Kinetics and mechanism of the gas-phase reaction of the cyclohexadienyl radical c-C6H7 with O2

Article abstract of DOI:10.1039/b308107a

The kinetics and mechanism of the gas-phase reaction of the cyclohexadienyl radical c-C₆H₇ with O₂ have been investigated using both experimental and theoretical approaches. The rate constant has been measured using conventional flash photolysis in the temperature range 302-456 K, 1 atm pressure. c-C₆H₇ radicals were produced by reacting Cl atoms with 1,4-cyclohexadiene. The rate expression is k₁ = (1.4 ± 0.26) x 10^-13 exp[-(300 ± 74) K/T] cm³ molecule^-1 s^-1 (2σ error bars). The reaction can proceed either by association, yielding a peroxy radical RO₂ or by H-abstraction, yielding benzene + HO₂, the two reaction channels involving two distinct transition states. In contrast to what is observed for the c-C₆H₆OH radical, no equilibrium with the peroxy radical could be characterised. The theoretical approach, involving both DFT and ab initio methods, was used to determine if the measured rate constant should be assigned to the association or to the H-abstraction channel. Comparison of experimental and theoretical results shows that H-abstraction must be the only significant reaction channel.

Full text of DOI:10.1039/b308107a

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Kinetics and mechanism of the gas-phase reaction of the
cyclohexadienyl radical c-C6H7 with O2
´
˜
E. Estupinan, E. Villenave, S. Raoult, J. C. Rayez, M. T. Rayez and R. 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 17th July 2003, Accepted 15th September 2003
First published as an Advance Article on the web 3rd October 2003
The kinetics and mechanism of the gas-phase reaction of the cyclohexadienyl radical c-C6H7 with O2 have been
investigated using both experimental and theoretical approaches. The rate constant has been measured using
conventional flash photolysis in the temperature range 302–456 K, 1 atm pressure. c-C6H7 radicals were
produced by reacting Cl atoms with 1,4-cyclohexadiene. The rate expression is k1 ¼ (1.4 ꢀ 0.26) ꢁ 10ꢂ13
exp[ꢂ(300 ꢀ 74) K/T] cm3 moleculeꢂ1 sꢂ1 (2s error bars). The reaction can proceed either by association,
yielding a peroxy radical RO2 or by H-abstraction, yielding benzene + HO2 , the two reaction channels
involving two distinct transition states. In contrast to what is observed for the c-C6H6OH radical, no
equilibrium with the peroxy radical could be characterised. The theoretical approach, involving both DFT and
ab initio methods, was used to determine if the measured rate constant should be assigned to the association or
to the H-abstraction channel. Comparison of experimental and theoretical results shows that H-abstraction
must be the only significant reaction channel.
the two possible reaction channels. Concerning branching
Introduction
ratios, the only information has been reported by Ohta7 who
provided possible evidence for channel (1b) to be the principal
reaction pathway at room temperature, but the occurrence of
channel (1a) could not be totally eliminated. A similar work
was recently published by Tuazon et al.16
Cyclohexadienyl type radicals, c-C6H6–X, are important inter-
mediates in reacting systems involving aromatic compounds,
whereas their reactivity in the gas phase has been poorly char-
acterised. In particular, reactions of the simplest radical, the
cyclohexadienyl c-C6H7 (C6H6–H adduct), have only been
the subject of a few investigations: recombination with other
radicals,1–4 self reaction,5 reaction with NO and O2
decomposition reaction.5
Most studies have concerned the hydroxycyclohexadienyl
radicals, in particular the OH–benzene and the OH–toluene
adducts, because of their role in atmospheric chemistry.8
Recent studies involved either theoretical,9–11 experimental12–14
or both approaches.15 Concerning the reaction with oxygen,
the c-C6H6–OH adduct reacts very slowly with O2 , k ꢃ 10ꢂ15
cm3 moleculeꢂ1 sꢂ1 at room temperature12,15 and it is now
demonstrated that the association reaction with O2 , yielding
the peroxy radical, is equilibrated under conditions of the tro-
posphere, in competition with the hydrogen abstraction, yield-
ing phenol and HO2 .12,15 The same behaviour is observed for
the OH–toluene adduct.13 Quantum calculations of thermo-
chemical parameters have corroborated the experimental
observations.15
The rate constant k1 was measured in this work as a function
of temperature, using flash photolysis combined with UV
detection of the c-C6H7 radical, along with a new chemical sys-
tem for radical generation. In addition, quantum calculations
were combined with experiments in order to provide informa-
tion on thermochemical parameters of reaction channels and
on branching ratios.
6,7
or
Experimental
Cyclohexadienyl radicals were generated using a new reaction
system, simpler than the one used in the previous work,6 which
simultaneously generated HO2 radicals, resulting in inter-
ferences with the reaction of interest. The new system consists
of photolysing molecular chlorine in the presence of 1,4-cyclo-
hexadiene. The photolytically formed chlorine atoms react
with 1,4-cyclohexadiene both by hydrogen abstraction and
addition, the hydrogen abstraction channel (3a) yielding the
cyclohexadienyl radical:
The objective of the present work is to provide a detailed
description of the kinetics, mechanism and thermochemistry
of the cyclohexadienyl radical c-C6H7 reaction with oxygen,
Cl2 þ hn ! 2 Cl
Cl þ 1; 4-c-C6H8 ! HCl þ c-C6H7
Cl þ 1; 4-c-C6H8 ! c-C6H8Cl
ð2Þ
ð3aÞ
ð3bÞ
M
*
cꢂC6H7 þ O2 )
c-C6H7 þ O2
ð1a; ꢂ1aÞ
ð1bÞ
c-C6H7 þ O2 ! C6H6 þ HO2
The rate constant k1 for the global reaction has been already
measured in our laboratory, but only at room temperature and
with fairly poor accuracy: k1 ¼ (4 ꢀ 2) ꢁ 10ꢂ14 cm3 moleculeꢂ1
Since the UV absorption cross section of c-C6H7 is known,
s ¼ 2.55 ꢁ 10ꢂ17 cm2 moleculeꢂ1 at 302 nm,5 it was possible
to estimate the branching ratio of reaction (3a) which was
found to be 0.38 ꢀ 0.06. In the absence of oxygen, a chain
reaction initiated by reaction (4),
s
ꢂ1.6 Due to the use of a complex reaction system for radical
generation, this first work did not allow us to measure the tem-
perature dependence of the rate constant, nor to provide infor-
mation on the equilibrium (1a) and on the branching ratios of
c-C6H8Cl þ Cl2 ! c-C6H8Cl2 þ Cl
ð4Þ
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DOI: 10.1039/b308107a

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k4 ꢃ 1 ꢁ 10ꢂ12 cm3 moleculeꢂ1 sꢂ1 17
,
resulted in an apparent
the electronic state of the system at the transition state, the
CCSD(T) method in its standard version is unable to calculate
reliable activation energies. A simple but efficient way to over-
come this shortcoming 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, originally introduced
by Marcus for proton transfer in the gas phase25 and extended
by Murdoch to atom transfer.26 The intrinsic barrier DHint is
the enthalpy of activation that the reaction would have if it
were thermoneutral. DHint is linked to the true enthalpy of
increase of the branching ratio. However, the chain reaction
was quenched by small amounts of oxygen ([O2] ꢄ 1.5 ꢁ 1016
molecule cmꢂ3), which scavenged all c-C6H8Cl radicals,
whereas reaction (1) did not occur to a significant extent
for such O2 concentrations, due to its lower rate constant
(see below). No measurements were performed at concentra-
tions lower than 2 ꢁ 1016 molecule cmꢂ3 in order to prevent
any perturbation by the chain reaction. The reaction of
c-C6H7 with Cl2 is much slower5 and does not play any signifi-
cant role.
The experimental set-up has already been described18 and
only the principal features, specific of this work, are given here.
Flash photolysis of Cl2 , 1,4-cyclohexadiene, N2 and O2 mix-
tures was performed through Pyrex (l > 290 nm). The cylind-
rical reaction cell, 70 cm long, could be temperature controlled
from 295 to 500 K. Cyclohexadienyl radicals were monitored
via their time-resolved absorption at 302 nm, corresponding
to the maximum of the absorption band (s(302 nm) ¼
2.55 ꢁ 10ꢂ17 cm2 moleculeꢂ1).5 The analysis beam, provided
by a stabilised high pressure xenon lamp, passed twice
through the reaction cell. The resulting decay profiles were
averaged, typically over 30 to 50 flashes, and stored in a micro-
computer for subsequent analysis via numerical integration/
non-linear least squares fitting. The corresponding reaction
mechanism is detailed below. All experiments were performed
at atmospheric pressure.
activation DHy298 and to the reaction enthalpy DHꢅ
by the
298
following empirical relationship:
DH2y98 ¼ DHint þ DH2ꢅ98=2 þ ðDHꢅ298Þ =16DHint
ðIÞ
2
Then, the procedure used to estimate the corrected activa-
tion enthalpy of a given reaction is the following: (i) DHint is
calculated from (I) using the DFTy values of DHy298 and
DHꢅ
and (ii) a corrected value DH298 is obtained from (I)
298
using the previously calculated value DHint and the CCSD(T)
value of DHꢅ298 . The activation energy Ea is then determined
using relation (II):
Ea ¼ DHyT þ nRT
ðIIÞ
with n ¼ 2 for a bimolecular reaction, R being the gas con-
Nitrogen (Messer, 99.995%), oxygen (Messer, 99.995%), Cl2
(Messer, 99.8%, 5% in N2 , 99.995%) and 1,4-cyclohexa-
diene (Aldrich, 97%) were used without further purification.
1,4-Cyclohexadiene was injected into the gas stream by using
a bubbler maintained at 273 K.
stant.
This method has been used for reactions (1a) and (1b), in the
case of the c-C6H6OH + O2 reaction. It has yielded kinetic
parameters in good agreement with experimental data which
are available for this reaction (see below).
Rate constants were calculated using the well-estalished
expressions of the Transition State Theory (TST).27
Based on comparisons of experimental and calculated rate
constants, we consider with reasonable confidence that the
agreement is good when the values differ by less than a factor
of 10 (corresponding to only an error of 1.4 kcal molꢂ1 on cal-
culated activation energies). Similarly, we consider that the
competition between two reaction channels is possible when
the corresponding calculated rate constants differ by less than
a factor of 10 and is not possible if they differ by a factor larger
than 100. In between, no conclusion can be reached.
Theoretical methods
Theoretical calculations were performed in order to determine
the characteristics (geometries, vibrational frequencies, rota-
tional constants and energetics) of the specific points (stable
species and transition states) of the potential energy surfaces
(PES) involved in reactions (1a) and (1b). Due to the large
number of electrons present in the molecular system investi-
gated, the density functional theory (DFT) was used. 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 calcu-
lations were performed with the coupled cluster CCSD(T)/
6-31G(d,p) method,20 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
Experimental results
Typical decay traces, recorded at 302 nm and for various O2
concentrations, are shown in Fig. 1. In addition to reaction
(1), the following reaction mechanism was used in the
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). In fact, ab initio
calculations describe the relevant reactions as being more
exothermic than DFT calculations do. Moreover, CCSD(T)
values are in good agreement with experimental data in the
particular case of the c-C6H6OH + O2 reaction.15 According
to the ‘‘Hammond postulate’’,22 we therefore expect that
actual activation energies are in fact lower than those calcu-
lated by the 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 multi-
configurational character23 of the wave function describing
Fig. 1 Typical decay traces recorded at 302 K and their simulations.
The trace corresponding to the absence of oxygen is calculated.
Phys. Chem. Chem. Phys., 2003, 5, 4840–4845
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Table 1 Pseudo-first order rate constants (kI1) and k1 values obtained
for various oxygen concentrations and at various temperatures
computer simulation of the traces:
c-C6H8Cl þ O2 ! c-C6H8ClO2
ð5Þ
ð6Þ
O2/1016
k1/10ꢂ14 cm3
moleculeꢂ1 sꢂ1
c-C6H7 þ c-C6H7 ! products
molecule cmꢂ3
kI a /sꢂ1
c-C6H7 þ RO2 ! products ðwith RO2
T ¼ 302 K
2.22
2.87
3.18
3.51
4.14
4.75
5.37
6.36
1170
1460
1620
1740
2150
2360
2870
3150
5.27
5.09
¼ c-C6H7O2 þ c-C6H8ClO2Þ
ð7Þ
ð8Þ
5.09
4.95
RO2 þ RO2 ! products
Products of reaction (1) are stable molecular species (see
below) which are not involved in the reaction mechanism and
do not absorb significantly at 302 nm. Nevertheless, a small resi-
dual absorption was always observed but was too small to assign
it to the products of a particular reaction using current simula-
tions. Residual absorptions were arbitrarily assigned to the pro-
ducts of reaction (8) (or reaction (7) with no difference in the
results). The rate constants used in the simulations for this set
5.19
5.00
5.34
4.95
k1 ¼ (5.09 ꢀ 0.14)b
T ¼ 354 K
2.19
2.88
3.50
4.15
1370
1920
2040
2450
6.25
6.66
of reactions were (units of cm3 moleculeꢂ1
s
(estimated from rate constant values for similar reactions and
ꢂ1): k5 ꢃ 2 ꢁ 10ꢂ12
5.82
5.90
k1 ¼ (6.07 ꢀ 0.58)b
adjusted at low O2 concentrations), k6 ¼ 3.1 ꢁ 10ꢂ11 5
k7 ¼
,
3.5 ꢁ 10ꢂ11 (adjusted at low O2 concentrations), k8 ꢃ 1 ꢁ 10ꢂ12
(estimated from recommendations28). Reaction (5) occurs on a
time scale of 10–50 ms, which is much shorter than the time scales
of other reactions ( > 1 ms). Thus, radical–radical reactions
involving the c-C6H8Cl radical were neglected. The value of k8
is a rough estimation but, as the oxygen concentration was
increased, radical–radical reactions became rapidly of negligible
importance and the uncertainty could not be a significant
source of error. Nevertheless, all the above reactions were
included in the reaction mechanism used in simulations.
T ¼ 406 K
2.19
2.81
3.11
3.42
4.07
1460
1750
2200
2350
2890
6.66
6.22
7.07
6.87
7.10
k1 ¼ (6.86 ꢀ 0.42)b
T ¼ 456 K
2.21
3.14
3.45
4.08
1580
2140
2440
2900
7.15
6.82
7.07
7.10
The principal observation was that the kinetics were consis-
tent with a pseudo-first-order reaction, whatever the experi-
mental conditions. No indication of an equilibrated reaction
could be observed, as was the case for the hydroxycyclohexa-
dienyl radicals obtained from benzene12,15 and toluene13 and
for the chlorocyclohexadienyl radical.29 Thus, no equilibrium
can be seen in the case of the c-C6H7 radical, which means that
either the c-C6H7O2 radical is stable or that reaction (1a) does
not occur to a significant extent under our experimental condi-
tions. It must be pointed out that, under similar experimental
conditions, the equilibrium was observed, in the case of the
hydroxycyclohexadienyl radicals, for O2 concentrations about
two orders of magnitude larger.12,13,15 The pseudo-first-order
behaviour is illustrated in Fig. 2 where the pseudo-first-order
rate constant is plotted against the O2 concentration. Details
about this set of experiments are given in Table 1.
k1 ¼ (7.04 ꢀ 0.22)b
a
b
Pseudo-first-order rate constants. Obtained by forcing the regres-
sion line to go through the origin (2s error bars).
yielding:
k1ð298 KÞ ¼ ð5:1 ꢀ 0:3Þ ꢁ 10ꢂ14 cm3 moleculeꢂ1 sꢂ1
in agreement with our preceding value, (4 ꢀ 2) ꢁ 10ꢂ14 cm3
moleculeꢂ1 sꢂ1,5 within uncertainties. As stated above, the pre-
ceding value was fairly inaccurate as a result of the presence of
HO2 radicals formed in the generation system of the c-C6H7
radicals. Such interferences are absent in the chemical system
used in the present work.
Similar experiments were performed at four different
temperatures, from 302 to 456 K. The details of results are
included in Table 1 and the corresponding Arrhenius plot is
represented in Fig. 3. The rate expression is (2s error bars):
One of the principal sources of error in the present measure-
ments is the difficulty, in the cases of fastest decays, to locate
accurately the starting point of decay traces, due to the initial
k1 ¼ ð1:4 ꢀ 0:26Þ ꢁ 10ꢂ13
ꢁ exp½ꢂð300 ꢀ 74Þ K=Tꢆ cm3 moleculeꢂ1 sꢂ1
Fig. 2 Pseudo-first-order rate constants plotted as a function of O2
concentration.
Fig. 3 Arrhenius plot for reaction (1).
4842
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dead time resulting from the scattered flash light and to the
fact that the initial radical concentration could not be rigo-
rously kept constant during a set of runs performed at various
O2 concentrations. A large part of this error is included in the
statistical errors quoted above but it is estimated that about
5% of systematic error on k1 may arise from this problem.
Other sources of errors essentially come from uncertainties
on radical–radical reactions, less than 10%, and from errors
on the oxygen concentration, <3%. Thus, the total uncer-
tainty, including the statistical error, is estimated to be around
15%.
of the equilibrium constants K1a should also be close to each
other for both systems and thus, the equilibrium (1a,ꢂ1a)
should be observed for the c-C6H7 radical at around room
temperature, with oxygen concentrations similar to those used
for the c-C6H6OH radical equilibrium study,12,15 i.e., about
two orders of magnitude larger than those actually used in
the present study. Therefore, with the low oxygen concentra-
tions used here, the equilibrium is totally shifted towards reac-
tants and thus, we can conclude that another reaction, different
from reaction (1a), must take place in the case of the
c-C6H7 + O2 system.
Kinetic parameters. Activation energies, corrected using the
IM approach described above, are listed in parentheses in
Table 2. The value, calculated for the C6H6OH + O2 reaction,
leads to a k1a value of 4.1 ꢁ 10ꢂ16 cm3 moleculeꢂ1 sꢂ1, in fairly
good agreement with the experimental value of 12 ꢁ 10ꢂ16 cm3
moleculeꢂ1 sꢂ1 (see Table 2). This good agreement provides an
interesting validation of our theoretical approach which can
therefore be considered reliable for describing the present sys-
tems. Thus, it can be expected that kinetic data calculated for
reaction (1a) in the case of the c-C6H7 radical, with the activa-
tion energy value corrected as described above, are also reli-
able. It is seen in Table 2 that the calculated k1a values are
very similar for both the c-C6H7 and c-C6H6OH reactions
and then, the actual values are also expected to be similar,
Results of calculations
The principal objective of the calculations was to help to deter-
mine if the measured rate constant should be assigned to the
association channel (1a) or to the H-abstraction channel
(1b). For this purpose, thermochemical and kinetic parameters
were calculated for both channels in order to estimate their
relative rates and the equilibrium constant K1a . The present
experimental study shows that the c-C6H7 radical reacts with
O2 differently compared to the c-C6H6OH radical,12,15 which
reacts much more slowly, the reaction being equilibrated under
atmospheric conditions. Thus, it was of interest to compare the
results of the calculations performed at the same level of
theory for both radicals. All results are listed in Table 2.
Some of the results obtained for the c-C6H6OH radical have
already been published.15
around 1 ꢁ 10ꢂ15 cm3 moleculeꢂ1
s
ꢂ1. This is a factor of
around 50 smaller than the k1 value measured in this work,
which exceeds the uncertainty range of calculated rate
constants (estimated at around a factor 10). It follows that,
as in the case of the thermochemical parameters above, kinetic
parameters indicate that the measured rate constant cannot
be assigned to reaction channel (1a).
Channel (1a)
Thermochemical parameters. Calculations were performed
for each stable species involved in reaction (1a) in order to
determine the reaction enthalpy and reaction entropy. As
mentioned in the ‘‘Theoretical methods’’ section, a significant
difference between the DFT and ab initio values of the reaction
enthalpy is observed (ab initio values are given in parentheses
in Table 2 for both reactions and for both c-C6H7 and
c-C6H6OH radicals). It was shown, in the case of the
Channel (1b)
Channel (1b) is a bimolecular reaction forming benzene and
HO2 . In the case of the c-C6H6OH radical, it corresponds to
the channel forming phenol, in competition with channel
(1a), with a yield estimated to be around 25–50% under tropo-
spheric conditions.8,15,30
For this abstraction channel, it is seen that the situation is
quite different for the two systems, c-C6H7 + O2 and
c-C6H6OH + O2 . The values of reaction enthalpies (Table 2)
are not significantly different and thus, cannot be the source
of any difference in the kinetic behaviour of the two systems.
c-C6H6OH radical, that the ab initio value (ꢂ11.4 kcal molꢂ1
)
was in good agreement with the value determined experi-
mentally (ꢂ12.4 kcal molꢂ1).15 It is reasonable to assume that
the same situation holds in the case of the c-C6H7 radical, since
the calculated reaction enthalpy DHꢅ
and reaction entropy
are similar for both systems. It results that the value
298
DSꢅ
298
Table 2 Thermochemical and kinetic parameters calculated for reactions (1a) and (1b) and for the corresponding reaction of c-C6H6OH, at the
DFT-B3LYP/6-31G(d) level and, for stable species only, at the ab initio CCSD(T)/6-31G(d,p)//B3LYP/6-31G(d) level (values in parentheses).
For transition states, the activation energy values shown in brackets are obtained by correcting the DFT values, as explained in the text
Reaction (1a)
c-C6H7 + O2 Ð c-C6H7O2
c-C6H6OH + O2 Ð HOC6H6O2
DHꢅ298/kcal molꢂ1
ꢂ5.5 (ꢂ10.1)
ꢂ36.6
ꢂ7.0 (ꢂ11.4)a
DSꢅ298/cal molꢂ1 Kꢂ1
Ea/kcal moleꢂ1
ꢂ38.6a
3.9 (2.4)
2.3 ꢁ 10ꢂ14
3.8 (2.5)b
A/cm3 moleculeꢂ1 sꢂ1
kTST(298 K)/cm3 moleculeꢂ1 sꢂ1
kexp(298 K)/cm3 moleculeꢂ1 sꢂ1
2.7 ꢁ 10ꢂ14 b
3.8 ꢁ 10ꢂ17 (3.9 ꢁ 10ꢂ16
)
4.4 ꢁ 10ꢂ17 (4.1 ꢁ 10ꢂ16 b
)
Expected to be ca. 1 ꢁ 10ꢂ15 (see text)
1.2 ꢁ 10ꢂ15 b
Reaction (1b)
c-C6H7 + O2 ! benzene + HO2
c-C6H6OH + O2 ! phenol + HO2
DHꢅ298/kcal molꢂ1
ꢂ20.4 (ꢂ23.1)
ꢂ25.6 (ꢂ26.5)b
DSꢅ298/cal molꢂ1 Kꢂ1
Ea/kcal molꢂ1
1.6
ꢃ0
1.4b
3.2 (3.0)b
A/cm3 moleculeꢂ1 sꢂ1
kTST(298 K)/cm3 moleculeꢂ1 sꢂ1
kexp(298 K)/cm3 moleculeꢂ1 sꢂ1
–
2.2 ꢁ 10ꢂ14 b
Expected to be > 1.4 ꢁ 10ꢂ16 (see text)
1.0 ꢁ 10ꢂ16 (1.4 ꢁ 10ꢂ16 b
)
5.1 ꢁ 10ꢂ14 c
0.6 ꢂ 1.1 ꢁ 10ꢂ16 b d
a
b
c
d
From ref. 15. To be reported in a forthcoming publication. This work. Derived from the global rate constant for the c-C6H6OH + O2
reaction, taking a phenol yield of 25–50%.
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In the case of the c-C6H6OH reaction, a barrier is localised and
the calculated features of the transition state yield the values
reported in Table 2 for the pre-exponential factor, activation
energy and rate constant at 298 K. As stated above, this is
totally consistent with the experimental observations since, in
air, it corresponds to a calculated pseudo-first-order rate con-
stant of about 500 sꢂ1, to be compared with the experimental
rate constant of 1000–2000 sꢂ1 measured for the total loss of
c-C6H6OH (ref. 12 and preliminary results obtained in our
laboratory). This corresponds to a yield of 25–50% for phenol,
consistent with experimental observations.
In the case of the c-C6H7 radical, no potential barrier has
been found for the reaction channel (1b), the potential energy
surface being found to decrease continuously along the reac-
tion path to benzene + HO2 products. This shows that, even
if a barrier does exist, it should be very small and difficult to
localise with sufficient reliability from DFT calculations. It
results, that any rate constant calculated with a small barrier
would be significantly larger than that calculated in the case
of the c-C6H6OH + O2 system. This compares favourably with
the rate constant measured in this work, which exhibits a weak
temperature dependence corresponding to a small activation
energy (0.6 kcal molꢂ1) and which is much larger than the
k1b value measured for c-C6H6OH. Thus, the comparison of
experimental and calculated data strongly favours the assign-
ment of the measured rate constant to channel (1b).
was the only effective channel in reaction (1). However, com-
bined with the present results, we can conclude with good con-
fidence that it is actually the case. It must be emphasised that
other reaction channels, in addition to channels (1a) and (1b),
such as those producing phenol + OH or benzene oxide + OH
are unfavourable. Despite the fact that they are exothermic,
they would involve very complex molecular rearrangements
corresponding to multi-step reactions and probably to high
activation energies.
It must be emphasised that the reaction of c-C6H7 with O2
is quite different from the corresponding reactions of the
hydroxycyclohexadienyl radicals formed from OH addition to
benzene, toluene, dimethylbenzenes or trimethylbenzenes. As
shown in refs. 12–15 and in preliminary results from this
laboratory, the equilibrium (1a,ꢂ1a) is observed for those
OH-adducts under conditions close to those of the tropo-
sphere, in competition with channel (1b) which is much slower
than for c-C6H7 . Nevertheless, the latter reaction is an impor-
tant source of phenol and cresol in the atmospheric oxidation
of benzene and toluene, along with other oxidation products
formed from subsequent reactions of peroxy radicals.
The present result has a consequence on the product distri-
bution in oxidation processes where the cyclohexadienyl radi-
cal is an intermediate. Benzene is a product with a yield equal
to that of the c-C6H7 radical. In particular, this is the case of
1,3- and 1,4-cyclohexadiene for which hydrogen abstraction
is an important channel in their reaction with OH (8–15%
and 12–20%, respectively).7,16,31 It may also be the case for ter-
penes, such as a-terpinene, g-terpinene, a-phellandrene, . . .,
which have the same ring structure as those of 1,3- and
1,4-cyclohexadiene.
Discussion and conclusions
The principal objectives of the present work were the determi-
nation of the temperature dependence of the rate constant k1
and the identification of the channel, (1a) or (1b), to which
the measured rate constant k1 must be assigned. It is shown
that the two channels are separate reaction paths involving
two distinct transition states. The comparison of the results
obtained both from experiments and from calculations is
strongly in favour of channel (1b) since, (i) the equilibrium
(1a,ꢂ1a) should be almost totally shifted towards reactants
under the experimental conditions used in the present work,
(ii) the calculated rate constant k1a is almost two orders of
magnitude smaller than the measured rate constant k1 , which
exceeds the combined uncertainties on both rate constants, as
can be seen from the good agreement obtained in the case of
the c-C6H6OH + O2 system and (iii) calculations predict that
the rate constant k1b should be much faster for the
c-C6H7 + O2 reaction than for the c-C6H6OH + O2 reaction,
due to an activation energy close to zero, which is observed
experimentally. Therefore, we can conclude with a good degree
of confidence that the products of the cyclohexadienyl radical
reaction with O2 in the gas phase are essentially benzene and
HO2 .
Acknowledgements
The authors wish to thank the Commission of the European
Union and the French National Program for Atmospheric
Research for funding this work.
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