2. 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 benzene-
OH 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-2,4-
cyclohexadienyl-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 benzene-
OH-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.
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
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 con-
sistency and accurate steady state species concentrations. It also
allows use of elementary rate constants in the reaction mech-
anism.
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
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 thermo-
dynamic data base. This scaling factor is obtained from the
comparison between PM3-determined enthalpies and experi-
mentally 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
6544 J. Phys. Chem., Vol. 100, No. 16, 1996 Lay et al.
3. 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 param-
eters 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 chemi-
cally 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 thermo-
chemical 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 unimo-
lecular 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:
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∞
reaction A∞ (s-1 or cm3/(mol s)) Ea,∞ (kcal/mol)
(4) benzene + OH w benzene-OHc 2.29 × 1012 0.68
(-4) benzene-OH w benzene + OHd 1.77 × 1014 19.2
(5) benzene-OH w phenol + He
1.95 × 1013
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) benzene + OH w benzene-OH 4.65 × 10+15
-1.18 1.23 7.03 × 1011
(-4) benzene-OH w benzene + OHf 0.146
(5) benzene + OH w phenol + H 3.34 × 10-5 5.62 2.59 3.39 × 107
(6) benzene-OH w phenol + Hg
2.04 × 10+25
-4.2 24.54 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.
Atmospheric Oxidation of Benzene J. Phys. Chem., Vol. 100, No. 16, 1996 6545
4. (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.
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∞
reaction A∞ (s-1 or cm3/(mol s)) Ea,∞ (kcal/mol)
(7) benzene-OH + O2 w benz-OH-O2
c 1.21 × 1012 0.0
(-7) benz-OH-O2 w benzene-OH + O2
d 2.27 × 1014 11.4
(8) benz-OH-O2 w 2,4-hexadiene-1,6-dial + OHe
4.77 × 1011
19.4
(9) benz-OH-O2 w phenol + HO2
f 2.62 × 1011 15.0
(10) benz-OH-O2 w adduct IIIg 1.41 × 1011 14.0
(11) benz-OH-O2 w adduct IVg
1.76 × 1011
14.0
(12) benz-OH-O2 w adduct Vg 2.49 × 1011 15.6
(13) benz-OH-O2 w adduct VIg
1.69 × 1011
39.6
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))
(7) benz-OH + O2 w benz-OH-O2 3.55 × 1036 -8.86 3.79 7.08 × 1011
(-7) benz-OH-O2 w benz-OH + O2
h 5.87 × 105
(8) benz-OH + O2 w hexadienedial + OH 1.73 × 1010
-0.26 8.28 3.26 × 103
(9) benz-OH + O2 w phenol + HO2 7.06 × 1014 -1.83 5.36 2.49 × 106
(10) benz-OH + O2 w adduct III 2.14 × 1015
-2.05 4.69 6.56 × 106
(11) benz-OH + O2 w adduct IV 2.67 × 1015 -2.05 4.69 8.19 × 106
(12) benz-OH + O2 w adduct V 6.07 × 109
-0.16 4.64 9.61 × 105
(13) benz-OH + O2 w adduct VI 8.68 × 106
0.69 27.78 1.83 × 10-12
(14) benz-OH-O2 w hexadienedial + OHi
4.43 × 1035
-9.27 22.44 1.75 × 10-4
(15) benz-OH-O2 w phenol + HO2
i 6.30 × 1040 -10.86 19.45 0.47
(16) benz-OH-O2 w adduct IIIi 1.43 × 1042 -11.34 18.80 2.01
(17) benz-OH-O2 w adduct IVi 1.78 × 1032 -11.34 18.80 2.51
(18) benz-OH-O2 w adduct Vi 2.46 × 1037 -9.81 18.93 0.17
(19) benz-OH-O2 w adduct VIi 1.44 × 1024 -5.83 41.02 4.52 × 10-21
a 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, ∆Sq
298 ) -7.09 cal/(mol K) (∆Sq
vib ) +2.0 eu and ∆Sq
rot ) -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), ∆Sq
298 ) -8.28
cal/(mol K) (∆Sq
vib ) +0.84 eu and ∆Sq
rot ) -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., Sq
298 ≈ S°298(product)), plus one optical isomer gained at TSs. ∆Sq
298 )
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.
6546 J. Phys. Chem., Vol. 100, No. 16, 1996 Lay et al.
5. 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
TABLE 3: Mechanism of Benzene Photooxidation
reactionsa,b A n Ea (cal/mol) comment
(1) XX + hv w YY+OH 1.54 × 10-6 0 0 c
(2) YY + OH w XX 2.00 × 10+13
0 0 c
(3) C6H6 + OH ) Ph + H2O 6.03 × 10+11 0 4948 d
(4) C6H6 + OH ) benzene-OH 4.65 × 10+15 -1.18 1228 e
(5) C6H6 + OH ) PhOH + H 3.34 × 10-5
5.62 2588 e
(6) benzene-OH ) PhOH + H 2.04 × 10+25 -4.2 24536 f
(7) benzene-OH + O2 ) benzene-OH-O2 3.55 × 10+36 -8.86 3789 e
(8) benzene-OH + O2 ) HDEDA+OH 1.73 × 10+10 -0.26 8277 e
(9) benzene-OH + O2 ) PhOH+HO2 7.06 × 10+14 -1.83 5356 e
(10) benzene-OH + O2 ) adduct III 2.14 × 10+15
-2.05 4690 e
(11) benzene-OH + O2 ) adduct IV 2.67 × 10+15 -2.05 4690 e
(12) benzene-OH + O2 ) adduct V 6.07 × 10+9
-0.16 4637 e
(13) benzene-OH + O2 ) adduct VI 8.68 × 10+6
0.69 27780 e
(14) benzene-OH-O2 ) HDEDA+OH 4.43 × 10+35 -9.27 22444 f
(15) benzene-OH-O2 ) PhOH+HO2 6.30 × 10+40 -10.86 19447 f
(16) benzene-OH-O2 ) adduct III 1.43 × 10+42
-11.34 18798 f
(17) benzene-OH-O2 ) adduct IV 1.78 × 10+42 -11.34 18798 f
(18) benzene-OH-O2 ) adduct V 2.46 × 10+37
-9.81 18927 f
(19) benzene-OH-O2 ) adduct VI 1.44 × 10+24 -5.83 41023 f
(20) adduct III + O2 ) adduct VIIO 1.20 × 10+12
0 0 g
(21) adduct VIIO + NO ) adduct VII + NO2 5.36 × 10+12 0 0 h
(22) adduct VII ) BDA + GLYH 3.07 × 10+13 0 8180 i
(23) adduct IV + O2 ) adduct VIIIO 1.20 × 10+12 0 0 g
(24) adduct VIIIO + NO ) adduct VIII + NO2 5.36 × 10+12
0 0 h
(25) adduct VIII ) BDAH + GLY 3.45 × 10+13
0 8020 i
(26) adduct V + O2 ) adduct IXO 1.20 × 10+12 0 0 g
(27) adduct IXO + NO ) adduct IX + NO2 5.36 × 10+12 0 0 h
(28) adduct IX ) BDA + GLYH 2.75 × 10+13 0 8630 i
(29) GLYH + O2 ) GLY+HO2 5.66 × 10+12 0 0 j
(30) BDAH + O2 ) BDA+HO2 5.66 × 10+12 0 0 j
a
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.
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.
Atmospheric Oxidation of Benzene J. Phys. Chem., Vol. 100, No. 16, 1996 6547
6. 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 high-
pressure 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 benzene-
OH 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
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)
speciesa ∆Hf°298 S°298 Cp300 Cp400 Cp500 Cp600 Cp800 Cp1000 formula
1 H 52.10 27.36 4.97 4.97 4.97 4.97 4.97 4.97 H1
2 O 59.55 38.47 5.23 5.14 5.08 5.04 5.01 5.01 O1
3 OH 9.49 43.88 7.15 7.10 7.07 7.06 7.13 7.33 H1 O1
4 O2 0.00 49.01 7.02 7.23 7.44 7.65 8.04 8.35 O2
5 H2O -57.80 45.10 8.02 8.19 8.41 8.66 9.24 9.85 H1 O2
6 glyoxal (GLY) -50.60 65.42 14.90 17.54 19.64 21.40 24.28 25.80 C2 H2 O2
7 CH(O)CHOH (GLYH) -34.60 67.38 15.54 18.62 21.25 23.40 26.66 29.00 C2 H3 O2
8 CH(O)CH2OH -73.50 73.57 17.53 20.07 22.34 24.41 28.32 31.01 C2 H4 O2
9 2-butene-1,4-dial (BDA) -53.16 78.18 23.82 29.12 33.14 36.24 40.98 44.02 C4 H4 O2
10 4-hydroxy-1-oxo-2-buten-4-yl (BDAH) -32.60 82.27 25.01 30.91 35.48 38.96 44.03 47.40 C4 H5 O2
11 CH(O)CHCHCH2OH -62.65 86.62 25.49 30.95 35.52 39.34 45.38 49.55 C4 H6 O2
12 benzene 19.81 64.37 19.92 27.09 33.25 38.38 45.87 51.05 C6 H6
13 cyclohexa-1,3-dien-5-yl 49.93 73.19 21.86 29.48 35.99 41.26 49.09 54.57 C6 H7
14 cyclohexa-1,3-diene 3.89 72.49 22.66 30.72 37.76 43.56 52.27 58.42 C6 H8
15 I (benzene-OH) 10.17 84.11 25.51 33.94 40.94 46.17 54.13 59.52 C6 H7 O1
16 I+H -13.73 84.79 26.31 35.18 42.71 48.47 57.31 63.37 C6 H8 O1
17 II (benzene-OH-O2) -1.20 100.65 32.72 42.33 50.06 55.56 64.08 70.13 C6 H7 O3
18 II+H -37.30 100.43 34.77 45.17 53.61 59.65 68.8 75.1 C6 H8 O3
19 III -13.2 87.17 30.00 40.16 48.58 54.74 63.75 69.65 C6 H7 O3
20 III+H -44.93 87.11 30.36 40.93 49.88 56.6 66.65 73.35 C6 H8 O3
21 IV 2.10 88.81 30.44 40.65 48.94 55.03 63.95 69.83 C6 H7 O3
22 IV+H -43.9 86.63 30.41 41.20 50.16 56.9 66.93 73.61 C6 H8 O3
23 V 3.86 90.28 30.23 40.24 48.53 54.63 63.58 69.49 C6 H7 O3
24 V+H -42.14 88.10 30.20 40.79 49.75 56.5 66.56 73.27 C6 H8 O3
25 VI 12.59 89.55 30.66 40.72 48.97 55.08 64.06 69.98 C6 H7 O3
26 VI+H -19.14 89.49 31.02 41.49 50.27 56.94 66.96 73.68 C6 H8 O3
27 VII -32.11 94.19 32.90 44.10 53.27 59.68 69.36 75.52 C6 H7 O4
28 VII+H -84.07 96.65 34.01 45.39 54.83 61.51 71.69 78.28 C6 H8 O4
29 VII+O -32.40 102.97 36.77 48.08 57.23 63.69 73.42 80.11 C6 H7 O5
30 VII+OH
b -68.50 102.75 38.82 50.92 60.78 67.78 78.14 85.08 C6 H8 O5
31 VIII -29.84 114.61 33.60 44.41 53.42 60.3 70.62 77.46 C6 H7 O4
32 VIII+H -81.8 117.07 34.71 45.70 54.98 62.13 72.95 80.22 C6 H8 O4
33 VIII+O -30.13 123.39 37.47 48.39 57.38 64.31 74.68 82.05 C6 H7 O5
34 VIII+OH
b -66.23 123.17 39.52 51.23 60.93 68.40 79.40 87.02 C6 H8 O5
35 IX -30.35 94.29 32.69 43.69 52.86 59.28 68.99 75.18 C6 H7 O4
36 IX+H -82.31 96.75 33.80 44.98 54.42 61.11 71.32 77.94 C6 H8 O4
37 IX+O -30.64 103.07 36.56 47.67 56.82 63.29 73.05 79.77 C6 H7 O5
38 IX+OH
b -66.74 102.85 38.61 50.51 60.37 67.38 77.77 84.74 C6 H8 O5
39 Ph 79.44 69.83 21.01 27.06 32.43 37.05 43.90 47.77 C6 H5
40 PhO 10.36 74.89 24.79 31.31 37.08 42.01 49.25 53.28 C6 H5 O1
41 phenol (PhOH) -23.03 75.43 24.90 32.45 38.64 43.54 50.62 55.49 C6 H6 O1
42 PhOO 37.04 85.62 26.76 34.25 40.07 44.82 51.76 56.48 C6 H5 O2
43 PhOOH 0.94 85.40 28.81 37.09 43.62 48.91 56.48 61.45 C6 H6 O2
44 2,4-hexadiene-1,6-dial -37.60 92.32 30.06 38.52 45.02 49.86 56.98 61.72 C6 H6 O2
a See footnote b of Table 3 for the representations of species symbols. b Adduct VIIOH ) 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.
6548 J. Phys. Chem., Vol. 100, No. 16, 1996 Lay et al.
7. 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.
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 ∆Sq
298 ) 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 benzene-
OH + 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, ring-
opening 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. Unimo-
lecular 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-OH-
O2 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,
Figure 4. Potential energy diagram for benzene-OH adduct + O2.
Figure 5. Potential energy diagram for reaction 14: benzene-OH-
O2 w 2,4-hexadiene-1,6-dial + OH.
Figure 6. Potential energy diagram for reaction 15: benzene-OH-
O2 w phenol + HO2.
Atmospheric Oxidation of Benzene J. Phys. Chem., Vol. 100, No. 16, 1996 6549
8. 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 benzene-
OH + 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-OH-
O2 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
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)
reaction kf (cm3
/(mol s)) Keq kr
(7) benz-OHa
+ O2 w benz-OH-O2
b 7.08 × 1011
1.21 × 106
(cm3
/mol) 5.85 × 105
(s-1
)
(8) benz-OH + O2 w hexadienedial + OH 3.26 × 103 1.56 × 1029 2.09 × 10-26 (cm3/(mol s))
(9) benz-OH + O2 w phenol + HO2 2.49 × 106 2.31 × 1023 9.28 × 10-18 (cm3/(mol s))
(10) benz-OH + O2 w adduct III 6.56 × 106
8.55 × 1011
(cm3
/mol) 7.67 × 10-6
(s-1
)
(11) benz-OH + O2 w adduct IV 8.19 × 106 1.19 × 1001 (cm3/mol) 6.90 × 105 (s-1)
(12) benz-OH + O2 w adduct V 9.61 × 105 1.28 (cm3/mol) 7.51 × 105 (s-1)
(13) benz-OH + O2 w adduct VI 1.82 × 10-12
3.52 × 10-7
(cm3
/mol) 5.17 × 10-6
(s-1
)
Dissociation of Stabilized Benzene-OH Adduct
kf (s-1
) Keq kr
(15) benz-OH-O2 ) PhOH + HO2 0.47 1.92 × 1017
(mol/cm3
) 2.45 × 10-18
(cm3
/(mol s))
(16) benz-OH-O2 ) adduct III 2.01 7.09 × 105 2.83 × 10-6 (s-1)
(17) benz-OH-O2 ) adduct IV 2.51 9.84 × 10-6
2.55 × 105
(s-1
)
(18) benz-OH-O2 ) adduct V 0.17 1.06 × 10-6 1.60 × 105 (s-1)
a
Benzene-OH adduct. b
Benzene-OH-O2 adduct.
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.
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.
6550 J. Phys. Chem., Vol. 100, No. 16, 1996 Lay et al.
9. (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, ∆Sq
298, since ∆Sq
298 ≈ ∆Sq
298,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: ∆Sq
298 ) 1.18 cal/(mol K); A22 ) 3.07 × 1013
s-1; Ea22 ) 8.18 kcal/mol.
Reaction 25: ∆Sq
298 ) 1.41 cal/(mol K); A25 ) 3.45 × 1013
s-1; Ea25 ) 8.02 kcal/mol.
Reaction 28: ∆Sq
298 ) 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 20-
30. 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 com-
pared 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 proper-
ties 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 revers-
ibility, 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 re-
versibility.
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
Figure 9. Potential energy diagram for β-scission of adducts VII, VIII,
and IX.
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.
Atmospheric Oxidation of Benzene J. Phys. Chem., Vol. 100, No. 16, 1996 6551
10. 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 intermedi-
ate 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 Spe-
cies. 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 esti-
mated from those parameters of its parent molecule, hydroxyl-
2,4-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.,
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 conforma-
tions, 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.
TABLE 6: Calculation Details of HBI ∆S°298 (cal/(mol K)) and ∆Cp(T) (cal/(mol K)) Values for the Alperoxy Group
S°int,298 Cp300 Cp400 Cp500 Cp600 Cp800 Cp1000
-1 × O-H 3400 cm-1 0.000 0.000 -0.001 -0.010 -0.037 -0.161 -0.357
-1 × H-O-O 1050 cm-1
-0.075 -0.326 -0.672 -0.970 -1.195 -1.484 -1.645
-1 × rotor RO-OH -1.997 -1.929 -2.079 -2.193 -2.269 -2.300 -2.208
-1 × rotor R-OOH -5.134 -2.073 -2.198 -2.286 -2.324 -2.253 -2.097
+1 × rotor R-OO 6.047 2.274 2.113 1.914 1.732 1.482 1.337
spin degeneracy 1.377
total increment 0.219 -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
∆S°int,298 ∆Cp°300 ∆Cp°400 ∆Cp°500 ∆Cp°600 ∆Cp°800 ∆Cp°1000
CHD -0.68 -0.8 -1.24 -1.77 -2.3 -3.18 -3.85
CHENE 2.18 0.03 -0.55 -1.22 -1.87 -2.98 -3.78
CHENEA 0.06 -0.36 -0.77 -1.3 -1.86 -2.9 -3.7
PEROXY 0.22 -2.05 -2.84 -3.55 -4.09 -4.72 -4.97
ALKOXY -1.46 -0.98 -1.3 -1.61 -1.89 -2.38 -2.8
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)
6552 J. Phys. Chem., Vol. 100, No. 16, 1996 Lay et al.
11. 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 experi-
mentally determined enthalpies (∆Hf°298,expt) for relevant mono-
cyclic 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
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
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 cyclo-
hexane (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:
4.3. Enthalpy, Entropy, and Heat Capacities of Com-
pounds III+H, IV+H, V+H, and VI+H. The three bicyclic ring
∆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)
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-1,2-
dioxin, C4H6O2; 5, oxirane, C2H4O; 6, 3,4-dihydro-2H-pyran, C4H6O2;
7, 3,6-dihydro-2H-pyran, C4H6O2; 8, oxitane, C3H6O; 9, 3,6-dihydro-
1,2-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)
Sint°298(BCYA) ) Sint°298(A) -
∑S°298{all groups of A except BCYA}
Cp(T)(BCYA) ) Cp(T)(A) -
∑Cp(T){all groups of A except BCYA}
Atmospheric Oxidation of Benzene J. Phys. Chem., Vol. 100, No. 16, 1996 6553
12. 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
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 cyclohexa-
dienyl) 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.
(2) Atkinson, R.; Ashmann, S. M.; Arey, J.; Carter; W. P. L. Int. J.
Chem. Kinet. 1989, 21, 801.
(3) Knispel, R.; Koch, R.; Siese, M.; Zetzch, C. Ber. Bunsen-Ges. Phys.
Chem. 1990, 94, 1375.
(4) Atkinson, R.; Carter, W. P. L.; Darnell, K. R.; Winer, A. M.; Pitts,
J. N. Int. J. Chem. Kinet. 1980, 12, 779.
(5) Atkinson, R.; Carter, W. P. L.; Winer, A. M. J. Phys. Chem. 1983,
87, 1605.
(6) Shepson, P. B.; Edney, E. O.; Corse, E. W. J. Phys. Chem. 1984,
88, 4122.
(7) Gery, M. W.; Fox, D. L.; Jeffries, H. E. Int. J. Chem. Kinet. 1985,
17, 931.
(8) Leone, J. A.; Flagan, R. C.; Grosjean, D.; Seinfeld, J. H. Int. J.
Chem. Kinet. 1985, 17, 177.
(9) Takagi, H.; Washida, N.; Akimoto, H.; Nagasawa, K.; Usui, Y.;
Okuda, M. J. Phys. Chem. 1980, 84, 478.
(10) Atkinson, R.; Aschmann, S. M.; Arey, J. Int. J. Chem. Kinet. 1991,
23, 77.
(11) Lonneman, W. A.; Kopczynski, S. L.; Darley, P. E.; Sutterfield, F.
D. EnViron. Sci. Technol. 1974, 8, 229.
(12) Grosjean, D.; Fung, K. J. Air Pollut. Control Assoc. 1984, 34, 537.
(13) Hendry, D. G.; Baldwin, A. C.; Golden, D. M. Computer Modeling
of Simulated Photochemical Smog; EPA-600/3-80-029; U.S. Environmental
Protection Agency: Washington, DC, 1980.
(14) Killus, J. P.; Whitten, G. Z. Atmos. EnViron. 1982, 16, 1973.
(15) Leone, J. A.; Seinfeld, J. H. Int. J. Chem. Kinet. 1984, 16, 159.
(16) Atkinson, R.; Lloyd, A. C. J. Phys. Chem. Ref. Data 1984, 13,
315.
(17) Atkinson, R. J. Phys. Chem. Ref. Data 1991, 20, 459.
(18) Benson, S. W. Thermodynamic Kinetics, 2nd ed.; Wiley-Inter-
science: New York, 1976.
(19) Ritter, E.; Bozzelli, J. W. Int. J. Chem. Kinet. 1991, 23, 767.
(20) (a) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209. (b) Stewart,
J. J. P. J. Comput. Chem. 1989, 10, 221.
(21) MOPAC: A General Molecular Orbital Package (QCPE 445):
QCPE Bull. 1983, 3, 43. MOPAC 6.0: Frank J. Seiler Research Lab., U.S.
Air Force Academy, CO, 1990.
(22) Coolidge, M. B.; Marlin, J. E.; Stewart, J. J. P. J. Comput. Chem.
1991, l12, 948.
(23) Lay, T. H.; Bozzelli, J. W.; Dean, A. M.; Ritter, E. R. J. Phys.
Chem. 1995, 99, 14514.
(24) Kondo, O.; Benson, S. W. J. Phys. Chem. 1984, 88, 6675.
(25) (a) Dean, A. M. J. Phys. Chem. 1987, 89, 4600. (b) Dean, A. M.;
Bozzelli, J. W.; Ritter, E. R. Combust. Sci. Technol. 1991, 80, 63. (c) Chang,
A. Y.; Chiang, H. M.; Bozzelli, J. W.; Dean, A. M. To be submitted for
publication in J. Phys. Chem.
(26) Gilbert, R. G.; Luther, K.; Troe, J. Ber. Bunsen-Ges. Phys. Chem.
1983, 87, 169.
(27) Bozzelli, J. W.; Chang, A. Y.; Dean, A. M. Molecular Density of
States from Estimated Vapor Phase Heat Capacities. Submitted for
publication in Int. J. Chem. Kinet.
(28) Ritter, E. R., J. Chem. Info. Comput. Sci. 1991, 31, 400
(29) Reid, R. C.; Prausinitz, J. M.; Sherwood, T. K. The Properties of
Gases and Liquids; McGraw-Hill Co.: New York, 1979.
(30) Kee, R. J.; Miller, J. A.; Jefferson, T. H. CHEMKIN: Fortran
Chemical Kinetics Code Package. Sandia Report SAND80-8003. UC-4;
Livermore, CA, 1980.
(31) Seinfeld, J. H. Atmospheric Chemistry and Physics of Air Pollution;
John Wiley & Sons: New York, 1986.
(32) Baulch L. D.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just,
Th.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J. J.
Phys. Chem. Ref. Data 1992, 21, 411.
(33) Kerr, J. A.; Parsonage, M. J. EValuated Kinetic Data on gas Phase
Addition Reactions; Butterworth: London, 1972.
(34) Bozzelli, J. W.; Dean, A. M. J. Phys. Chem. 1990, 94, 3313. (b)
Bozzelli, J. W.; Dean, A. M. J. Phys. Chem. 1993, 97, 4427.
(35) Berkowitz, J.; Ellison, G. B.; Gutman, D. J. Phys. Chem. 1994,
98, 2744.
(36) Tsang, W. J. Phys. Chem. 1986, 90, 1152.
(37) Tsang, W.; Hampson, R. F. J. Phys. Chem. Ref. Data 1986, 15,
1087.
(38) Stull, D. R.; Prophet, H. JANAF Thermochemical Tables, 2nd ed.;
NSRDS-NBS37; U.S. Goverment Printing Office: Washington, DC, 1970.
(39) Dorofeeva, O. V.; Gurvich, L. V.; Jorish, V. S., J. Phys. Chem.
Ref. Data 1986, 15, 437.
(40) Seakins, P. W.; Pilling, M. J.; Nitranen, J. T.; Gutman, D.;
Krasnoperov, L. N. J. Phys. Chem. 1992, 96, 9847.
(41) Tsang, W. J. Phys. Chem. 1992, 96, 8378.
JP951726Y
∆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)
6554 J. Phys. Chem., Vol. 100, No. 16, 1996 Lay et al.
