DFT evidence for a stepwise mechanism in the O-neophyl rearrangement of 1,1-diarylalkoxyl radicals

Article abstract of DOI:10.1021/jo070125n

(Chemical Equation Presented) Hybrid DFT calculations of the potential energy surface (PES) relative to the O-neophyl rearrangement of a series of ring-substituted 1,1-diarylalkoxyl radicals have been carried out at the UB3LYP/6-31G(d) level of theory. On the basis of the computational data, the rearrangement can be described as a consecutive reaction of the type a ? b → c (see above graphic), and the steady-state approximation could be applied in all cases to the intermediate b. The first-order rearrangement rate constants [k_obs = k₁k₂/(k_-1 + k ₂)] were thus obtained from the computed activation free-energies and were compared with the experimental rate constants measured previously in MeCN solution by laser flash photolysis. An excellent agreement is observed along the two series, which strongly supports the hypothesis that the O-neophyl rearrangement of 1,1-diarylalkoxyl radicals proceeds through the formation of the reactive 1-oxaspiro [2,5]octadienyl radical intermediate. This is in contrast to previous hypotheses that involve either a long-lived intermediate or the absence of this intermediate along the reaction path. The calculated rearrangement free-energies decrease upon going from the methoxy-substituted radical (ΔG° = -16.4 kcal·mol^-1) to the nitro-substituted one (ΔG° = -21.8 kcal·mol^-1), which follows a trend that is similar to the one observed for the C _Ar-O bond dissociation enthalpies (BDEs) of ring-substituted anisoles. This evidence indicates that in the O-neophyl rearrangement the effect of ring substituents on the strength of the newly formed C_Ar-O bond plays an important role.

Full text of DOI:10.1021/jo070125n

DFT Evidence for a Stepwise Mechanism in the O-Neophyl
Rearrangement of 1,1-Diarylalkoxyl Radicals
Massimo Bietti,* Gianfranco Ercolani,* and Michela Salamone
Dipartimento di Scienze e Tecnologie Chimiche, UniVersita` “Tor Vergata”, Via della Ricerca Scientifica,
00133 Roma, Italy
bietti@uniroma2.it; ercolani@uniroma2.it
ReceiVed January 22, 2007
Hybrid DFT calculations of the potential energy surface (PES) relative to the O-neophyl rearrangement
of a series of ring-substituted 1,1-diarylalkoxyl radicals have been carried out at the UB3LYP/6-31G(d)
level of theory. On the basis of the computational data, the rearrangement can be described as a consecutive
reaction of the type a / b f c (see above graphic), and the steady-state approximation could be applied
in all cases to the intermediate b. The first-order rearrangement rate constants [kobs ) k1k2/(k-1 + k2)]
were thus obtained from the computed activation free-energies and were compared with the experimental
rate constants measured previously in MeCN solution by laser flash photolysis. An excellent agreement
is observed along the two series, which strongly supports the hypothesis that the O-neophyl rearrangement
of 1,1-diarylalkoxyl radicals proceeds through the formation of the reactive 1-oxaspiro [2,5]octadienyl
radical intermediate. This is in contrast to previous hypotheses that involve either a long-lived intermediate
or the absence of this intermediate along the reaction path. The calculated rearrangement free-energies
decrease upon going from the methoxy-substituted radical (∆G° ) -16.4 kcal‚mol-1) to the nitro-
substituted one (∆G° ) -21.8 kcal‚mol-1), which follows a trend that is similar to the one observed for
the CAr-O bond dissociation enthalpies (BDEs) of ring-substituted anisoles. This evidence indicates that
in the O-neophyl rearrangement the effect of ring substituents on the strength of the newly formed CAr-O
bond plays an important role.
SCHEME 1
Introduction
The 1,2-migration of an aryl group in arylcarbinyloxyl
radicals, known as the O-neophyl (or neophyl-like) rearrange-
ment, has been the subject of several studies.1 This process
converts an oxygen centered radical into an isomeric carbon
centered radical, and it has been observed only for radicals that
bear at least two R-aryl substituents, such as the triarylmethoxyl
and 1,1-diarylalkoxyl radicals. The mechanism of this re-
arrangement is still not entirely understood; the main question
is whether the bridged 1-oxaspiro[2,5]octadienyl radical is an
intermediate or a transition-state in this process (Scheme 1).
respectively. After LFP of a MeCN solution containing tert-
butyl 1,1-diphenylethylperoxide, Schuster observed the forma-
tion of a transient that was characterized by an absorption band
centered at 535 nm and assigned this transient to the bridged
radical.2 Later, Scaiano showed by LFP studies that Schuster’s
assignment was not correct and reassigned the 535 nm transient
to the 1,1-diphenylethoxyl radical (1a).4,5 He further concluded
that the bridged radical was either not an intermediate in the
rearrangement of 1a or was a short-lived intermediate that was
not detectable with nanosecond LFP techniques. Grossi reported
EPR spectra, which were obtained during a ceric ammonium
nitrate (CAN) induced photooxidation of triphenylmethanol and
Evidence in favor of the intermediacy of a 1-oxaspiro[2,5]-
octadienyl radical was provided by Schuster2 and Grossi3 by
means of laser flash photolysis (LFP) and EPR spectroscopy,
(1) For an excellent review on radical aryl migration reactions, see Studer,
A.; Bossart, M. Tetrahedron 2001, 57, 9649-9667.
(2) Falvey, D. E.; Khambatta, B. S.; Schuster, G. B. J. Phys. Chem. 1990,
94, 1056-1059.
(3) Grossi, L.; Strazzari, S. J. Org. Chem. 2000, 65, 2748-2754.
(4) Banks, J. T.; Scaiano, J. C. J. Phys. Chem. 1995, 99, 3527-3531.
10.1021/jo070125n CCC: $37.00 © 2007 American Chemical Society
Published on Web 05/08/2007
J. Org. Chem. 2007, 72, 4515-4519
4515

Bietti et al.
CHART 1
1,1-diphenylethanol, that were assigned to the corresponding
1-oxaspiro[2,5]octadienyl radicals that formed after O-neophyl
rearrangement of the triphenylmethoxyl and 1,1-dipenylethoxyl
radicals.3 However, Ingold reexamined these EPR data to
provide, in both cases, an unambiguous reassignment from
1-oxaspiro[2,5]octadienyl radicals to phenoxyl radicals.6
Our own results that have been obtained recently for a series
of symmetric and non-symmetric ring-substituted 1,1-diaryl-
alkoxyl radicals, by means of product and time-resolved (LFP)
kinetic studies, were instead interpreted in terms of a concerted
mechanism.7
To obtain additional evidence on the concerted or stepwise
nature of this rearrangement, we carried out hybrid DFT
calculations of the potential energy surface (PES) relative to
the reactions of the radicals 1a-6a (see Chart 1). Although most
of the experimental data are available for cyclopropyl-substituted
radicals,7 most of the calculations were carried out on the
corresponding methyl-substituted ones. The substitution of
methyl for cyclopropyl reduces the number of distinct confor-
mational minima of the involved species but does not signifi-
cantly affect the experimental and calculated rate constants (see
below the results of 1a vs 6a).
FIGURE 1. Gas-phase potential energy profile for the reaction of
radical 1a with reference to Scheme 2, calculated at the UB3LYP/6-
31G(d) level of theory.
In the case of the unsymmetrically substituted radicals 5a
and 9a, Scheme 3 holds.
The electronic energies, the electronic energies plus the
corresponding zero-point vibrational energy (zpve) corrections,
and the gas-phase free-energy differences (∆G°) for all the
species are reported in Table 1 and take the corresponding
reactant as a reference. When a given species exists as
populations over multiple conformers (see Supporting Informa-
tion), the data reported in Table 1 refer to the lowest-energy
conformer. It has been verified that ∆G° values of the lowest-
energy conformers and of the entire conformer populations differ
by less than 0.1 kcal‚mol-1
.
The computed kinetic results here obtained have been
compared with the experimental ones previously reported for
1a and 6a-8a7 and with the additional experimental data,
reported in Supporting Information, relative to the reaction of
radical 9a.
In all of the cases, with the possible exception of 5d, the
bridged 1-oxaspiro[2,5]octadienyl radical has been shown to be
a minimum along the reaction coordinate, which corresponds
to a short-lived intermediate. When an allowance is made for
the zpve correction, the case of 5d is ambiguous because its
energy is practically coincident with that of the transition-state
preceding its formation (TS5a-5d). This indicates the absence
of any energy barrier that separates the low-energy vibrational
levels of 5d and TS5a-5d. Apart from this possible exception,
the overall picture, at the temperature of 0 K appears to be quite
consistent. The matter is not so clear-cut at 298 K, be-
cause a potential energy barrier less than rt (about 0.6
kcal‚mol-1) is negligible. From this point of view the existence
of the bridged 1-oxaspiro[2,5]octadienyl radical as a distinct
intermediate might be questionable in some of the cases reported
in Table 1.
Results
Hybrid DFT calculations, at the UB3LYP/6-31G(d) level of
theory, have been carried out for the reactions of the radicals
1a-6a in the gas-phase. This level of theory was used because
the results it provides for radicals have generally been found to
be very reliable not only for equilibrium species but also for
transition-states, as long as no sudden spin localization is
required for the adiabatic passage from reactants to products.8
The geometry optimization of reactants, intermediates, and
products, followed by location of the transition-states, has
allowed for the calculation of all the stationary points of the
potential energy curves. For the sake of illustration, the curve
relative to the reaction of the radical 1a, with reference to
Scheme 2, is shown in Figure 1.
When focused on the overall energetics of the reaction series
1a-4a, it is evident that the reaction depends on the energetic
balance due to the cleavage of a CAr-C bond in the starting
1,1-diarylalkoxyl radical (1a-4a) and accompanied by the
formation of a CAr-O bond in the rearranged carbon centered
SCHEME 2
4516 J. Org. Chem., Vol. 72, No. 12, 2007

O-Neophyl Rearrangement of 1,1-Diarylalkoxyl Radicals
SCHEME 3
TABLE 1. Thermodynamic Data for the Reactions of the Radicals
SCHEME 4
1a-6aa
electronic
energy
electronic energy
structure
+ zpve
∆G° b
1a
TS1a-1b
1b
0
8.9
8.2
0
7.6
7.2
0
8.1
7.4
TS1b-1c
1c
10.4
-17.0
8.9
-17.4
9.2
-18.3
2a
TS2a-2b
2b
0
8.7
8.4
0
7.5
7.4
0
8.0
7.6
TABLE 2. Absolute and Relative Gas-Phase CAr-C and CAr-O
BDEs of Para Substituted Benzyl Alcohols (4-XC6H4-CH2OH) and
Anisoles (4-XC6H4-OCH3)a
TS2b-2c
2c
11.5
-14.8
10.0
-15.4
10.4
-16.4
X
4-XC6H4-CH2OH
4-XC6H4-OCH3
3a
TS3a-3b
3b
TS3b-3c
3c
0
8.5
7.1
8.9
-18.7
0
7.3
6.3
7.6
-19.0
0
7.6
6.5
7.7
-21.1
H
OCH3
CF3
94.3 (0)
95.3 (0)
95.4 (+1.1)
94.8 (+0.5)
95.2 (+0.9)
94.8 (-0.5)
96.5 (+1.2)
97.7 (+2.4)
NO2
4a
TS4a-4b
4b
TS4b-4c
4c
0
7.4
4.9
6.4
-21.2
0
6.3
4.2
5.1
-21.3
0
6.9
4.6
5.4
-21.8
a
Calculated at the UB3LYP/6-31G(d) level of theory, at 298.15 K, and
at 1 atm. Reported in kcal‚mol-1. ∆BDEs values, in parentheses, are relative
to X ) H.
5a
TS5a-5b
5b
TS5b-5c
5c
TS5a-5d
5d
0
10.6
9.2
10.6
-15.8
9.1
8.8
11.7
-15.3
0
9.3
8.2
9.2
-16.3
7.8
7.8
10.2
-15.8
0
9.7
8.0
9.5
-17.5
8.3
7.8
10.5
-17.3
to the cancellation of errors, differences in BDEs (∆BDEs)
within a closely related family of compounds are much more
reliable than the absolute values.9 Absolute and relative BDEs
thus obtained for CAr-C and CAr-O bond cleavage of ring-
substituted benzyl alcohols and anisoles are collected in Table
2.
TS5d-5e
5e
6a
TS6a-6b
6b
0.0
8.9
8.5
0.0
7.7
7.6
0.0
8.2
7.7
Discussion
TS6b-6c
6c
10.6
-17.2
9.2
-17.4
9.5
-18.3
Before getting to the heart of the discussion of the compu-
tational results, it is important to validate them by comparison
against the available experimental data. Because most of the
experimental data are available for cyclopropyl-substituted
radicals,7 whereas most of the calculations have been carried
out, for practical convenience, on the corresponding methyl-
substituted ones, the first question to resolve is the lack of a
significant change of effects upon the substitution of methyl
for cyclopropyl. It was already evidenced in a previous work
that this substitution produces only a minor change in the
observed rate constant of O-neophyl rearrangement on passing
Reported in kcal‚mol-1. Calculated at the B3LYP/6-31G(d) level of
a
theory relative to the corresponding reactant. b In the gas-phase at 298.15
K and 1 atm.
radical (1c-4c). Thus to properly discuss this balance, we have
felt that it is also necessary to evaluate the gas-phase bond
dissociation enthalpies (BDEs), at the same level of theory, for
the cleavages of the two series of compounds, 4-XC6H4-
CH2OH and 4-XC6H4-OCH3 (X ) OCH3, H, CF3, NO2),
respectively, as described in Scheme 4.
BDEs calculated at the UB3LYP/6-31G(d) level of theory
are sufficiently reliable for the discussion presented here. It has
been pointed out that the B3LYP functional offers an attractive
and seemingly accurate alternative to the expensive conventional
ab initio methods for the computation of BDEs8 and that, thanks
(6) Ingold, K. U.; Smeu, M.; DiLabio, G. A. J. Org. Chem. 2006, 71,
9906-9908.
(7) Aureliano Antunes, C. S.; Bietti, M.; Ercolani, G.; Lanzalunga, O.;
Salamone, M. J. Org. Chem. 2005, 70, 3884-3891.
(8) Bally, T.; Borden, W. T. In ReViews in Computational Chemistry;
Lipkowitz, K. B., Boyd, D. B. Eds.; Wiley-VCH: New York, 1999; Vol.
13, pp 1-97.
(5) Avila, D. V.; Ingold, K. U.; Di Nardo, A. A.; Zerbetto, F.; Zgierski,
M. Z.; Lusztyk, J. J. Am. Chem. Soc. 1995, 117, 2711-2718.
(9) Pratt, D. A.; DiLabio, G. A.; Mulder, P.; Ingold, K. U. Acc. Chem.
Res. 2004, 37, 334-340 and references therein.
J. Org. Chem, Vol. 72, No. 12, 2007 4517

Bietti et al.
TABLE 3. Calculated Gas-Phase and Experimental
Solution-Phase First-Order Rate Constants for the Rearrangement
of Radicals 1a-9a
Microscopic rate constants appearing in eqs 1-3 have been
calculated from the free-energies of activation reported in Table
1 by the canonical transition-state theory.10,11 The gas-phase rate
constants reported in Table 3 are calculated on the basis of either
eq 1 or eq 2, and the available experimental rate constants are
measured in a MeCN solution. In the case of unsymmetrically
substituted radicals, the molar ratio Q is also reported.
kcalc
kexp
radical
s-1 a
s-1 b
1a
2a
3a
4a
5a
R ) Me; X ) Y ) H
9.3 × 105
1.5 × 105
7.5 × 106
5.3 × 107
3.8 × 105
(Q ) 2.2)
5.9 × 105
2.8 × 106 c
R ) Me; X ) Y ) OMe
R ) Me; X ) Y ) CF3
R ) Me; X ) Y ) NO2
R ) Me; X ) OMe, Y ) CF3
Direct comparison between kexp and kcalc for 1a and 6a shows
that, in both cases, the experimental value is ≈3 times larger
than the calculated one. Moreover, as indicated above, it is
legitimate to compare kexp for the cyclopropyl-substituted
radicals 7a-9a with kcalc relative to the corresponding methyl-
substituted ones, 2a, 3a, and 5a, respectively; the kexp values
are from 1.3 to 2.4 times larger than the kcalc ones. The
conclusion is that the accordance between theoretically evaluated
and experimental rate constants is extraordinarily good on the
energy scale, which lends support to the reliability of the PESs
evaluated at the UB3LYP/6-31G(d) level of theory. Further
support comes from the comparison of the molar ratio Q in the
case of the rearrangement of the unsymmetrically substituted
radicals 5a and 9a; indeed the theory predicts that isomer 5c is
preferentially formed with respect to isomer 5e, which is
analogous to the experimentally observed predominance of
isomer 9c with respect to isomer 9e (see Scheme 3 and Table
3).
6a
7a
8a
9a
R ) c-Pr; X ) Y ) H
2.0 × 106 c
2.6 × 105 c
1.8 × 107 c
5.1 × 105 d
(Q ) 4.3) d,e
R ) c-Pr; X ) Y ) OMe
R ) c-Pr; X ) Y ) CF3
R ) c-Pr; X ) OMe, Y ) CF3
a Gas-phase at 298.15 K and 1 atm. b MeCN solution at 295.15 K. c Ref
7. d This work (see Supporting Information). e Molar ratio of products
obtained in CH2Cl2 at 293.15 K.
from radical 6a to 1a in a CH3CN solution at 295.15 K (see
Table 3).7 Comparison between the ∆G° values for the reactions
of radicals 1a and 6a, displayed in Table 1, shows that the data
differ by e 0.3 kcal‚mol-1. This is evidence that the substitution
of methyl for cyclopropyl does not significantly affect the overall
computational results. Validation of the computed data can
therefore be realized, aside from the direct comparison with
experimental data in the case of the radicals 1a and 6a, by
comparing the computational data obtained for the methyl-
substituted radicals 2a, 3a, and 5a with the experimental data
relative to the cyclopropyl-substituted ones 7a-9a, respectively.
To carry out such a comparison, the computed ∆G° values
shown in Table 1 must be translated into rate constants.
According to Hammett, in a consecutive reaction of the type
shown in Scheme 2, it is only necessary for the free-energy of
the intermediate (b) to be a couple of kilocalories or more higher
than that of the reactant (a) for the Bodenstein steady-state
approximation to apply.10 This condition is largely verified for
the cases at hand. Accordingly, the overall first-order rearrange-
ment rate constants for the radicals that follow Scheme 2 will
be given by eq 1.
The DFT computations thus provide strong support for the
hypothesis that the O-neophyl rearrangement of 1,1-diaryl-
alkoxyl radicals proceeds through the reversible formation of
the reactive 1-oxaspiro[2,5]octadienyl radical intermediate. A
reactive intermediate is typically present at very low, often
undetectable, concentrations during the reaction course. In this
sense, the above results are in contrast with the observations of
Schuster2 and Grossi,3 which were successively challenged by
Scaiano4,5 and Ingold,6 respectively, who suggested the ac-
cumulation of a relatively long-lived intermediate.
The above results are also in contrast to our own previous
hypothesis of a concerted mechanism that appeared suitable to
interpret the observed substituent electronic effects.7 Indeed in
our previous work we found excellent Hammett-type correla-
tions between the σ+ substituent constants and both the visible
absorption band maxima of the reacting radicals and the
rearrangement rate constants. These results were unduly inter-
preted as significant evidence of a reactant-like transition-state,
and the latter was in contrast with a stepwise mechanism in
which the formation of a high-energy intermediate is rate-
determining.
k1k2
k )
(1)
k-1 + k2
One possible objection to the use of the steady-state ap-
proximation for all of the cases reported in Table 1 is that, at
298 K, in some of the examined cases, it is not absolutely clear
if the 1-oxaspiro[2,5]octadienyl radical is actually an intermedi-
ate (see Results). However, we wish to point out that this
objection is irrelevant because in these dubious cases k-1 . k2
so that the overall rate constant is determined by the free-energy
of the second transition-state, which is exactly the same result
that one would obtain by considering a concerted reaction in
which the first transition-state is ignored.
The data in Table 1 provide a significant basis for the critical
discussion of substituent effects on a consecutive reaction of
the type a / b f c. To this end we will focus on ∆G° values
relative to the reactions of radicals 1a-4a. The data relative to
the 1-oxaspiro[2,5]octadienyl radical intermediates 1b-4b show
that the presence of methoxy ring substituents in 2b determines
a negligible effect with respect to the unsubstituted intermediate
1b (7.6 vs 7.4 kcal‚mol-1), whereas a significant stabilizing
effect is observed in the presence of electron-withdrawing
substituents, which increases upon going from the CF3-
substituted radical 3b (6.5 kcal‚mol-1) to the NO2-substituted
Analogously, for the case of an unsymmetrically substituted
radical following Scheme 3, eqs 2 and 3 hold, where Q is the
molar ratio c/e of the rearranged products.
k1k3
k2k4
k )
+
(2)
k-1 + k3 k-2 + k4
k1k3
k-1 + k3
k2k4
(10) Hammett, L. P. In Physical Organic Chemistry, 2nd ed.; McGraw-
Hill: New York, 1970. Chapter 5.
(11) Cramer, C. J. Essentials of Computational Chemistry - Theories
and Models, 2nd ed.; Wiley: Chichester, UK, 2004; pp 524-527.
Q )
(3)
k-2 + k4
4518 J. Org. Chem., Vol. 72, No. 12, 2007

O-Neophyl Rearrangement of 1,1-Diarylalkoxyl Radicals
one 4b (4.6 kcal‚mol-1). A similar trend is observed, although,
as expected, to a lesser degree, for the free-energies of the first
transition-state TSa-b relative to the formation of the bridged
radical intermediate from the 1,1-diarylalkoxyl radical. In
contrast, the second transition-state TSb-c, relative to the
transformation of the radical intermediate into the corresponding
final carbon centered radical, appears to be much more sensitive
to electronic effects, which spans about 5 kcal‚mol-1 upon going
from the OMe to the NO2 group. Interestingly, this large
sensitivity changes the relative importance of the two transition-
states in affecting the observed reaction rate. Indeed, according
to the steady-state approximation, the reaction rate is mostly
affected by the transition-state which has the higher free-energy,
no matter whether it is the first or the second transition-state.10
The second transition-state, TSb-c, has a higher free-energy than
the first one, TSa-b, in the cases of X ) MeO and H and has
comparable free-energy in the case of X ) CF3. Its free-energy
decreases below the level of TSa-b in the case of X ) NO2.
The final carbon centered radical is also largely sensitive to
electronic effects; its free-energy decreases by 5.4 kcal‚mol-1
upon going from the OMe to the NO2 group. The main
contribution to the energetics of the process can be reasonably
ascribed to the cleavage of a CAr-C bond in the starting 1,1-
diarylalkoxyl radical (1a-4a) that is accompanied by the
formation of a CAr-O bond in the rearranged carbon centered
radical (1c-4c). Along this line, relative gas-phase CAr-C and
CAr-O BDEs of para-substituted benzyl alcohols and anisoles,
collected in Table 2, can help to shed light on the relative
importance of the two processes. The data indeed show that,
although all substituents determine a small but comparable
increase in the CAr-C BDE for the benzyl alcohol series,
opposite effects are instead observed in the anisole series. The
CAr-O BDE slightly decreases in the presence of the OMe ring
substituent and progressively increases upon going to the
electron-withdrawing CF3 and NO2 substituents. Very impor-
tantly, the latter trend is analogous to that observed for the
calculated reaction free-energy differences, ∆G°, for the rear-
rangement of radicals 1a-4a (Table 1) discussed above, which
indicates that in the rearrangement the effect of ring substituents
on the strength of the newly formed CAr-O bond plays an
important role. Along this line, the observations that the free-
energy differences calculated for the bridged radical intermediate
and the activation free-energies relative to its conversion into a
carbon centered radical, ∆G°TSb-c, increase in the presence of
electron-releasing substituents and decrease in the presence of
electron-withdrawing ones (see above) can be interpreted
similarly in terms of the substituent effect on the strength of
the CAr-O bond.
reaction path. The present study, moreover, indicates that, among
the factors that govern the rearrangement, the strength of the
CAr-O bond that is formed during the rearrangement appears
to play an important role.
Experimental Section
Computational Details. Hybrid DFT calculations have been
carried out at the UB3LYP/6-31G(d) level of theory using the
Gaussian 03 program package.12 All species have been fully
geometry optimized in the gas-phase and characterized as minima
or transition-states by frequency calculations; the Cartesian coor-
dinates are supplied in Supporting Information. The calculated spin-
squared expectation values (<S2>) were, after spin annihilation,
e0.751 in all cases, which is in good agreement with the
theoretically expected value of 0.75 for a pure doublet state.
Transition-states have been located by the quadratic synchronous
transit method (QST2). The eigenvector relative to the imaginary
frequency of each transition-state has been carefully inspected with
the help of the program GaussView13 to check that it corresponded
to the expected reaction coordinate. IRC calculations have been
also carried out to confirm that the located transition-state actually
connected the reactants and products from which it had been
generated by the QST2 algorithm. Zero-point energies and gas-
phase thermodynamic data at 298.15 K and 1 atm have been
calculated by the standard harmonic approximation without any
correction to vibrational frequencies.
Gas-phase BDEs at 298.15 K and 1 atm relative to the processes
in Scheme 4, with X ) OCH3, H, CF3, and NO2, were also
calculated by geometry optimization and frequency calculations of
the involved species at the UB3LYP/6-31G(d) level of theory [BDE
) H° (p-XC6H4 ) + H° (Y•) - H° (p-XC6H4Y)].
•
298
298
298
Acknowledgment. Financial support from the Ministero
dell’Istruzione dell’Universita` e della Ricerca (MIUR) is grate-
fully acknowledged.
Supporting Information Available: Results and experimental
details of product and time-resolved studies for radical 9a. Cartesian
coordinates, potential energy, and thermodynamic data for all of
the stationary points of the reaction of radicals 1a-6a calculated
at the UB3LYP/6-31G(d) level of theory. This material is available
free of charge via the Internet at http://pubs.acs.org.
JO070125N
(12) Gaussian 03, Revision B.01, Frisch, M. J.; Trucks, G. W.; Schlegel,
H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.,
Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.;
Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.;
Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda,
R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai,
H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken,
V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.;
Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.;
Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski,
V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D.
K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui,
Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.;
Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith,
T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; and
Pople, J. A.; Gaussian, Inc.: Wallingford CT, 2004.
In conclusion, the results presented above show that DFT
computational methods based on the hybrid B3LYP functional
and on a basis set of moderate size such as 6-31G(d) can be
conveniently used for the determination of kinetic data relative
to neutral free-radical reactions. This is evidenced by the close
adherence of the computational gas-phase rate constants to the
experimental ones obtained in solution. The results point out
to the reliability of the computed gas-phase mechanism of
reaction. The bridged 1-oxaspiro[2,5]octadienyl radical has
generally been shown to be a minimum along the reaction
coordinate, which corresponds to a reactive intermediate. This
is in contrast with previous hypotheses involving either a long-
lived intermediate or the absence of this intermediate along the
(13) Dennington, R., II; Keith, T.; Millam, J.; Eppinnett, K.; Hovell, W.
L.; and Gilliland, R.; GaussView, Version 3.09, Semichem, Inc.: Shawnee
Mission, KS, 2003.
J. Org. Chem, Vol. 72, No. 12, 2007 4519