Solvent effect on the rate of β-scission of the tert-butoxyl radical

Article abstract of DOI:10.1021/jp9822236

The transient absorption spectrum of the tert-butoxyl radical in the UV region was obtained by the laser flash photolysis technique. The rate constants for β-scission and self-termination reactions of tert-butoxyl radicals were measured in five solvents; the Arrhenius parameters of the rate constant for β-scission k_β were determined. It was shown that both the solvent polarity and ability for hydrogen bonding accelerate the reaction of β-scission. The solvent effect on the rate constant of the β-scission reaction is discussed in terms of a simple Onzager-Betcher model, a point dipole model, and a model of the H-bonded complex of the radical with the solvent molecule.

Full text of DOI:10.1021/jp9822236

J. Phys. Chem. A 1998, 102, 7975-7980
7975
Solvent Effect on the Rate of â-Scission of the tert-Butoxyl Radical
Yuri P. Tsentalovich,* Leonid V. Kulik, Nina P. Gritsan,† and Alexandra V. Yurkovskaya‡
International Tomography Center, Institutskaya 3a, 630090, NoVosibirsk, Russia, and Institute of Chemical
Kinetics and Combustion, Institutskaya 3, 630090, NoVosibirsk, Russia
ReceiVed: May 12, 1998; In Final Form: August 6, 1998
The transient absorption spectrum of the tert-butoxyl radical in the UV region was obtained by the laser flash
photolysis technique. The rate constants for â-scission and self-termination reactions of tert-butoxyl radicals
were measured in five solvents; the Arrhenius parameters of the rate constant for â-scission kâ were determined.
It was shown that both the solvent polarity and ability for hydrogen bonding accelerate the reaction of â-scission.
The solvent effect on the rate constant of the â-scission reaction is discussed in terms of a simple Onzager-
Betcher model, a point dipole model, and a model of the H-bonded complex of the radical with the solvent
molecule.
Introduction
for the fragmentation differs significantly from that of the initial
radical, the activation energy of this reaction becomes solvent
Spectroscopy and reaction kinetics of alkoxyl radicals have
been extensively studied over the past decade. In these studies,
special attention was given to the solvent effect on the main
reactions of alkoxyl radicals: the â-scission and hydrogen
abstraction:
dependent. Direct evidence of the solvent effect was obtained
for â-scission of 2-phenylethoxyl,12 cumyloxyl,3,13 and decar-
bonylation of some acyl radicals.14,15 However, to the best of
our knowledge, direct measurements of the rate constant for
â-scission in different solvents have never been performed for
one of the most important alkoxyl radicals, tert-butoxyl. Most
likely, it is mainly caused by experimental difficulties. tert-
Butoxyl has no absorption bands in the visible,16-18 and its
absorption in the near-UV is rather small. To our knowledge,
only weak “tail-end” absorption of tert-butoxyl radicals at
wavelengths above 300 nm has been published17,18 until now.
Additionally, as follows from indirect measurements,2,19 the rate
constant of â-scission for tert-butoxyl is rather low, and at the
high radical concentrations this reaction is strongly suppressed
by the second-order reactions.
In the present work we are pleased to report the electronic
absorption spectrum of the tert-butoxyl radical in the UV region
and the measurements of the rate constant for its â-scission in
variety of solvents. To decrease the contribution of the second-
order reactions, we carried out the flash photolysis measurements
at the lowest possible initial radical concentrations. Despite
this, for some solvents at room temperature the radical
recombination still remained the main channel of radical decay.
Thus, for all solvents the measurements were performed at
temperatures ranging from 295 to 345 K, and the rate constants
of â-scission at room temperature were determined from the
Arrhenius parameters obtained.
kâ
R1R2R3CO˙
98 R1COR2 + R˙ 3
(1)
(2)
ka
R1R2R3CO˙ + RH 98 R1R2R3COH + R˙
The first observation of the effect of media on the reaction rate
constants of alkoxyl radicals has been made in pioneering works
of Walling and Wagner.1,2 Studying the distribution of the
products of the reactions of tert-butoxyl radicals generated
during the photolysis of tert-butyl hypochlorite, they found1,2
that the ratio of the rate constants for hydrogen abstraction and
â-scission, ka/kâ, strongly depends on the polarity of the solvent.
This effect could be attributed to either an increase in kâ with
increasing solvent polarity or a decrease in ka, or both.3 To
separate the contributions of these two processes, direct
measurements of the rate constants for â-scission and hydrogen
abstraction were required.
A recent investigation of the solvent effect on the rate constant
for hydrogen abstraction by alkoxyl radicals has been performed
by Ingold, Lusztyk, and co-workers.3-8 It has been shown that
the solvent effect on the hydrogen abstraction from substrates
RH is mainly determined by hydrogen bonding between RH
and solvent molecules and, in general, does not depend on the
nature of the attacking radical.
Experimental Section
The solvent effect on the rate constants of radical fragmenta-
tion is usually negligibly small;9 that is why this reaction was
often considered as a kinetic standard (“chemical clock”) for
the quantitative determination of the rate constants of competi-
tive reactions.10,11 Nevertheless, if the solvent stabilization (due
to solvent polarity or hydrogen bonding) of the transition state
The detailed description of our LFP setup has been published
earlier.20 Solutions placed in a rectangular cell 10 × 10 mm2
were irradiated by the light pulses of a Lambda Physik EMG
101 excimer laser (308 nm, pulse energy up to 100 mJ). The
dimensions of the laser beam at the cell front are 4 × 9 mm2.
The monitoring system includes a xenon short-arc lamp DKSh-
120 connected to a high-current pulser, two monochromators,
a Hamamatsu R955 photomultiplier, a digitizer LeCroy 9310A,
and sets of filters and shutters. The monochromator placed
between the lamp and the cell allows to completely avoid
* To whom correspondence should be addressed.
† Institute of Chemical Kinetics and Combustion.
‡ At present, a research fellow of Humboldt foundation at Free University
of Berlin, Germany.
S1089-5639(98)02223-3 CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/19/1998

7976 J. Phys. Chem. A, Vol. 102, No. 41, 1998
Tsentalovich et al.
“tail-end” absorption of tert-butoxyl reported by Avila et al.17
Ab initio calculations show that the tert-butoxyl radical has two
absorption bands, the first one being in a vacuum-UV region
(141 nm, oscillator strength f ) 2.6 × 10-2) and the second, of
rather low intensity (f ) 4 × 10-4), at 277 nm. This band very
well coincides with the experimental spectrum (Figure 1). Thus,
the obtained spectrum can be reliably attributed to the tert-
butoxyl radical (BO•). The spectrum obtained in benzene is
more intensive (solid squares) and demonstrates a red shift as
compared with the case of nonaromatic solvents. The red shift
in spectra of alkoxyl radicals in aromatic solvents has been
observed earlier18 and was attributed to the formation of
π-complexes between radicals and solvent.
To determine the absolute values of absorption coefficient
of BO• in different solvents, for every solvent carefully matched
pairs of experiments17,18,35 have been performed: (1) during the
photolysis of 0.11 M DTBP, the kinetics of BO• at the absorption
maximum (300 nm for benzene and 275 nm for other solvents)
were measured; (2) during the photolysis of 0.11 M DTBP and
0.3 M diphenylmethanol (DPH) the kinetic traces of ketyl
radicals DP were obtained at 545 nm, where the absorption
coefficient of these radicals ꢀDP ) 3220 M-1 cm-1 is well-
known.36 In these experimental conditions, the rise time of the
signal at 545 nm (in experiment 2) was more than 10 times
shorter than the decay of BO• (in experiment 1). Thus, most
of BO• abstracts the hydrogen atom from diphenylmethanol
forming benzophenone ketyl radicals:
Figure 1. Absorption spectrum of the tert-butoxyl radical: open circles,
solvent acetonitrile; solid squares, solvent benzene.
depletion of the solution by the monitoring light and increases
the spectral selectivity of the monitoring system; besides, it
easily allows to compensate for the wavelength-dependent shift
of the focus caused by the lens chromatic aberration and to form
the monitoring beam inside the cell into a distinct rectangle of
area 3 × 1 mm2.
All solutions were purged with argon for 15 min prior to use
and during the irradiation. For high-temperature measurements
the cell was warmed by a hot air flow; the temperature was
controlled by a thermocouple placed inside the cell just above
the irradiated zone.
(CH3)3CO˙ + DPH f (CH3)3COH + DP˙
(3)
The absorption coefficient of BO• was determined from the ratio
Quantum chemical calculations of the geometry and enthalpy
of formation of the reactants, products, and transition states were
performed using AM121 and PM322,33 methods based on a
modified MNDO-85 program.24 Properties of the radical species
were determined by both unrestricted (UHF) and restricted
(RHF) Hartree-Fock techniques in a “half-electron” ap-
proximation.25 The transition states were found according to
ref 26. The free energies of solvation were estimated using a
simple Onzager-Betcher model or a point dipole model.27,28
Since the PM3 method is better adopted to the calculation of
the geometry and enthalpy of formation of H-bonded com-
plexes,23,29 we used only this technique for the study of the
influence of the protic solvents on the activation energy of the
â-scission reaction.
The UV-vis absorption spectrum of the tert-butyl radical
was calculated using a single excitation configuration interaction
(CIS) method30 with 6-311+G* basis set. The geometry was
optimized by a DFT method31 (B3LYP/6-31G*). Free energy
of solvation of tert-butyl was calculated in terms of the UHF
approximation (UHF/6-31G*) using an Onsager model32 and a
polarized continuum model33 (PCM). The calculations were
performed using the GAUSSIAN94 program.34
BO
in
DP
OD
C
max
ꢀBO ) ꢀDP
(4)
DP
max
BO
OD
C
in
BO
in
BO
in
where C and OD are the initial concentration and optical
absorption of BO• at 275 nm (300 nm in benzene); CDmPax and
DP
max
OD are the maximal concentration and optical absorption of
DP at 545 nm. The actual ratio CDmPax/CBO was determined
in
taking into account the rate of initial growth of absorption at
545 nm and the rate of BO• decay in absence of diphenylmetha-
nol. The small absorption of DPH at 308 nm was also taken
into account. For every solvent, these sets of experiments were
carried out for 3-5 different laser energies (in the range 10-
70 mJ per pulse), and the results were averaged. For four
nonaromatic solvents, the absorption coefficient of BO• at 275
nm was the same within the experimental error, ꢀΒÃ ) 560 (
70 M-1 cm-1; for benzene solvent at 300 nm ꢀΒÃ ) 800 ( 50
M-1 cm-1
.
Kinetic Data. The general scheme of DTBP photolysis can
be presented as follows:
DTBP
9
hV8 2BO•
(5)
(6)
Results
kâ
BO• 98 (CH3)2CO + C˙ H3
Spectral Data. Figure 1 shows the transient absorption
spectra obtained during the photolysis of 0.07 M di-tert-butyl
peroxide (DTBP) in different solvents 300 ns after the laser
flash. For four solvents, tetrachloromethane, acetonitrile, tert-
butyl alcohol, and acetic acid, the transient spectra were
practically identical (open circles in Figure 1, only spectrum
for acetonitrile solvent is shown), and the time profiles of the
signal decay in all solvents were wavelength-independent. The
spectrum at wavelengths above 320 nm well coincides with the
2k2
2BO• 8 DTBP
(7)
(8)
2k3
2C˙ H3 8 C2H6
k4
BO• + C˙ H3
9
8 (CH3)3COCH3
(9)
Besides, BO• can abstract a hydrogen atom from a solvent or

Rate of â-Scission of tert-Butoxyl Radical
J. Phys. Chem. A, Vol. 102, No. 41, 1998 7977
Figure 2. Transient absorption kinetics of the tert-butoxyl radical in
benzene (trace 1) and acetonitrile (trace 2): (a) at T ) 295 K, (b) at T
) 335 K. For the fitting procedure, see text.
Figure 3. Arrhenius plots for the â-scission rate constant of the tert-
butoxyl radical. Solvents: open circles, tetrachloromethane; triangles,
benzene; squares, acetonitrile; diamonds, tert-butyl alcohol; solid circles,
acetic acid.
from the parent peroxide:
ka
TABLE 1: Rate Constants for the Reactions of â-Scission
and Self-Termination of tert-Butoxyl Radicals at T ) 295 K
and Arrhenius Parameters for kâ
BO• + RH
98 (CH3)3COH + R˙
(10)
Figure 2a shows the kinetics of BO• decay obtained at room
temperature for two solvents, benzene (trace 1) and acetonitrile
(trace 2); both traces are scaled to unity. For benzene solvent,
the absorption of BO• decays practically by pure second-order
law until the lowest detectable initial concentrations of radicals.
It means that the rate of â-scission (6) is too small to compete
with the reaction (7) of radical termination. On the other hand,
the BO• decay in acetonitrile presents a mixture of the first-
order and second-order reactions. When the same experiments
were carried out at T ) 61 °C, the admixture of the first-order
reaction was observed for both benzene and acetonitrile (Figure
2b).
Ea,
kJ/mol
kâ(295 K)
2k2(295 K)
solvent
gas phaseb
CCl4
C6H6
CH3CN
log(A/s-1
)
× 104,a s-1 × 109, M-1 s-1
14.04
62.5
0.163c
13.4 ( 0.5 53 ( 4
13.4 ( 0.6 52 ( 4
13.2 ( 0.4 48 ( 3
1.0 ( 0.2
1.4 ( 0.3
6.4 ( 1.1
19 ( 4c
34 ( 6
140 ( 15
2.8 ( 0.4
3.4 ( 0.3
4.1 ( 0.8
1.5 ( 0.4c
2.7 ( 0.6
(CH3)3COH 12.4 ( 0.6 40 ( 5
CH3COOH
12.1 ( 0.3 37 ( 3
H2Od
a Values of the observed rate constant for first-order decay. b Data
from ref 50. c For T ) 303 K. d Data from ref 49.
The rate constants for â-scission kâ of BO• at different
temperatures were determined in the following way. For every
given temperature, the kinetics of BO• decay have been obtained
for at least three different laser energies (typical values are 50,
35, and 20 mJ per pulse). These kinetic data were treated
simultaneously according to the reaction scheme (5)-(9), taking
into account the known absorption coefficient of BO• (see
above). Thus, the contribution of the first-order reaction into
the radical decay was determined.
In an additional experiment, the dependence of radical decay
on the concentration of the initial substrate has been measured.
The independence of the first-order component of decay on
DTBP concentration testifies that the hydrogen abstraction from
DTBP is negligibly small.
The temperature dependencies of the first-order rate constant
for five solvents in Arrhenius coordinates are shown in Figure
3. For all solvents, the data lay on a straight line fairly well.
The corresponding frequency factors and activation energies are
collected in Table 1. This table also presents the rate constants
for BO• self-termination reaction at room temperature and the
first-order rate constants at room temperature. (For nonpolar
solvents the last is an extrapolation from the higher tempera-
tures.)
Figure 4. Calculated (solid lines) and experimental yields of acetone
(circles) and tert-butyl methyl ether (triangles) during the photolysis
of 0.11 M DTBP in deuterated acetonitrile. In calculations, the kinetic
parameters were taken from Table 1; the initial radical concentration
was 1 × 10-4 M.
measurements, the depletion of the parent peroxide was kept
below 5%. The formation of the main reaction products, acetone
and tert-butyl methyl ether, was linear with respect to the
irradiation dose. The concentrations of the reaction products
have been determined from the integration of NMR spectra and
then recalculated into the product yield per laser shot in the
irradiated volume. The results are shown in Figure 4.
Product Yields. The analysis of the product yields at
different temperatures was carried out by means of NMR
spectroscopy. The 0.11 M solution of DTBP in deuterated
acetonitrile placed in a quartz cell was irradiated by an excimer
laser under exactly the same experimental conditions as in LFP
1
measurements, and then the H NMR spectra of the irradiated
We tried to carry out the same experiment using deuturated
benzene as a solvent. However, in testing experiments, we
revealed that under our experimental conditions during the
samples were obtained. For every temperature, 3-4 samples
with the different dose of irradiation were taken. In all

7978 J. Phys. Chem. A, Vol. 102, No. 41, 1998
Tsentalovich et al.
irradiation at temperatures above 50 °C a significant amount of
the forming acetone evaporates from the cell. (In the associating
solvent acetonitrile the evaporation of acetone was below 10%
at highest temperatures used.) Thus, the results obtained for
benzene solvent were disregarded.
Solid lines in Figure 4 show the calculated temperature
dependence of the product yield according to the reaction
scheme (5)-(9). The Arrhenius parameters for the rate constant
of â-scission were taken from the kinetic measurements. For
radical termination reactions, two reasonable assumptions have
been made:
abstraction from acetic acid and tert-butyl alcohol. However,
if for any of the solvent used the hydrogen abstraction was the
main channel of BO• decay, one would expect a significantly
smaller frequency factor for this solvent. This statement is also
confirmed by the absence of tert-butyl alcohol formation during
the photolysis of DTBP in acetonitrile and benzene. Unfortu-
nately, it is difficult to provide the product analysis for the most
probable hydrogen donor solvent tert-butyl alcohol, because in
this case the product of the hydrogen abstraction coincides with
the solvent. Thus, for this particular solvent the role of hydrogen
abstraction remains somewhat uncertain.
(i) The radical termination rate constants kt are close to the
diffusional limit, kt ∼ D, where D is the diffusion coefficient.37,38
The dependence of the diffusion coefficient on the solvent
viscosity η and temperature T can be expressed39,40 as D ) kT/
6πrηf, where r is the radical hydrodynamic radius and f is the
microfriction factor. Thus, in our calculations, we used the
relation kt ∼ T/η.
The analysis of the product yield in acetonitrile confirms the
reaction scheme (5)-(9). Solid lines in Figure 4 show the
computer simulations of the yields of acetone and ether
according to this scheme. Rather good agreement between
calculated and experimental product yields has been achieved.
The calculated ratio of acetone/ether concentrations also coin-
cides well with the experimental data. From these results, the
following conclusions could be extracted: (a) under our
experimental conditions the hydrogen abstraction is of minor
importance, and the main channels of BO• decay are the
reactions of â-scission and radical termination; (b) the agreement
between calculated and experimental temperature dependencies
of the product yields is also a good confirmation of the kinetic
results obtained by LFP.
(ii) We presumed that the self-termination rate constants for
the radicals of different size (e.g., BO• and methyl) are
proportional to the microfriction factors:
k2/k3 ) rBODBO/rMeDMe ) fBO/fMe
The microfriction factors were estimated as39,40
The values of the rate constants kâ and k2 reported in this
work can be compared with the previous indirect measurements.
Walling and Kurkov45 estimated 2k2 as 2.8 × 109 M-1 s-1 at
313 K in CCl4; Wong19 reported 2k2 ) 1.6 × 109 M-1 s-1
measured by the EPR technique. However, since in the last
work the measurement of 2k2 was based on a probably
underestimated rate constant for hydrogen abstraction,44 this
value for 2k2 is likely underestimated as well.
f ) 0.16 + 0.4r/rs
where rs is the radius of the solvent molecule, which leads to
the ratio k2/k3 ≈ 0.45. The cross-termination rate constant can
be described40,41 by the geometric mean rule: k4 ) 2(k2k3)1/2
1.3k3.
≈
During the calculations, the initial radical concentration taken
from the kinetic measurements was adjusted within 20% in order
to obtain the best fit to the experimental results.
It is noteworthy that the product analysis in both solvents
(acetonitrile and benzene) has revealed only the trace amounts
of tert-butyl alcohol, the main product of the hydrogen abstrac-
tion reaction (10).
We have not found in the literature the data on the direct
measurements of the rate constant for â-scission of the tert-
butoxyl radical, so we can compare our results only with the
related data from the different sources. Walling and Wagner2
measured the yields of acetone and tert-butyl alcohol during
the photolysis of mixtures of tert-butyl hypochlorite and
cyclohexane and determined in this way the ratios of ka/kâ
(reactions 10 and 6, RH ) cyclohexane) for the different
solvents. In particular, the ka/kâ ratios were equal 48.6 M-1 in
benzene, 19.8 M-1 in acetonitrile, and 4.87 M-1 in acetic acid
at temperature 298 K. The rate constants for hydrogen
abstraction by alkoxyl radicals from cyclic hydrocarbons ka were
measured by different authors.42-44,46,47 For the reaction of tert-
butoxyl with cyclopentane the reported values of ka are 3.45 ×
Discussion
Generally speaking, the first-order decay of BO• can be caused
by two reactions: â-scission of BO• (reaction 6) and hydrogen
abstraction from the solvent or from the starting peroxide
(reaction 10). The independence of the first-order rate constant
of radical decay on the concentration of initial compound
testifies that under our experimental conditions (concentration
of DTBP about 0.1 M, initial radical concentrations 10-5-10-4
M) the hydrogen abstraction from DTBP is insignificant.
The reaction with solvents cannot be ruled out completely.
Paul et al.42 revealed that tert-butoxyl radicals can react with
even such an inert solvent as acetonitrile. Avila and co-workers3
reported the hydrogen abstraction by cumyloxyl radicals from
tert-butyl alcohol. Here, we have only indirect evidence that,
for the solvents used in the present work, the reactions with
the solvents do not play a significant role. Table 1 shows that
for all solvents the frequency factors for the first-order rate
constant are similar, but the activation energy is solvent-
dependent. The typical frequency factors for H abstraction are
105 M-1 s-1 44
,
8.57 × 105 M-1 s-1 43
,
and 8.8 × 105 M-1 s-1 42
,
and with cyclohexane ka ) 1.6 × 106 M-1 s-1 47
.
Avila et al.
reported ka ) 1.2 × 106 M-1 s-1 for the reaction of cumyloxyl
radical with cyclohexane;3 besides, in this work3 it was shown
that the rate constant ka for hydrogen abstraction from cyclo-
hexane is solvent-independent. Thus, we can estimate the rate
constant of the reaction of BO• with cyclohexane as ka ≈ 1.0 ×
106 M-1 s-1. The combination of this value with ka/kâ ratios
reported by Walling and Wagner2 (see above) gives kâ ) 2.0
× 104 s-1 in benzene, 5.0 × 104 s-1 in acetonitrile, and 2.0 ×
105 s-1 in acetic acid, which is in good agreement with our
results (Table 1).
108-109 M-1 s-1 43,44 for the neat solvent it corresponds to 109-
;
1010 s-1, which is 2-3 orders of magnitude smaller than the
frequency factors for the first-order rate constants determined
in the present work. Somewhat smaller frequency factors in
(CH3)3COH and CH3COOH, as compared with the other
solvents, indicate that some radicals can be lost due to hydrogen
For further analysis, our results can be presented as a
correlation between the most commonly used solvent parameter
ET(30)9,48 and the logarithm of the rate constant for â-scission
(Figure 5). Figure 5 presents also the data reported by Erben-
Russ et al.49 for water solvent. The data for all solvents except

Rate of â-Scission of tert-Butoxyl Radical
J. Phys. Chem. A, Vol. 102, No. 41, 1998 7979
activation energy 62.5 kJ/mol for this reaction in the gas phase.
However, the experimental difference in activation energies for
the polar and nonpolar solvents is much larger than calculated.
The same holds true for the activation energies in solutions and
in the gas phase (compare Tables 1 and 2). We suppose that
this discrepancy is probably connected with the simplicity of
the model: a radical is considered as a dipole of radius r,
whereas in the real radical the dipole moment is mainly
concentrated along the C-O bond.
To account for the charge distribution in the molecule, we
also used the more sophisticated point dipole model.27,28 The
empirical parameter of this model, the energy of interaction
between two neighboring solvent molecule, was estimated as
the energy of dipole-dipole interaction between acetonitrile
molecules, 12.5 kJ/mol. In this model, the calculated value of
activation energy in acetonitrile is 46 kJ/mol, which qualitatively
agrees with the experimental value.
Ab initio calculations of the free energy of solvation of BO•
confirm the importance of the charge distribution in radical.
The calculations were performed using the GAUSSIAN94
program34 and UHF approximation (UHF/6-31G*) in two
models: an Onsager model32 and a more sophisticated polarized
continuum model (PCM).33 In the Onsager model, the calcu-
lated value of free energy of BO• solvation in acetonitrile was
only 3.1 kJ/mol, whereas PCM, which takes into account the
charge distribution, gives 19.2 kJ/mol. Thus, the simple Onsager
model significantly underestimates the solvent stabilization of
molecules.
Formulas 11 and 12 and the point dipole model describe only
the nonspecific interactions of the solute molecule with the
solvent. To account for the effect of the hydrogen bonding,
we performed the calculation of the activation enthalpy for the
complex of tert-butoxyl radical with H2O (as a typical example
of protic solvent). The activation enthalpy of â-scission reaction
in the H-bonded complex was estimated as 57.7 kJ/mol, which
is 8.8 kJ/mol lower than for the reaction of nonbonded radical.
The reason for this effect is the higher energy of H-bond
formation for transition state (18.4 kJ/mol) compared with that
of the radical (9.6 kJ/mol). The difference in the activation
energies of the â-scission reaction in CH3CN and in protic
solvents (tert-butyl alcohol and acetic acid) can be attributed
to the effect of H-bond formation in the latter solvents (Table
1). This difference (7-10 kJ/mol) is in a very good agreement
with our theoretical estimation.
Figure 5. Correlation of log(kâ) with ET(30) (kcal/mol) in tetrachlo-
rmethane (1), benzene (2), acetonitrile (3), tert-butyl alcohol (4), acetic
acid (5), and water49 (6).
TABLE 2: Data of Semiempirical Quantum Chemical
Calculations of the Activation Enthalpy (∆H#) for the
Reaction of â-Scission of tert-Butoxyl Radical, Values of
Dipole Moment of Reactant (µR) and Transition State (µTS),
and Solvation Part of Free Energy of Activation in Benzene
(∆G#b) and Acetonitrile (∆Ga#c)
∆H#,
kJ/mol
∆G#b,
kJ/mol
∆G#ac,
kJ/mol
method
µR, D
µ
TS, D
AM1 (RHF)
AM1 (UHF)
PM3 (RHF)
PM3 (UHF)
67.0
59.1
66.6
65.4
2.59
1.96
2.22
1.76
3.23
2.76
3.00
2.61
1.13
1.14
1.22
1.13
2.14
2.18
2.35
2.14
tert-butyl alcohol show a reasonably good linear relationship.
The unexpectedly high value of kâ in tert-butyl alcohol points
to the possible contribution of the hydrogen abstraction from
this solvent into BO• decay.
More quantitatively, the solvent effect on the rate constant
for â-scission can be explained in terms of different solvent
stabilization of the radical and the transition state for radical
fragmentation, caused by the different polarity of the solvents
and their ability to form the hydrogen bonds. The influence of
the solvent polarity can be accounted for as a dipole-dipole
interaction of the parent radical and the transition state for
â-scission with the solvent medium treated as a continuum of
dielectric constant ꢀ. According to Kirkwood’s formula,9 the
solvent influence on the activation energy of the reaction can
be considered as the difference of the solvation energies for
the transition state (TS) and reactant (R):
Acknowledgment. This work was supported by State
Program “Actual directions in physics of condensed states”
(Project 96141 “Flash”) and by INTAS (Project No. 96-1269).
A.V.Yu. thanks Alexander von Humbold Foundation for the
research fellowship at the Free University of Berlin, Germany.
∆G#sol ) ∆GTS - ∆GsRol
(11)
(12)
sol
µ2 ꢀ - 1
TS,R
sol
∆G
)
r3
2ꢀ + 1
References and Notes
(1) Walling, C.; Wagner, P. J. Am. Chem. Soc. 1963, 85, 2333-2334.
(2) Walling, C.; Wagner, P. J. Am. Chem. Soc. 1964, 86, 3368-3375.
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where µ is the dipole moment and r is the radical radius.
We performed the semiempirical calculations of the reaction
and activation enthalpies and the dipole moments of the radical
and the transition state using AM1 and PM3 methods. The
results of the calculations are presented in Table 2. Our
calculations show that the dipole moment of the transition state
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