LIF Spectra of Cyclohexoxy Radical and Direct Kinetic Studies of Its Reaction with O2

Article abstract of DOI:10.1021/jp036891p

The laser-induced fluorescence (LIF) excitation spectrum of cyclohexoxy radical has been measured for the first time. The dominant vibrational progression is consistent with computations, at CIS/6-31+G(d), of the C-O stretch frequency of the axial conformer of cyclohexoxy radical. LIF intensity was used as a probe in direct kinetic studies of the reaction of cyclohexoxy radicals with O₂. The Arrhenius expression obtained was k _O2 = (5.8 ± 2.3) × 10^-12 exp[(-14.3 ± 0.8) kJ/mol/RT] cm^-3 molecule^-1 s^-1 (225-302 K), independent of pressure in the range 50-125 Torr. The room temperature rate constant for this reaction is a factor of 2 higher than the commonly recommended value, but the observed activation energy is 9 times larger than the recommended value of 1.6 kJ/mol. Combining our results with the ratio of rate constants, k_O2/k_scission, measured in chamber experiments, we obtained an Arrhenius expression for k_scission, the rate constant for β C-C scission of cyclohexoxy radical. However, the resulting Arrhenius preexponential factor of 4.5 × 10¹⁵ s ^-1 is unreasonably high compared with the value of ～2 × 10¹³ s^-1 obtained in our RRKM/Master Equation calculations as well as in calculations and experiments reported for other alkoxy radicals. The apparent discrepancy is resolved by examining the uncertainties in the values of k_scission and the limited temperature range spanned by the relative rate experiments. A part of the discrepancy might also be explained by the observation that the O₂ rate constant measured here is only for a single conformer of cyclohexoxy radical, whereas the relative rate experiments represent some averaging over both conformers.

Full text of DOI:10.1021/jp036891p

J. Phys. Chem. A 2004, 108, 447-454
447
LIF Spectra of Cyclohexoxy Radical and Direct Kinetic Studies of Its Reaction with O2
Lei Zhang, Katherine A. Kitney, Melissa A. Ferenac, Wei Deng, and Theodore S. Dibble*
Department of Chemistry, SUNYsEnVironmental Science and Forestry, 1 Forestry DriVe,
Syracuse, New York 13210
ReceiVed: September 28, 2003; In Final Form: NoVember 12, 2003
The laser-induced fluorescence (LIF) excitation spectrum of cyclohexoxy radical has been measured for the
first time. The dominant vibrational progression is consistent with computations, at CIS/6-31+G(d), of the
C-O stretch frequency of the axial conformer of cyclohexoxy radical. LIF intensity was used as a probe in
direct kinetic studies of the reaction of cyclohexoxy radicals with O2. The Arrhenius expression obtained was
kO2 ) (5.8 ( 2.3) × 10-12 exp[(-14.3 ( 0.8) kJ/mol/RT] cm3 molecule-1 s-1 (225-302 K), independent of
pressure in the range 50-125 Torr. The room temperature rate constant for this reaction is a factor of 2
higher than the commonly recommended value, but the observed activation energy is 9 times larger than the
recommended value of 1.6 kJ/mol. Combining our results with the ratio of rate constants, kO2/kscission, measured
in chamber experiments, we obtained an Arrhenius expression for kscission, the rate constant for â C-C scission
of cyclohexoxy radical. However, the resulting Arrhenius preexponential factor of 4.5 × 1015 s-1 is unreasonably
high compared with the value of ∼2 × 1013 s-1 obtained in our RRKM/Master Equation calculations as well
as in calculations and experiments reported for other alkoxy radicals. The apparent discrepancy is resolved
by examining the uncertainties in the values of kscission and the limited temperature range spanned by the
relative rate experiments. A part of the discrepancy might also be explained by the observation that the O2
rate constant measured here is only for a single conformer of cyclohexoxy radical, whereas the relative rate
experiments represent some averaging over both conformers.
I. Introduction
SCHEME 1
The formation of ozone and organic aerosols in polluted air
is controlled by the degradation of volatile organic compounds
(VOCs). Alkoxy radicals are important intermediates in the
degradation of most VOCs.1 The atmospheric fate of large
alkoxy radicals (gC4) is usually determined by competition
among â C-C scission, reaction with O2, and isomerization,2
as shown in Scheme 1. Each reaction pathway contributes
differently to the formation of ozone and secondary organic
aerosols.3 Therefore, understanding alkoxy radical chemistry in
the atmosphere is of crucial importance for understanding and
modeling smog chemistry.
Vehicle exhaust and evaporation of gasoline are important
sources for the emission of alkanes and cycloalkanes in urban
areas. Cyclohexane constitutes 0.1-1.0 wt % of the gasoline
sold in the U.S., Germany, and the U.K.4 In the polluted
troposphere, alkanes and cycloalkanes react with OH· in the
presence of O2 and NO to form alkoxy radicals. The kinetics
of small, acyclic alkoxy radicals have received much attention,
but, although there are several smog chamber studies inferring
information about cyclohexoxy radicals,5-8 there have been no
direct studies of any gas-phase alkoxy radicals containing a six-
membered ring. This is a significant gap because the most
abundantly emitted terpenes (alkenes with molecular formula
C10H16) possess six-membered rings; terpenes are very important
in atmospheric chemistry due to their large emissions and their
role in aerosol formation. Kinetic studies of cyclohexoxy radicals
may provide insight into the chemistry of alkoxy radicals from
terpenes.
Although alkoxy radicals in general can react via three
channels in the atmosphere, isomerization of the cyclohexoxy
radical is slow in comparison to â C-C scission and reaction
with O2. This is attributed to the high energy of the boat-twist
conformation required for the transition state for isomerization.7
Reaction of cyclohexoxy radical with O2 to produce cyclohex-
anone competes with the â C-C scission reaction under
atmospheric conditions (cyclohexanone yield 25-35%).5-8
The technique of laser-induced fluorescence (LIF) has long
been used to monitor small alkoxy radicals (C1-C3) in direct
kinetic studies due to its excellent sensitivity, selectivity, and
time resolution.9-18 More recently, spectroscopic and kinetic
investigations have been extended to larger alkoxy radicals,19-25
and spectroscopic experiments of many of these larger alkoxy
radicals have been carried out under jet-cooled conditions.26-28
Due to the lack of any LIF (or other) spectra for cyclohexoxy
radical, there have been no direct studies of its reaction kinetics.
This paper first discusses the experimental and computational
methods employed. Next the LIF excitation spectrum of
cyclohexoxy radical is presented, followed by computational
results on the relative energies of the conformers of cyclohexoxy
* To whom correspondence should be addressed. FAX: (315) 470-6856.
E-mail: tsdibble@syr.edu.
10.1021/jp036891p CCC: $27.50 © 2004 American Chemical Society
Published on Web 12/23/2003

448 J. Phys. Chem. A, Vol. 108, No. 3, 2004
Zhang et al.
and the vibrational spectra of their second excited (B˜) states.
The discussion then turns to the absolute rate constant, kO2, for
the reaction of cyclohexoxy radical with O2 versus temperature
(and pressure). The calculated rate constant for â C-C scission
is presented and compared to that inferred from relative rate
experiments using both the previously recommended and the
present results for kO2. Finally, discrepancies arising from these
comparisons are discussed.
II. Experimental and Theoretical Methods
An excimer (GAM Laser, Inc., EX100H) laser operating at
351 nm was used to photolyze cyclohexyl nitrite and generate
the cyclohexoxy radical. A dye laser (Lambda Physik, FL3002)
pumped by another excimer laser (Lambda Physik, Lextra 100,
308 nm) was used to excite the radicals. The beams of the two
lasers counter-propagated through the cell in most experiments,
but a few experiments were carried out with the two lasers
perpendicular to each other. The delay time between the dye
laser and the photolysis laser is adjusted by a digital delay
generator. The lasers were operated at 2 Hz. The fluorescence
signal is converted into electric signal by a PMT perpendicular
to both lasers. The electric signal is monitored by a boxcar that
transfers a digital signal to a computer for data acquisition. The
gate width on the boxcar used to record the signal intensities is
20 ns, and the gate is delayed by 70 ns with respect to the
scattered light.
LIF spectra of cyclohexoxy were obtained at 226 K in N2
buffer gas by measuring the integrated fluorescence signal
intensity while continuously scanning the excitation laser
wavelength at 0.03 nm/s. The spectral ranges were 345-370
and 363-403 nm covered by the laser dyes DMQ and PPI,
respectively. We verified that the spectrum only appeared in
the presence of the photolysis laser and that the signal strength
decreased significantly when the delay time between the
photolysis and excitation lasers were extended from 5 to 300
µs; both observations suggest the reported spectra are due to
radicals produced by cyclohexyl nitrite photolysis rather than
wall reactions or secondary chemistry. All the spectral intensities
were corrected by subtracting the background obtained with the
photolysis laser blocked and normalized by dividing by the laser
power. Flow rates and pumping rates were fixed in all
spectroscopic experiments to maintain 13 mTorr partial pressure
of cyclohexyl nitrite and 50 Torr total pressure (at 226 K).
In the kinetic experiments, the dye laser was fixed at one of
four different excitation wavelengths: 349.749, 356.161, 373.586,
and 374.460 nm. These wavelengths are marked by a star in
Figure 1. The pseudo-first-order rate constants for radical loss
were determined from the rate of change of the signal intensity
with delay time. We recorded signal intensities at 16 different
delay times ranging from 5 µs to 10 ms. At each delay time
100 measurements were made and averaged. The partial pressure
of cyclohexyl nitrite was maintained at 13 mTorr in most
experiments. Recently, we have improved the signal-to-noise
ratio sufficiently that we can carry out experiments with about
one-third the concentration of cyclohexyl nitrite (and cyclo-
hexoxy radical), and rate constants were remeasured at three
temperatures using this lower cyclohexyl nitrite concentration.
Cyclohexyl nitrite was synthesized by the dropwise addition
of a mixture of sulfuric acid and cyclohexanol to an aqueous
sodium nitrite solution29 and purified by trap-to-trap distillation.
FTIR30 and NMR30 spectra were obtained to verify the structure
and purity of the product. Based on the NMR experiment, the
major impurity (∼13%) in the nitrite sample was found to be
cyclohexanol, which does not produce any fluorescence at the
Figure 1. Laser-induced fluorescence (LIF) spectrum of cyclohexoxy
radical at 226 K and 50 Torr N2. Peaks used in the kinetics experiments
are marked with an asterisk.
wavelengths used in our experiment. The liquid nitrite sample
was kept at -20 °C when not in use. In the experiment, the gas
mixture was prepared by diluting the vapor of nitrite precursor
to a mole fraction of 1% (or 0.3%) in N2 (Haun Welding
Supplies, 99.999%) in a 10-L darkened glass bulb at room
temperature.
To estimate the concentration of cyclohexyl nitrite photolyzed,
we carried out a single measurement of the UV spectrum of
cyclohexyl nitrite in a 10-cm Pyrex cell with quartz windows.
The resultant (approximate) absorption cross section at 351 nm
was 1.8 × 10-19 cm2. Using this value and the photolysis laser
fluence of 20 mJ/cm2, we estimate the initial alkoxy radical
concentration to be 5.2 × 1012 molecules/cm3 (or 1.7 × 1012
molecules/cm3 at the lower cyclohexyl nitrite concentration).
The temperature of the gases inside the cell was varied between
225 and 302 K. The partial pressure of O2 (Messer, 99.999%)
varied from 0.7 Torr (2.3 × 1016 molecules/cm3 at 298 K) to
4.0 Torr. The high partial pressure of O2 ensures that the kinetic
experiments are carried out under pseudo-first-order conditions.
N2 was added to set the total pressure at 50 Torr (or 125 Torr
in a few experiments).
Temperatures of gases in the cell were measured by a Type
T thermocouple located 1-2 cm below the height of the laser
beams at the point where the fluorescence is monitored. At 50
Torr and 225 K, the displacement of the thermocouple from
the center of the flow results in reported temperatures that
understate the gas temperature in the relevant volume by 2 deg.
The error is less than 2 deg at all other temperatures used in
these experiments.
Quantum calculations employed the Gaussian98 series of
programs31 and examined both conformers of cyclohexoxy
radical. All radicals were treated with the spin-unrestricted
formalism. Different computational methods were used for
different purposes. The relative energy of the axial and equatorial
conformers was studied by second-order Møller-Plesset per-
turbation theory (MP2) with all orbitals correlated. MP2 theory,
unlike most density functional approaches, includes a good
representation of dispersion forces, which are critical to
determining the energy difference between the conformers.
Harmonic vibrational frequencies were computed with the
geometry optimized using the 6-31G(d,p) basis set, and elec-

Spectra of Cyclohexoxy Radical
J. Phys. Chem. A, Vol. 108, No. 3, 2004 449
TABLE 1: Absolute Energies (Hartrees), Zero Point Energies (in parentheses, kJ/mol), and Relative Energies (kJ/mol) of Axial
and Equatorial Conformers of the Cyclohexoxy Radical
equatorial
absolute energy
axial
level of theory
relative energy
absolute energy
relative energy
B3LYP/6-31G(d,p)
B3LYP/6-311G(2df,2p)
MP2/6-31G(d,p)
-310.441 30 (421.5)
-310.527 19
-309.482 46 (436.1)
-308.536 05
0
0
0
0
-310.440 68 (421.5)
-310.526 76
-309.482 48 (436.3)
-308.534 94
1.7
1.2
0.1
3.1
MP2/6-311++G(2d,2p)
tronic energy differences were refined by reoptimizing the
geometry using the 6-311++G(2d,p) basis set.
peak in progression A: progression B with four (triplet) peaks,
∼135 cm-1 higher; progression C with three (doublet) peaks,
∼193 cm-1 higher; progression D with three (doublet) peaks,
∼290 cm-1 higher; progression E with three (triplet) peaks,
∼361 cm-1 higher; progression F with three strong (triplet)
peaks, ∼458 cm-1 higher; and progression G with three (triplet)
peaks, ∼575 cm-1 higher. It is reasonable to identify these
progressions as possessing between zero and three quanta in
the mode with frequency ∼685 cm-1 and one quantum of
excitation in one of several different modes (with frequencies
of ∼135, ∼193, ∼290, ∼361, ∼458, and ∼575 cm-1. However,
this assignment cannot be confirmed without better-resolved
(i.e., jet-cooled) spectra as well as an understanding of possible
confounding factors (e.g., excitation out of the vibrationally
excited ground state, axial vs equatorial conformers).
We carried out computations on the â C-C scission reaction
of cyclohexoxy radical because of its importance to the
atmospheric fate of cyclohexoxy and to help determine the
Arrhenius preexponential factor independently of experiment.
To characterize the C-C scission reaction we used density
functional theory, specifically, the correlation functional of Lee,
Yang, and Parr combined with the three-parameter HF exchange
functional of Becke (B3LYP).32,33 The basis sets used were
6-31G(d,p) and 6-311G(2df,2p). B3LYP, unlike MP2, has been
fairly successful in computing activation barriers to â C-C
scission reactions of alkoxy radicals, especially with the
6-31G(d,p) basis set.34-37 We carried out RRKM/Master Equa-
tion calculations using the UNIMOL program38 and the B3LYP/
6-31G(d,p) relative energies to compute the rate constants for
â C-C scission at a range of temperatures and pressures. These
computations enable us to calculate the corresponding activation
energies and Arrhenius preexponential factors.
Cyclohexoxy radical possesses two dominant conformers,
axial and equatorial,41 as shown below.
The reaction of alkoxy radicals with O2 presents some
difficulties which preclude a calculation as part of this paper.
It has been shown that the O2 reaction of alkoxy radicals
involves a highly spin-contaminated transition state, for which
CASSCF calculations may be necessary.39 Moreover, the
reaction rate is highly sensitive to tunneling and the detailed
dynamics.39,40
To characterize the vibrational structure of the excited state
of cyclohexoxy radical we employed the method of configu-
ration interaction with single excitations (CIS) with the 6-31+G(d)
basis set. This method has been fairly successful in previous
analyses of alkoxy radical vibrational spectra.26 The adiabatic
excitation energies from CIS are not reported because they are
expected to be less accurate than empirical estimates based on
experimental results for other secondary alkoxy radicals.20,26
The MP2/6-311++(2d,2p) calculations indicate that the
equatorial conformer is more stable than the axial conformer
by 3.1 kJ/mol (see Table 1). The other calculations also favor
the equatorial conformer, albeit to lesser extents. The structure
obtained for the equatorial conformer possesses Cs symmetry
and an A′ ground state.
The C-O stretch mode typically dominates the near-
ultraviolet (B˜ state) spectra of alkoxy radicals because the C-O
bond distance in the excited state is extended by 0.1-0.25 Å
over the ground-state value.42,43 Most alkoxy radical spectra
show strong progressions from C-O stretch modes with
III. Results and Discussion
vibrational frequencies in the range 520-600 cm-1 26,44-49
.
1. LIF Detection of Cyclohexoxy Radical. Figure 1 shows
the fluorescence excitation spectrum of cyclohexoxy radicals
from 345 to 403 nm at 226 K and 50 Torr total pressure. Note
that Figure 1 shows two overlapping spectra using different dyes;
large intensity differences in the region of overlap are due to
errors in normalizing the spectra in the wings of the tuning
curves of the two laser dyes. Four pairs of peaks, split by ∼60
cm-1, are found in the dominant progression (marked as A in
Figure 1) starting at 26 702 cm-1. Note that the apparent origin
bands of secondary alkoxy radicals fall at about 26500 ( 250
However, recent analyses suggest that conformers of linear
alkoxy radicals may possess C-O stretch frequencies as high
as 671-676 cm-1 27,28
Therefore, our analysis of the computa-
.
tions on the excited-state focuses on the modes with C-O
stretch character and modes in the region 520-700 cm-1. Our
CIS/6-31+G(d) calculations on the A′B˜ state of the equatorial
conformer indicated that the C-O stretch mode was at 817
cm-1, which is very different from that found for other alkoxy
radicals or in our experiments. A vibrational mode of A′
symmetry with significant C-O stretch component was also
found at 574 cm-1 (similar to the C-O stretch mode frequency
in other alkoxy radicals) but this mode was dominated by a
CCC bending motion. The calculated vibrational frequencies
suggest that the equatorial conformer of cyclohexoxy radical
do not include any modes between 574 and 817 cm-1. Therefore,
the calculations appear inconsistent with the observed ∼685-
cm-1 interval which dominates the observed LIF spectrum.
We optimized a B˜ state of A′ symmetry for the axial
conformer of cyclohexoxy at CIS/6-31G(d,p), but it had one
cm-1 20,26 so the strong peak at 26 702 cm-1 or the two weaker
,
peaks to the red are consistent with the expected location of
the origin band. In progression A, the intervals are 689, 686,
and 682 cm-1. The intensity of peaks decreases with the
increasing wavenumber. No obvious progression was found
involving peaks at lower energy than 26 702 cm-1. In addition
to progression A, there are six reproducible progressions which
also possess ∼685-cm-1 intervals. The apparent origins of these
transitions are displaced to higher frequency with respect to each

450 J. Phys. Chem. A, Vol. 108, No. 3, 2004
Zhang et al.
Figure 2. Typical linear decay of ln(LIF intensity) as a function of
the delay time for cyclohexoxy reacting with O2 at total pressure 50
Torr and 268 K. O2 concentrations in molecules/cm3 are, 9 1.6 × 1014,
b 3.1 × 1014, 2 4.7 × 1014, 4 6.3 × 1014, and O 8.5 × 1014.
Figure 3. Linear fit of the pseudo-first-order rate constant versus the
O2 concentration for selected data at 225, 240, 260, and 268 K.
imaginary frequency. When symmetry was relaxed, we opti-
mized a structure with near-Cs symmetry. Unfortunately, the
frequency calculations did not converge in several attempts. We
present here the results of J. Liu, who graciously allowed us to
report his results prior to his submitting them for publication.50
His results show modes with C-O stretch character at 812 cm-1
(A′′) and 694 cm-1 (A′). The presence of a mode near 690 cm-1
in the computed spectrum of the axial conformer and its absence
in the calculated spectrum of the equatorial conformer suggest
that the dominant features in the experimental spectrum should
be assigned to the axial conformer. Further investigation is
needed before one can be confident in this assignment.
2. The Reaction of Cyclohexoxy Radical with O2. The
reaction with O2 is considered to be a major pathway for the
degradation of cyclohexoxy radical in the atmosphere.2
Figure 2 shows a typical plot of the natural logarithm of LIF
intensity versus delay time for cyclohexoxy reacting with various
concentrations of O2. The slopes of each of the lines in Figure
2 represents a pseudo-first-order rate constant for loss of
cyclohexoxy radical. We note here that vibrational structure of
the spectrum does not change with delay time, so that there is
no significant fluorescence from the products of reaction 1 or
other reactions. Bimolecular reaction rate constants were
obtained from the slopes of the linear correlation between the
pseudo-first-order rate constant and different concentrations of
O2 in the experiments, as shown in Figure 3. The high linearity
of the data shown in Figures 2 and 3 confirms that the pseudo-
first-order approximation is valid here. The rate constant at 301
K (averaged over two determinations) is (2.1 ( 0.5) × 10-14
cm3 molecule-1 s-1, which is 2.6 times greater than the
suggested 298 K value for all secondary alkoxy radicals:2 kO2
Figure 4. Arrhenius plot showing the temperature dependence of the
rate constant for the reaction of cyclohexoxy with O2.
the noise. By linearly fitting all the data in Figure 4, the
Arrhenius expression is found to be
kO2 ) (5.8 ( 2.3) × 10-12 exp[(-14.3 (
0.8) kJ/mol/RT] cm3 molecule-1 s-1 (225-302 K)
where the cited errors represent two standard deviations of the
statistical error. A summary of kinetic data for other alkoxy
radical reactions with O2 is listed in Table 2. Our Arrhenius
preexponential factor of cyclohexoxy reaction with O2 is 300-
400 times larger than that for other secondary alkoxy radicals.
Our activation energy is ∼6 kJ/mol larger than the next highest
value (that for methoxy radical) and 9 times higher than that
recommended for secondary alkoxy radicals.2
) 0.8 × 10-14 cm3 molecule-1 s-1
.
Bimolecular reaction rate constants of cyclohexoxy reaction
with O2 increase from 2.5 × 10-15 at 226 K to 2.1 × 10-14
cm3 molecule-1 s-1 as the temperature is raised from 225 to
302 K. An Arrhenius plot of the data is shown in Figure 4. The
uncertainties in the individual rate determinations are typically
8%, and the trend in the rate constant stands out clearly above
Since the temperature dependence measured here for the
reaction of cyclohexoxy with O2 is so very different from that
expected for a secondary alkoxy radical, it is extremely
important to consider possible sources of error. This reaction
has the potential for extensive secondary chemistry. HO2 is
created by the abstraction reaction of O2 (reaction 1). In the

Spectra of Cyclohexoxy Radical
J. Phys. Chem. A, Vol. 108, No. 3, 2004 451
TABLE 2: Arrhenius Parameters for the Reactions of
Various Alkoxy Radicals with O2
TABLE 3: B3LYP Absolute Energies (Hartrees) and Zero
Point Energies (kJ/mol) of Transition States (TS) for â C-C
Scission of Cyclohexoxy Radical, for O2, and for products of
the â C-C Scission and O2 Reactions of Cyclohexoxy
Radical
A, cm3
radical
CH3O
C2H5O
molecule-1 s-1 Ea, kJ/mol temp range, K
ref
55 × 10-15
71 × 10-15
24 × 10-15
14 × 10-15
25 × 10-15
10 × 10-15
15 × 10-15
16 × 10-15
1.25 × 10-15
23 × 10-15
4.1 × 10-15
8.3
4.6
2.7
0.9
2.0
1.8
1.6
2.2
-4.6
1.4
-2.6
14.3
298-450
295-411
295-354
223-303
289-381
218-313
298-383
288-364
221-266
223-305
220-285
225-302
11
13
18
15
18
15
12
18
25
54
25
species
6-31G(d,p)
ZPE 6-311G (2df,2p)
TS scission (equatorial) -310.419 936 413.4
-310.508 73
-310.509 62
-310.520 33
-150.372 86
-309.993 47
-150.959 19
TS scission (axial)
6-oxo-1-hexyl radical
O2
-310.420 72
-310.429 23
-150.319 13
-309.905 25
-150.904 00
414.3
406.8
9.9
396.8
37.0
1-C3H7O
2-C3H7O
cyclohexanone
HO2
2-C4H9O
are accurate, then the difference between the reactivity of O2
with cyclohexoxy and with acyclic alkoxy radicals must have
some physical/chemical basis. We note that cyclohexanone,
which is the product of the O2 reaction, possesses about 12 kJ/
mol of strain energy, whereas cyclohexoxy radical, itself, is
expected to have almost no strain energy.41 If this amount of
extra energy is present in the transition state for the O2 reaction
of cyclohexoxy and absent in the transition state for the O2
reactions of acyclic alkoxy radicals, it would neatly explain the
observed activation energy. It should be noted that tunneling is
believed to contribute significantly, or even to dominate, the
room-temperature rate constant,39,40 so that the Arrhenius
preexponential factor would be strongly affected by large
changes in the activation barrier.
3. Rate Constant for â C-C Scission. Tables 3 and 4 list
absolute and relative energies for the â C-C scission of the
axial and equatorial conformers of cyclohexoxy radical, and
Figure 5 shows the potential energy profile for â C-C scission
to produce 6-oxo-1-hexyl radical. The less stable axial conformer
possesses a lower barrier to â C-C scission. We carried out
RRKM/Master Equation calculations of the rate constant using
the B3LYP/6-31G(d,p) activation energies, which have previ-
ously proven more reliable than those obtained with larger basis
sets.34-37,51 RRKM calculations suggest Arrhenius expressions
for the C-C scission rate constant of the axial and equatorial
conformers at 1 atm of N2:
3-pentoxy
cyclohexoxy 5850 × 10-15
this work
presence of the NO generated by the photolysis of cyclohexyl
nitrite, O3 is produced:
HO2 + NO f OH + NO2
NO2 + hV f NO + O
O + O2 +M f O3 + M
(2)
(3)
(4)
This chemistry is the same as that which produces O3 in the
polluted atmosphere. The presence of radicals such as OH, HO2,
and atomic oxygen give rise to concerns about secondary
chemistry affecting the determination of kO2. However, the three
rate constants obtained using one-third the initial radical
concentration (at 239, 267, and 302 K) are indistinguishable
from those obtained at the higher radical concentration used in
most of the experiments. This makes it extremely unlikely that
secondary radical chemistry is affecting our determination of
kO2
.
Another source of secondary chemistry is the accumulation
of closed-shell (nonradical) reaction products such as cyclo-
hexanone. The cyclohexyl nitrite flows along the paths of the
photolysis and probe laser beams for ∼10 s before reaching
the area which is in the viewing zone of the photomultiplier
tube. To minimize accumulation of photoproducts, we repeated
the experiments using a perpendicular alignment of photolysis
and detecting lasers (at 238 K and 125 Torr). The rate constants
are (4.2 ( 0.2) × 10-15 cm3 molecule-1 s-1 for counter-
propagating alignment and (4.5 ( 0.7) × 10-15 cm3 molecule-1
s-1 for the perpendicular alignment, which is consistent within
the error bars. Also, a single experiment was carried out at 276
K and 50 Torr in which the data acquisition frequency was
increased from 2 to 3 Hz. The resulting rate constant of (1.4 (
0.4) × 10-14 cm3 molecule-1 s-1 at 3 Hz is virtually the same
as that obtained at 2 Hz: (1.4 ( 0.2) × 10-14 cm3 molecule-1
s-1. These results further confirm that the rate constants reported
here are not affected by secondary chemistry.
As noted previously and depicted in Figure 4, the kinetic
experiments used four different excitation (detection) wave-
lengths. Results from all four wavelengths are consistent within
the error bars. It is reasonable to conclude that all these peaks
in the LIF spectrum arise from cyclohexoxy radical. This result
is also consistent with our conclusion, based on the spectroscopic
analysis, that all major peaks are due to a single conformer
(axial).
kscission,axial ) 2.0 × 1013 exp[-47.5 kJ/mol/RT] s-1
kscission,equatorial ) 2.4 × 1013 exp[-50.5 kJ/mol/RT] s-1
As with any computed rate constant, the activation barriers have
considerable uncertainty, which we roughly estimate at 10 kJ/
mol (2 sd). Figure 6 shows the pressure dependence of the rate
constant for both conformers at 300 K; the pressure dependence
is modest over range from 50 to 760 Torr. As the pressure drops
from 760 to 50 Torr, the computed activation energy drops by
1-1.5 kJ/mol and the preexponential factor drops by a factor
of 2-2.5.
Ideally, we could obtain C-C scission rate constants from
experiment. One possible interpretation of the intercepts of our
plots of k′ versus [O2] (such as Figure 3) is that they represent
the rate of â C-C scission of the cyclohexoxy radical. To
evaluate this possibility, we plotted the natural logarithm of all
the intercepts (of our plots of k′ versus [O2]) versus 1/T in Figure
7. Although the plot is consistent with an Arrhenius temperature
dependence, the implied activation energy of ∼30 kJ/mol and
preexponential factor of 109.5(1.0 are far different than those
obtained by our calculation. At room temperature and 50 Torr,
the pseudo-first-order loss rate of about 1 × 104 s-1 is consistent
with the rate of C-C scission of axial cyclohexoxy radical
inferred from our computations (8 × 104 s-1, with an uncertainty
The above discussion suggests no obvious sources of error
that would explain the difference between the temperature
dependence we observe for cyclohexoxy radical and that
common to other secondary alkoxy radicals. If our observations

452 J. Phys. Chem. A, Vol. 108, No. 3, 2004
Zhang et al.
TABLE 4: B3LYP Reaction Enthalpies (∆Hr) and Activation Barriers (Eo) for â C-C Scission and O2 Reaction of
Cyclohexoxy Radical (kJ/mol)
∆Hr (0 K)
6-311G(2df,2p)
Eo
reaction
6-31G(d,p)
6-31G(d,p)
6-311G(2df,2p)
â scission (equatorial)
17.3
15.6
-125.7
3.5
2.4
-135.7
48.2
45.4
40.5
38.0
â scission (axial)
equatorial + O2 f cyclohexanone + O2
TABLE 5: Experimental Pressure Dependence of the Rate
Constant for Cyclohexoxy + O2 at Three Temperatures
T, K
total pressure, Torr
K, cm3 molecule-1 s-1
239
50
125
50
125
50
(4.2 ( 0.1) × 10-15
(4.5 ( 0.3) × 10-15
(1.4 ( 0.2) × 10-14
(1.3 ( 0.2) × 10-14
(2.0 ( 0.2) × 10-14
(2.3 ( 0.5) × 10-14
276
301
125
and â C-C scission for 273 K e T e 296 K:
Figure 5. Potential energy profile for the â C-C scission of the
equatorial and axial conformers of cyclohexoxy radical.
kO2/kscission ) (1.3 ( 0.3) × 10-27
exp[(46.1 ( 9.1) kJ/mol/RT] cm3 molecule-1 s-1
Based on this result and Atkinson’s recommendation for the
rate constant, kO2 ) 1.5 × 10-14 exp(-1.6 kJ/mol/RT) cm3
molecule-1 s-1, Orlando et al., calculated the Arrhenius expres-
sion for the â C-C scission reaction rate constant as
kscission
)
(1.2 ( 0.3) × 1013 exp[-(47.7 ( 9.1) kJ/mol/RT] s-1
The agreement between our theoretical results and the analysis
of Orlando, Iraci, and Tyndall is much better than could be
expected given the significant uncertainties inherent in both
values.
Just as Orlando, Iraci, and Tyndall use Atkinson’s recom-
mended value of kO2 to determine kscission, the present experi-
Figure 6. Pressure dependence of the rate constants for â C-C scission
of the axial and equatorial conformers of cyclohexoxy radical at 300
K.
mental results can also be combined with Orlando et al.’s kO2
/
kscission ratio to give
kscission
)
(4.5 ( 2.2) × 1015 exp[-(60.4 ( 9.5) kJ/mol/RT] s-1
The activation energy we infer from the relative rate measure-
ment of Orlando, Iraci, and Tyndall is somewhat higher than
the calculated value, but the difference is less than the combined
uncertainties. However, because the Arrhenius preexponential
for the O2 reaction determined here is about 300 times larger
than Atkinson’s recommended value, the inferred Arrhenius
preexponential factor for â C-C scission is about 300-400
times higher than that obtained by our theoretical calculation.
This dramatic difference is very disconcerting!
Let us consider some possible causes for this discrepancy.
The A-factor obtained by theory is very similar to those obtained
from previous experimental and computational studies,24,52
which strongly suggests that the error does not lie in the
theoretical work. One possible explanation is that the rate
constant for the cyclohexoxy + O2 reaction, unlike those for
other alkoxy radicals, is different at 50 Torr (where our
measurements were made) than at 1 atm (where Orlando et al.
made their measurements). We therefore remeasured the rate
constant for the cyclohexoxy + O2 reaction at 125 Torr at three
temperatures, 239, 276, and 301 K. As can be seen from Table
5, the measured rate constant is essentially unchanged by this
Figure 7. Arrhenius plot showing the temperature dependence of the
intercepts of our plots of pseudo-first-order rate constant versus the O2
concentration at two total pressures (50 and 125 Torr) and two
concentrations of cyclohexyl nitrite at 50 Torr total pressure.
of at least a factor of 10). At lower temperatures, the intercepts
are much higher than the computed rate of C-C scission. It is
reasonable to think that C-C scission is contributing to the
intercepts of our plots of k′ versus [O2] but that other chemical
losses must also be important, particularly at low temperatures.
Orlando, Iraci, and Tyndall6 experimentally measured the
ratio, kO2/kscission, of the reaction rate constants for O2 reaction

Spectra of Cyclohexoxy Radical
J. Phys. Chem. A, Vol. 108, No. 3, 2004 453
increase in pressure. This result strongly suggests that the rate
constant is not significantly different at 1 atm than at 50 Torr.
Another possible cause of this discrepancy arises from the
presence of two conformers of cyclohexoxy radical or their
interconversion on time scale of our experiment. Our experi-
mental spectrum is consistent with the computed spectrum of
the axial conformer of cyclohexoxy radical. In our experiments,
the time scale for kinetic measurements is 5-400 µs. The barrier
to axial-equatorial interchange (inversion) of substituted cy-
clohexanes (in solution) is about 45 kJ/mol and the Arrhenius
If our interpretation of the LIF spectra as being due to a single
conformer is correct, it is not valid to compare our kinetic results
to those of Orlando, Iraci, and Tyndall. A proper comparison
would probably require knowledge of the temperature and
pressure dependence of the rate of the axial-equatorial conver-
sion in cyclohexoxy radical, confirmation (or correction) of our
assignment of the spectrum to the axial conformer, and, perhaps,
direct studies of the rate of the â scission reaction.
Acknowledgment. This research was supported by the
National Science Foundation under Grant ATM-0087057 and
by a Research Experience for Undergraduates supplement for
K. A. K. This research was further supported by the National
Computational Science Alliance under Grant ATM010003N,
utilizing the HP-N4000 cluster at the University of Kentucky.
We thank B. S. Hudson for the loan of the hardware for data
acquisition, and J. Liu and T. A. Miller for permission to report
a portion of their results prior to publication. We thank T. A.
Miller and K. M. Callahan for helpful discussions, R. Atkinson,
A. R. Ravishankara, S. P. Sander, and C. Anastasio for forcefully
questioning our first explanations for the apparent discrepancy,
and the anonymous reviewers for many very helpful comments.
preexponential factor is inferred to be 3 × 1013 s-1 41,53
.
At 225
K, the implied lifetime of the inversion reaction is ∼1 ms, so
our observations are probably undisturbed by the interconver-
sion. At 250 K and higher, the implied lifetime for the inversion
reaction is comparable to, or shorter than, the time scale of our
kinetic measurements (using rate parameters obtained from
solution phase). However, if conformational interchange was
affecting the concentration of the axial conformer, we would
expect to see nonlinearities in some of our plots of ln(intensity)
versus time or strongly non-Arrhenius behavior of the ln(k)
versus 1/T plot. Since we observe neither of these behaviors,
we conclude that conformational interchange is not affecting
our kinetic results.
References and Notes
Let us take a closer look at the determinations of kscission from
the relative rate data. The original data of Orlando, Iraci, and
Tyndall consists of relative rate measurements at four temper-
atures in the range 273-296 K, each with uncertainties (2 sd)
of ∼40%. The uncertainty they assigned to the Arrhenius
preexponential factor was explicitly stated to be that of the 296
K data, rather than being derived from statistical analysis.
Because of the limited temperature range spanned by the relative
rate data, a more realistic estimate of the uncertainty in the fitted
Arrhenius preexponential factor is a factor of 10. Another issue
is that the results of the relative rate experiments necessarily
reflect some averaging of the reactivity of both conformers. The
two conformers could have significantly different rates of
reaction with O2, and our calculations suggest they have
significantly different rates of â C-C scission reactions. Our
spectra, and therefore, our kinetic results, seem to arise only
from the less stable (axial) conformer; if so, it is not valid to
combine our value of kO2 with the relative rate constants in order
to extract a rate constant for C-C scission.
(1) Atkinson, R. J. Phys. Chem Ref. Data Monograph No. 2 1994.
(2) Atkinson, R. Int. J. Chem. Kinet. 1997, 29, 99.
(3) Jenkin, M. E.; Hayman, G. D. Atmos. EnViron. 1999, 33, 1275.
(4) Schauer, J.; Kleeman, M.; Cass, G.; Simoneit, B. R. T. EnViron.
Sci. Technol. 2002, 36, 1169.
(5) Platz, J.; Sehested, J.; Nielsen, O. J. J. Phys. Chem. A 1999, 103,
2688.
(6) Orlando, J. J.; Iraci, L. T.; Tyndall, G. S. J. Phys. Chem. A 2000,
104, 5072.
(7) Aschmann, S. M.; Chew, A. A.; Arey, J.; Atkinson, R. J. Phys.
Chem. A 1997, 101, 8042.
(8) Takagi, H.; Washida, N.; Bandow, H.; Akimoto, H.; Okuda, M. J.
Phys. Chem. 1981, 85, 2701.
(9) Sanders, N.; Butler, J. E.; Pasternack, L. R.; McDonald, J. R. Chem.
Phys. 1980, 48, 203.
(10) Gutman, D.; Sanders, N.; Butler, J. E. J. Phys. Chem. 1982, 86,
66.
(11) Lorenz, K.; Rhasa, D.; Zellner, R.; Fritz, B. Ber. Bunsen-Ges. Phys.
Chem. 1985, 89, 341.
(12) Balla, R.; Nelson, H. H.; McDonald, J. R. Chem. Phys. 1985, 99,
323.
(13) Hartmann, D.; Karthauser, J.; Sawerysyn, J. P.; Zellner, R. Ber.
Bunsen-Ges. Phys. Chem. 1990, 94, 639.
(14) Frost, M. J.; Smith, I. W. M. J. Chem. Soc., Faraday Trans. 1990,
86, 1757.
(15) Mund, C.; Fockenberg, C.; Zellner, R. Ber. Bunsen-Ges. Phys.
IV. Conclusion
We have reported the first observation of the LIF excitation
spectrum of cyclohexoxy radical. The spectrum is consistent
with a single conformer and comparison of the calculated and
experimental spectrum suggests that the dominant features in
the spectrum arise from the axial conformer of the cyclohexoxy
radical. A direct study of the rate constant for cyclohexoxy
radicals reacting with O2 has been carried out using LIF to
monitor the disappearance of cyclohexoxy radicals. The activa-
tion energy for kO2 is markedly higher than expected, a result
which may arise from strain energy in the transition state.
Our theoretical calculation of the rate constant for â C-C
scission, kscission, is similar to that inferred by Orlando, Iraci,
and Tyndall from their experimental measurement of kO2/kscission
and Atkinson’s recommended kO2. However, using our kO2 and
Orlando’s kO2/kscission, the calculated Arrhenius preexponential
factor for kscission appears inconsistent with our calculations or
with values found for other alkoxy radicals. The discrepancy
between the Arrhenius preexponential factor derived from
calculation and inferred by comparison of our kO2 and Orlando’s
Chem. 1998, 102, 709.
(16) Devolder, P.; Fittschen, Ch.; Frenzel, A.; Hippler, H.; Poskrebyshev,
G.; Striebel, F.; Viskolcz, B. Phys. Chem. Chem. Phys. 1999, 1, 675.
(17) Caralp, F.; Devolder, P.; Fittschen, C.; Gomz, N.; Hippler, H.;
Mereau, R.; Rayez, M. T.; Striebel, F.; Viskolcz, B. Phys. Chem. Chem.
Phys. 1999, 1, 2935.
(18) Fittschen, C.; Frenzel, A.; Imrik, K.; Devolder, P. Int. J. Chem.
Kinet. 1999, 31, 860.
(19) Wang, C.; Shemesh, L. G.; Deng, W.; Lilien, M. D.; Dibble, T. S.
J. Phys. Chem. A. 1999, 103, 8207.
(20) Wang, C.; Deng, W.; Shemesh, L. G.; Lilien, M. D.; Katz, D. R.;
Dibble, T. S. J. Phys. Chem. A. 2000, 104, 10368.
(21) Deng, W.; Wang, C. J.; Katz, D. R.; Gawinski, G. R.; Davis, A. J.;
Dibble, T. S. J. Phys. Chem. A 2000, 104, 10368.
(22) Blitz, M.; Pilling, M. J.; Robertson, S. H.; Seakins, P. W. Phys.
Chem. Chem. Phys. 1999, 1, 73.
(23) Fittschen, C.; Hippler, H.; Viskolcz, B. Phys. Chem. Chem. Phys.
2000, 2, 1677.
(24) Lotz, C.; Zellner, R. Phys. Chem. Chem. Phys. 2000, 2, 2353.
(25) Deng, W.; Davis, A. J.; Zhang, L.; Katz, D. R.; Dibble, T. S. J.
Phys. Chem. A. 2001, 105, 8985.
(26) Carter, C. C.; Gopalakrishnan, S.; Atwell, J. R.; Miller, T. A. J.
Phys. Chem. A 2001, 105, 2925.
(27) Gopalakrishnan, S.; Carter, C. C.; Zu, L.; Stakhursky, V.; Tarczay,
G.; Miller, T. A. J. Chem. Phys. 2003, 118, 4954.
k
O2/kscission is due, at least in part, to the uncertainty in the
Arrhenius preexponential factor for kO2/kscission
.

454 J. Phys. Chem. A, Vol. 108, No. 3, 2004
Zhang et al.
(28) Gopalakrishnan, S.; Zu, L.; Miller, T. A. J. Phys. Chem A 2003,
107, 5189.
(29) Blatt, A. H. Organic Syntheses; Wiley: New York, 1966; pp 108-
109.
(30) Typical alkylnitrite IR and NMR spectra may be found in the Sadtler
Index, Bio-Rad Laboratories Inc., 1973.
(31) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G.
A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski,
V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P. Head-
Gordon, M. Gonzalez, C. Pople, J. A. Gaussian98, Revision D.3 Gaussian,
Inc.: Pittsburgh, PA, 1995.
(40) Setokuchi, O.; Sato, M. J. Phys. Chem. A 2002, 106, 8124.
(41) Eliel, E. L.; Wilen, S. H. Stereochemistry of Organic Compounds;
Wiley: New York, 1994.
(42) Powers, D. E.; Pushkarsky, M.; Miller, T. A. J. Chem. Phys. 1997,
106, 6863.
(43) Tan, X. Q.; Williamson, J. M.; Foster, S. C.; Miller, T. A. J. Phys.
Chem. 1993, 97, 9311.
(44) Foster, S. C.; Misra, P.; Lin, T. Y.; Damo, C. P.; Carter, C. C.;
Miller, T. A. J. Phys. Chem. 1988, 92, 5914.
(45) Liu, X.; Damo, C. P.; Lin, T. Y.; Foster, S. C.; Mistra, P.; Yu, L.;
Miller, T. A. J. Phys. Chem. 1989, 93, 2266.
(46) Powers, D. E.; Pusharsky, M.; Miller, T. A. J. Phys. Chem. 1997,
106, 6863.
(47) Inoue, G.; Akimoto, H.; Okuda, M. Chem. Phys. Lett. 1979, 63,
(32) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785.
(33) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
213.
(48) Ohbayashi, K.; Akimoto, H.; Tanaka, I. J. Phys. Chem. 1977, 81,
(34) Orlando, J. J.; Tyndall, G. S.; Bilde, M.; Ferronato, C.; Wallington,
T. J.; Vereecken, L.; Peeters, J. J. Phys. Chem. A 1998, 102, 8116.
(35) Dibble, T. S. J. Phys. Chem. A 1999, 103, 8559.
(36) Dibble, T. S. Chem. Phys. Lett. 1999, 301, 297.
(37) Peeters, J.; Fantechi, G.; Vereecken, L. J. Atmos. Chem., submitted
2003.
(38) Gilbert, R. G.; Smith, S. C.; Jordan, M. J. T. UNIMOL program
suite (calculation of falloff curves for unimolecular and recombination
reactions), 1993. Available from the authors: School of Chemistry, Sydney
University, NSW 2006, Australia. E-mail: gilbert_r@summer.chem.su.oz.au.
(39) Bofill, J. M.; Olivella, S.; Sole´, A.; Anglada, J. M. J. Am. Chem.
Soc. 1999, 121, 1337.
798.
(49) Wendt, H. R.; Hunziker, H. E. J. Phys. Chem. 1979, 71, 5202.
(50) Liu, J.; Miller, T. A., manuscript in preparation.
(51) Jungkamp, T. P. W.; Smith, J. N.; Seinfeld, J. H. J. Phys. Chem.
A 1997, 101, 4392;
(52) Devolder, P. J. Photochem. Photobiol A 2003, 157, 137.
(53) Carey, F. A.; Sundberg, R. J. AdVanced Organic Chemistry, 2nd
ed.; Part A: structure and mechanisms.
(54) Zellner, R.; Lotz, Ch. In Transport and Chemical Transformation
in the Troposphere, Proceedings of the 7th EUROTRAC Symposium, 2002;
Midgley, P.M., Reuther, M., Eds.; pp 464-467.