gation is less effective in 7-norbornyl because of the geo-
metrical constraints. As a result, the C7-C1 and C7-C4
bond distances shorten only by 3 pm. The C1-C7-C4 angle
is about 4° wider than the same angle in norbornane. Again,
the radical center is trying to attain a planar geometry but is
hindered by a rigid structure. As a result, DH°(C7-H) >
DH°(C2-H).
Table 2. Experimental Values (kJ mol-1) for the C1-H BDE
in Norbornane
authors (year)
methoda DH°(C1-H) ref
Applequist, Kaplan (1965)
O’Neal, Bagg, Richardson (1970)
Danen, Tipton, Saunders (1971)
SPK
GPK
GPK
408.8
403.3 ( 9.6
416
24
25
22
In the 1-norbornyl radical, hyperconjugation is achieved
by delocalizing the spin through three C-H bonds. There-
fore, the spin density at the radical center is smaller than in
the other two radicals (Table 3), implying that the 1-norbor-
nyl radical should be the most stable. However, spin density
is not the only parameter required to explain the observed
stability trend (see below). As a result of the rigid structure
around C1, the radical cannot attain the optimal planar (or
nearly planar) geometry. The bond distances around C1
shorten by 2-3 pm, but the rest of the bond distances become
stretched by 1-2 pm. On the other hand, the angle at the
radical center is wider than in norbornane, but an opposite
trend is observed for several other angles. These changes
make 1-norbornyl the least stable of the three norbornyl
radicals and therefore the C1-H BDE has the highest value.
An alternative method to understand the stability trend of
the norbornyl radicals, is using natural bond orbital (NBO)
analysis to calculate the p% character associated with each
one of the three C-H bonds in norbornane and with the odd
electron of the corresponding radical atom. This has been
proposed by Feng et al.,3 who showed that the C-H BDEs
in hydrocarbons are dependent not only on the spin density
but also on the hybridization of the radical and the parent
molecule. Ring strain influences the hybridization in nor-
bornane and in the corresponding radicals, as it forces these
species to assume a certain geometry. The p% character data
in Table 3 are in excellent agreement with the values
computed by Feng et al. As observed, the p% character for
the three carbon atoms is similar in norbornane but signifi-
cantly different in the radicals. The smallest deviation from
the pure p character in norbonyl radicals is observed for C2
in the 2-norbornyl radical, justifying a C2-H BDE smaller
than C1-H and C7-H BDEs. On the other hand, the p%
character in the radical center of 1-norbornyl has the highest
deviation from a pure p orbital. Therefore, C1-H BDE has
the highest value among the three BDEs. An intermediate
situation is observed for C7. Hence, the C7-H BDE lies
between the C1-H and C2-H BDEs.
a SPK ) solution-phase kinetics; GPK ) gas-phase kinetics.
the C1-H BDE (416 kJ mol-1) determined by Danen et al.22
is recalculated using recent data for C-H BDEs in
t-Bu-H, Me-H, Et-H, i-Pr-H, and s-Bu-H,21,23 we
obtained DH°(C1-H) ) 427 kJ mol-1.
The trend DH°(C1-H) > DH°(C7-H) > DH°(C2-H)
can be easily rationalized considering the relative stability
of the resulting carbon-centered radicals. The 2-norbornyl
radical is stabilized by hyperconjugation with the neighboring
C1-H and C3-H bonds. This leads to a 6 and 4 pm
shortening, respectively, in the C2-C3 and C2-C1 bonds
in 2-norbornyl radical, relative to the corresponding bond
lengths in norbornane (Figure 1). This shortening is in good
agreement with previously reported bond length data.26 On
the other hand, as shown in Figure 1, the C1-C2-C3 angle
in 2-norbornyl radical is about 5° wider than the same angle
in norbornane. This seems to indicate that the radical center
is trying to achieve a planar geometry but is constricted by
the rigid carbon frame. Nonetheless, this is the largest angle
widening for the three norbornyl radicals.
As expected, the 7-norbornyl radical is less stabilized by
hyperconjugation than the 2-norbornyl radical. This is in
keeping with the spin density values for the two radicals
(Table 3). The spin density in the radical center of 7-nor-
Table 3. Spin Densities at the Radical Centers of Norbornyl
Radicals and NBO Analyis Results for p% Character Associated
with the C-H Bond in Norbornane and with the Odd Electron
of the Radical Atom
spin density p% in norbornane p% in radical
1-norbornyl
2-norbornyl
7-norbornyl
+0.907
+0.967
+0.970
0.75
0.77
0.76
0.83
0.98
0.93
Comparing the selected results in Table 1 with other C-H
BDEs in simple hydrocarbons, we find that DH°(C7-H) is
similar to the C-H BDE in methane (439.1 ( 0.5 kJ
mol-1),23 supporting the limited hyperconjugation of the
C7 carbon with vicinal C-H bonds. The value for
DH°(C2-H) matches the C2-H BDE in propane (412.5 (
1.7 kJ mol-1)21 corroborating the conclusion that the 2-nor-
bornyl radical is stabilized by hyperconjugation with both
C1-H and C3-H bonds.
Remarkably, the DH°(C1-H) is ∼10 kJ mol-1 higher than
the C-H BDE in methane but similar to the calculated
bridgehead C-H BDEs in bicyclo[1.1.1]pentane and bicyclo-
[2.1.1]hexane.3 This is consistent with the hypothesis that
bornyl is higher than the corresponding value for the
2-norbornyl. Both of these radicals may delocalize spin
through two neighboring C-H bonds, but the hyperconju-
(22) Danen, W. C.; Tipton, T. J.; Saunders, D. G. J. Am. Chem. Soc.
1971, 93 (20), 5186-5189.
(23) Ruscic, B.; Boggs, J. E.; Burcat, A.; Csaszar, A. G.; Demaison, J.;
Janoschek, R.; Martin, J. M. L.; Morton, M. L.; Rossi, M. J.; Stanton, J.
F.; Szalay, P. G.; Westmoreland, P. R.; Zabel, F.; Berces, T. J. Phys. Chem.
Ref. Data 2005, 34 (2), 573-656.
(24) Applequist, D. E.; Kaplan, L. J. Am. Chem. Soc. 1965, 87 (10),
2194-2200.
(25) O’Neal, H. E.; Bagg, J. W.; Richardson, W. H. Int. J. Chem. Kinet.
1970, 2, 493-496.
(26) Agapito, F.; Nunes, P. M.; Costa Cabral, B. J.; Borges dos Santos,
R. M.; Martinho Simo˜es, J. A. J. Org. Chem. 2007, 72, 8770-8779.
Org. Lett., Vol. 10, No. 8, 2008
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