The β C-C bond scission in alkoxy radicals: Thermal unimolecular decomposition of t-butoxy radicals

Article abstract of DOI:10.1039/b000009o

The temperature and pressure dependence of the unimolecular decomposition of t-butoxy radicals was studied by the laser photolysis/laser induced fluorescence technique. Experiments have been performed at total pressures between 0.04 and 60 bar of helium and in the temperature range 323- 383 K. The low and the high pressure limiting rate constants as well as the broadening factor F(c) have been extracted from a complete falloff analysis of the experimental results: k₀ = [He] x 1.5 x 10^-8 exp(- 38.5 kJ mol^{- 1}/RT) cm³ s^-1, k∞ = 1.0 x 10¹⁴ exp(-60.5 kJ mol^-1/RT) s^-1, and F(c) = 0.87 - T/870 K. We anticipate an uncertainty for these rate constants of ± 30%. Important features of the potential energy surface have been computed by ab initio methods. The Arrhenius parameters for the high pressure limiting rate constant for the β C-C bond scission of t-butoxy radicals have been computed from the properties of a transition state based on the results of G2(MP2) ab initio calculation. The results from density functional theory (DFT) with a small basis set (B3LYP/SVP) are very similar. Excellent agreement between the calculated and the experimental rate constants has been found. We suggest a common pre-exponential factor for β C-C bond scission rate constants of all alkoxy radicals of A = 10(14±0.3) s^-1. Thus we express the high pressure limiting rate constant for ethoxy and i-propoxy radicals by k∞ = 1.0 x 10¹⁴ exp(-78.2 kJ mol^-1/RT) and 1.0 x 10¹⁴ exp(-63.1 kJ mol^-1/RT) s^-1, respectively. For the reverse reactions, the addition of CH₃ radicals to CH₂O, CH₃CHO, and (CH₃)₂CO, we obtained activation enthalpies of 32, 42, and 52 kJ mol^-1, respectively.

Full text of DOI:10.1039/b000009o

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The b C–C bond scission in alkoxy radicals: thermal unimolecular
decomposition of t-butoxy radicals
Christa Fittschen,a Horst Hippler*b and Bela Viskolczb
a L aboratoire de Cinetique et Chimie de la CombustionÈUMR 8522, Centre dÏEtudes et de
Recherches L asers et Applications Universite de L ille 1, F-59655 V illeneuve dÏAscq Cedex,
France
b L ehrstuhl fur Molekulare Physikalische Chemie, Universitat Karlsruhe, Kaiserstrasse 12,
D-76128 Karlsruhe, Germany. E-mail: horst.hippler=chemie.uni-karlsruhe.de;
Fax: ]49 721 608 6524; T el: ]49 721 608 3301
Received 4th January 2000, Accepted 11th February 2000
The temperature and pressure dependence of the unimolecular decomposition of t-butoxy radicals was studied
by the laser photolysis/laser induced Ñuorescence technique. Experiments have been performed at total
pressures between 0.04 and 60 bar of helium and in the temperature range 323È383 K. The low and the high
pressure limiting rate constants as well as the broadening factor F have been extracted from a complete fallo†
c
analysis of the experimental results: k \ [He] ] 1.5 ] 10~8 exp([38.5 kJ mol~1/RT ) cm3 s~1, k \ 1.0
0
=
] 1014 exp([60.5 kJ mol~1/RT ) s~1, and F \ 0.87 [ T /870 K. We anticipate an uncertainty for these rate
constants of ^30%. Important features of the potential energy surface have been computed by ab initio
c
methods. The Arrhenius parameters for the high pressure limiting rate constant for the b CÈC bond scission of
t-butoxy radicals have been computed from the properties of a transition state based on the results of
G2(MP2) ab initio calculation. The results from density functional theory (DFT) with a small basis set
(B3LYP/SVP) are very similar. Excellent agreement between the calculated and the experimental rate
constants has been found. We suggest a common pre-exponential factor for b CÈC bond scission rate
constants of all alkoxy radicals of A \ 1014B0.3 s~1. Thus we express the high pressure limiting rate constant
for ethoxy and i-propoxy radicals by k \ 1.0 ] 1014 exp([78.2 kJ mol~1/RT ) and 1.0 ] 1014 exp([63.1 kJ
=
mol~1/RT ) s~1, respectively. For the reverse reactions, the addition of CH radicals to CH O, CH CHO, and
3
2
3
(CH ) CO, we obtained activation enthalpies of 32, 42, and 52 kJ mol~1, respectively.
3 2
and i-propoxy9 the radical center is connected to a primary
and secondary carbon atom, respectively. The t-butoxy radical
is a prototype for the b CÈC bond dissociation of larger
alkoxy radicals since b CÈH bond dissociation does not exist
and 1,3-hydrogen transfer isomerizations are energetically dis-
favored because of the high strain energy of the cyclic tran-
sition state resulting in a threshold energy about 40 kJ mol~1
higher than for the b CÈC bond dissociation.
Introduction
In the photo-oxidation of saturated hydrocarbons in the
atmosphere alkoxy radicals are important intermediates from
NO oxidation to NO . Low temperature combustion as well
2
as pyrolysis of oxygen containing compounds proceed via
alkoxy radicals. Therefore, many experimental studies have
been devoted to alkoxy radical reactions and several review
articles have appeared.1h5 Earlier data on the decomposition
of alkoxy radicals are mainly based on the work of Batt2 and
were focused on atmospheric pressure conditions.6,7
Recently, new experimental8h11 and theoretical12h14 studies
have been carried out on the unimolecular reactions of alkoxy
radicals. It was found that for ethoxy, i-propoxy and t-butoxy
the b CÈC bond dissociation dominates over all other intra-
molecular processes. For ethoxy11 and i-propoxy,9 the fallo†
is centered near 1 bar and the studied pressure range extends
over several orders of magnitude in pressure up to 60 bar.
Also for the t-butoxy radical decomposition a pressure depen-
dence has been reported15h18 and recently8 it was found that
the fallo† was centered near 200 mbar. However, since t-
butoxy is a relatively large radical we expected a broad fallo†
range and the pressure dependence to continue above atmo-
spheric pressure.
t-C H O~ ] M ] ~CH ] CH COCH ] M
(1)
4
9
3
3
3
The ab initio study of the potential energy surface for two
di†erent decomposition channels enabled us to theoretically
analyze the fallo† curves and also to predict the high pressure
limiting rate constant from a RRKM calculation using a
simple transition state model (TST).
In the present work we have investigated the decomposition
of t-butoxy radicals at di†erent temperatures over several
orders of magnitude in pressure. Our intention was to experi-
mentally access most of the fallo† range which will then allow
for a reliable determination of the limiting high and low pres-
sure rate constants. We combined our experiments with ab
initio calculations and identiÐed the unimolecular b CÈC bond
scission as the dominant decomposition channel. The experi-
mental high pressure limiting rate constant will be compared
to the result from a simple RRKM calculation using the ab
initio transition state. The analysis of the low pressure limiting
rate constant should deliver valuable information on the col-
lisional energy transfer. Based on our present and earlier
This study on the thermal decomposition of t-butoxy rad-
icals completes the di†erent cases for b CÈC bond dissociation
of alkoxy radicals. In t-butoxy the radical center at the oxygen
atom is connected to a tertiary carbon atom while in ethoxy11
DOI: 10.1039/b000009o
Phys. Chem. Chem. Phys., 2000, 2, 1677È1683
This journal is ( The Owner Societies 2000
1677

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experimental results on the b CÈC bond scission of alkoxy
radicals, we predict Arrhenius parameters for b CÈC bond
cleavage of many other alkoxy radicals and also for the corre-
sponding reverse reaction.
Experimental
Experiments have been performed by laser Ñash photolysis
(LFP) of t-butylnitrite (t-C H ONO) under high helium pres-
4
9
sures (0.04È60 bar) and t-butoxy radicals were detected by
laser induced Ñuorescence. Details of the experimental set-up
have been described recently9,11 so only some principal fea-
tures are given here:
Like all alkyl nitrites, t-butylnitrite has two absorption
bands in the UV region particularly suitable for excimer laser
photolysis: one broad band with a maximum at 223 nm and a
decadic absorption coefficient of e(223 nm) \ 1750 l mol~1
cm~1 and a second weaker and more structured transition
near 360 nm [e(353.6 nm) \ 37 l mol~1 cm~1].19 The t-
butylnitrite has mostly been photolysed at 351 nm and only
few experiments with 248 nm photolysis have been performed.
However, at low pressures thermalization of the t-butoxy rad-
icals from 248 nm photolysis could not be achieved.
Fig. 2 Fluorescence lifetime q of t-butoxy radicals excited at 335
fl
nm as a function of the precursor concentration (T \ 323 K; …:
p(He) \ 26 Torr; >: p(He) \ 100 Torr; =: p(He) \ 316 Torr; +:
p(He) \ 737 Torr).
found to be q \ (1.0 ^ 0.1) ] 10~6 s. As seen in Fig. 2 quen-
rad
ching is more or less independent on helium addition between
26 and 737 Torr and we estimate an upper limit of the quen-
ching rate constant at room temperature of k
\ 5 ] 10~15
q, He
The photolysis laser beam (Lambda Physik LPX 202i) was
focused with two cylindrical lenses, leading to average pulse
energies of 50 mJ cm~2 at 351 nm. The t-C H ONO concen-
cm3 s~1. Our radiative lifetime is much longer than previously
reported lifetimes of 500 ns by Blitz et al.8 and of 150 ns by
Wang et al.20 The shorter lifetimes might result from the effi-
cient quenching by the parent molecules or from uncompleted
thermalization of the t-butoxy radicals when the excitation
laser has been Ðred.
4
9
trations have been varied up to 5 ] 1015 cm~3. With a
decadic absorption coefficient of e(351 nm) \ 27 l mol~1
cm~119 and an assumed photodissociation quantum yield of
unity the t-C H O~ radical concentration was always below
The t-butylnitrite (Aldrich, 96%) was used without further
puriÐcation after extensive degasing in various freeze pump
cycles. Gaseous mixtures, highly diluted in He, did not mark-
edly decompose at room temperature in a darkened glass bulb
or stainless steel cylinder. The carrier gas He (99.995%, Air
Liquide) was used without further puriÐcation.
The helium pressure in the experiments extended from 0.04
to 60 bar and the temperature range was restrained between
323 and 383 K. At the high temperature limit t-butoxy radical
decomposition approached the time resolution of the experi-
ments while below the low temperature limit unimolecular
decomposition could no longer be separated from t-butoxy
loss in bimolecular reactions.
4
9
4.5 ] 1013 cm~3.
We followed the temporal evolution of the t-C H O~
4
9
radical concentration by laser induced Ñuorescence (LIF),
excited near 335 nm. The Ñuorescence was collected perpen-
dicular to the Ñuorescence excitation laser beam through a
cut-o† Ðlter at j [ 375 nm. The room temperature Ñuores-
cence excitation spectrum has been normalized with respect to
the energy of the excitation laser pulse and is displayed in Fig.
1. As expected, the structure in our spectrum is much more
congested compared to the low temperature spectra at 203 K
from Blitz et al.8 and at 213 K from Wang et al.20 The Ñuores-
cence lifetime q is given by the following expression:
fl
q~1 \ q~1 ] k [t [ C H ONO] ] k
[He]
(2)
fl
rad
q
4 9
q, He
Theoretical methods
in which q is the radiative lifetime and k and k
are the
rad
q
q, He
Ñuorescence quenching rate constant with the precursor t-
butylnitrite and with He, respectively. Quenching by t-
butylnitrite was very efficient and from the shortening of the
Ñuorescence lifetime (see Fig. 2) we found a rate constant of
Di†erent theoretical methods were tested in two recent papers
to obtain reliable potential energy surfaces for b CÈC bond
dissociation of ethoxy11 and i-propoxy radicals.9 Consequent-
ly, we selected the modiÐed G2(MP2) method for the t-butoxy
decomposition, expecting the most accurate results. All ab
initio calculations were carried out using the GAUSSIAN 94
program package.21
k \ (4.3 ^ 0.2) ] 10~10 cm3 s~1. The radiative lifetime was
q
The equilibrium geometries, transition structures, and har-
monic vibrational frequencies were obtained on the MP2/6-
311G** level. The height of the barriers were calculated from
the classical barrier heights (obtained as the ab initio energy
di†erences) by adding the di†erence of the vibrational zero-
point energies scaled by the factor of 0.9748 as recommended
by Scott and Radom22. Activation enthalpies were obtained
by adding the thermal contributions. The standard enthalpy
of reaction at 298.15 K was taken as the enthalpy di†erence
between the products and the t-butoxy radical.
For comparison we also performed DFT calculations as
undertaken before for the ethoxy radical.11 We found again
that extended basis sets deÐnitely underestimate the barrier
heights and reaction enthalpies and that the predicted tran-
sition state structures are relatively loose. These loose tran-
sitions states will lead to an overestimation of the
preexponential factor of the high pressure limiting dissociation
Fig. 1 Fluorescence excitation spectrum of t-butoxy radicals at
298 K.
1678
Phys. Chem. Chem. Phys., 2000, 2, 1677È1683

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rate constant. However, very good agreement with energies
from the expensive G2(MP2) method has been obtained using
the much cheaper B3LYP hybrid functional23 combined with
the SVP basis set from Ahlrichs and co-workers.24
Results
Experimental results
Under our experimental conditions t-butoxy radicals decay
predominantly by unimolecular decomposition in reaction (1)
and to a lesser extent by a bimolecular reaction with the pre-
cursor
t-C H O~ ] t-C H ONO ] other products
(3)
4
9
4 9
Accordingly, the t-butoxy radical decay follows a pseudo-Ðrst-
Fig. 4 Pseudo-Ðrst-order rate constant k as a function of precur-
obs
order rate law
sor concentrations (T \ 323 K; >: p(He) \ 7500 Torr; =:
p(He) \ 200 Torr; …: p(He) \ 30 Torr).
d[t-C H O~]
4
9
\ [k [t-C H O~]
obs
(4)
4
9
dt
the b CÈC bond scission and the 1,3 hydrogen atom shift. It
has been shown that the 1,3 isomerization transition states for
the ethoxy10 and the n-butoxy radical13 contain high strain
energies. We conclude, that for the t-butoxy radical the situ-
ation is similar and that under our conditions only the b CÈC
bond scission has to be considered.
The calculated MP2/6-311G(d,p) optimized geometries of
the t-butoxy radical and the transition state (TS) are shown in
Fig. 6. At the transition state the length of the breaking CÈC
bond has increased by about 30%, with respect to its lengths
in the parent radical while the length of the CÈO bond has
already shortened and approaches the characteristic length of
the CÈO double bond. All other bond lengths remain almost
unchanged during the reaction. The transition state structure
is very much product-like as found previously for the b CÈC
where the total pseudo-Ðrst-order rate constant k is given
by
obs
k
\ k ] k [t-C H ONO].
(5)
obs
1
3
4 9
Total pseudo-Ðrst order rate constants k for the t-butoxy
radical decay were obtained from plots of the Ñuorescence
yields vs. the delay time between the two laser pulses. Typical
decay curves of the t-C H O~ Ñuorescence yield at 323 K and
obs
4
9
di†erent total pressures are shown in Fig. 3.
The inÑuence of reaction (3) on the total pseudo-Ðrst-order
rate constant has carefully been investigated by running
experiments with di†erent precursor concentrations at all
pressures
and
temperatures.
The
pseudo-Ðrst-order
has been
unimolecular decomposition rate constant
obtained by an extrapolation of k to a zero precursor con-
centration. An example of this procedure at 323 K and di†er-
k
1
obs
ent total pressures is shown in Fig. 4. We obtained for the rate
constant k \ (5 ^ 2) ] 10~12 cm3 s~1, temperature indepen-
3
dent between 323 and 383 K. The extrapolation of k was
obs
always straightforward but at low temperatures the relative
contribution of reaction (3) to k was generally larger than at
obs
high temperatures. The experimental conditions and the
results of this procedure are represented in the supplementary
Table S1.¤ The individual fallo† curves for the Ðrst-order
decomposition rate constant k are illustrated in Fig. 5.
1
Ab initio calculations
There is a large variety of possible decomposition channels of
the t-butoxy radical. The two energetically lowest channels are
Fig. 5 Fallo† curves of the Ðrst-order rate constants k at di†erent
1
temperatures (= and K: T \ 383 K; … and L: T \ 363 K; > and
|: T \ 343 K; + and ): T \ 323 K; lines: best Ðt by eqn. (6) using
the fallo† parameters from Table 2; full symbols: this work; open
symbols: ref. 8).
Fig. 3 Decay of t-butoxy Ñuorescence yields at di†erent helium pres-
sures [T \ 323 K; K: 30 Torr; |: \ 219 Torr; =: \ 750 Torr; solid
lines: best Ðt according to eqn. (4)].
Fig. 6 Equilibrium geometry of the t-butoxy radical and structure of
the transition state for the decomposition channel (1) optimized by
MP2/6-311G**.
¤ Available as electronic supplementary information. See http://
www.rsc.org/suppdata/cp/b0/b000009o
Phys. Chem. Chem. Phys., 2000, 2, 1677È1683
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bond scission in ethoxy11 and in i-propoxy.9 The TS geometry
from the B3LYP/SVP method is somewhat more product-like
than from the optimized MP2/6-311G(d,p) calculation.
by Troe et al.30,31
A
k
B A
k
/k
B
log F
1
1, 0 1, =
c
log
\ log
]
k
1 ] k /k
1 ] (log(k /k )/N)2
The reaction barriers (E ), activation enthalpies [*H0E (298
1, =
1, 0 1, =
1, 0 1, =
0
K)], and activation entropies [*S0E (298 K)] obtained at
(6)
various levels of theory are presented in Table 1. There are
signiÐcant di†erences in the barriers heights from various
levels of theory. The lowest barrier of b CÈC bond scission
was always predicted by DFT with the extended basis set.
However, the barrier predicted by B3LYP with smaller basis
sets is in very good agreement with the higher level G2(MP2)
barrier. The agreement between the barriers for the reverse
reaction from the various methods was not very good. The
reasons can be found in the reaction enthalpies which are cor-
rectly predicted to be positive by QCISD(T) and G2(MP2)
and incorrectly predicted to be negative by the DFT and MP2
methods. The activation entropies [*S0E (298 K)] using the
di†erent TS geometries and the scaled vibrational frequencies
were always about 3 J mol~1 K~1 higher from the DFT cal-
culation than from the MP2/6-311G** method.
In this expression the parameters k , k
and F are
1, 0 1, =
C
respectively the low pressure rate constant, the high pressure
rate constant and the broadening factor. The procedure of the
analysis of the experimental results has been described in
detail in previous publications.9,11
The experimental results allow for a reliable determination
of the high pressure limiting rate constants (see Fig. 5) which
are also given in Table 2. We represent these rate constants in
an Arrhenius expression and account for an uncertainty in the
rate constant of ^30% comprehending essentially the reli-
ability of the fall o† extrapolation:
k
\ 1.0 ] 1014 exp([60.5 kJ mol~1/RT ) s~1
1, =
(323 K \ T \ 383 K) (7)
The ab initio reaction enthalpies are also listed in Table 1.
From standard reference data bases the reaction enthalpy
* H¡ (298 K) \ 19.2 kJ mol~1 is obtained, using * H¡ (CH ,
Our high pressure Arrhenius parameters are slightly di†erent
from the values given by Blitz et al.8 Presumably this di†er-
ence has its source in the smaller range of pressure covered by
Blitz et al. It should be pointed out that the experimental
accessible temperature range is much too small to reliably
separate the A-factor from the activation energy. We therefore
Ðxed the A-factor to A \ 1.0 ] 1014 s~1 in agreement with the
transition state model from the ab initio calculations (see
below). Although the absolute rate constants of the two
studies agree reasonably well, it should be pointed out that
our dissociation rate constants are moderately and systemati-
cally higher than the values from Blitz et al.8 (see Fig. 5). The
reason for this di†erence is yet unknown and may be due to
slightly di†erent temperatures in the two experiments. It is
very well known that fast gas Ñows into thermalized reactors
do not instantaneously thermally equilibrate. To check this we
have varied the Ñow rate at constant pressure and carefully
determined the rate of unimolecular decomposition as pre-
viously undertaken for the i-propoxy radical.9 At low Ñow
rates we found a constant Ñow independent t-butoxy decom-
position rate which considerably decreased with increasing the
Ñow rate thus reÑecting incomplete heating of the gas Ñow.
We conclude that the systematic di†erence in the two experi-
mental results is in conformity with a temperature di†erence
of about 3 K in the two experimental arrangements.
R
f
3
298 K) \ 145.5,25,26 * H¡(t-C4H9O, 298 K) \ [90.8,27 and
f
* H¡(acetone, 298 K) \ [217.1 kJ mol~1,28 respectively.
f
From our G2(MP2) calculation we obtain a reaction enthalpy
of * H¡ (298 K) B 7.4 kJ mol~1 which is about 12 kJ mol~1
R
lower. For comparison, we computed the standard enthalpy of
formation of t-C H O radicals by the modiÐed G2(MP2)
4
9
method combined with the tabulated heat of formation of the
atoms. We obtained * H¡ (t-C H O, 298 K) \ [81.3 kJ
f
4 9
mol~1 about 10 kJ mol~1 higher than the recommended
value in ref. 27. For comparison, similarly 10 kJ mol~1 higher
heats of formation of ethoxy11 and i-propoxy9 radicals than
currently accepted have recently been found. These higher
values are in close agreement with results from ab initio calcu-
lations of the heats of formation of alkoxy radicals within the
Gaussian-n29 series.
Discussion
The fallo† analysis of the t-butoxy decomposition rate con-
stant is straightforward since we know from our ab initio
treatment that the b CÈC bond scission is the energetically
distinctly favored pathway. We therefore describe the experi-
mentally obtained fallo† curves by the expression developed
Table 1 Activation barriers E , activation enthalpies *H0E(298 K), activation entropies *S0E(298 K) and standard reaction enthalpies
0
* H0(298 K) of the CÈC bond dissociation as well as the high pressure limiting rate constant (energies and enthalpies in kJ mol~1; entropies in J
R
K~1 mol~1)
Method
E
*H0E(298 K)
*S0E(298 K)
* H0(298 K)
k /103 s~1 (T \ 323 K)
0
R
=
B3LYP/SVP
56.7
49.4
79.6
67.5
69.8
57.6
58.3
50.5
80.8
68.7
70.9
58.8
54.5
58.0
14.0
11.0
11.0
11.0
11.0
11.0
14
170
0.002
0.2
0.09
7.8
B3LYP/6-311 ] G(3df,2p)a
MP2/6-311G(d,p)a
MP2/6-311 ] G(3df,2p)a
QCISD(T)/6-311G(d,p)a
G2(MP2)-likea
Experiment (ref. 7)
This work
[9.6
[1.8
[8.5
14.1
7.4
8.4
18
a MP2/6-311G(d,p) geometries and frequencies.
Table 2 Fallo† parameters for the thermal decomposition of the t-butoxy radical for di†erent temperatures
T /K
(k /[He])/10~14 cm3 s~1
k
/104 s~1
F
b
[S*ET /cm~1
1, 0
1, =
c
c
all
323
343
363
383
0.90
1.78
4.41
9.32
1.75
6.14
18.8
48.4
0.50
0.47
0.45
0.43
0.050
0.040
0.0345
0.031
21
18
17
16
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The high pressure limiting rate constant has almost been
reached at the highest pressures of 60 bar helium. We
analyzed this rate constant in terms of a simple transition
state theory analysis.
temperature range of our experiments does not allow for a
good separation of the pre-exponential factor from the activa-
tion energy of eqn. (9). The agreement with the recently
published extrapolated low pressure expression8 is satisfactory
although our A-factor is about 10 times higher, which is
mostly compensated by our 6 kJ mol~1 higher activation
energy. In Fig. 8 we compare the strong collision as well as
the weak collision low pressure rate constants as a function of
temperature.
k T
h
A
*SE0B A *HE0
B
B
k
\
] exp
] exp [
(8)
th, =
R
RT
Using the parameters of Table 1 we calculate on the
G2(MP2) level at 323 K high pressure limiting rate constants
From our fallo† analysis we extracted the broadening factor
of k
\ 7.8 ] 103 s~1 in excellent agreement with the
th, =
experimental value of k
F
and the collision efficiencies b between 323 and 383 K,
\ 1.7 ] 104 s~1 from eqn. (7).
C
c
1, =
respectively (see Table 2). Within the temperature range of our
experiments the slightly negative temperature dependence of
From the B3LYP/SVP method which is computationally
much cheaper we obtain k \ 1.4 ] 104 s~1 also in excel-
th, =
the broadening factor F is expressed as:
lent agreement with the experiment. However, B3LYP with
larger basis sets overestimates the high pressure rate constant
by about a factor of 10. A comparison of experimental and
theoretically predicted high pressure limiting rate constants
for the b CÈC bond scission of t-butoxy is represented in Fig.
7. For the b CÈC bond scission of small alkoxy radicals the
reliability of the results from the cheap DFT small basis set
calculations has been demonstrated. We conclude that this
method can be used to predict rate constants for the b CÈC
bond scission of larger alkoxy radicals which are difficult to
measure and very expensive to calculate with a high level ab
initio method.
C
F \ 0.87 [ T /870 K (323 K \ T \ 383 K)
(10)
C
According to the expression31
b
[S*ET
c
\
(11)
F kT
1 [ Jb
E
c
very low average energies transferred per collision with helium
of S*ET \ 21 and [16 cm~1 at 323 and 383 K, respectively,
are found (see Table 2). One might state that the [S*ET
values are low, however, they are in perfect agreement with
the almost temperature independent S*ET values of about
[22 and [24 cm~1 for i-propoxy and ethoxy radicals in
helium.9,11
The strong collision low pressure limiting rate constant was
calculated using the formalism proposed by Troe32 by taking
the molecular parameters from the ab initio calculations as
given in the Appendix. The density of states was calculated
with the WhittenÈRabinovitch approximation33 and the cor-
Implications for b C–C bond scission of alkoxy radicals
rection factors F and F
refs. 30 and 31. We did not explicitly take into account inter-
were determined as described in
The excellent agreement between the experimental high pres-
sure limiting rate constant and the theoretical result from a
simple transition state treatment (TST) based on ab initio
methods is very satisfactory. In particular, as the transition
state properties from expensive G2 and G2(MP2) ab initio cal-
culations are very similar to the energy and structure of the
transition state from cheap small basis set DFT (B3LYP/SVP)
calculations. The agreement between the results from high
level ab initio treatments and small basis set DFT calculations
holds for the three classes of alkoxy radicals, in which the
radical center is connected to a primary (ethoxy),11 secondary
(i-propoxy)9 and tertiary (t-butoxy) carbon atom, respectively.
For t-butoxy decomposition the experimental and theoreti-
cally predicted high pressure limiting rate constants agree
within the experimental uncertainty of about ^30%. A com-
parison is given in Fig. 7. We have shown, that for the three
classes of b CÈC bond scission of alkoxy radicals cheap small
basis set DFT calculations provide reliable transition state
structures and energies. On this evidence we calculated the
E
anh
nal rotations but used the maximum F . The collision effi-
rot
ciency b was obtained from a comparison with the low pres-
c
sure limiting rate constant extrapolated from the experimental
data. Since the collision efficiency e†ects the total broadening
factor F we repeated this procedure until a theoretically con-
C
sistent fallo† curve was obtained. The Ðnal individual fallo†
curves are shown in Fig. 5 together with the experimental
results. The fallo† parameters are given in Table 2. We
expressed the low pressure limiting rate constant as:
k
\ [He] ] 1.5 ] 10~8 exp([38.5 kJ mol~1/RT ) cm3 s~1
(323 K \ T \ 383 K) (9)
1, 0
Taking into account the experimental uncertainties and the
fact that fallo† e†ects do inÑuence the extrapolation of the low
pressure rate constant, we estimate an uncertainty of this rate
constant of 30%. It should be pointed out, that the limited
Fig. 7 Experimental and theoretical high pressure limiting rate con-
stant for reaction (1) (L: from ref. 8; =: this work; solid line: high
pressure limit as given in eqn. (7); dotted line: TST-calculation based
on the G2MP2; dashed line: TST-calculation based on the B3LYP/
SVP).
Fig. 8 Strong and weak collision second-order low pressure limiting
rate constants k /[He] (=: this work; solid line: weak collision rate
1, 0
constant as given by eqn. (9); dashed line: calculated strong collision
rate constant).
Phys. Chem. Chem. Phys., 2000, 2, 1677È1683
1681

View Article Online
Table 3 Activation barriers E , activation enthalpies *H0E(298 K), activation entropies *S0E(298 K), and high pressure Arrhenius preexponen-
0
tial factor of the CÈC bond dissociation as well as the Arrhenius activation energy from B3LYP/SVP calculations (energies and enthalpies in kJ
mol~1; entropies in J K~1 mol~1)
Reaction
E
*H0E
*S0E
log(A/s)
E
0
A
C H O~ ] ~CH ] CH O
71.2
63.4
58.8
57.0
47.5
35.8
72.7
64.7
60.2
58.5
48.7
36.3
13.4
14.8
16.5
17.4
13.3
7.7
14.0
14.1
14.2
14.2
14.0
13.7
75.6
67.6
63.1
61.4
51.6
39.2
2
5
3
2
1-C H O~ ] CH CH~ ] CH O
3
7
3
2
2
1-C H O~ ] CH CH CH~ ] CH O
4
9
3
2
2
2
1-C H O~ ] CH (CH ) CH~ ] CH O
11 2 2
(CH ) CHCH O~ ] CH C~HCH ] CH O
3 2
(CH ) CCH O~ ] (CH ) C~ ] CH O
3 3 3 3
5
3
2
2
2
3
3
2
2
2
2-C H O~ ] CH~ ] CH CHO
62.2
48.7
51.3
70.0
70.7
63.7
50.3
52.7
71.8
72.5
13.0
14.8
14.5
16.5
16.7
14.0
14.2
14.1
14.2
14.2
66.5
63.1
55.6
74.7
75.4
3
7
3
3
2-C H O~ ] ~CH CH ] CH CHO
4
9
3
2
3
2-C H O~ ] ~CH CH CH ] CH CHO
11
2-C H O~ ] ~CH ] CH CH CHO
5
3
2
2
3
4
9
3
3
2
2-C H O~ ] ~CH ] CH (CH ) CHO
5
11 2 2
3
3
t-C H O~ ] ~CH ] CH COCH
56.7
58.3
14.0
14.0
D14.0 ^ 0.3
61.2
4
9
3
3
3
b CÈC bond scission of alkoxy radicals
transition state properties for the b CÈC bond scission reac-
tions of several larger alkoxy radicals. The activation
entropies and enthalpies as well as the corresponding Arrhe-
nius parameters are presented in Table 3.
of [6.0, [45.2 and [81.3 kJ mol~1 for the ethoxy,11 i-
propoxy9 and t-butoxy radicals from our ab initio calculations
we obtain reaction enthalpies of 39.2, 20.1 and 7.4 kJ mol~1,
respectively. Activation barriers of 32, 42, and 52 kJ mol~1 are
calculated for the addition of CH radicals to CH O,
For all the transition states we found the length of the
breaking CÈC bond signiÐcantly increased with respect to
their lengths in the parent radical together with a considerably
shortening of the CÈO bond approaching the characteristic
length of the CÈO double bond. Generally, all transition state
structures for the b CÈC bond scission are very much product
like, but this feature is less compelling with increasing the
alkyl size. For smaller alkoxys the transition state structures
from di†erent methods can be compared and regularly the
B3LYP/SVP geometry is somewhat more product-like than
the optimized MP2/6-311G(d,p) geometry. This is reÑected in
systematically slightly higher activation entropies from the
DFT calculations. However, these di†erences are generally
small and lead to about 10% higher A-factors. The properties
of the transition states of the 12 reactions are very similar and
the small geometrical di†erences caused a di†erence in the
activation entropy of less than 2 J mol~1 K~1. The (O)CÈC
bond lengths at the transition state decrease very moderately
with the increasing size of the alkyl rest, but a similar e†ect is
seen for the equilibrium conÐguration of the alkoxy radical.
Since the transition state structures of the 12 reactions are
very much alike, the activation entropies and Arrhenius pre-
exponential factors are also very close (see Table 3). Conse-
quently, we propose a unique A-factor for the b CÈC bond
scission of all alkoxy radicals of A \ 1014B0.3 s~1. This seems
to be somewhat surprising in particular when the number of
methyl groups in ethoxy (1) and t-butoxy (3) decomposition
are compared. The degeneracy of the three equivalent methyl
groups in the t-butoxy radical cancels with the degeneracy of
the three indistinguishable transition states structure of the
decomposition path. This is generally true and holds also for
all other cases. For the decomposition of ethoxy radicals we
consequently reevaluate the Arrhenius expression and now
3
2
CH CHO, and (CH ) CO, respectively. Using the current lit-
3
3 2
erature values for the heat of formation of the alkoxy
radicals26,27 the activation barriers would be even lower and
reduce to 21, 35, and 42 kJ mol~1, respectively. These addi-
tion reactions will compete with the currently suggested
hydrogen abstraction reactions.4,34,35
Conclusions
In the present study, the pressure dependence of the thermal
unimolecular decomposition of the t-butoxy radical has been
studied in the temperature range between 323 and 383 K. The
high pressure limit has been reached at a total pressure of 60
bar helium and the fallo† analysis allowed for an extrapo-
lation of the low pressure limiting rate constant. From ab
initio calculations we conclude that the decomposition is com-
pletely controlled by the b CÈC bond scission.
A simple transition state treatment of the results of high
level ab-initio calculations (G2(MP2) and B3LYP/SVP) pro-
vided high pressure limiting rate constants in excellent agree-
ment with the experiment. From the results of this work and
from our work on ethoxy11 and i-propoxy9 thermal decompo-
sition we suggest that the literature data on the thermal
decomposition of all other alkoxy radicals should be critically
re-evaluated. We have extensively studied the unimolecular b
CÈC bond scission of di†erent alkoxy radicals using theoreti-
cal methods, based on calibrated cheap B3LYP/SVP calcu-
lations. The transition state structures were all very similar
and we propose a unique preexponential factor for the b CÈC
bond scission of all alkoxy radical of A \ 1014B0.3 s~1. The
corresponding Arrhenius activation energies are generally
lower than the currently accepted values in the literature. The
extended study of the thermochemistry of alkoxy radicals is in
progress.
prefer k \ 1.0 ] 1014 exp([78.2 kJ mol~1/RT ) s~1 instead
=
of the previously published expression of 1.1 ] 1013
exp([70.3 kJ mol~1/RT ) s~1.11 For i-propoxy the new Arr-
henius expression of k \ 1.0 ] 1014 exp([63.1 kJ mol~1/
=
RT ) s~1 is very similar to the recently published of 1.2 ] 1014
Acknowledgements
exp([63.7 kJ mol~1/RT ) s~1.9 The new activation energies
are somewhat higher, however, the individual rate constants
remain unchanged within the limited temperature range of the
experiments.
We thank the Deutsche Forschungsgemeinschaft (SFB 551,
““Kohlensto† aus der Gasphase: Elementarreaktionen, Struk-
turen, Werksto†eÏÏ), the Commission of European Com-
munities (contract SARBVOC) and CERLA (Centre dÏEtude
et Recherches Lasers et Applications) for Ðnancial support.
CERLA is supported by Ministere charge de la Recherche,
Region Nord/Pas de Calais and the Fonds Europeen de
We obtain the activation barriers for the corresponding
back reactions, the addition of alkyl radicals to aldehydes, by
subtracting the heat of reaction from the activation enthalpy
for the decomposition direction. Using the heat of formation
1682
Phys. Chem. Chem. Phys., 2000, 2, 1677È1683

View Article Online
12 T. P. W. Jungkamp, J. N. Smith and J. H. Steinfeld, J. Phys.
Chem. A, 1997, 102, 4392.
13 G. Lendvay and B. Viskolcz, J. Phys. Chem., 1998, 102, 10777.
14 T. Yamada, J. W. Bozzelli and T. Lay, J. Phys. Chem. A, 1999,
103, 7646.
Developpement Economique des Regions (FEDER). B.V.
thanks the Alexander von Humboldt Stiftung for a postdocto-
ral fellowship and the Hungarian ScientiÐc Research Found
(OTKA F030436).
15 T. Kortvelyesi and L. Seres, J. Chim. Phys., 1996, 93, 253.
16 J. M. Park, N. W. Song and K. Y. Choo, Bull. Korean Chem. Soc.,
1990, 11, 343.
Appendix
L J-parameters:
17 L. Batt, M. W. M. Hisham and M. Mackay, Int. J. Chem. Kinet.,
1989, 21, 535.
18 J. Heicklen, Adv. Photochem., 1988, 14, 177.
He: p \ 2.55 ] 10~10 m e/k \ 10 K
B
19 J.-M. Avez, PhD Thesis, University of Lille, France, 1978.
20 C. Wang, L. G. Shemesh, W. Deng, M. D. Lilien and T. S.
Dibble, J. Phys. Chem. A, 1999, 103, 8207.
t-C H O~: p \ 5.26 ] 10~10 m e/k \ 402 K
4
9
B
(LJ-parameters for t-butoxy radicals have been estimated by
taking the values for alcohols. All LJ-parameters have been
taken from ref. 36).
21 M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G.
Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Peterss-
on, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G.
Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Ste-
fanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y.
Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R.
Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J.
Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A.
Pople, Gaussian Inc., Pittsburgh PA, 1995.
22 A. P. Scott and L. Radom, J. Phys. Chem., 1996, 100, 16502.
23 A. D. Becke, J. Chem. Phys., 1993, 101, 5648.
24 A. Schaefer, H. Horn and R. Ahlrichs, J. Chem. Phys., 1992, 97,
2571.
25 N. J. Cohen, Phys. Chem. Ref. Data, 1996, 25, 1411.
26 J. Berkowitz, G. B. Ellison and D. Gutman, J. Phys. Chem., 1994,
98, 2744.
27 D. F. McMillen and D. M. Golden, Annu. Rev. Phys. Chem.,
1984, 80, 4065.
28 CRC Handbook of Chemistry and Physics, ed. D. R. Lide, CRC
Press, Boca Raton, 77th edn., 1997.
Molecular parameters calculated from the ab initio methods
Molecular frequencies were scaled by the factor 0.95:
(a) C H O
4
9
Vibrational frequencies in cm~1: 165, 239, 251, 317, 319, 388,
391, 413, 730, 865, 877, 898, 923, 974, 985, 1166, 1185, 1226,
1327, 1332, 1359, 1414, 1422, 1428, 1439, 1439, 1460, 2917,
2921, 2927, 3005, 3010, 3017, 3018, 3023 and 3027
Rotational constants in cm~1: 0.1653, 0.1652 and 0.1500
(b) Transition state
Vibrational frequencies in cm~1: i ] 732, 91, 215, 228, 241,
252, 368, 459, 492, 623, 662, 752, 851, 908, 909, 1031, 1060,
1175, 1326, 1329, 1374, 1390, 1414, 1419, 1421, 1431, 1577,
2923, 2926, 2981, 3008, 3012, 3042, 3044, 3148 and 3159
Rotational constants in cm~1: 0.1603, 0.1507 and 0.1374
Threshold energy: e \ 57.7 kJ mol~1
29 L. A. Curtiss, K. Raghavachari, G. W. Trucks and J. A. Pople, J.
Chem. Phys., 1991, 94, 7221; L. A. Curtiss, K. Raghavachari, P. C.
Redfern, V. Rassolov and J. A. Pople, J. Chem. Phys., 1998, 109,
7764; L. A. Curtiss, P. C. Redfern, K. Raghavachari, V. Rassolov
and J. A. Pople, J. Chem. Phys., 1999, 110, 4703; A. G. Baboul,
L. A. Curtiss, P. C. Redfern and K.Raghavachari, J. Chem. Phys.,
1999, 110, 7650.
References
1
A. C. Baldwin, J. R. Barker, D. M. Golden and D. G. Hendry, J.
Phys. Chem., 1977, 81, 2483.
2
3
4
L. Batt, Int. Rev. Phys. Chem., 1987, 6, 53.
J. Heicklen, J. Adv. Photochem., 1988, 14, 177.
D. L. Baulch, C. J. Cobos, R. A. Cox, C. Esser, P. Frank, Th. Just,
J. A. Kerr, M. J. Pilling, J. Troe, R. W. Walker and J. Warnatz, J.
Phys. Chem. Ref. Data, 1992, 21, 411.
R. Atkinson, Int. J. Chem. Kinet., 1997, 29, 99.
L. Batt, Int. J. Chem. Kinet., 1979, 11, 977.
L. Batt and R. T. Milne, Int. J. Chem. Kinet., 1977, 9, 549.
M. Blitz, M. J. Pilling, S. H. Robertson and P. W. Seakins, Phys.
Chem. Chem. Phys., 1999, 1, 73.
P. Devolder, Ch. Fittschen, A. Frenzel, H. Hippler, G. Poskreby-
shev, F. Striebel and B. Viskolcz, Phys. Chem. Chem. Phys., 1999,
1, 675.
30 J. Troe, Ber. Bunsen-Ges. Phys. Chem., 1983, 87, 161.
31 R. G. Gilbert, K. Luther and J. Troe, Ber. Bunsen-Ges. Phys.
Chem., 1983, 87, 169.
32 J. Troe, J. Chem. Phys., 1977, 66, 4758.
5
6
7
8
33 G. Z. Whitten and B. S. Rabinovitch, J. Chem. Phys., 1963, 38,
2466; G. Z. Whitten and B. S. Rabinovitch, J. Chem. Phys., 1964,
41, 1883.
34 D. L. Baulch, C. J. Cobos, R. A. Cox, P. Frank, G. Hayman, Th.
Just, J. A. Kerr, T. Murrells, M. J. Pilling, J. Troe, R. W. Walker
and J. Warnatz, J. Phys. Chem. Ref. Data, 1994, 23, 847.
35 A. C. Kinsman and J. M. Roscoe, Int. J. Chem. Kinet., 1994, 26,
191.
9
10 K. Hoyermann, M. Olzmann, J. Seeba and B. Viskolcz, J. Phys.
Chem., 1999, 103, 5692.
36 R. C. Reid, J. M. Prausnitz and B. E. Poling, T he Properties of
Gases and L iquids, McGraw-Hill, New York, 4th edn., 1987.
11 F. Caralp, P. Devolder, Ch. Fittschen, N. Gomez, H. Hippler, R.
Mereau, M. T. Rayez, F. Striebel and B. Viskolcz, Phys. Chem.
Chem. Phys., 1999, 1, 2935.
Paper b000009o
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1683