Solvent effect on the decarbonylation of acyl radicals

Article abstract of DOI:10.1039/b103422g

The rate constants of the decarbonylation reaction of phenylacetyl and 2-hydroxy-2-methyl-propanoyl radicals were determined in various solvents, e.g., hexane, chloroform, acetic acid, acetonitrile, etc., over a wide temperature range. For the first time, it was shown that the electrostatic interactions with solvent and hydrogen bonding could influence the reaction in different ways: the decarbonylation of phenylacetyl proceeded more slowly in polar solvents while hydrogen bonding decreased the activation barrier and increased the reaction rate constant. The scale of the solvent effect was determined by the change of the radical polarity in the course of the reaction rather than by radical polarity itself. The solvent effect for phenylacetyl was significantly distinct than that for the 2-hydroxy-2-methyl-propanoyl radical of similar polarity. A linear relationship existed between the enthalpy of the reaction of decarbonylation and the barrier to the reaction for most acyl radicals.

Full text of DOI:10.1039/b103422g

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Solvent e†ect on the decarbonylation of acyl radicals
Olga A. Kurnysheva,ab Nina P. Gritsanbc and Yuri P. Tsentalovich*a
a International T omography Center, Siberian Branch of Russian Academy of Sciences,
630090 Novosibirsk, Russia. E-mail: yura=tomo.nsc.ru
b Novosibirsk State University, 630090 Novosibirsk, Russia
c Institute of Chemical Kinetics and Combustion, Siberian Branch of Russian Academy of
Sciences, 630090 Novosibirsk, Russia
Received 17th April 2001, Accepted 20th June 2001
First published as an Advance Article on the web 7th August 2001
The rate constant k of decarbonylation of phenylacetyl and 2-hydroxy-2-methylpropanoyl radicals,
CO
generated by photolysis of dibenzyl ketone and 2,4-dihydroxy-2,4-dimethyl-3-pentanone, was measured in a
number of solvents over a wide temperature range. The pre-exponential factors A and activation energies E
a
were found for all solvents. The rate constant of phenylacetyl decarbonylation decreases with the increase of
the solvent relative permittivity e, but increases in protic solvents. The results of quantum chemistry
calculations conÐrm the mutual cancellation of the contributions of speciÐc and nonspeciÐc solvations to the
activation energy of the decarbonylation reaction in alcohols. For the 2-hydroxy-2-methylpropanoyl radical,
the solvent e†ect on the decarbonylation rate constant is very small.
polarity and hydrogen bonding on the rate constant of radical
fragmentation.
Introduction
Solvent e†ects on the mechanism and rate constants of chemi-
cal reactions have attracted the attention of many physical
chemists. A recent book by Reichardt1 includes more than
Experimental
2300 references on this subject. The solvent e†ect is most pro-
Materials
nounced in reactions involving cations and anions. In this
case, the change of reaction rate constants in di†erent solvents
can reach many orders of magnitude,2 and reaction mecha-
nisms can change drastically.
All solvents used in this work were doubly distilled. 2,4-
Dihydroxy-2,4-dimethyl-3-pentanone was synthesized follow-
ing ref. 13 and puriÐed by distillation. Dibenzyl ketone
(Aldrich) was used as received.
The inÑuence of solvent on radical reactions is most signiÐ-
cant when the radicals are charged, or when polar radicals
participate in bimolecular reactions.1 The inÑuence of solvent
on the monomolecular reactions of polar radicals is con-
sidered as very weak, and even negligible in the case of non-
polar radicals. In particular, the decarbonylation of the
phenylacetyl radical was suggested as a ““chemical clockÏÏ, i.e.
a reaction for which the rate constant does not depend on the
solvent, and which can be used for the determination of the
absolute rate constants of parallel reactions.3h5 However,
recently a solvent e†ect has been revealed in the reactions of
b-scission of some alkoxyl radicals6h9 and of decarbonylation
of acyl radicals.10,11
It was shown that the rate constant of b-scission of alkoxyl
radicals increases with the increase in solvent polarity. This
e†ect can be accounted for as follows: polar solvents stabilize
the transition state for fragmentation more strongly than the
initial radical. Thus, in polar solvents the activation energy of
the reaction decreases, and the rate constant increases. Both
the solvent polarity and its ability for hydrogen bonding
accelerate the rate constant of b-scission. A good linear
relationship was found between the commonly used solvent
Apparatus
A detailed description of the laser Ñash photolysis equipment
has been published earlier.3,14 Solutions in a rectangular cell
(10 mm ] 10 mm) were irradiated with a Lambda Physik
EMG 101 excimer laser (308 nm, pulse energy up to 100 mJ,
pulse duration 15 ns). The dimensions of the laser beam at the
front of the cell were 3 mm ] 8 mm. The monitoring system
includes a DKSh-120 xenon short-arc lamp connected to a
high current pulser, two synchronously operating monochro-
mators, a Hamamatsu R955 photomultiplier, and a LeCroy
9310A digitizer. All solutions were purged with argon for 15
min prior to, and during, irradiation.
Computational methods
Radical geometry optimization and transition state search
were performed at the B3LYP15 level of theory using the
6-31G* basis set. The nature of the stationary point (i.e., either
minimum or transition state) was determined by calculating
the vibrational frequencies, and the unscaled frequencies were
used to obtain corrections for the zero-point vibrational ener-
gies. Free energies of solvation of radicals and transition states
were calculated using the PCM model.16 Geometries and
heats of formation of radicals, transition states and their com-
plexes with methanol were calculated also by semi-empirical
PM3 method.17 All calculations were performed using the
GAUSSIAN98 program.18
parameter1,12 E (30) and the logarithm of the rate constant
T
for b-scission of cumyloxyl6 and tert-butoxyl9 radicals.
In the present work, the rate constants of the decarbonyla-
tion reaction of phenylacetyl and 2-hydroxy-2-methyl-
propanoyl radicals have been measured in a number of
solvents over a wide temperature range. The main goal of this
work is the quantitative analysis of the inÑuence of solvent
DOI: 10.1039/b103422g
Phys. Chem. Chem. Phys., 2001, 3, 3677È3682
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Results
The phenylacetyl and 2-hydroxy-2-methylpropanoyl radicals
were generated by the laser Ñash photolysis (LFP) of dibenzyl
ketone (DBK) and 2,4-dihydroxy-2,4-dimethyl-3-pentanone
(
DHDMP), respectively. These reactions have been studied
previously3,4,10,19h41 and can be described by the scheme:
~
8
hl
R CO ÈÈ
2
:10
s
Õ
R CO (S ) ÈÈÈÈ
Õ
R CO (T )
(1)
(2)
(3)
(4)
(5)
(6)
2
1
2
1
~
:10
9
s
R CO (T ) ÈÈÈÈ
Õ
RC
] CO
products
0
O ] R
0
2
1
kCO
RC0 O ÈÈÕ R0
2
k1
2
RC
0
O ÈÈ
Õ
2
k2
2
R
0
ÈÈ
Õ
products
Fig. 1 Transient absorption kinetics of benzyl radicals (314 nm) in
hexane (1), methanol (2) and acetonitrile (3) at room temperature.
Bold lines show the best Ðt to eqn. (9).
kx
RC
0
O ] R
0
ÈÈ
Õ
products
performed in the following way. At every given temperature
three or four kinetic traces were obtained with the laser power
varying between 1 and 10 mJ per pulse. Typical concentration
of DBK was 3 ] 10~3 M, and 2 ] 10~2 M for DHDMP.
Thus, the initial radical concentration in the intersection of
the exciting and monitoring beams varied in the range from
where
R
stands for PhCH (LFP of DBK) and for
2
(
CH ) COH (LFP of DHDMP).
The absorption spectra of benzyl PhCH and ketyl
3
2
2
(
CH ) COH radicals, formed in these reactions, were
3
2
published earlier. Benzyl has absorption bands with maxima
at 260 and 314 nm,10,24,42 whereas the absorption of ketyl
radical in the near-UV region gradually increases toward
short wavelengths.11,43h46 The transient absorption kinetics
was measured at 314 nm in the LFP of DBK, and at 270 nm
in the LFP of DHDMP.
2
] 10~6 M to 2 ] 10~5 M in the LFP of DBK and in the
range from 2 ] 10~5 M to 2 ] 10~4 M for DHDMP. The
experimental traces were treated according to eqn. (9). The
absorption coefficients 6500 M~1 cm~1 for phenyl-
acetyl10,24,42 and 860 M~1 cm~1 for 2-hydroxy-2-
methylpropanoyl11 radicals were taken from the literature,
whereas the rate constants k and k and the initial radical
An example in Fig. 1 shows the kinetic traces obtained by
the LFP of DBK in three solvents at room temperature. The
observed kinetics reÑects the evolution of benzyl radical
according to the reaction scheme (1)È(6): the initial absorp-
tion jump corresponds to the generation of benzyl radicals in
the geminate reaction (2) followed by benzyl radical formation
due to decarbonylation of phenylacetyl (3). Further signal
decrease corresponds to the radical decay in the termination
reactions (4)È(6). At the minimal laser energies used (about 1
mJ per pulse) the reactions of radical termination become
much slower than decarbonylation, and the rate of the signal
growth practically coincides with the rate of the reaction (3). It
can be readily seen that the decarbonylation of the phenyla-
cetyl radical is fastest in the nonpolar hexane and slowest in
the polar aprotic acetonitrile.
CO
t
concentration R were Ðtting parameters. The deviations of
0
the calculated k values within each set of data usually did
not exceed 5È7%. Some of the simulations are shown in Fig. 1
CO
(the bold line corresponds to the calculated curves).
Results of the Arrhenius treatment of the decarbonylation
rate constants in three solvents are shown in Fig. 2 (LFP of
DBK) and Fig. 3 (LFP of DHDMP). Similar temperature
dependences were obtained for other solvents as well. As one
can see, the experimental data show good linear dependences
in Arrhenius coordinates, which allowed for the determination
of pre-exponential factors (A) and activation energies (E ). The
a
Arrhenius parameters are collected in Tables 1 and 2 for the
decarbonylation of phenylacetyl and 2-hydroxy-2-methyl-
propanoyl radicals, respectively. The tables also include the
Decarbonylation of the 2-hydroxy-2-methylpropanoyl
radical at ambient temperature is too fast to be measured by
conventional nanosecond Ñash photolysis, but at lower tem-
peratures traces similar to those shown in Fig. 1 were
observed.
values of k at ambient temperature, which for phenylacetyl
CO
are in a good agreement with the previous reports.4,5,10 For
Since the reactions of radical termination (4)È(6) are di†u-
sion controlled, and the radicals are of similar size, we can use
the approximation39 2k \ 2k B 2k B k . In this case, the
t
1
2
x
kinetics of radical formation and decay can be described by
eqns. (7) and (8):
d[ R0 ]
dt
\
k
[RC
0
O] [ 2k [R
0
]2 [ 2k [R
0
][RC
0
O]
(7)
CO
t
t
d[RC
0
O]
\
[k [RC
0
O] [ 2k [RC
0
O]2 [ 2k [R
0
][RC
0
O] (8)
dt
CO
t
t
Solution of this system yields the time dependence of benzyl
(
ketyl) radical concentration:47
[
R
0
] \ R M2 [ exp([k t)N/(1 ] 4k R t)
(9)
0
CO
t 0
Fig. 2 Arrhenius plots for the rate constant of phenylacetyl decarb-
onylation in hexane (squares), isopropanol (triangles) and acetonitrile
(circles).
where R is the initial radical concentration, R \ [ R0 ](t \ 0).
0
0
Determination of the decarbonylation rate constant k
CO was
3678 Phys. Chem. Chem. Phys., 2001, 3, 3677È3682

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Table 1 Rate constants k
solvents
CO of decarbonylation of phenylacetyl radicals at ambient temperature and Arrhenius parameters for kCO in various
e [ 1
Solvent
2e ] 1
EN
k
(295 K)/s~1
log(A/s~1)
E /kJ mol~1
T
CO
a
Hexane
0.188
0.356
0.388
0.420
0.460
0.470
0.477
0.480
0.009
0.259
0.648
0.309
0.546
0.654
0.762
0.460
(4.5 ^ 0.3) ] 106
(3.0 ^ 0.3) ] 106
(2.0 ^ 0.2) ] 106
(1.9 ^ 0.1) ] 106
(2.6 ^ 0.2) ] 106
(2.4 ^ 0.2) ] 106
(2.2 ^ 0.2) ] 106
(1.4 ^ 0.1) ] 106
12.2 ^ 0.6
12.9 ^ 0.6
11.7 ^ 0.6
13.1 ^ 0.5
12.5 ^ 0.6
11.5 ^ 0.4
12.1 ^ 0.6
13.1 ^ 0.7
31.5 ^ 1.1
36.4 ^ 1.4
30.5 ^ 1.2
38.3 ^ 1.4
34.2 ^ 1.5
28.9 ^ 0.9
32.2 ^ 1.3
39.6 ^ 1.5
Chloroform
Acetic acid
Dichloromethane
Isopropanol
Ethanol
Methanol
Acetonitrile
the 2-hydroxy-2-methylpropanoyl radical these values are esti-
mated by extrapolation of the low-temperature data to 295 K.
Discussion
The results obtained for the decarbonylation of the phenyl-
acetyl radical agree qualitatively with the earlier conclusions10
that the decarbonylation rate constant decreases in polar sol-
vents. According to the transition state theory, the inÑuence of
media on a rate constant is due to the di†erence in the free
energies of solvation of an initial radical and a transition state.
If the initial radical is more polar than the transition state, the
di†erence in the free energy of solvation increases with
increase in the solvent polarity. That results in the increase of
the activation energy E and decrease of the rate constant in
a
polar solvents as compared to nonpolar ones. Thus, the
Fig. 3 Arrhenius plots for the rate constant of 2-hydroxy-2-methyl-
experimental results have a simple qualitative explanation:
since in the course of fragmentation the polar phenylacetyl
radical transforms into the nonpolar benzyl radical and CO
molecule, the transition state for the decarbonylation reaction
should also be less polar than the initial radical.
propanoyl decarbonylation in methanol (squares), ethyl acetate
(
triangles) and acetonitrile (circles).
In the simplest Onsager model, the solvent polarity can be
characterized by the dielectric constant e, and the solvent
e†ect on the reaction rate constant k can be described with the
use of KirkwoodÏs formula:1
ln(k) [ ln(k ) \ [ Gtsolv \ [
*
RT
1
N
A
e [ 1
A
k2 k2
a [ t ,
B
(10)
0
4pe RT 2e ] 1 r3 r3
0
a
t
where k corresponds to the hypothetical solvent with e \ 1,
0
k , k , r and r are the dipole moments and the radii of the
a
t
a
t
initial radical and the transition state, respectively. According
to this formula, the change in activation energy of the reaction
is proportional to the parameter (e [ 1)/(2e ] 1).
Fig. 4 shows the plot of the activation energies of the
decarbonylation reaction of the phenylacetyl radical in di†er-
ent solvents vs. (e [ 1)/(2e ] 1). A good linear correlation can
be found only for aprotic solvents, whereas the data for alco-
hols and acetic acid lay far away from the values expected
Fig. 4 Correlation between KirkwoodÏs parameter (e [ 1)/(2e ] 1)
and the activation energy of phenylacetyl decarbonylation in di†erent
solvents.
Table 2 Rate constants k of decarbonylation of 2-hydroxy-2-methylpropanoyl radicals at room temperature and Arrhenius parameters for k
CO
CO
in various solvents
e [ 1
Solvent
2e ] 1
EN
k
(295 K)/s~1
CO
log(A/s~1)
E /kJ mol~1
T
a
Methylcyclopentane
Diethyl ether
Ethyl acetate
Methanol
0.198
0.341
0.385
0.477
0.480
0.010
0.117
0.228
0.762
0.460
4.4 ] 107
1.1 ] 108
8.2 ] 107
6.9 ] 107
4.1 ] 107
11.2 ^ 1.6
12.0 ^ 0.5
12.1 ^ 0.4
11.7 ^ 0.4
11.3 ^ 0.9
20.3 ^ 1.8
22.5 ^ 1.1
23.8 ^ 1.2
21.9 ^ 0.9
21.0 ^ 0.9
Acetonitrile
Phys. Chem. Chem. Phys., 2001, 3, 3677È3682
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The dipole moment calculated using the B3LYP/6-31G*
method changes from 2.3 D in phenylacetyl to 1.6 D in the
transition state. PM3 calculations also demonstrate a similar
decrease of the dipole moment in the transition state. Thus,
the electrostatic interactions with solvents should increase the
activation barrier and decrease the decarbonylation rate con-
stant, which agrees qualitatively with the experimental Ðnd-
ings (see data for aprotic solvents in Table 1 and Figs. 4 and
5).
To account quantitatively for the inÑuence of the electro-
static interactions with solvent on the rate constant, we used
the more sophisticated polarized continuum model (PCM),16
which takes into account the more realistic shape of a solvent
cavity and real charge distribution in a radical. Free energies
of solvation were calculated in two solvents, hexane and ace-
tonitrile. The calculated di†erence in the free energy of activa-
tion in these two solvents *Gt [ *Gt \ 4.2 kJ mol~1 is in
Fig. 5 Correlation between parameter EN and the activation energy
T
of phenylacetyl decarbonylation in di†erent solvents.
ACN
hex
a fairly good agreement with the experimental data.
The inÑuence of hydrogen bonding on the reaction rate
constant was calculated taking into account the di†erence in
the enthalpies of complex formation of the radical and the
transition state with solvent molecules. Methanol was used as
a typical molecule forming hydrogen bonds. The heat of
complex formation with the radical (7.2 kJ mol~1) was notice-
ably lower than that with the transition state (12.9 kJ mol~1).
Thus, the stabilization of the transition state by hydrogen
bonding is stronger than the stabilization of the initial radical.
This result conÐrms that hydrogen bonding, in contrast to
nonspeciÐc solvation, decreases the activation energy and
accelerates the rate of the decarbonylation. The calculated
e†ects of electrostatic interactions and hydrogen bonding on
the decarbonylation rate constant are of similar scales and of
di†erent signs in the case of typical protic solvent methanol,
which is in good agreement with the experimental Ðndings:
the activation energies is alcohols and in acetic acid are close
to that in nonpolar solvent hexane (Table 1).
according to formula (10). That is not surprising since the
Kirkwood formula is oversimpliÐed and takes into account
only electrostatic interactions between solvent and solute,
leaving aside all other interactions, most importantly, hydro-
gen bonding. Besides, the Onsager model treats the molecule
as a sphere with a point dipole in the center and does not take
into account the real shape of the molecule and the charge
distribution.
The other commonly used approach to describe the solvent
e†ect on reaction rate constants is the use of empirical param-
eters characterizing the solvent polarity, among which the
most popular is the DimrothÏs E scale.1 Empirical param-
T
eters take into account not only the electrostatic interactions,
but also the speciÐc interactions between solute and solvents.
Indeed, a good linear correlation has been found between
solvent parameter E (30) and the logarithm of the rate con-
T
stant for some reactions, in particular for the reaction of b-
scission of alkoxyl radicals.6,9
Thus, the quantum chemical calculations conÐrm the
hypothesis about mutual compensation of e†ects of speciÐc
and nonspeciÐc solvation on the rate constant of decarbonyla-
tion of the phenylacetyl radical.
The dependence of the phenylacetyl decarbonylation rate
constant on the parameter EN is shown in Fig. 5. It is obvious
T
that a linear correlation can be found only for aprotic sol-
vents, as well as with the use of KirkwoodÏs formula.
Comparison of Tables 1 and 2 shows that, although 2-
hydroxy-2-methylpropanoyl and phenylacetyl radicals have
similar dipole moments, the solvent e†ect on the rate constant
of decarbonylation of the former is much smaller than that of
the latter. The qualitative explanation of this is that both
polarity and hydrogen bonding abilities of the 2-hydroxy-2-
methylpropanoyl are associated with the hydroxy group,
present in the initial radical as well as in the transition state
and in the ketyl radical formed after decarbonylation. The
quantum chemical calculations conÐrm this statement.
One should note that the parameter EN is proportional to
T
the energy of the electronic transition of a standard com-
pound in di†erent solvents,1 and it grows with the increase of
both solvent relative permittivity and its ability for hydrogen
bonding. Thus, a linear correlation between EN and the reac-
T
tion activation energy can take place only if the electrostatic
interactions and hydrogen bonding inÑuence the reaction rate
constant in a similar manner. It is possible that the initial
radical is more polar than the transition state, whereas the
hydrogen bonding stabilizes the transition state more strongly
than the initial radical. In this case the mutual compensation
of speciÐc and nonspeciÐc solvation can occur. Most likely,
just this situation takes place in the case of phenylacetyl
decarbonylation. In order to conÐrm this assumption, we per-
formed quantum chemical calculations of the solvent e†ect on
the barrier to decarbonylation of the phenylacetyl radical.
The geometries of the phenylacetyl radical and of the tran-
sition state were optimized at the B3LYP/6-31G* level. The
length of the RÈCO bond, which cleaves during the reaction,
Elongation of the RÈCO bond in the transition state of the
2-hydroxy-2-methylpropanoyl radical is even larger than that
for phenylacetyl, whereas the redistributions of the spin den-
sities in both radicals are similar (Fig. 7). The energy di†erence
Fig. 6 Geometries and spin density distribution in the phenylacetyl
radical (R) and in the transition state of its decarbonylation (TS).
in the transition state was found to be about 0.5 AŽ longer than
that in the initial radical, and the lengths of the other bonds
change insigniÐcantly (Fig. 6). Also, redistribution of spin
density from carbonyl group to methylene group takes place.
The energy di†erence between the transition state and the
initial radical is 37.9 kJ mol~1 or 29.9 kJ mol~1 with zero-
point energy (ZPE) correction, and the enthalpy di†erence is
equal to 30.4 kJ mol~1. The latter values are in very good
agreement with the experimental activation energy in non-
polar solvent hexane (31.5 ^ 0.5 kJ mol~1).
Fig. 7 Geometries and spin density distribution in the 2-hydroxy-2-
methylpropanoyl radical (left) and in the transition state of its decarb-
onylation (right).
3680
Phys. Chem. Chem. Phys., 2001, 3, 3677È3682

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between the transition state and the initial radical is 32.5 kJ
mol~1 or 24.4 kJ mol~1 with ZPE correction. The latter value
is in fairly good agreement with the experimental activation
energy (20.3 ^ 0.9 kJ mol~1 in hexane). In contrast to phenyl-
acetyl, the dipole moment of the transition state (2.1 D) is a
little larger than that of the initial radical (1.8 D). The di†er-
ence in the free energy of activation in acetonitrile and hexane,
experimental data used in this study49 were taken from di†er-
ent sources and were obtained in di†erent experimental condi-
tions. As a result, data scatter for some radicals exceeded two
orders of magnitude. Besides, the enthalpy of RÈCO bond
cleavage was estimated in a relatively rough way.
We have performed B3LYP/6-31G* calculations of the
reaction enthalpy and the barrier to the decarbonylation of
some acyl radicals. The results are presented in Table 3. First
of all, we have to mark a very good agreement between our
calculations and estimations of the reaction enthalpies made
by Vollenweider and Paul.49 Second, the calculated reaction
barriers coincide well with the experimental values of the acti-
vation energies for nonpolar solvents.
calculated using the PCM model, is very small: *Gt
ACN
[
*Gt \ [0.7 kJ mol~1. This theoretical result is in good
hex
agreement with the experimental Ðnding that the activation
energies of the reaction in hexane and acetonitrile are very
close.
We also performed calculations of the enthalpies of complex
formation of the initial radical and transition state with meth-
anol, using the PM3 model. Two types of complex can be
formed: (a) an alcohol is a hydrogen donor; (b) an alcohol is a
hydrogen acceptor (see Fig. 8).
Finally, the deviation from the linear relationship between
bond dissociation enthalpy and reaction barrier for the phenyl-
acetyl radical becomes apparent (Fig. 9). The deviations for
phenyl-containing radicals can be explained in the following
way. The reaction coordinate for this reaction is a com-
bination of the CÈC bond stretch and libration motion of the
methylene carbon. The barrier heights for this reaction are
mainly determined by stretching of the CÈC bond and are
similar for phenylacetyl and 2-hydroxy-2-methylpropanoyl
radicals. In the transition states R R R C fragments are pyr-
In case (a) the heat of complex formation with the radical
(
7.0 kJ mol~1) is a little larger than that with the transition
state (6.2 kJ mol~1). The heat of complex formation is much
higher in the case of (b) type complex: 17.8 kJ mol~1 with the
initial radical and 13.4 kJ mol~1 with the transition state.
Therefore the activation energy should increase and the rate
constant decrease for the decarbonylation of the 2-hydroxy-2-
methylpropanoyl radical in solvents forming hydrogen bonds
due to electron pair donation. Indeed, the activation energy of
decarbonylation is a little higher in ether and ethyl acetate,
but the e†ect is very small.
1
2 3
amidal and in the case of PhCH hydrogen atoms are 22¡ out
2
of the phenyl plane. When moving along the decaying branch
of the phenylacetyl reaction coordinate a large part of the
whole energy decrease (16.4 kJ mol~1) is associated with the
relaxation of PhCH geometry (14 kJ mol~1). Note that the
2
Experiment (Tables 1 and 2) and calculations show that the
activation energies of the decarbonylation reaction of the
phenylacetyl radical (30È40 kJ mol~1) are signiÐcantly higher
than those of the 2-hydroxy-2-methylpropanoyl radical (20È24
kJ mol~1). We also calculated the energy di†erence between
the initial radicals and Ðnal products of the decarbonylation
reaction (Table 3). Opposite to the commonly valid relation-
ship between the enthalpies of activation and reaction,48 the
thermally neutral reaction has higher activation energy than
the endothermic one (Table 3).
di†erence in ZPE between the products and the transition
state is 15.5 kJ mol~1. The energy decrease due to the relax-
ation of (CH ) COH or CH radicals is very small (3È4 kJ
3
2
3
mol~1). Therefore we conclude that the reason for the devi-
ation from the linear relationship for phenyl-containing acetyl
radicals49 is the aromaticity of benzyl radicals (PhCR R ).
1
2
Earlier the relationship between log(k ) and the enthalpy
CO
of the decarbonylation reaction was considered by Vollenwei-
der and Paul.49 A usual linear correlation has been found for
all acyl radicals except phenyl-containing ones. However, the
Fig. 9 Data of quantum chemical calculations by the B3LYP/6-
3
1G* method: dependence of the reaction barrier (*Et) on the energy
Fig. 8 Structures of the two types of complexes of 2-hydroxy-2-
methylpropanoyl radical with methanol.
di†erence (*E ) between product (R ] CO) and reactant (RCO)
0
(corrected for ZPE).
Table 3 Data of quantum chemical calculations of the bond dissociation enthalpy [*H(RÈCO)], the reaction barrier to dissociation (*Et), the
enthalpy of activation at 298 K (*Ht), the CÉ É ÉCO bond length in the transition state, and the dipole moment in the initial (d ) and transition
rad
(d
) states
TS
*H(RÈCO)/kJ mol~1
B3LYP/6-31G* calculations
R
B3LYP/6-31G*
Ref. 49
*Et(*Ht)/kJ mol~1
R(CÉ É ÉCO)/A
drad/D
dTS/D
PhÈCH
[2.1
21.7
25.3
48.9
61.8
117.7
[6 ^ 2
18 ^ 8
25 ^ 5
43
61
109
29.8(30.4)
24.3(26.0)
36.3(38.0)
59.2(61.5)
73.3(75.8)
È
2.052
2.134
2.189
2.300
2.347
È
2.3
1.8
2.5
2.5
2.4
3.5
1.6
2.1
1.8
1.4
1.0
È
2
HO(CH ) C
3 2
(
CH ) C
3
3
C H
CH
3
2
5
Ph
Phys. Chem. Chem. Phys., 2001, 3, 3677È3682
3681

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1
6
7
(a) S. Miertus, E. Scrocco and J. Tomasi, Chem. Phys., 1981, 55,
Conclusion
1
17; (b) S. Miertus and J. Tomasi, Chem. Phys., 1982, 65, 239; (c)
V. Barone, M. Cossi and J. Tomasi, J. Chem. Phys., 1997, 107,
In the present paper, the importance of the solvent e†ect on
the rate constant of acyl radical decarbonylation has been
conÐrmed. It has been shown for the Ðrst time that the elec-
trostatic interactions with solvent and hydrogen bonding can
inÑuence this reaction in di†erent ways: the decarbonylation
of phenylacetyl proceeds more slowly in polar solvents,
whereas hydrogen bonding decreases the activation barrier
and increases the reaction rate constant. It was also shown
that the scale of the solvent e†ect is determined by the change
of the radical polarity in the course of the reaction rather than
by radical polarity itself: the solvent e†ect for phenylacetyl is
much more pronounced than that for the 2-hydroxy-2-methyl-
propanoyl radical of similar polarity. For most acyl radicals a
linear relationship exists between the enthalpy of the reaction
of decarbonylation and the barrier to the reaction. Deviations
from this linear dependence, found for phenyl-containing rad-
icals, can be explained as the result of pronounced energy
decrease due to the relaxation of PhCR R radical structure.
3
1
210; (d) V. Barone, M. Cossi and J. Tomasi, J. Comput. Chem.,
998, 19, 404.
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Acknowledgements
Support of this work by the Russian Foundation for Basic
Research (Projects No. 00-15-97450, No. 99-04-49879 and No.
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