A R T I C L E S
Antonello et al.
DET can be expressed as a function of the bond dissociation
free energy (BDFE) of the cleaving bond and the E° of the
leaving group:2
of radical anions occurring by fragmentation of a σ bond have
been published.2,3,8,11b,13-24 Except for a few systems,21-24
however, the antibonding orbital initially hosting the electron
(most often a π* orbital) is often very strongly coupled to the
σ* orbital of the cleaving bond, which makes the description
of the overall process in terms of electron uptake followed by
intramolecular π* f σ* ET as not quite realistic.25 On the other
hand, it is well known that fascinating results have been obtained
in the area of intramolecular nondissociative ETs, leading to
the building of a sound experimental-theoretical framework
to understand how electrons are transferred through bonds and
space.1c,26 This knowledge was reached by using well-devised
D-Sp-A molecular systems, in which a donor (D) and an
acceptor (A) are spatially separated by a spacer (Sp) having
specifically tailored properties. Very recently, we studied the
∆G° dependence of intramolecular DETs in D-Sp-A mol-
ecules (eq 4) in which a tertiary bromide functional group was
E˚AB/A ,B- ) E˚ - - BDFE/F
(2)
•
•
B /B
What characterizes concerted DETs is that they are energetically
very demanding and thus intrinsically slow processes. This is
q
because of their large intrinsic barrier (∆G0 ), which is the
activation free energy (∆Gq) at ∆G° ) 0. In fact, concerted
DETs requires significant stretching of the cleaving bond as
the reacting system evolves toward the transition state. Save´ant
developed a simple but nevertheless very useful model to
describe these ET reactions and showed that, besides the usual
solvent reorganization energy, one-fourth of the bond dissocia-
tion energy (BDE) of the cleaving bond contributes to determin-
ing ∆G0q.11 In its most used and practical form, the model leads
to a quadratic ∆Gq - ∆G° relationship that is formally identical
to the well-known Marcus equation. Thus, the adiabatic DET
rate constant expression can be simply written as
q
2
∆G o
∆G0
k ) Z exp -
1 +
(3)
q
(
)
[
RT
]
4∆G0
chosen as the acceptor, ring-substituted benzoates were the
donors, and cyclohexyl was the spacer.24 For these systems,
comparison of the intramolecular and the intermolecular log k
versus ∆G° plots revealed that the intramolecular rate constants
are more sensitive to variation of ∆G° than observed for the
bimolecular reaction. Typically, when the driving force was
decreased by ∼15 kcal mol-1, the rate was found to drop 1
order of magnitude more rapidly than expected. This experi-
q
Besides ∆G0 , concerted DETs may also be slow for other
reasons. In particular, we have recently shown that the actual
prefactor of DETs can be much smaller than the value Z
expected for an adiabatic process characterized by the same
∆G0q and studied in the same ∆G° range.4,6,7 This behavior was
hypothesized to be related to the failure of the Born-
Oppenheimer approximation near the transition state,7 which
would cause the avoided crossing of the reactant and product
curves to be only narrowly avoided.12 In conclusion, because
of small preexponential values (which cause the log k vs ∆G°
(13) (a) Maslak, P. In Topics in Current Chemistry; Mattay, J., Ed.; Springer-
Verlag: Berlin, 1993; Vol. 168, p 1. (b) Maslak, P.; Vallombroso, T. M.;
Chapman, W. H., Jr.; Narvaez, J. N. Angew. Chem., Int. Ed. Engl. 1994,
33, 73.
q
(14) (a) Severin, M. G.; Are´valo, M. C.; Maran, F.; Vianello, E. J. Phys. Chem.
1993, 97, 150. (b) Daasbjerg, K.; Jensen, H.; Benassi, R.; Taddei, F.;
Antonello, S.; Gennaro, A.; Maran, F. J. Am. Chem. Soc. 1999, 121, 1750.
(c) Antonello, S.; Benassi, R.; Gavioli, G.; Taddei, F.; Maran, F. J. Am.
Chem. Soc. 2002, 124, 7529.
(15) (a) Save´ant, J.-M. J. Phys. Chem. 1994, 98, 3716. (b) Andrieux, C. P.;
Robert, M.; Save´ant, J.-M. J. Am. Chem. Soc. 1995, 117, 9340. (c) Andrieux,
C. P.; Save´ant, J.-M.; Tallec, A.; Tardivel, R.; Tardy, C. J. Am. Chem.
Soc. 1996, 118, 9788. (d) Andrieux, C. P., Save´ant, J.-M.; Tallec, A.;
Tardivel, R.; Tardy, C. J. Am. Chem. Soc. 1997, 119, 2420. (e) Andrieux,
C. P., Combellas, C.; Kanoufi, F.; Save´ant, J.-M.; Thie´bault, A. J. Am.
Chem. Soc. 1997, 119, 9527.
(16) (a) Andersen, M. L.; Mathivanan, N.; Wayner, D. D. M. J. Am. Chem.
Soc. 1996, 118, 4871. (b) Andersen, M. L.; Long, W.; N.; Wayner, D. D.
M. J. Am. Chem. Soc. 1997, 119, 6590. (c) Andersen, M. L.; Wayner, D.
D. M. Acta Chem. Scand. 1999, 53, 830.
(17) (a) Christensen, T. B.; Daasbjerg, K. Acta Chem. Scand. 1997, 51, 307.
(b) Jakobsen, S.; Jensen, H.; Pedersen, S. U.; Daasbjerg, K. J. Phys. Chem.
A 1999, 103, 4141. (c) Enemærke, R. J.; Christensen, T. B.; Jensen, H.;
Daasbjerg, K. J. Chem. Soc., Perkin Trans. 2 2001, 1620.
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(19) Zheng, Z.-R.; Evans, D. H.; Chan-Shing, E. S.; Lessard, J. J. Am. Chem.
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(20) Janssen, R. G.; Utley, J. H. P., Carre´, E.; Simon, E.; Schirmer, H. J. Chem.
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(21) (a) Pearl, D. M.; Burrow, P. D.; Nash, J. J.; Morrison, H.; Jordan, K. D. J.
Am. Chem. Soc. 1993, 115, 9876. (b) Pearl, D. M.; Burrow, P. D.; Nash,
J. J.; Morrison, H.; Nachtigallova, D.; Jordan, K. D. J. Phys. Chem. 1995,
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(22) (a) Kimura, N.; Takamuku, S. Bull. Chem. Soc. Jpn. 1991, 64, 2433. (b)
Kimura, N.; Takamuku, S. Bull. Chem. Soc. Jpn. 1992, 65, 1668. (c)
Kimura, N.; Takamuku, S. J. Am. Chem. Soc. 1994, 116, 4087. (d) Kimura,
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curve to shift downward) and/or large ∆G0 s (which flattens
the parabola), the rate constants of concerted DETs are smaller
and much less sensitive to ∆G° changes than observed with
common nondissociative outer sphere ETs. The most important
conclusion, however, is that, once these factors are taken into
account, the shape of the log k versus ∆G° relationship and
thus the value of k at any given ∆G° value can be predicted
satisfactorily.
In recent years several groups have collected data and
provided relevant insights into the dynamics of intermolecular
DETs, as recently reviewed.2,3,8,9,11b On the other hand, less
information is available on the corresponding intramolecular
processes. Indeed, interesting results and analyses of the decay
(5) (a) Donkers, R. L.; Workentin, M. S. J. Phys. Chem. B 1998, 102, 4061.
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(c) Magri, D. C.; Donkers, R. L.; Workentin, M. S. J. Photochem. Photobiol.
A: Chem. 2001, 138, 29. (b) Donkers, R. L.; Workentin, M. S. Chem.
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Antonello, S.; Maran, F. J. Am. Chem. Soc. 1999, 121, 9668.
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Chem. Soc. 2001, 123, 9577.
(8) Eberson, L. Acta Chem. Scand. 1999, 53, 751.
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(10) (a) Andrieux, C. P.; Gallardo, I.; Save´ant, J.-M.; Su, K. B. J. Am. Chem.
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1. (c) Save´ant, J.-M. J. Am. Chem. Soc. 1992, 114, 10595.
(11) (a) Save´ant, J.-M. J. Am. Chem. Soc. 1987, 109, 6788. (b) Save´ant, J.-M.
In AdVances in Electron-Transfer Chemistry; Mariano, P. S., Ed.; JAI
Press: Greenwich, CT, 1994; Vol. 4, p 53. (c) Andrieux, C. P.; Save´ant,
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(25) Burrow, P. D.; Gallup, G. A.; Fabrikant, I. I.; Jordan, K. D. Aust. J. Phys.
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(26) For example, see: (a) Closs, G. L.; Miller, J. R. Science 1988, 240, 440.
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9
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