 53.27 54.83 57.23 60.78 53.42 54.98 57.38 60.93 52.86 54.42 56.82 60.37 32.43 37.08 38.64 40.07 43.62 45.02

4.97 5.04 7.06 7.65 8.66 21.40 23.40 24.41 36.24 38.96 39.34 38.38 41.26 43.56 46.17 48.47 55.56 59.65 54.74 56.6 55.03 56.9 54.63 56.5 55.08 56.94 59.68 61.51 63.69 67.78 60.3 62.13 64.31 68.40 59.28 61.11 63.29 67.38 37.05 42.01 43.54 44.82 48.91 49.86

4.97 5.01 7.13 8.04 9.24 24.28 26.66 28.32 40.98 44.03 45.38 45.87 49.09 52.27 54.13 57.31 64.08 68.8 63.75 66.65 63.95 66.93 63.58 66.56 64.06 66.96 69.36 71.69 73.42 78.14 70.62 72.95 74.68 79.40 68.99 71.32 73.05 77.77 43.90 49.25 50.62 51.76 56.48 56.98

4.97 5.01 7.33 8.35 9.85 25.80 29.00 31.01 44.02 47.40 49.55 51.05 54.57 58.42 59.52 63.37 70.13 75.1 69.65 73.35 69.83 73.61 69.49 73.27 69.98 73.68 75.52 78.28 80.11 85.08 77.46 80.22 82.05 87.02 75.18 77.94 79.77 84.74 47.77 53.28 55.49 56.48 61.45 61.72

H1 O1 H1 O1 O2 H1 O2 C2 H2 O2 C2 H3 O2 C2 H4 O2 C4 H4 O2 C4 H5 O2 C4 H6 O2 C6 H6 C6 H7 C6 H8 C6 H7 O1 C6 H8 O1 C6 H7 O3 C6 H8 O3 C6 H7 O3 C6 H8 O3 C6 H7 O3 C6 H8 O3 C6 H7 O3 C6 H8 O3 C6 H7 O3 C6 H8 O3 C6 H7 O4 C6 H8 O4 C6 H7 O5 C6 H8 O5 C6 H7 O4 C6 H8 O4 C6 H7 O5 C6 H8 O5 C6 H7 O4 C6 H8 O4 C6 H7 O5 C6 H8 O5 C6 H5 C6 H5 O1 C6 H6 O1 C6 H5 O2 C6 H6 O2 C6 H6 O2

a See footnote b of Table 3 for the representations of species symbols. b Adduct VII OH ) the parent molecule (alcohol) of adduct VIIO (alkoxy radical) with one more hydrogen, as are adduct VIIIOH and adduct IXOH.

Figure 3. Selected product profiles of subsystem BM1. Initial mixing ratios (v/v): [C6H6], 1.0 × 10-6; [OH], 4.1 × 10-14; [AA], 4.1 × 10-7; [YY], 4.1 × 10-8; [O2], 0.22.

benzene-OH adduct reaches a pseudo SS of 7.0 × 10-6 ppm within 0.5 min. The stabilized benzene-OH adducts from reaction 4 in this step decomposed back to reactants at k-4 )

0.15 s-1. Phenol grows steadily because reactions 5 and 6 serve as a removal (bleed) path to deplete benzene, at k5 ) 3.4 × 107 cm3/(mol s) and k6 ) 8.4 × 10-4 s-1, respectively. Benzene-OH Adduct + O2. High-Pressure Limit Rate Constants as QRRK Input Parameters. The potential energy diagram for the reaction of benzene-OH adduct with O2 is illustrated in Figure 4. The well depth of benzene-OH + O2 w benzene-OH-O2 is 12.0 kcal/mol. The shallow energy well suggests that its reverse reaction (-7), the dissociation back to benzene-OH + O2, is relatively fast. We estimate the highpressure limit rate constant k∞,7 to be 1.21 × 1012 cm3/(mol s), in accord with several investigations on the addition of alkyl radicals to molecular oxygen: R + O2 w ROO.34 The barrier for reaction -7 is 11.4 kcal/mol; k∞,-7 is then determined as (2.27 × 1014 s-1) exp(-11.4 kcal mol-1/RT), that is, ca. 105 s-1 at 298 K. This leads to a lifetime of the benzene-OH-O2 adduct of only 10-5 s because of the fast (reverse) dissociation. Knispel et al.3 report the overall rate constant for benzeneOH adduct + O2 is 1.1 × 108 cm3/(mol s). This small overall rate constant is mainly due to the fast adduct formation combined with rapid reverse reaction. Reaction 14 occurs Via hydrogen transfer from OH to the peroxy group followed by a series of rapid β-scissions to form

Atmospheric Oxidation of Benzene

Figure 4. Potential energy diagram for benzene-OH adduct + O2.

Figure 5. Potential energy diagram for reaction 14: benzene-OHO2 w 2,4-hexadiene-1,6-dial + OH.

2,4-hexadiene-1,6-dial + OH. The first step of this reaction (the hydrogen transfer) has a barrier of 19.4 kcal/mol, which is mostly due to endothermicity (the cleavage of the CO-H bond requires ca. 104 kcal/mol,35 and the formation of the OO-H bond gains only ca. 88 kcal/mol).24 This is the rate-determining step of reaction 14 because the subsequent steps are β-scissions to form strong carbonyl bonds, CdO, which have lower barriers (see Figure 5) and higher A factors.

Reaction path 15 occurs Via transfer of the hydrogen bonded from the carbon with OH substituent (C1) to the peroxy group and subsequent β-scission to form phenol + HO2. The hydrogen transfer step of reaction 15 has a smaller barrier of 15.0 kcal/mol than that of reaction 14, because this C1-H bond is doubly allylic with a lower bond energy (76 kcal/mol).36 Again this is the rate-determining step of reaction 15 since the following β-scission step is highly exothermic with a low barrier; see Figure 6. Evaluations of high-pressure limit rate constants for reactions 14 and 15 are given in Table 2.

Reaction paths 16-19 take place Via intramolecular addition of the terminal oxygen to π bond sites on the cyclohexadiene ring, forming four isomers of peroxy bicyclic hexenyl adducts.

J. Phys. Chem., Vol. 100, No. 16, 1996 6549

Figure 6. Potential energy diagram for reaction 15: benzene-OHO2 w phenol + HO2.

These cyclization reactions have product-like TSs, according to the TS molecular geometries obtained by the PM3/UHF method. A∞ factors of these four reactions are estimated by TST and ∆Sq298 ) S°298,product - S°298,reactant + R ln 2, since S°298,TS ≈ S°298,product and the peroxide bridge of the TS has two optical isomers.18 This results in A∞ factors equal to ca. 2.0 × 1011 cm3/(mol s) (see Table 2). The reaction barriers for these cyclization channels primarily result from ring strain energy (ERS) and the barrier of peroxy radical addition to a CdC double bond. The ERS of adducts III, VI, and V are similar (13-15 kcal/mol; see Appendix, section 4.2), while that of adduct VI is much higher (39 kcal/mol). This results in an activation energy of reaction 19 higher by ca. 25 kcal/mol than those of reactions 16-18. QRRK Analysis Results. The apparent rate constants at different temperatures (200 e T/K e 2000) and 1 atm obtained using QRRK calculations are illustrated in Figure 7. The parameters of k ) A(T/K)n exp(-Ea/RT) in Table 2 for each reaction channel are obtained by fitting the rate constants from 200 to 400 K. The apparent rate constant, k7, for benzeneOH + O2 w benzene-OH-O2 adduct is calculated to be 7.1 × 1011 cm3/(mol s) at 298 K. The apparent rate constants k9, k10, k11, and k12 are similar, ca. 106 cm3/(mol s) at 298 K. Formation of 2,4-cyclohexadiene-1,6-dial Via reaction 8 at k8 ) 3.3 × 103 cm3/(mol s) is relatively slow at room temperature. Path 13 with k13 ) 1.8 × 10-12 cm3/(mol s) is too slow to compete with cyclization channels 10-12. Reaction 13 is therefore not an effective path leading to subsequent, ringopening products. The stabilized benzene-OH-O2 adduct formed at this step can dissociate back to benzene-OH + O2 (-7), react to form 2,4-hexadiene-1,6-dial + OH (14), react to form phenol + HO2 (15), isomerize to the bicyclic adducts (16, 17, 18, 19), or react with other active species, such as O2 (20, 23, 26; see below). The apparent rate constants of reactions 14-19 are calculated using unimolecular QRRK and are listed in Table 2. Unimolecular reactions of the benzene-OH-O2 adduct to form hexadienedial + OH and adduct VI are rather slow with k14 ) 1.8 × 10-4 s-1 and k19 ) 4.5 × 10-21 s-1. Apparent rate constants k15, k16, k17, and k18 vary from 0.17 to 2.51 s-1. Model Computation (BM2). The mechanism for subsystem BM2 includes reactions 1-18. Figure 8 presents the calculated product profile using mechanism BM2. The benzene-OHO2 adduct is in SS with its concentration (10-7 ppm) 1 order of magnitude higher than that of the benzene-OH adduct (10-8 ppm). Adduct III reaches a concentration level 10-4 ppm,

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TABLE 5: Forward Rate Constants (kf), Equilibrium Constants in Concentration Units (Keq), and Reverse Rate Constants (kr) for Benzene-OH + O2 Adduct System of Reactions Addition (Elimination or Isomerization) (7) (8) (9) (10) (11) (12) (13)

(15) (16) (17) (18) a

reaction

kf (cm3/(mol s))

Keq

kr

benz-OHa + O2 w benz-OH-O2b benz-OH + O2 w hexadienedial + OH benz-OH + O2 w phenol + HO2 benz-OH + O2 w adduct III benz-OH + O2 w adduct IV benz-OH + O2 w adduct V benz-OH + O2 w adduct VI

7.08 × 1011 3.26 × 103 2.49 × 106 6.56 × 106 8.19 × 106 9.61 × 105 1.82 × 10-12

1.21 × 106 (cm3/mol) 1.56 × 1029 2.31 × 1023 8.55 × 1011 (cm3/mol) 1.19 × 1001 (cm3/mol) 1.28 (cm3/mol) 3.52 × 10-7 (cm3/mol)

5.85 × 105 (s-1) 2.09 × 10-26 (cm3/(mol s)) 9.28 × 10-18 (cm3/(mol s)) 7.67 × 10-6 (s-1) 6.90 × 105 (s-1) 7.51 × 105 (s-1) 5.17 × 10-6 (s-1)

Dissociation of Stabilized Benzene-OH Adduct kf (s-1) Keq benz-OH-O2 ) PhOH + HO2 0.47 1.92 × 1017 (mol/cm3) benz-OH-O2 ) adduct III 2.01 7.09 × 105 benz-OH-O2 ) adduct IV 2.51 9.84 × 10-6 benz-OH-O2 ) adduct V 0.17 1.06 × 10-6

kr 2.45 × 10-18 (cm3/(mol s)) -6 2.83 × 10 (s-1) 2.55 × 105 (s-1) 1.60 × 105 (s-1)

Benzene-OH adduct. b Benzene-OH-O2 adduct.

Figure 8. Selected product profiles of subsystem BM2. Initial mixing ratios (v/v): [C6H6], 1.0 × 10-6; [OH], 4.1 × 10-14; [XX], 1.8 × 10-6; [YY], 4.1 × 10-8; [NO], 1.0 × 10-6; [O2], 0.22.

Figure 7. Rate constants at different temperatures and 1 atm for chemically activated reactions: benzene-OH + O2 w products: (9) benzene-OH + O2 ) benzene-OH-O2; (0) the dissociation of energized benzene-OH adduct to benzene-OH + O2; (*) reaction 8; (() reaction 9; (O) reaction 10; (+) reaction 11; (#) reaction 12; (b) reaction 13.

which is 8-9 orders of magnitude higher than those of adducts IV (10-13 ppm) and V (10-12 ppm). Adduct III

is therefore the most important bicyclic adduct leading to the subsequent ring-cleavage reactions. Previous studies5,6,16 have assumed, without thermochemical or detailed quantum chemical calculations, that the preferred bicyclic adduct is V,

The very low SS levels of adducts IV and V result directly from thermodynamic considerations. Forward rate constants, equilibrium constants in concentration units, and reverse rate constants at 298 K for elementary reactions following benzeneOH + O2 are listed in Table 5. The rate constant of stabilization channel 7, k7, is about 5 orders of magnitude higher than k9, k10, k11, and k12 are 8 and 23 orders of magnitude higher than k8 and k13, respectively. Benzene-OH-O2 is therefore the primary intermediate in the reaction sequence of benzene-OH + O2. This benzene-OH-O2 adduct, however, dissociates back to benzene-OH and O2 faster than its transformation to products, because k-7, 5.9 × 105 s-1, is at least 5 orders of magnitude higher than k15, k16, k17, and k18 (0.17-2.51 s-1). This repeated formation and dissociation of the benzene-OHO2 adduct amplifies the importance of chemical activation paths 8-13. The rate contestants k9, k10, k11, and k12 are all similar, ca. 106 cm3/(mol s); k8 and k13 are about 3 and 18 orders of magnitude smaller, as 103 and 10-12 cm3/(mol s), respectively. The high exothermicity of reaction 9 leads to the small reverse rate constant, k-9, of 9.3 × 10-18 cm3/(mol s). Reaction 9 is therefore an effective path to phenol formation. For other reactions, k-10 is also small, 7.7 × 10-6 s-1, but k-11 and k-12 are large, 6.9 × 105 s-1 and 7.5 × 105 s-1, respectively, because of the very low equilibrium constants Keq,11 and Keq,12. This means adducts IV and V formed Via paths 11 and 12 quickly dissociate back to benzene-OH + O2 since there are no other

Atmospheric Oxidation of Benzene

J. Phys. Chem., Vol. 100, No. 16, 1996 6551

Figure 10. Selected product profiles of system BM3. The concentration of glyoxal, CHOCHO, is equal to that of butenedial. Initial mixing ratios (v/v): [C6H6], 1.0 × 10-6; [OH], 4.1 × 10-14; [XX], 1.8 × 10-6; [YY], 4.1 × 10-8; [NO], 1.0 × 10-6; [O2], 0.22.

Figure 9. Potential energy diagram for β-scission of adducts VII, VIII, and IX.

(fast) reactions for IV and V in this system. Adduct III therefore reaches a high concentration level, while adducts IV and V are present at very low concentration in this subsystem BM2. The allylic (resonance-stabilized) structure of adduct III lowers its enthalpy and causes the equilibrium of reactions 10 and 16 to favor the forward direction. Reactions Resulting in Ring Cleavage. Rate Constants. Potential energy diagrams of reactions 22, 25, and 28 are illustrated in Figure 9. The potential energy diagrams indicate that each first step of these reactions is rate-determining because the subsequent β-scission steps to form strong carbonyl bonds are highly exothermic with low barriers. Rate constants of these three reactions are therefore determined via the TS of first β-scission steps. The determination of TS structure for each initial β-scission step is carried out using the PM3/UHF method. The TS structures confirmed by the appearance of only one imaginary frequency are reactant-like. The PM3-determined vibrational frequencies of reactants and TSs are used to calculate the entropy difference, ∆Sq298, since ∆Sq298 ≈ ∆Sq298,vibration, by assuming that the hindered rotation of the OH group on the ring body and the overall molecular rotations have the identical contributions to the entropies of the reactant and the respective TS. The A factors and reaction barriers are as follows: Reaction 22: ∆Sq298 ) 1.18 cal/(mol K); A22 ) 3.07 × 1013 s-1; Ea22 ) 8.18 kcal/mol. Reaction 25: ∆Sq298 ) 1.41 cal/(mol K); A25 ) 3.45 × 1013 s-1; Ea25 ) 8.02 kcal/mol. Reaction 28: ∆Sq298 ) 0.96 cal/(mol K); A28 ) 2.75 × 1013 s-1; Ea28 ) 8.63 kcal/mol. The barriers determined above are nearly identical to those for alkyl radical addition to olefinic and carbonyl π bonds, 7-8 kcal/mol,32,37 which adds support to these calculated values.

Model Computation (BM3). Mechanism BM3 consists of BM2 and the reactions leading to ring cleavage, reactions 2030. The reactions of transformation from III, IV, and V to VII, VIII, and IX, respectively, and ring-cleavage reactions are included in BM3. Product profiles of select species as a function of reaction time using this mechanism are illustrated in Figure 10. The main ring fragments considered in the present simulation are 2-butene-1,4-dial and glyoxal. Prediction of mechanism BM3 for the benzene oxidation shows a phenol yield of 13.5%. Present modeling results cannot be properly compared to experimental values, since the reactions of NO and NO2 with the benzene-OH adduct and peroxy radicals are not considered in these calculations. Summary We have applied the group additivity and semiempirical molecular orbital methods to determine thermodynamic properties of species important in the study of initial steps of benzene photochemical oxidation in the atmosphere. High-pressure limit rate constants (k∞) are taken from generic reactions in the literature, estimated from the principles of microscopic reversibility, or determined from transition state theory and principles of thermodynamic kinetics.18 Calculations using Quantum Rice-Ramsperger-Kassel (QRRK) theory coupled with a modified strong collision model are performed to evaluate temperature and pressure effects (falloff) for unimolecular reactions and to obtain apparent rate constants of chemically activated reactions resulting from energized adduct formation. The thermodynamic and kinetic parameters are then used as input to build the reaction mechanisms of three subsystems for benzene photooxidation in the atmosphere. These mechanisms are used in the CHEMKIN230 suite of computer codes under the constant temperature and constant pressure conditions. Both forward and reverse reactions are included in the mechanism by incorporating thermodynamic properties and principles of microscopic reversibility. Reverse reactions are important, and equilibrium is observed for OH addition to the aromatic ring and for the benzene-OH adduct + O2 reaction systems. Equilibrium levels and product formation rates are controlled by thermodynamic and kinetic parameters and are found to play a significant role in the overall reaction process. Stabilization is the dominant forward path in the benzene-OH adduct + O2 reaction system, but dissociation of the stabilized benzene-OH-O2 adduct back to reactants also

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TABLE 6: Calculation Details of HBI ∆S°298 (cal/(mol K)) and ∆Cp(T) (cal/(mol K)) Values for the Alperoxy Group -1 × O-H 3400 cm-1 -1 × H-O-O 1050 cm-1 -1 × rotor RO-OH -1 × rotor R-OOH +1 × rotor R-OO spin degeneracy total increment

S°int,298

Cp300

Cp400

Cp500

Cp600

Cp800

Cp1000

0.000 -0.075 -1.997 -5.134 6.047 1.377 0.219

0.000 -0.326 -1.929 -2.073 2.274

-0.001 -0.672 -2.079 -2.198 2.113

-0.010 -0.970 -2.193 -2.286 1.914

-0.037 -1.195 -2.269 -2.324 1.732

-0.161 -1.484 -2.300 -2.253 1.482

-0.357 -1.645 -2.208 -2.097 1.337

-2.054

-2.837

-3.545

-4.094

-4.716

-4.970

TABLE 7: Selected HBI Group Values, ∆S°int,298, and ∆Cp(T) (cal/(mol K)) in Use for Thermodynamic Properties of Radicals CHD CHENE CHENEA PEROXY ALKOXY

∆S°int,298

∆Cp°300

∆Cp°400

∆Cp°500

∆Cp°600

∆Cp°800

∆Cp°1000

-0.68 2.18 0.06 0.22 -1.46

-0.8 0.03 -0.36 -2.05 -0.98

-1.24 -0.55 -0.77 -2.84 -1.3

-1.77 -1.22 -1.3 -3.55 -1.61

-2.3 -1.87 -1.86 -4.09 -1.89

-3.18 -2.98 -2.9 -4.72 -2.38

-3.85 -3.78 -3.7 -4.97 -2.8

dominates. This repeated formation and dissociation of the benzene-OH-O2 adduct amplifies the importance of chemical activation paths 8-13. The most important bicyclic intermediate leading to ring-cleavage products is adduct III. It is an allylic radical (i.e., resonance-stabilized) with an intermediate ring strain energy (ca. 14 kcal/mol), while other bicyclic adducts, IV and V, are nonallylic radicals with the similar ring strain energies. Acknowledgment. The authors gratefully acknowledge funding from the NJIT-MIT USEPA Northeast Research Center and the USEPA MIT-CALTECH-NJIT Research Center on Airborne Organics. Appendix 1. Hydrogen-Atom-Bond-Increment (HBI) Groups for Calculation of Thermodynamic Properties of Radical Species. Hydrogen-atom-bond-increment (HBI) groups23 are derived for estimating S°298 and Cp(T) (300 e T/K e 1500) on generic classes of free radical species. The HBI group technique is based on the changes that occur upon formation of a radical Via loss of a H atom from its parent molecule. The HBI approach incorporates (i) calculated entropy and heat capacity increments resulting from loss and/or change in vibrational frequencies including frequencies corresponding to inversion of the radical center, (ii) increments from changes in barriers to internal rotation and/or loss of the internal rotors, and (iii) spin degeneracy. For example, loss of the H atom in ROOH results in loss of one O-H stretch, one H-O-O bend, and one internal rotation about the RO-OH bond, and the barrier for the rotation about the C-O bond is changed from 7 to 2.5 kcal/mol. These changes are incorporated in the determination of ∆S°298(peroxy) and ∆Cp(T)(peroxy) values, see Table 6. The HBI groups, when coupled with thermodynamic properties of the appropriate “parent” molecule, are found to yield accurate thermodynamic properties for the respective radicals.23 The groups values of all HBI groups used in this work are listed in Table 7. 2. Thermodynamic Properties for the Benzene-OH Adduct. The thermodynamic properties of the benzene-OH adduct (I), the hydroxyl-2,4-cyclohexadienyl radical, are estimated from those parameters of its parent molecule, hydroxyl2,4-cyclohexadiene (denoted as I+H), which are calculated using the GA method. The enthalpy of compound I+H is calculated as -13.73 kcal/mol. The allylic HC-H bond energy for cyclohexadienyl was evaluated by Tsang as 76.0 kcal/mol,36 which results in ∆Hf°298(I) equal to 10.17 kcal/mol along with ∆Hf°298(H) ) 52.1 kcal/mol.38 The S°298 and Cp(T) increments of the HBI(chd) group which corresponds to cyclohexadienyl radical is used to determine S°298

and Cp(T)s of radical I. Thermodynamic properties for species I and I+H are given in Table 4. The values of S°298 and Cp(T)s for 1,3-cyclohexadiene determined by Dorofeeva et al.39 and the S°298 and Cp(T)s determined by PM3 MO calculations for cyclohexadienyl are used to derive the groups values (∆S°298 and ∆Cp(T)s) of HBI(chd). The thermodynamic parameters of 1,3-cyclohexadiene and cyclohexadienyl are listed in Table 4. The HBI(chd) group values are obtained by subtracting the intrinsic entropy (Sint°298, where Sint°298 indicates the entropy not including the correction of symmetry number) and heat capacities of cyclohexadiene from those of cyclohexadienyl, e.g.,

S°298(chd) ) Sint°298(1,3-cyclohexadiene) Sint°298(cyclohexadienyl) ) -0.68 cal/(mol K) Cp(T)(chd) ) Cp(T)(1,3-cyclohexadiene) Cp(T)(cyclohexadienyl) It should be noted that I+H has two optical isomers. The thermodynamic properties considered in this work are referred to a standard state which is defined as an equilibrium mixture of enantiomers of an ideal gas at 1 atm. The value R ln 2 (1.38 cal/(mol K)) is added to the entropy values of I+H. Entropies of all other species with optical isomers considered in this work are calculated in the same manner. 3. Thermodynamic Properties of Benzene-OH-O2 (II). The thermodynamic properties of the parent molecule of II, II+H, is calculated using the GA method. The enthalpy of II is then determined as -1.2 kcal/mol from ∆Hf°298(II+H) ) -37.3 kcal/mol along with the bond energy D°298(ROO-H), equal to 88.0 kcal/mol. The entropy and heat capacities for II are estimated from II+H with the HBI(peroxy) group.

There exist cis and trans conformations which both have two optical isomers for II and II+H. The cis and trans conformations, for simplification of modeling, are considered to have identical thermodynamic properties and are not distinguished. The value R ln 4 (2.75 cal/(mol K)) is therefore added to both the entropy values of II and II+H.

Atmospheric Oxidation of Benzene

J. Phys. Chem., Vol. 100, No. 16, 1996 6553

4. Thermodynamic Properties and Ring Strain Energy for Species with Bicyclic Peroxy Rings. Enthalpies and entropies of the bicyclic adducts III, IV, V, and VI are extremely important in evaluating the branching ratio of aromatic ring-reforming reaction 9 and ring-opening reactions 10-13. Thermodynamic properties of these bicyclic peroxy hexenyl species and their parent molecules, III+H, IV+H, V+H, and VI+H, have not been previously studied. Three special “ring groups”, which correspond to the three types of bicyclic peroxy hexene rings (III+H and IV+H have the same type of bicyclic ring) are needed. We derive these three ring groups from the thermodynamic parameters of compounds A, B, and C and denote them as groups BCYA, BCYB, and BCYC, respectively. The calculations of ring-group values for BCYA, BCYB, and BCYC, ring strain energies, and the thermodynamic parameters of parent compounds III+H-VI+H and radical adducts III-X are described below.

4.1. Scaling Factor of PM3-Determined Enthalpies of Compounds A, B, and C. We utilize the PM3 MO method to determine the theoretical enthalpies (∆Hf°298,PM3) of compounds A, B, and C. An extensive analysis is also performed to determine a correction factor for the ∆Hf°298,PM3s with experimentally determined enthalpies (∆Hf°298,expt) for relevant monocyclic and bicyclic oxygenated hydrocarbons. This analysis, ∆Hf°298,expt vs ∆Hf°298,PM3, is illustrated in Figure 11. The regressed line is found to pass through (0,0) with a slope of 0.83, resulting in ∆Hf°298,expt ) 0.83∆Hf°298,PM3. The empirical factor 0.83 is used to scale the ∆Hf°298,PM3 values of A, B, and C. Enthalpies of formation of A, B, and C (after scaling) are therefore determined as: ∆Hf°298(A) ) -1.97 kcal/mol; ∆Hf°298(B) ) -4.76 kcal/mol; ∆Hf°298(C) ) +20.00 kcal/mol. 4.2. Ring Strain Energies and Group Values of Three Bicyclic Peroxy Hexene Groups: BCYA, BCYB, and BCYC. The ring strain energies are usually assigned as the same values as the enthalpy corrections of the corresponding ring groups used in the group additivity method.18 The “strain energy” can only have meaning when it is relative to some reference state which is arbitrarily assigned zero strain. The “unstrained” standards can be assigned as the enthalpies estimated from group additivities using the groups values derived from the unstrained compounds.18 The ring strain energies (ERS) of A, B, and C are therefore assigned as the enthalpy correction values of ring groups BCYA, BCYB, and BCYC, respectively. The enthalpy correction of the BCYA group, for instance, is calculated as follows

Figure 11. Analysis of correlation factors for PM3-determined enthalpies to experimentally determined enthalpies. The plus signs represent cyclic oxygenated hydrocarbons: 1, oxirene, C2H2O; 2, dioxirane, C2H2O2; 3, 1,3-dioxirane, C4H8O2; 4, 3,6-dioxirane-1,2dioxin, C4H6O2; 5, oxirane, C2H4O; 6, 3,4-dihydro-2H-pyran, C4H6O2; 7, 3,6-dihydro-2H-pyran, C4H6O2; 8, oxitane, C3H6O; 9, 3,6-dihydro1,2-dioxin, C4H6O2; 10, 2,3-dihydro-1,2-dioxin, C4H6O2.

∆Hf°298(BCYA) ) ∆Hf°298(A) -

∑∆Hf°298{all groups of A except BCYA} ) ERS(A)

The bicyclic ring strain energies are calculated as: ERS(A) ) 14.77 kcal/mol; ERS(B) ) 13.01 kcal/mol; ERS(C) ) 38.80 kcal/mol. The results indicate that the ERS of A and B are about the same, although B contains a five-member ring and A is composed of six-member rings. This is different from the relative ERS of other five-ring and six-ring systems quoted by Benson18 (ERS in kcal/mol): (i) cyclopentane (6.3) and cyclohexane (0); (ii) cyclopentene (5.9) and cyclohexene (1.4); (iii) tetrahydrofuran (C4H8O, 5.9) and tetrahydro-2H-pyran (C5H10O, 0.5); (iv) 1,3-dioxolane (C3H6O2, 6.0); 1,3-dioxepane (C5H10O2, 0.2). Compound C has a high ERS due to the four-member ring. These ERS values are important in evaluating the reaction barrier of cyclization reactions (see footnotes of Table 2). The entropies and heat capacities for A, B, and C are also calculated by means of the PM3 method. The S°298 and Cp(T) corrections of the bicyclic ring groups BCYA, BCYB, and BCYC are then derived in the same manner as are the enthalpy corrections. The entropy and heat capacity corrections of ring group BCYA, for example, are derived as follows:

Sint°298(BCYA) ) Sint°298(A) -

∑S°298{all groups of A except BCYA}

∆Hf°298(A) ) ∆Hf°298{2(Cd/C/H) + 2(C/C/Cd/H/O) + 2(O/C/O) + (C/C2/H/O) + (O/C/H) + (C/C2/H2) + (BCYA)} (GA1)

Cp(T)(BCYA) ) Cp(T)(A) -

where the symbols Cd/C/H, C/C/Cd/H/O, ..., etc., are the terms of the GA approach used in the THERM package.23 Enthalpy correction for the bicyclic ring group (BCYA) is calculated as

4.3. Enthalpy, Entropy, and Heat Capacities of Compounds III+H, IV+H, V+H, and VI+H. The three bicyclic ring

∑Cp(T){all groups of A except BCYA}

6554 J. Phys. Chem., Vol. 100, No. 16, 1996 groups BCYA, BCYB, and BCYC enable the calculation of thermodynamic parameters for compounds III+H, IV+H, V+H, and VI+H using the GA method. It needs group BCYB for compounds III+H and IV+H, BCYA for compound V+H, and BCYC for compound VI+H. Enthalpy of III+H, for example, is calculated as

∆Hf°298(III+H) ) ∆Hf°298{2(Cd/C/H) + (C/C/Cd/H2) + (C/C/Cd/H/O) + 2(O/C/O) + (C/C2/H/O) + (O/C/H) + (BCYB)} (GA2) The enthalpies for these four compounds are determined as: ∆Hf°298(III+H) ) -44.93 kcal/mol; ∆Hf°298(IV+H) ) -43.90 kcal/mol; ∆Hf°298(V+H) ) -42.14 kcal/mol; ∆Hf°298(VI+H) ) -19.14 kcal/mol. Enthalpies of compounds III+H, IV+H, and V+H are similar (-42 to -45 kcal/mol), and VI+H has a much higher enthalpy due to its high ERS. 4.4. Thermodynamic Properties of Radicals III, IV, V, VI, VII, VIII, IX, and X. Adducts IV and V are secondary alkyl radicals, and adducts III and VI are secondary allylic radicals that are stabilized by the conjugation of unpaired electrons with the adjacent π bond. The generic secondary C-H bond energy is experimentally determined as 98.45 kcal/mol,40 which results in ∆Hf°298(IV) as 2.10 kcal/mol and ∆Hf°298(V) as 3.86 kcal/mol. The secondary allylic C-H bond energy (85.6 kcal/mol) is estimated from primary allylic C-H bond energy (88.2 kcal/mol)41 plus the increment of C-H bond energy from primary alkyl (101.1 kcal/mol)40 to secondary alkyl (98.45 kcal/ mol)40 C-H bond energy. The secondary allylic C-H bond energy is therefore evaluated as 85.6 kcal/mol, which results in ∆Hf°298(III) ) -13.2 kcal/mol and ∆Hf°298(VI) ) 12.6 kcal/ mol. Adduct III has the lowest enthalpy because it is an allylic radical with resonance stabilization, while adducts IV and V have similar ERS energies but no resonance. Adduct VI has the highest enthalpy because of its high ERS, although it is allylic. Entropies and heat capacities of III and VI are calculated using the HBI(CHENEA) group and those of IV and V using the HBI(CHENE) group. The HBI groups CHENE (secondary cyclohexadienyl, nonallylic) and CHENEA (allylic cyclohexadienyl) are used in the estimation of the S°298 and Cp(T)s for the 4-cyclohexenyl type and 3-cyclohexenyl type of radicals, respectively. Group values (∆S°298 and ∆Cp(T)s) of HBI(CHENE) and HBI(CHENEA) are obtained from the increments of ∆S°298 and ∆Cp(T)s from cyclohexene to 4-cyclohexenyl and 3-cyclohexenyl, respectively. The ∆S°298 and ∆Cp(T)s data for cyclohexene are taken from the work of Dorofeeva et al.;39 these parameters of two cyclohexenyl radicals are obtained using the PM3 method. Entropies, heat capacities, and enthalpies of formation of these four radical adducts and their parent molecules are given in Table 4. Calculations of thermodynamic properties for the alkoxy radical species VI, VIII, IX, and X follow the procedure described above, i.e., using the GA method to obtain the thermodynamic parameters of their parents and using the HBI groups to obtain those of the radicals. The HBI(ALKOXY) group in Table 6 is used for estimating thermodynamic properties of these alkoxy radicals along with the corresponding values of their parent molecules. References and Notes (1) Perry, R. A.; Atkinson; R.; Pitts, Jr., J. N. J. Phys. Chem. 1977, 81, 296.

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