Rate Constants for Reactions of Alkyl Radicals
plexation will accelerate a 5-exo radical cyclization such as that
in radical 3.21 The computational results suggest that an alkali
metal ion will accelerate the radical cyclization in the gas phase,
but little evidence for such an acceleration in condensed phase
is available, probably because the binding constants for forma-
tion of complexes between an alkene and an alkali metal ion
are small. For the ring opening reaction of radical 8, Lewis acids
should not affect the reaction because a complex will not be
present in condensed phase.
With the caveat that the rate constant for cyclization of radical
3 might be affected by the Lewis acid Et3B, we used estimated
rate constants for cyclization of 3 and ring opening of 8 to
calculate second-order rate constants for the H-atom transfer
reactions. Both the 5-hexenyl radical and the 1-methyl-5-hexenyl
radical cyclize at 20 °C with rate constants of kR ) 2 × 105
FIGURE 1. Product ratios from reactions of radical 8 in the presence
of Et3B with water (b), with deuterium oxide (9), or with methanol
(2). U/R is the ratio of the cyclobutyl product 10 to ring opened product
11. The lines are least-squares fits for each data set.
s-1 17,18,22,23
and we assumed that this would be equal to the
,
rate constant for cyclization of 3. For the ring opening of radical
8, we assumed that the rate constant would be equal to that for
ring opening of the cyclobutylcarbinyl radical at 20 °C, kR )
trapping agents at varying concentrations, and the products were
determined by GC analysis. Hydrocarbon products 10 and 11
were identified by comparison to authentic samples. The yields
of hydrocarbons 10 and 11 were high (>70%) with Et3B-H2O,
consistent with expectations that the generation of 8 from a
radical chain reaction of 7 would be relatively efficient. Also
as expected, the ratios of unrearranged to rearranged products
were considerably larger than those from reactions of radical 3.
Figure 1 shows representative results for the reactions of
radical 8 in the presence of Et3B with additives. The ratio of
10 to 11 is plotted against the concentration of the Et3B complex,
and the slope of these plots is the ratio of rate constants kH/kR.
The near-zero intercepts of these plots are noteworthy because
they show that the radical reaction is not reversible (see below).
Complete results for the studies with radical 8 are given in the
Supporting Information, and the ratios of rate constants obtained
in these studies are listed in Table 2. In most of the experiments,
the relative amount of unrearranged product was in the range
of 20-80%, and good precision was obtained in the relative
rate constants.
1000 s-1 4,19,24
These values for kR and the experimental ratios
.
of rate constants gave the values for kH that are listed in Table 2.
The values of the absolute rate constants kH might have
systematic errors due to the assumed rate constants for the
rearrangements, but those errors are not likely to be as large as
a factor of 2. More importantly, the relative rate constants for
two trapping agents reacting with the same radical clock will
have good accuracy. Thus, triethylborane complexed with water
reacted with radical 8 five times as fast as the uncomplexed
borane reagent, and the presence of the Lewis basic solvent THF
as an additive had little effect on the reactivity of the
R-hydrogens of Et3B. Assuming that the R-hydrogen atoms in
Et3B complexed with H2O and D2O have the same reactivity
as in the uncomplexed borane, one can factor out an equal
contribution to the kinetics of reactions of the borane R-hydro-
gens from the H2O and D2O reactions to give a kinetic isotope
effect for reaction of the water complexes with radical 8 of kH/
kD ) (2.0 - 0.4)/(0.8 - 0.4) ) 4.
The rate constants we determined are for reactions at room
temperature, but one can make qualitative predictions about the
rate constants at other temperatures because various second-
order hydrogen atom transfer reactions have relatively consistent
entropy demands. More importantly for synthetic considerations,
one can predict that the hydrogen atom transfer reactions from
the triethylborane-water and -methanol complexes should
become increasingly competitive with radical rearrangements
such as we used for the radical clocks in this work. For example,
the log A values for many hydrogen atom transfer reactions to
carbon-centered radicals are in the range of 8-9.4,13 The 5-exo
radical cyclization reactions, such as the cyclization of radical
clock 3, have entropy of activation terms that are less negative
than those for second-order bimolecular H-atom transfer reac-
tions; one can use an approximate value of log A ) 10 for such
When a radical clock study is performed with a relatively
slow trapping agent, one should determine whether the clock
reaction is reversible under the reaction conditions. That can
be established in the type of study performed here because the
intercepts of the plots of product ratios versus concentration of
trapping agent would be non-zero if the radical reaction was
reversible.13 As indicated in Figure 1 and listed in the Supporting
Information, we found zero intercepts within experimental error
for all reactions with radical 8, thus ensuring that the reactions
were not reversible.
The ratios of rate constants determined experimentally can
be used to calculate absolute rate constants kH if the rate constant
for the rearrangement reaction is known. This “radical clock”
method is commonly employed with the assumption that the
rate constants for the rearrangement reactions are not affected
by any special reaction conditions. The rate constants for simple
radical cyclization and ring opening reactions such as those used
here are generally not subject to noticeable solvent effects.13
Nonetheless, it is possible, in principle, that Lewis acids will
affect the kinetics of radical reactions, and Horn and Clark
explored computationally the possibility that Lewis acid com-
(23) Lusztyk, J.; Maillard, B.; Deycard, S.; Lindsay, D. A.; Ingold, K.
U. J. Org. Chem. 1987, 52, 3509-3514.
(24) In the original study of ring openings of cyclobutylcarbinyl radical
ring openings, the value obtained for the rate constant for cyclobutylcarbinyl
ring opening was k ) 500 s-1 at ambient temperature, but the value assumed
for the rate constant for the competing reaction, Bu3SnH trapping of an
alkyl radical, was 1 × 106 M-1 s-1 (ref 19). The currently accepted value
for the rate constant for the Bu3SnH reaction is 2 × 106 M-1 s-1 (ref 4).
(25) For a reaction with ∆Sq ) 0 eu at room temperature, the equivalent
Arrhenius function term is log A ) 13.1.
(21) Horn, A. H. C.; Clark, T. J. Am. Chem. Soc. 2003, 125, 2809-
2816.
(22) Chatgilialoglu, C.; Ingold, K. U.; Scaiano, J. C. J. Am. Chem. Soc.
1981, 103, 7739-7742.
(26) Wilt, J. W.; Lusztyk, J.; Peeran, M.; Ingold, K. U. J. Am. Chem.
Soc. 1988, 110, 281-287.
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