Gas phase oxidation of benzene: Kinetics, thermochemistry and mechanism of initial steps

Article abstract of DOI:10.1039/b315953a

Volatile aromatic compounds participate to a significant extent to the pollution of the troposphere and to ozone formation. A new investigation of the primary steps of the benzene oxidation, involving complementary experimental and theoretical approaches,

Full text of DOI:10.1039/b315953a

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R E S E A R C H P A P E R
Gas phase oxidation of benzene: Kinetics, thermochemistry and
mechanism of initial steps
´ ´ `
Severine Raoult, Marie-Therese Rayez, Jean-Claude Rayez and Robert Lesclaux*
´
Laboratoire de Physico-Chimie Moleculaire, Universite Bordeaux I-UMR 5803 CNRS,
33405 Talence Cedex, France. E-mail: r.lesclaux@lpcm.u-bordeaux1.fr
´
Received 9th December 2003, Accepted 24th February 2004
F|rst published as an AdvanceArticle on the web 31st March 2004
A new investigation of the primary steps of the benzene oxidation, involving complementary experimental
and theoretical approaches, is presented. The reactions of the OH-adduct (hydroxy-cyclohexadienyl radical
c-C6H6-OH) were investigated using laser flash photolysis and producing OH radicals by H2O2 photolysis at
248 nm. It is confirmed that the adduct is in equilibrium with the corresponding peroxy radical RO2 , near
atmospheric conditions, the measured equilibrium constant being: Kc,2b ¼ (2.62 ꢀ 0.24) ꢁ 10ꢂ19 cm3 moleculeꢂ1
at 295 K, with the temperature dependent expression: ln(Kc,2b/cm3 moleculeꢂ1) ¼ ꢂ63.29 þ 6049/T, obtained
by using the calculated entropy of reaction. The rate constant of the association reaction yielding RO2 is:
k2b ¼ (1.31 ꢀ 0.12) ꢁ 10ꢂ15 cm3 moleculeꢂ1
s
ꢂ1. Calculated data are in agreement with those values. In
addition, data analysis shows that the reaction c-C6H6-OH þ O2 involves an irreversible loss of radical species,
yielding phenol and other oxidation products, with the global rate constant: kloss ¼ (2.52 ꢀ 0.40) ꢁ 10ꢂ16 cm3
moleculeꢂ1 sꢂ1. Quoted errors are statistical (2s), the possible total errors on the above values being estimated at
around 40%. By comparison with the kloss value, the rate constant for phenol formation, calculated using a
combination of DFT and ab initio CCSD(T) methods, corresponds to a phenol yield of about 55%, in
reasonable agreement with experimental observations. Thermochemical and kinetic parameters have been
calculated for the formation and for the reactions of the two RO2 stereoisomers, cis and trans. They show that
the observed equilibrium must involve the trans isomer, which is more stable and is formed more rapidly
than the cis isomer. Calculations show that the only possible reactions of peroxy radicals, under atmospheric
conditions, is cyclisation yielding a bicyclic radical. However, cyclisation of the RO2(trans) is calculated to
be too slow, compared to the rate of the irreversible radical loss, whereas it is very fast in the case of the cis
isomer and can lead readily to oxidation products. On the basis of those results, a reaction mechanism is
proposed for the first steps of benzene oxidation, consistent with all experimental and theoretical data, and
which accounts for the principal oxidation products observed.
than the value previously reported by Bohn and Zetzsch,
. Thus, one of the objectives of
1. Introduction
2.7 ꢁ 10ꢂ19 cm3 moleculeꢂ1 2
It is now recognised that volatile aromatic compounds partici-
pate to a significant extent to the pollution of the troposphere
and to ozone formation.1 Consequently, several works have
been published recently with the aim of providing a detailed
description of the oxidation mechanisms, particularly those
concerning the initial steps. Works have involved either experi-
mental,2–4 theoretical5–8 or both approaches.9 A synthetic
presentation of the results is provided in the most recent
publications2,3,9–11 and all the possible reaction paths are
presented by Calvert et al.1 and Volkamer et al.11,12 One of
the most recent findings is that the OH-adducts (hydroxy-
cyclohexadienyl type radicals) are in equilibrium with the
corresponding peroxy radical RO2 , under tropospheric
conditions.2,3,9 In the case of benzene, the presently accepted
reaction mechanism is:
the present work is to understand the origin of this disagree-
ment. In addition to the channel forming phenol, another possi-
ble pathway of reaction (2a) is the formation of benzene oxide/
oxepin intermediates.13 However, those products have not been
detected experimentally10 and the thermochemistry of this reac-
tion path has been shown to be unfavourable.14 Thus, it is not
considered anymore as a possible reaction pathway. Concerning
the peroxy radical RO2 , despite the publication of several theo-
retical works5–8 aiming at describing the thermochemical and
kinetic properties of the various possible reaction paths, there
is no definite proposed mechanism for the actual reactions pre-
vailing under atmospheric conditions and leading to oxidation
products (reaction (3)). Only Tonachini et al.6,7 have proposed
the reaction of RO2 with NO followed by ring opening and for-
mation of muconaldehyde, a reaction path which was shown to
be unlikely under atmospheric conditions.2 In fact the use of the
complementarity between experimental and theoretical results
has not really been explored. In particular, the role played by
each of the RO2 stereoisomers, cis or trans, has not been
accurately characterised.
OH þ C6H6 Ð c-C6H6-OH
c-C6H6-OH þ O2 ! C6H5OH þ HO2
c-C6H6-OH þ O2 Ð RO2
ð1Þ
ð2aÞ
ð2b, ꢂ2bÞ
ð3Þ
RO2 ! ꢃ ꢃ ꢃ ! oxidation products
The peroxy radical RO2 can undergo various reaction paths,
in addition to the decomposition back to the OH-adduct þ O2
reactants (reaction (ꢂ2b)):
Hydrogen abstraction, which is a minor channel of reaction (1),
is neglected in this work. In our preceding work,9 the equili-
brium constant of reaction (2b) was measured as a function
of temperature and found to be equal to 1.15 ꢁ 10ꢂ19 cm3
moleculeꢂ1 at room temperature, a factor of about 2.5 smaller
—reaction with NO;
—H-atom transfer from the OH group to the –OO radical
centre, followed by ring opening of the oxy radical formed;
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by using a high pressure xenon lamp (75 W), instead of the
—HO2 elimination yielding phenol;
—cyclisation yielding a new bicyclic radical bearing an
–O–O– bridge (Fig. 1).
deuterium lamp, powered by batteries which provided very
stable voltage and current. In addition, the analysis beam
was passed twice through the cell, which corresponded to an
optical path length of 140 cm. This allowed us to work with
radical concentrations significantly smaller than in our pre-
vious work,9 with good signal to noise ratio, as shown by
the typical decay traces in Fig. 2. The c-C6H6-OH radical con-
centrations, measured using reported cross sections9 (s(315
nm) ¼ 5.40 ꢁ 10ꢂ18 cm2 moleculeꢂ1) were usually in the range
(2–8) ꢁ 1012 molecule cmꢂ3 for initial OH concentrations of 4
to 25 ꢁ 1012 molecule cmꢂ3, using laser fluences of 5 to 15 mJ
cmꢂ2. This is a factor of about 5, in average, smaller than in
our previous work, resulting in a smaller contribution of radi-
cal–radical reactions and in the possibility of a more accurate
analysis of the first stages of the decays which provide kinetic
information on reaction (2b).
Considering the fairly fast global loss rate of the c-C6H6-
OH/RO2 species in air (pseudo-first-order rate constant of
1000–2000 sꢂ1 , as determined in ref. 2 and confirmed in the
present work), the reaction with NO is not possible, consider-
ing the usual atmospheric NO concentrations (more than 1
ppm of NO would be necessary). The H-atom transfer from
the OH group to the –OO radical centre has been shown to
involve a too high activation energy, > 20 kcal molꢂ1 5,15
to
,
play a significant role and a similar situation has been charac-
terised for the HO2 elimination yielding phenol (Ea > 24 kcal
molꢂ1).5,15 The cyclisation yielding a bicyclic radical bearing
an O–O bridge has been shown to exhibit favourable thermo-
kinetic parameters5,6 and appears to be the only possible reac-
tion pathway for RO2 radicals. As the subsequent reactions of
the bicyclic radical lead to some of the principal benzene oxi-
dation products (glyoxal, butenedial), the cyclisation reaction
is examined again in detail in the present work, for both the
RO2(cis) and the RO2(trans).
New experiments have been performed in this work, using
the same method as in our preceding work,9 but with an
improved detection system, in order to clarify the situation
concerning the equilibrium constant of reaction (2b) and to
provide new data on the kinetics of the OH-adduct/RO2 reac-
tions. Quantum calculations of thermochemical and kinetic
parameters have also been performed in parallel, allowing us
to validate the theoretical methods. Since the RO2 reactions
could not be investigated experimentally, the theoretical
approach was particularly appropriate for determining the
reaction pathways of this radical which can be expected to
occur under atmospheric conditions. A reaction mechanism,
which is likely to occur under those conditions, is proposed
for the first steps of the benzene oxidation. This mechanism
is consistent with present and previous experimental and
theoretical results.
All experiments were carried out at 1 atm/295 K and gas
mixtures consisted of passing N2 through separate bubblers
containing benzene and aqueous H2O2 solution and intro-
ducing these controlled flows into a known fast flow of N2 ,
or N2 and O2 . The resultant steady-state concentration
of H2O2 in the cell was determined by its absorption at
240 nm (s ¼ 12.4 ꢁ 10ꢂ20 cm2 moleculeꢂ1 17
)
and the concen-
tration of benzene was derived from its vapour pressure.
Typically, concentrations of (1–6) ꢁ 1015 molecule cmꢂ3
H2O2 and (2–6) ꢁ 1015 molecule cmꢂ3 benzene were employed
in all experiments. Hydrogen peroxide (ACROS Organics,
50 wt.% ), benzene (Aldrich, HPLC grade, 99.9þ%), nitrogen
(Messer, 99.995%) and oxygen (Messer, 99.995%) were used
without further purification. Data were processed using
numerical simulations of decay traces, based on the reaction
mechanism detailed in Table 1, associated to a non-linear least
square fitting procedure.
2b. Theoretical
Theoretical methods have been presented in a previous publi-
cation.18 However, for greater convenience, they are repeated
here. Theoretical calculations were performed in order to
determine the characteristics (geometries, vibrational frequen-
cies, rotational constants and energetics) of the specific points
(stable species and transition states) of the potential energy
surfaces (PES) involved in each reaction investigated. Due to
the large number of electrons present in the molecular system
investigated, the density functional theory (DFT) was used.
2. Methods
2a. Experimental
Experiments were performed using the laser flash photolysis
technique. The apparatus and methods used have been des-
cribed more fully elsewhere16 and in our recent paper,9 but
briefly consisted of the following. Benzene-OH adduct was
formed by the reaction of OH (from the laser flash photolysis
of H2O2 at 248 nm) with benzene vapour and subsequently
monitored by time-resolved UV absorption spectrometry
in the wavelength range 275 to 320 nm. The gas mixture,
prepared using calibrated mass flow controllers, was flowed
through the reactor, a cylindrical glass reaction cell (70 cm
in length, 1.8 cm internal diameter, and fitted with Suprasil
grade quartz windows).
The photolysing radiation was provided by an KrF excimer
laser (Lambda Physik EMG 200), with l ¼ 248 nm, directed
longitudinally through the cell by dichroic mirrors. Compared
to our preceding work, the monitoring system was improved
Fig. 2 Transient absorptions of the adduct c-C6H6-OH recorded
at 315 nm. Experimental conditions were as follows (concentration
units of molecule cmꢂ3): [H2O2] ¼ 6.2 ꢁ 1015, [C6H6] ¼ 4.8 ꢁ 1015
,
[OH]0 ¼ 2.25 ꢁ 1013, total pressure ¼ 760 Torr. Smooth lines corre-
spond to the results of simulations. The lower simulation trace was
obtained by setting k1a ¼ 2 ꢁ 10ꢂ15 cm3 moleculeꢂ1
s
ꢂ1, as reported
Fig. 1 Formulas of cis and trans peroxy radicals and of the cis bicyc-
lic radical.
by Bohn and Zetzsch.2 The adduct absorption cross section was taken
as s(315 nm) ¼ 5.40 ꢁ 10ꢂ18 cm2 moleculeꢂ1 9
.
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Table 1 Reaction mechanism used in numerical simulations of experimental signals, for the determination of kinetic parameters and equilibrium
constant
Reaction
k295/cm3 moleculeꢂ1 sꢂ1 a
Ref.
OH þ C6H6 ! c-C6H6-OH
(1)
1.22 ꢁ 10ꢂ12
1.31 ꢁ 10ꢂ15
5000 sꢂ1
1
Adjusted, this work
b
c-C6H6-OH þ O2 ! RO2
(2b)
(ꢂ2b)
(loss)c
(3)
RO2 ! c-C6H6-OH þ O2
Adjusted, this work
Adjusted, this work
c-C6H6-OH þ O2 ! Productsc
OH þ H2O2 ! H2O þ HO2
OH þ HO2 ! H2O þ O2
2.52 ꢁ 10ꢂ16
1.7 ꢁ 10ꢂ12
1.1 ꢁ 10ꢂ10
3.8 ꢁ 10ꢂ12 d
4.0 ꢁ 10ꢂ11
1 ꢁ 10ꢂ10 e
5–10 ꢁ 10ꢂ11
5 ꢁ 10ꢂ11
30
30
(4)
(5)
HO2 þ HO2 ! H2O2 þ O2
c-C6H6-OH þ c-C6H6–OH ! Products
c-C6H6-OH þ OH ! Products
c-C6H6-OH þ HO2 ! Products
c-C6H6-OH þ RO2 ! Products
RO2 þ RO2 ! Products
31
Estimated in this work
(6)
(7)
Estimated
Adjusted for each run at low O2 concentration
Estimated in this work, see text
(8)
(9)
(10)
(11)
1.6 ꢁ 10ꢂ12 e f
32
31
RO2 þ HO2 ! Products
2 ꢁ 10ꢂ11 e f
a
Other units are indicated. b With R ¼ c-C6H6-OH. c Includes all irreversible radical loss reactions, see text. d Determined for the present experi-
e
mental conditions. Has a negligible influence on kinetic simulations. Value determined for peroxy radicals of similar structure.
f
Becke’s three parameter function, with non-local correlation
provided by the LYP expression (B3LYP), and the 6-31G(d)
basis set were used in the DFT calculations.19 Both energies
and optimised geometries were calculated using the same level
of theory i.e. DFT-B3LYP/6-31G(d). Single point energy cal-
culations were performed using the coupled cluster CCSD(T)/
6-31G(d,p) method20 based on the B3LYP/6-31G(d) opti-
mised structures. Zero-point energy corrections were obtained
from the calculated DFT-B3LYP frequencies. Using statistical
mechanics, thermal energy corrections as well as entropies
were obtained from vibrational frequencies and rotational con-
stants. All calculations were performed with the Gaussian98
package of programs.21
previously calculated value DHint and the CCSD(T) value of
DHꢄ298 . The activation energy Ea is then determined using
relation (II):
Ea ¼ DHy þ nRT
ðIIÞ
T
with n ¼ 1 or 2 for unimolecular or bimolecular reactions,
respectively, R being the gas constant. Note that the method
is only applicable if DHꢄ
298
is smaller than ꢅ4DHint ; other-
298
wise, DHy tends rapidly to zero.
This method has been used for all reactions investigated and
has yielded kinetic parameters in good agreement with experi-
mental data (see below) whereas, in the particular case of
reaction (2b), the non-corrected Ea values yield rate constant
values a factor of 15 to 30 too low. This shows the importance
of doing this correction for obtaining reliable calculated rate
constants. It must be emphasised, in addition, that this correc-
tion is very simple to apply.
It has been observed on similar systems that the DFT
method may yield significant differences on calculated enthal-
pies of reaction, compared to the values obtained from a more
sophisticated ab initio method like CCSD(T). For example, in
the particular case of reaction (2b), the CCSD(T) value is
ꢂ11.4 kcal molꢂ1, in good agreement with the experimental
value, ꢂ12.5 kcal molꢂ1, compared to the DFT value: ꢂ7.0
kcal molꢂ1.9 In fact, ab initio calculations describe the relevant
reactions as being more exothermic than DFT calculations do.
According to ‘‘Hammond postulate’’,22 we therefore expect
that actual activation energies are in fact lower than those cal-
culated by DFT method. A priori, one might think that an
approach like CCSD(T) would provide more accurate values
of activation energies. However, due to the multiconfigura-
tional character23 of the wave function describing the electro-
nic state of the system at the transition state, the CCSD(T)
method, in its standard version, is unable to provide this infor-
mation. A simple but efficient way to overcome this shortcom-
ing is to use an analytical approach, in line with the ISO-M
method developed in our laboratory.24 This approach, called
further ‘‘Intrinsic-Method’’ (IM), is based on the concept of
an intrinsic barrier, introduced by Marcus for proton transfer
in the gas phase25 and extended by Murdoch to atom trans-
fer.26 The intrinsic barrier DHint is the enthalpy of activation
that the reaction would have if it were thermoneutral. DHint
Rate constants were calculated using the well-established
relationships of the transition state theory (TST).27
On the basis of the results obtained so far, when comparison
is possible between calculated and experimental rate constants,
we consider with reasonable confidence that the agreement is
good when calculated and experimental values differ by less
than a factor of 10 (corresponding to an error of only 1.4 kcal
molꢂ1 on calculated activation energies). Similarly, we con-
sider that the competition between two reaction channels is
possible when the corresponding calculated rate constants dif-
fer by less than a factor of 10 and is not possible if they differ
by a factor larger than 100 (corresponding to an error of about
3 kcal molꢂ1 on calculated activation energies). Intermediate
values provide no definite information. In the present work,
two rate constants (k2a and k2b) are compared to experimental
data, yielding differences smaller than a factor of three.
3. Results
is linked to the true enthalpy of activation DHy and to the
3a. Experimental results
298
reaction enthalpy DHꢄ
ship:
by the following empirical relation-
298
As emphasised above, the objectives of the experimental work
were to measure the equilibrium constant for reaction (2b),
using the improved experimental conditions and to provide
kinetic data for reaction (2b) and for the reactions correspond-
ing to the irreversible loss of species, essentially (2a) and (3).
The data will then be used to validate calculations which in
turn will provide more details on reaction mechanisms.
Transient UV absorption traces of the benzene adduct c-
C6H6-OH (Fig. 2), were recorded at various wavelengths
2
DHy ¼ DHint þ DHꢄ298=2 þ ðDH2ꢄ98Þ =16DHint ðIÞ
298
Then, the procedure used to estimate the corrected activation
enthalpy of a given reaction is the following : (i) DHint is calcu-
lated from (I) using the DFT values of DHy298 and DHꢄ298 and
(ii) a corrected value DHy
is obtained from (I) using the
298
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between 270 and 320 nm (mostly at 315 nm). The UV absorp-
tion spectrum and cross section values were from our preced-
ing work.9 As explained in previous publications,2,9 a constant
absorption was generated by the direct photolysis of benzene
at 248 nm, presumably owing to the formation of benzene iso-
mers: benzvalene, prismane or Dewar benzene. It was shown
that this constant absorption could be taken as the baseline
for the adduct absorption signal, without significant error. In
simulations, it was fitted to the residual absorption at long
time (upper horizontal solid line in Fig. 2). Residual absorp-
tions due to the products of the reactions of interest may also
have to be taken into account, as discussed below. Data were
obtained from a series of traces recorded at different oxygen
partial pressures, from 8 to 760 Torr. A minimum amount of
oxygen (around 10 Torr) was necessary in order to suppress
the benzene photosensitised OH formation (see previous pub-
lications2,9).
Decay traces were modelled using the reaction mechanism
detailed in Table 1. Series of decays were recorded with differ-
ent O2 partial pressures and constant C6H6 , H2O2 and initial
OH concentrations. The OH initial concentration was deter-
mined at low O2 partial pressure, 8–10 Torr, for which reaction
(2) does not occur to significant extent, using the OH-adduct
absorption cross section determined previously.9 The same
decays were used for the estimation of rate constants k6 and
k8 , for the adduct self reaction and the adduct þ HO2 reaction,
respectively (under conditions where either [c-C6H6-OH] or
[HO2] were dominant, respectively).
RO2 : s(RO2) ꢅ 5 ꢁ 10ꢂ19 cm2 moleculeꢂ1 at 300 nm, increasing
up to ꢅ3 ꢁ 10ꢂ18 cm2 moleculeꢂ1 at 270 nm. Such values are
typical for peroxy radicals at those wavelengths.28
ꢆ At 275 nm, a strong residual absorption was observed, cor-
responding to a sharp absorption band, similar to that of phe-
nol recorded in the same conditions. However, the phenol yield
could not be measured accurately, it was only estimated to be
between 50 and 100%, in rough agreement with previous
observations (25–50%).1,4,11
ꢆ Most experiments were performed at 315 nm, where no
significant residual absorption was observed, whereas the
adduct absorption is still strong. However, it was observed
that the measured equilibrium constant decreased when the
oxygen partial pressure was increased over 150–200 Torr, by
a factor of about 1.5 at 1 atm pure oxygen. This may be due
to a small absorption of RO2 at that wavelength or to the
absorption of some oxidation product (resulting in a baseline
shift in our analysis method which, however, could never be
characterised). In order to cancel this effect, a small absorption
cross section of 5 ꢁ 10ꢂ19 cm2 moleculeꢂ1 at 300–315 nm was
assigned to RO2 . In the low range of O2 partial pressures
(100–300 Torr), where measurements were the most accurate,
this had the effect of increasing the measured equilibrium
constant by only 10 to 15% and kloss by about 10%.
Those observations show that the most accurate and reliable
results are obtained at l > 300 nm and for O2 partial pressures
smaller than ꢅ300 Torr. Thus, most experiments were per-
formed under those conditions. Nevertheless, a few data were
obtained in pure oxygen and yielded results in good agreement
with others, despite a fairly poor signal-to-noise ratio. The
results and experimental conditions are listed in Table 2. In
All experimental decays were analysed individually. At low
O2 concentration (upper trace in Fig. 2), traces were simulated
by setting the OH initial concentration and slightly adjusting
the values of k6 or k8 (for conditions where [c-C6H6-OH] or
[HO2] are dominant, respectively), from their mean values.
In the presence of increased oxygen, traces could be simulated
the cases where k2b , k
the returned values of k
and kloss were fitted simultaneously,
were fairly scattered, between
ꢂ2b
ꢂ2b
roughly 4000 and 6000 sꢂ1. Thus, for the data reported in
by adjusting three parameters simultaneously: k2b , k
k
and
loss . kloss is a pseudo-first-order rate constant, accounting
Table 2, a fixed value of 5000 sꢂ1 was assigned to k
and
ꢂ2b
ꢂ2b
only k2b and kloss were fitted. The corresponding pseudo-
first-order rate constants are plotted in Fig. 3 against oxygen
concentration. The average values of Kc,2b , obtained at 295
K and the k2b and kloss values derived from the regression lines
shown in Fig. 3, are the following:
for the global irreversible loss of c-C6H6-OH and RO2 , result-
ing from the reaction of c-C6H6-OH with O2 and excluding
radical–radical reactions. The elementary steps included in
the global loss reaction are identified below in the discussion.
The reaction with O2 is clearly illustrated by the lower experi-
mental trace in Fig. 2. The signal first rises as a result of reac-
tion (1) and, after the maximum, the signal decreases with a
rate (partly) determined by reaction (2b). Then, after ꢅ0.8
ms, the equilibrium is reached and the decay slows down, the
decay rate being now largely determined by kloss (and by k9 ,
to a lesser extent) and the intensity of the signal by the equili-
k2b ¼ ð1:31 ꢀ 0:12Þ ꢁ 10ꢂ15 cm3 moleculeꢂ1 sꢂ1
Kc;2b ¼ ð2:62 ꢀ 0:24Þ ꢁ 10ꢂ19 cm3 moleculeꢂ1
kloss ¼ ð2:52 ꢀ 0:39Þ ꢁ 10ꢂ16 cm3 moleculeꢂ1 sꢂ1
Error bars are statistical (2s). The latter value corresponds to
a pseudo-first-order rate constant for radical loss reactions of
about 1250 sꢂ1 in air at 1 atm, a parameter to which it will
be referred in the following for evaluating product yields
from calculated rate constants and thus, for determining which
of the possible reaction channels can occur to a significant
extent.
The actual uncertainties on those values are certainly larger
than indicated by the statistical error bar. One of the principal
sources of systematic error is probably the constant absorption
generated by the photolysis of benzene and which is taken as
the baseline for kinetic measurements. No clear dependence
of this constant absorption with H2O2 and O2 concentrations
could be characterised but small changes could be seen from
one run to the other. These changes were taken into account
in each analysis and, since there was no systematic variations,
a large part of the resulting errors were included in statistical
uncertainties. Nevertheless, we must take into account that this
constant absorption may introduce systematic errors of up to
20% on all measured parameters. In estimating uncertainties
below, we tended to overestimated them, as their main sources
(constant absorption, shape of the decay traces) cannot be
quantified for a more accurate determination. Note that radi-
cal–radical reactions have minor or negligible importance in
brium constant k2b/k
¼ Kc,2b . Smooth lines correspond to
ꢂ2b
the results of simulations. The best fit of the particular decay
corresponding to 150 Torr of oxygen was obtained with
k2b ¼ 1.20 ꢁ 10ꢂ15 cm3 moleculeꢂ1
s
ꢂ1, Kc,2b ¼ 2.40 ꢁ 10ꢂ19
cm3 moleculeꢂ1 and kloss ¼ 2.64 ꢁ 10ꢂ16 cm3 moleculeꢂ1 sꢂ1
.
The simulation trace below the best fit was obtained with
k2b ¼ 2.0 ꢁ 10ꢂ15 cm3 moleculeꢂ1
s
ꢂ1, showing that the simu-
lation is sensitive to the value of k2b , under those particular
conditions. However, in some cases and particularly at high
O2 concentrations, where the equilibrium is reached within
a short time, the individual value of k2b and k
be fitted separately and only their ratio (Kc,2b) could be
determined.
could not
ꢂ2b
The present experimental work has led to the following
observations.
ꢆ The equilibrium constant is larger than the value reported
in our previous work by a factor larger than 2. Possible reasons
for this difference are discussed below.
ꢆ The apparent value of the equilibrium constant decreases
when going to shorter monitoring wavelengths. This reveals
that the peroxy radical RO2 absorbs in the spectral range
investigated and the observed variation of Kc,2b can be
cancelled by assigning in simulations a cross section to
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Table 2 Details of results for the experimental study of the c-C6H6-OH þ O2 reaction
[H2O2]/1015
molecule cmꢂ3
[C6H6]/1015
molecule cmꢂ3
[O2]/1018
molecule cmꢂ3
[OH]0/1012
molecule cmꢂ3
k2ba /10ꢂ15 cm3
moleculeꢂ1 sꢂ1
Kc,2b/10ꢂ19 cm3
moleculeꢂ1
kloss/10ꢂ16 cm3
moleculeꢂ1 sꢂ1
l/nm
300
300
308
308
315
315
315
315
315
315
315
315
315
315
315
315
315
315
315
4.48
4.48
4.75
4.75
5.30
5.30
1.95
1.95
6.19
6.19
2.48
4.55
4.55
4.48
4.48
3.55
3.55
0.96
0.96
4.46
4.46
5.26
5.26
5.68
5.68
2.33
2.33
4.78
4.78
3.59
6.00
6.00
4.46
4.46
3.90
3.90
4.32
4.32
4.79
9.17
4.76
9.80
4.90
9.80
3.75
7.50
4.92
24.6
4.95
3.94
9.92
4.79
9.17
4.92
24.6
4.92
24.6
11.3
10.8
8.7
1.35
1.55
1.19
1.05
1.44
1.38
1.48
1.44
1.20
1.16
1.32
1.34
1.22
1.28
1.35
1.37
1.20
1.30
1.40
2.72
3.10
2.38
2.10
2.53
2.80
2.97
2.88
2.40
2.32
2.64
2.68
2.44
2.55
2.70
2.75
2.40
2.70
2.79
1.90
2.45
2.23
2.70
2.94
3.17
2.30
3.08
2.64
2.71
3.42
2.34
2.93
2.10
2.81
2.62
2.19
2.42
2.33
8.5
13.5
13.5
10.4
10.4
24.9
24.9
8.9
17.4
16.8
12.4
12.2
18.4
17.9
4.2
4.1
a
Determined with a fixed value of k
¼ 5000 sꢂ1
.
ꢂ2b
simulations, in the presence of significant amount of oxygen.
Only reaction (9) may contribute to small extent.
on s(RO2) (10%) and errors on kloss (15–20%), to which the
determination of Kc,2b is particularly sensitive in simulations.
Including statistical errors, the global uncertainty is estimated
at 40%.
Errors on kloss are directly linked to the shape of the decay
trace tail, which has a small intensity compared to the first part
of the signal and thus, is more sensitive to errors on the deter-
mination of the baseline. This explains the fairly large scatter
on the results and may also result in a 10–15% systematic
error. The shape of the tail is also influenced by the value of
the rate constant k9 , for the reaction between the OH-adduct
and RO2 , which is difficult to determine. It has been estimated
The dispersion of k2b values (Table 2) is fairly small but the
listed values have been obtained with a fixed value of 5000 sꢂ1
for kꢂ2b . As stated above, this value was observed to vary by
more than ꢀ20% from one run to the other, as both k2b and
k
were derived from the shape of decay traces around the
ꢂ2b
maximum, which cannot be accurate. It must be pointed out
that, for a given run, the ratio k2b/k was nearly constant,
ꢂ2b
whatever the rate constant absolute values in the ꢀ20% uncer-
tainty range. Other sources of errors may come from errors on
radical concentrations and, to a lesser extent, on radical–radi-
cal reaction rate constants. However, there was an internal
calibration performed at low O2 partial pressure (ꢅ10 Torr)
for each series of runs, so that the resulting error on k2b could
not be larger than 5%. It results that the global uncertainty on
k2b (and kꢂ2b) can be estimated at 40–50%.
at 5 ꢁ 10ꢂ11 cm3 moleculeꢂ1
s
ꢂ1, from the results of a few
simulations which, in reality, are more sensitive to the value
of kloss than to the value of k9 (reaction (10) contributes for less
than 200 sꢂ1 at the tail decay rate whereas the loss reaction
contributes for 1000 to 6000 sꢂ1). The value derived for kloss
looks reasonable, given the fairly good linear dependence
observed between the pseudo-first-order rate constant klIoss
and the oxygen concentration. Nevertheless, an error of about
5% may result from the uncertainty on k9 . The estimated
global error on kloss is about 30%.
Errors on the equilibrium constant come from baseline
changes (10%), radical concentration uncertainties (5%), errors
3b. Results of calculations
As emphasised in the Introduction, calculations have concen-
trated on the reactions which have been identified as being
the most important in the processes forming oxidation pro-
ducts. Those reactions are reactions (2a), (2b) and the unimo-
lecular reactions of RO2 (3), particularly the cyclisation
channel yielding the bicyclic radical shown in Fig. 1. One
important point is that the two stereisomers cis and trans of
RO2 have been taken into account. It will be shown that each
of them play different and critical roles in the formation of pro-
ducts. As stated in the Introduction, other RO2 unimolecular
reactions are unlikely to occur as they involve too high barriers
on the reaction path. All calculated parameters are gathered in
Table 3.
Reaction (2a) forming phenol. Kinetic parameters for phenol
formation (Table 3) have been calculated for a direct H-
abstraction by O2 since, as pointed out above, the HO2 elimi-
nation from the peroxy radical is too slow.5,15 They are in
Fig. 3 Pseudo-first-order rate constants corresponding to k2b and
kloss , plotted as a function of oxygen concentration.
T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 2 2 4 5 – 2 2 5 3
2249

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Table 3 Thermochemical and kinetic parameters calculated for reactions forming phenol and peroxy radicals and for cyclisation of peroxy
radicals
H abstraction
c-C6H6-OH þ O2 ! phenol þ HO2
DHꢄ298/kcal molꢂ1 (DFTa /ab initiob )
DSꢄ298/cal molꢂ1 Kꢂ1 a
ꢂ25.6/ꢂ26.5
1.4
3.2/3.0
Ea/kcal molꢂ1 (DFTa /IMc )
A/cm3 moleculeꢂ1 sꢂ1 a
kTST(298 K)/cm3 moleculeꢂ1 sꢂ1 (DFTa /IMc )
2.2 ꢁ 10ꢂ14
1.0 ꢁ 10ꢂ16/1.4 ꢁ 10ꢂ16 (experimental: 0.6–1.1 ꢁ 10ꢂ16 d
c-C6H6-OH þ O2 ! RO2(cis)
)
O2 addition
c-C6H6-OH þ O2 Ð RO2(trans)
DHꢄ298/kcal molꢂ1 (DFTa /ab initiob )
DSꢄ298/cal molꢂ1 Kꢂ1 a
ꢂ7.0e /ꢂ11.4 (experimental: ꢂ12.5) f
ꢂ5.9/ꢂ10.3
ꢂ39.3
ꢂ38.6e
Ea/kcal molꢂ1 (DFTa /IMc )
3.8/2.5
2.7 ꢁ 10ꢂ14
6.2/4.6
1.9 ꢁ 10ꢂ14
A/cm3 moleculeꢂ1 sꢂ1 a
kTST(298 K)/cm3 moleculeꢂ1 sꢂ1 (DFTa /IMc )
4.4 ꢁ 10ꢂ17/4.1 ꢁ 10ꢂ16 (experimental: 1.3 ꢁ 10ꢂ15 g
RO2(trans) ! trans bicyclic radical
)
5.5 ꢁ 10ꢂ19/8.6 ꢁ 10ꢂ18
Cyclisation
RO2(cis) ! cis bicyclic radical
DHꢄ298/kcal molꢂ1 (DFTa /ab initiob )
DSꢄ298/cal molꢂ1 Kꢂ1 a
ꢂ3.9/ꢂ5.9
ꢂ5.2
ꢂ8.3/ꢂ10.3
ꢂ4.3
Ea/kcal moleꢂ1 (DFTa /IMc )
A/sꢂ1 a
16.8/15.9
1.2 ꢁ 10ꢂ12
0.6/2.6
10.3/9.0
1.0 ꢁ 10ꢂ12
kTST(298 K)/sꢂ1 (DFTa /IMc )
2.8 ꢁ 104/2.5 ꢁ 105
Value calculated at the DFT-B3LYP/6-31G(d) level. b Value calculated at the CCSD(T)/6-31G(d,p)//B3LYP/6-31G(d) level. c DFT-B3LYP/
a
d
6-31G(d) value corrected by the IM method (see text). Derived from the global rate constant kloss for the c-C6H6-OH þ O2 reaction, taking a
e
f
phenol yield of 0.25–50%. From ref. 9. Derived from the measured equilibrium constant and the calculated DSꢄ298 values (third law method).
This work.
g
fairly good agreement with those reported by Ghigo and
Tonachini.14 The activation energy of 3.0 kcal molꢂ1 and
the low pre-exponential factor associated with this reaction
a new validation of our theoretical approach, since both the
thermochemistry and the kinetics of this reaction are
reasonably accounted for.
(2.2 ꢁ 10ꢂ14 cm3 moleculeꢂ1
s
ꢂ1), result in a fairly slow reac-
Calculations concerning the RO2 formation processes have
already been performed by Ghigo and Tonachini at the DFT
level.6 A good agreement with our DFT results is observed
for the cis isomer. However, a significant discrepancy is
observed for the trans isomer which is found less stable than
the cis isomer by these authors. The origin of this discrepancy
is not known, perhaps the internal H-bond in the trans isomer
was not correctly taken into account.
tion with k2a ¼ 1.4 ꢁ 10ꢂ16 cm3 moleculeꢂ1
s
ꢂ1. In air, 298
K, this results in a pseudo-first-order rate constant of
kI2a ¼ 700 sꢂ1. This reaction constitutes an irreversible loss
process for the radical species involved in the equilibrium
(2b) and thus, kI2a must be compared to the total loss rate con-
stant measured experimentally, kIloss ¼ 1250 sꢂ1. It results that
the calculated kI2a value corresponds to a yield of about 55%
for phenol, in good agreement with experimental observations
(25 to 50%).1,4,11 Since it can be compared to experimental
data, this is one of the results which shows that our calculation
methods are able to provide fairly reliable results.
Cyclisation reaction of the RO2 radical. Formulas of peroxy
radicals and of the bicyclic radical (cis) resulting from ring clo-
sure are shown in Fig. 1. The results of calculations are given
in the Table 3. It appears clearly that the situation is quite dif-
ferent for the two isomers. Cyclisation of the RO2(trans)
(k ¼ 3 sꢂ1) appears difficult if compared to the total radical
loss rate of 1250 sꢂ1. It would correspond to a yield of
ꢅ0.25% for the products formed through this reaction channel.
If this channel was actually efficient, an error of at least a fac-
tor 100 would have occurred in calculations. We estimate that
such an error is very unlikely (would correspond to an error of
nearly 3 kcal molꢂ1 on the activation energy), given the good
agreement observed for other reactions, when comparison with
experimental data is possible. Thus, under atmospheric condi-
tions, the only fate of the RO2(trans) radical is to stay in equi-
librium with the OH-adduct.
Reaction (2b) forming the peroxy radical RO2. Calculated
thermochemical and kinetic parameters are listed in Table 3,
both for the trans and cis stereo-isomers of the peroxy radical.
It is worth noting that optimised structures of both cis and
trans isomers present an internal H-bond between the –OH
and OO– groups.9 It is seen that the trans isomer is slightly
more stable than the cis one and that its formation rate is sig-
nificantly faster (a factor 50). Thus, the equilibrium observed
experimentally must essentially involve the trans-isomer. Con-
sidering the experimental value of the equilibrium constant,
Kc,2b ¼ (2.62 ꢀ 0.15) ꢁ 10ꢂ19 cm3 moleculeꢂ1 at 295 K and
the calculated DSꢄ
value of ꢂ38.6 cal molꢂ1
K
ꢂ1, one can
298
derive: DHꢄ
calc
¼ ꢂ12.5 kcal molꢂ1, in good agreement with
exp
DHꢄ
¼ ꢂ11.4 kcal molꢂ1 for the trans isomer. From those
In contrast, the ring closure is very fast (ꢅ105 sꢂ1) in the case
of the cis isomer and quasi instantaneous in comparison with
the rate of other reactions. Thus, this fast reaction prevents
any equilibrium of RO2(cis) with the OH-adduct to be
observed and it results that the RO2(cis) formation corre-
sponds to an irreversible loss of species involved in equilibrium
(2b). This reaction may well be the principal reaction channel
leading to oxidation products of benzene, different from
phenol (mainly glyoxal).
parameters, one can also derive the temperature dependent
expression for the equilibrium constant: ln(Kc,2b/cm3
moleculeꢂ1) ¼ 6049/T ꢂ 63.29, with the uncertainties dis-
cussed above for the measured value of Kc,2b at around room
temperature. The rate constant for the RO2(trans) formation is
calculated to be k2b ¼ 4.1 ꢁ 10ꢂ16 cm3 moleculeꢂ1
s
ꢂ1, again
in fairly good agreement with the experimental value k2b
¼
13.1 ꢁ 10ꢂ16 cm3 moleculeꢂ1
s
ꢂ1. Thus these results provide
T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4
2250
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 2 2 4 5 – 2 2 5 3

View Article Online
shown in Fig. 4, where rate constants for unimolecular
reactions and pseudo-first-order rate constants for bimolecular
reactions in air are compared.
It must be emphasised that our results (and previously pub-
lished results) do not definitely prove that this is the actual
mechanism, since it is based on the assumption stated above
about the errors on calculated rate constants. However, this
mechanism is consistent with experimental data and with the
results of calculations, including those of the literature,5–8
which show that other reaction routes are very unlikely.
However, the calculated RO2(cis) formation rate (ꢅ40 sꢂ1
)
is low and would correspond to a product yield of only a
few percent, if compared to the experimental total loss rate
of 1250 sꢂ1 in air and to the calculated phenol formation rate
of 700 sꢂ1. The value should be a factor of about 10 larger for
corresponding to a reasonable yield (20–30% for glyoxal).
However, if a factor of 100 is certainly over uncertainty limits
of calculated rate constants, as stated above, we consider that a
factor of 10 is still within those limits. A factor of 10 on rate
constants corresponds to an uncertainty of only 1.4 kcal molꢂ1
on activation energies. Such an error is certainly possible,
despite the good agreement observed with available experi-
mental data. Thus, we propose that this channel is the actual
channel leading to oxidation products, in addition to phenol,
since it appears that all other channels are much slower.
Consequently, our combined experimental and theoretical
results lead us to propose the following simple reaction
mechanism for the first steps of benzene oxidation in air.
4. Discussion
Experimental part
The kinetic study of the reaction between the adduct c-C6H6-
OH and oxygen has provided new values for the rate constants
of the association reaction k2b , for the rate constant of radical
loss (kloss ¼ k2a þ k2c in the proposed mechanism above) and
for the equilibrium constant Kc,2b
.
Our value k2b
¼
OH þ C6H6 ! c-C6H6-OH
c-C6H6-OH þ O2 ! C6H5OH þ HO2
c-C6H6-OH þ O2 Ð RO2ðtransÞ
ð1Þ
ð2aÞ
ð2bÞ
ð2cÞ
(1.31 ꢀ 0.12) ꢁ 10ꢂ15 cm3 moleculeꢂ1 sꢂ1 confirms the previous
determination of Bohn and Zetzsch,2 k2b ¼ (2 ꢀ 1) ꢁ 10ꢂ15
cm3 moleculeꢂ1 sꢂ1 and decreases the uncertainty. Note that
the calculated value is k2b,calc. ¼ 4.1 ꢁ 10ꢂ16 cm3 moleculeꢂ1
c-C6H6-OH þ O2 ! RO2ðcisÞ
s
ꢂ1 in reasonable agreement with the above values. The experi-
mental value corresponds to a pseudo-first-order rate constant
of 6500 sꢂ1 in air, significantly faster than the total radical loss
rate constant of 1250 sꢂ1. This shows that in air, the loss reac-
tion does not shift the equilibrium to significant extent, the
concentrations of the OH-adduct and of RO2(trans) being
nearly equal.
RO2ðcisÞ ! bicyclic radical and subsequent
oxidation products ð3Þ
This mechanism accounts for the principal oxidation pro-
ducts observed experimentally, phenol, formed in reaction
(2a) and glyoxal (and probably butenedial and epoxy-muco-
naldehyde), formed in the subsequent reactions of the bicyclic
radical (reaction (3)).1,11,12 The principal reaction paths are
The value kloss ¼ (2.52 ꢀ 0.5) ꢁ 10ꢂ16 cm3 moleculeꢂ1 sꢂ1
(1250 sꢂ1 in air) also confirms the value of Bohn and Zetzsch,
kloss ¼ (2.1 ꢀ 0.2) ꢁ 10ꢂ16 cm3 moleculeꢂ1 sꢂ1 2
.
This is an
important parameter since it allows us to determine which
reaction is likely to occur under atmospheric conditions, by
comparing the calculated rate constants with kloss (or kloss[O2]).
In particular, it shows that both the adduct and RO2(trans)
cannot react with NO or NO2 since the corresponding
pseudo-first-order rate constant cannot exceed 50 sꢂ1 for
NOx concentrations smaller than 200 ppb. It also shows that
cyclisation of the RO2(trans) is too slow to compete with other
loss reaction paths (Fig. 4). Thus, this value of kloss has consti-
tuted a key parameter for determining the proposed mechan-
ism presented above.
The value of the equilibrium constant determined in the
present work,
K
c,2b(295 K) ¼ (2.62 ꢀ 0.24) ꢁ 10ꢂ19 cm3
moleculeꢂ1 is in good agreement with that reported by Bohn
and Zetzsch,2 Kc,2b(297 K) ¼ 2.7 ꢁ 10ꢂ19 cm3 moleculeꢂ1. In
reality, Bohn and Zetzsch did not assign any cross section to
RO2 and thus, their value should be compared to the value
2.3 ꢁ 10ꢂ19 cm3 moleculeꢂ1 that we would have obtained in
the same conditions. However, taking uncertainties into
account, the agreement is still good. The value of Kc,2b
reported here is more than twice larger than our value reported
previously.9 We have identified the reasons of this discrepancy
as being the addition of errors which all contributed to
decrease the measured value of Kc in our previous work. The
principal reason is the much larger radical concentration that
was used which, as a result of fast radical–radical recombina-
tions, prevented the analysis of the first stages of the decay to
be done accurately. In addition, it was thought at that time
that k2b was larger than the value determined in the present
work and, since the equilibrium constant was essentially
derived from the decrease of the adduct absorption with
[O2], measured at the very beginning of the decay (Fig. 3 in
ref. 9) it appears now that the equilibrium was not totally
established at that short time, particularly at low O2 concen-
trations. This resulted in an apparent slower decrease of the
adduct absorption with [O2] and in a lower value of the
Fig. 4 Detailed mechanism for the adduct c-C6H6-OH reaction with
O2 . The pseudo-first-order rate constants indicated are derived from
quantum calculations and determined for air conditions, 1 atm. For
estimating which reactions are likely to occur, the corresponding rate
constants must be compared to the measured pseudo-first-order rate
constant for global radical loss kIloss ¼ 1250 sꢂ1. Rate constants for
HO2 elimination from either RO2(cis) or RO2(trans) have been calcu-
lated to be smaller than 10ꢂ5 ꢂ1. In the particular case of reactions
s
with NOx , pseudo-first-order rate constants have been estimated for
heavily polluted atmospheres, [NO] ꢅ [NO2] < 100 ppbv, using rate
constants of the order of 2 ꢁ 10ꢂ11 cm3 moleculeꢂ1 sꢂ1 1
.
T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4
P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 2 2 4 5 – 2 2 5 3
2251

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in RO2 , which have been shown by calculations to be un-
favourable, would necessitate additional OH reactions to form
glyoxal.
A similar work, both experimental and theoretical, has been
recently conducted in this laboratory in the case of toluene.
The results are very similar to those presented here for ben-
zene, meaning that the reaction mechanism must be the same.
Preliminary experimental data also indicate that a similar
mechanism is expected for p-xylene and 1,3,5-trimethylben-
zene. However, it must be pointed out that this mechanism is
not representative of all reactions of cyclohexadienyl-type
radicals with O2 . For example, the H-transfer reaction (corres-
ponding to reaction (2a) above) is dominant in the cases of the
cyclohexadienyl radical c-C6H6-H18,33,34 and of the phenol-OH
adduct, HOC6H5-OH.35,36
equilibrium constant. At high O2 concentration, the equili-
brium was established, even at the shortest times but, as stated
above, the equilibrium constant appears smaller due to RO2
(or product) absorption which was not taken into account.
By combining those two effects, the decrease of the adduct
absorption with [O2] could be nicely modelled with the low
value of the equilibrium constant, from the lowest to the high-
est O2 concentrations used. It can also be mentioned that the
low Kc,2b value was supported by the fact that the RO2 absorp-
tion at shorter wavelengths, which could not really be charac-
terised and taken into account, resulted in an apparent lower
value of the equilibrium constant (see above).
It must be emphasised that, as discussed above, the determi-
nation of the equilibrium constant is difficult as the resulting
value is sensitive to several parameters which are not accu-
rately characterised: shift of the baseline resulting from the
benzene photolysis, additional absorptions due to RO2 and
products, uncertainties on rate constants, etc.
Note added at proof
A new contribution to the kinetics of the system investigated in
the present paper has been published recently (S. Y. Grebenkin
and L. N. Krasnoperov, J. Phys. Chem. A, 2004, 108, 1953).
The results are in rough agreement with those reported here,
the main discrepancy being on the radical loss reaction which
was not really characterised in their work. This is surprising
since phenol and other oxidation products have to be formed
in some way. Probably that the absence of kloss in their reac-
tion mechanism is compensated by a value of k9 which is
obviously too large since it is over the gas kinetics rate
constant.
Theoretical part and mechanism of benzene oxidation
The identification of the mechanism proposed above is essen-
tially based on calculated kinetic parameters and on their com-
parison with available experimental data. Previous results of
theoretical works have also been used for discarding those pos-
sible reaction routes which involve high activation barriers,
such as the benzene oxide/oxepine channel14 or the H-atom
transfer from the OH group to the –OO radical centre.5,15
One of the principal interests of the comparison between
experimental and theoretical data is the validation of the the-
oretical methods which have been shown to provide fairly reli-
able data for the systems of interest in this work. In particular,
the IM method used for correcting the activation energies cal-
culated at the DFT level has been proved to be particularly
efficient for improving the accuracy of calculated rate con-
stants. This has been very useful for identifying with good
degree of confidence those of the reaction routes which can
possibly occur under atmospheric conditions and those which
cannot. In particular, calculations account well for the phenol
yield and for both the kinetics and thermodynamics of the
equilibrium (2b), measured experimentally. Thus, calculations
showing that the RO2(trans) cannot undergo any reaction,
apart from the decomposition (ꢂ2b) to reactants, can be con-
sidered to be reliable, as well as those showing that the
RO2(cis) readily undergoes ring closure. The difficulty of cycli-
sation of the RO2(trans), compared to that of the cis isomer, is
expected as it involves an interconvertion of the cycle for going
from the stable structure allowing the H-bond to be formed to
the structure which favours the ring closure. This adds an addi-
tional barrier. Such an interconvertion is not necessary in the
case of the cis isomer. Finally, the principal point that can
be debated about is the calculated rate constant for the
RO2(cis) formation which is a factor of about 10 too low for
being consistent with a reasonable yield of oxidation products
formed through this reaction channel. However, as already sta-
ted above, it can be considered that a factor of 10 is still within
the limits of uncertainties for calculated rate constants.
Acknowledgements
The authors wish to thank the Commission of the European
Union (Energy, Environment and Sustainable Development
programme, EXACT project) and the French National Pro-
gramme for Atmospheric Research for funding this work.
They are also grateful to the CNRS Computer Centre in
Orsay, France (I.D.R.I.S.), for providing computer time.
References
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J. G. Calvert, R. Atkinson, K. H. Becker, R. M. Kamens, J. H.
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B. Bohn and C. Zetzsch, Phys. Chem. Chem. Phys., 1999, 1, 5097.
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G. Ghigo and G. Tonachini, J. Am. Chem. Soc., 1999, 121, 8366.
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I. Garcıa-Cruz, M. Castro and A. Vivier-Bunge, J. Comput.
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8
9
In conclusion, it must be emphasised that the proposed
mechanism is consistent with experimental and calculated data
and with the final oxidation products which have been charac-
terised. Due to uncertainties on calculated parameters, it
cannot be claimed that this work provides a definite demon-
stration for this mechanism. The arguments provided in favour
of it are certainly strong but a confirmation is needed. It
must be noted, however, that in a recent paper, Volkamer
et al.29 have shown that one of the principal oxidation
product, glyoxal, is a primary product, i.e. only a single OH
reaction is involved in its formation. This is consistent with
our mechanism, since other reaction routes, benzene oxide/
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