Dependence of intramolecular dissociative electron transfer rates on driving force in Donor-Spacer-Acceptor systems

Article abstract of DOI:10.1021/ja9741180

The voltammetric reduction of a series of phenyl-substituted 4- benzoyloxy-1-methylcyclohexyl bromides has been investigated in DMF. The reduction leads to the cleavage of the C-Br bond. On a thermodynamic ground, the direct reduction of the tertiary C-Br function is easier than that of the selected benzoates by at least 0.5 V. However, since the direct reduction of bromides is affected by a large activation overpotential, the electron is first located in the benzoate moiety. The rate constant for the following exergonic intramolecular dissociative electron transfer was determined by kinetic analysis of the cyclic voltammetry curves. The intermolecular rate constants for the reaction between the radical anions of methyl benzoates and 4-tert-butyl-1-methylcyclohexyl bromide were also determined and found to correlate very well with related literature data pertaining to tert-butyl bromide. The intramolecular rate constants were found to be more sensitive to variation of driving force than the corresponding intermolecular data. This result can be attributed to a shift of the center of the π* orbital of the radical anion donor away from the acceptor moiety, the shift being larger for the most easily reduced donors. The resulting distance increase is therefore envisaged as responsible for a more rapid rate drop, compared to the intermolecular pattern, when smaller driving forces are considered.

Full text of DOI:10.1021/ja9741180

J. Am. Chem. Soc. 1998, 120, 5713-5722
5713
Dependence of Intramolecular Dissociative Electron Transfer Rates on
Driving Force in Donor-Spacer-Acceptor Systems
Sabrina Antonello and Flavio Maran*
Contribution from the Dipartimento di Chimica Fisica, UniVersita` di PadoVa, Via Loredan 2,
35131 PadoVa, Italy
ReceiVed December 4, 1997
Abstract: The voltammetric reduction of a series of phenyl-substituted 4-benzoyloxy-1-methylcyclohexyl bro-
mides has been investigated in DMF. The reduction leads to the cleavage of the C-Br bond. On a thermo-
dynamic ground, the direct reduction of the tertiary C-Br function is easier than that of the selected benzoates
by at least 0.5 V. However, since the direct reduction of bromides is affected by a large activation overpotential,
the electron is first located in the benzoate moiety. The rate constant for the following exergonic intramolecular
dissociative electron transfer was determined by kinetic analysis of the cyclic voltammetry curves. The
intermolecular rate constants for the reaction between the radical anions of methyl benzoates and 4-tert-butyl-
1-methylcyclohexyl bromide were also determined and found to correlate very well with related literature data
pertaining to tert-butyl bromide. The intramolecular rate constants were found to be more sensitive to variation
of driving force than the corresponding intermolecular data. This result can be attributed to a shift of the
center of the π* orbital of the radical anion donor away from the acceptor moiety, the shift being larger for
the most easily reduced donors. The resulting distance increase is therefore envisaged as responsible for a
more rapid rate drop, compared to the intermolecular pattern, when smaller driving forces are considered.
Introduction
tions in condensed media is available.9 On these grounds and
because of our interest in nonadiabatic dissociative ETs,10 we
have started to investigate the activation-driving force relation-
ships ruling the intramolecular dissociative ETs in well-defined
D-Sp-A systems (eq 1).
The distance dependence in electron transfer (ET) reactions
within D-Sp-A systems, in which an electron donor (D) and
electron acceptor (A) are separated by a saturated spacer (Sp),
has been the subject of several studies.1 Although A and D
are usually chosen to be chemically stable during the ET process,
some recent investigations have focused on acceptors designed
to undergo fast and irreversible chemical reactions as a tool to
provide further insight into the dynamics of intramolecular ET.2
Dissociative ET processes, i.e., those reactions in which the
acceptor molecule fragments synchronously with the electron
uptake, represent the fundamental limiting case of a fast,
irreversible follow-up reaction.3,4 However, although very
recent work has provided a clearer understanding of different
aspects of intramolecular dissociative ETs,5-8 no quantitative
information concerning the distance dependence of such reac-
•-D-Sp-A h D-Sp• + A-
(1)
Previous work on intramolecular dissociative ETs5-8 focused
on spacers consisting of either a single methylene group or a
(partially) π-conjugated molecular backbone. Under these
conditions, the free energy (∆G°) of the intramolecular ET (eq
1) may be difficult to estimate. Since the standard potential
•
-
for a dissociative ET (E°DSpA/DSp ,A ) can be expressed as a
function of the bond dissociation free energy (BDFE) of the
breaking σ bond (here, the Sp-A bond) and of the oxidation
11,12
-
•
potential of the leaving group (E°A /A ),
∆G° may be
(1) For example, see: (a) Closs, G. L.; Miller, J. R. Science 1988, 240,
440. (b) Wasiliewski, M. R. Chem. ReV. 1992, 92, 435. (c) Paddon-Row,
M. N. Acc. Chem. Res. 1994, 27, 18.
expressed by eq 2
(2) (a) Zhu, Y.; Schuster, G. B. J. Am. Chem. Soc. 1993, 115, 2190. (b)
Leon, W. J.; Whitten, D. G. J. Am. Chem. Soc. 1993, 115, 8038. (c) Maslak,
P. In Topics in Current Chemistry; Mattay, J., Ed.; Springer-Verlag: Berlin,
1993; Vol. 168, p 1. (d) Wang, Y.; Lucia, L. A.; Schanze, K. S. J. Phys.
Chem. 1995, 99, 1961. (e) Gaillard, E. R.; Whitten, D. G. Acc. Chem. Res.
1996, 29, 292.
∆G° ) -F(E°DSpA/DSp ,A- - E°
•-) )
•
DSpA/(DSpA)
-F(E°A /A- - E°
•-) + BDFE (2)
•
DSpA/(DSpA)
•-
where E°DSpA/(DSpA) is the standard potential for the donor redox
(3) Eberson, L. Acta Chem. Scand. 1982, B36, 533.
couple. In general, when D is varied while A is kept constant,
(4) (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.
(7) Maslak, P.; Vallombroso, T. M.; Chapman, W. H., Jr.; Narvaez, J.
N. Angew. Chem., Int. Ed. Engl. 1994, 33, 73.
(5) (a) Save´ant, J.-M. J. Phys. Chem. 1994, 98, 3716. (b) Addock, W.;
Andrieux, C. P.; Clark, C. I.; Neudeck, A.; Save´ant, J.-M.; Tardy, C. J.
Am. Chem. Soc. 1995, 117, 8285. (c) Andrieux, C. P.; Robert, M.; Save´ant,
J.-M. J. Am. Chem. Soc. 1995, 117, 9340. (d) Andrieux, C. P.; Save´ant,
J.-M.; Tallec, A.; Tardivel, R.; Tardy, C. J. Am. Chem. Soc. 1996, 118,
9788. (e) Andrieux, C. P., Save´ant, J.-M.; Tallec, A.; Tardivel, R.; Tardy,
C. J. Am. Chem. Soc. 1997, 119, 2420.
(6) (a) Andersen, M. L.; Mathivanan, N.; Wayner, D. D. M. J. Am. Chem.
Soc. 1996, 118, 4871. (b) Andersen, M. L.; Wayner, D. D. M. J. Electroanal.
Chem. 1996, 412, 53. (c) Andersen, M. L.; Long, W.; N.; Wayner, D. D.
M. J. Am. Chem. Soc. 1997, 119, 6590.
(8) (a) Harsanyi, M. C.; Lay, P. A.; Norris, R. K.; Witting, P. K. J. Org.
Chem. 1995, 60, 5487. (b) Harsanyi, M. C.; Lay, P. A.; Norris, R. K.;
Witting, P. K. Aust. J. Chem. 1996, 49, 581. (c) Lay, P. A.; Norris, R. K.;
Witting, P. K. Aust. J. Chem. 1996, 49, 1279.
(9) Some interesting results concerning the distance effects in gas-phase
dissociative electron attachments have been published: Pearl, D. M.;
Burrow, P. D.; Nash, J. J.; Morrison, H.; Nachtigallova, D.; Jordan, K. D.
J. Phys. Chem. 1995, 99, 12379.
(10) (a) Workentin, M. S.; Maran, F.; Wayner, D. D. M. J. Am. Chem.
Soc. 1995, 117, 2120. (b) Donkers, R. L.; Maran, F.; Wayner, D. D. M.;
Workentin, M. S. Work in progress.
S0002-7863(97)04118-8 CCC: $15.00 © 1998 American Chemical Society
Published on Web 06/02/1998

5714 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Antonello and Maran
•
-
the BDFE value and thus E°DSpA/DSp ,A also vary. In other
words, by changing the donor, one varies ∆G° not only because
ET processes, the mechanism of the reduction of halides
deserves further investigation. We believe that a good way to
tackle this problem is by using well-defined intramolecular
D-Sp-A systems, where any inner-sphere contributions to the
ET are precluded and where the distance and orientation of the
electron-exchanging centers are controlled.
We report here the results obtained on the intramolecular ET
rate in compounds 1 measured at 25 °C by cyclic voltammetry
in N,N-dimethylformamide (DMF) containing 0.1 M tetrabu-
tylammonium perchlorate (TBAP). The free-energy dependence
•-
•
-
of E°DSpA/(DSpA) but also through E°DSpA/DSp ,A . As a conse-
quence, if there is no practical way to know how the presence
of different D groups affects the BDFE of the DSp-A bond,
special caution must be exercised to deal with the result of an
activation-driving force analysis. This complication can be
minimized or even avoided by choosing a spacer that is not too
short nor one that leads to a π-conjugated system. Therefore,
along the lines described by the pioneering work by Closs,
Miller, and their co-workers,1a we decided to focus on spacers
formed by saturated and (relatively) rigid molecular frameworks.
In this study, the leaving group A has been selected to be a
tertiary bromide since the reduction of tert-butyl bromide is by
far the most studied molecule that undergoes a dissociative ET.
As a matter of fact, for this experimental system data are
available (homogeneous reduction in amide solvents) for an
overall variation of the intermolecular rate constant by 13 orders
of magnitude.13 In this reaction (and also in the ET to other
alkyl halides), the experimental data seems to fit almost equally
well to a parabola, as predicted by the theory,4 or to a straight
line.14,15 Consequently, the actual form of the activation-
driving force relationship for ET to tert-butyl bromide and
similar acceptors or the possible role of an inner-sphere
component when the ET becomes more endergonic15 are still
an open matter for discussion. This is primarily because these
reactions have large intrinsic barrier (∆G#0) values. To better
understand this point, one has to consider the Marcus-like
parabola underlying the dissociative ET theory4 and relating the
activation free energy (∆G#) to ∆G° (eq 3). Whereas the first
of the intramolecular ET rate constant (kET) in 1 (eq 6) was
determined by varying D, which was chosen as the activated
(i.e., reduced) form of an aromatic ester, while keeping constant
a 1,4-cyclohexanediyl moiety as the spacer. To define the free
(6)
2
∆G°
∆G# ) ∆G#0 1 +
(3)
(4)
(5)
#
(
)
4∆G0
∂∆G#
∂∆G°
∆G°
energy of the process and the heterogeneous ET kinetics, we
studied also the voltammetric reduction of the corresponding
D-Sp-OH (2) and D-Sp-H (3) systems. 4-tert-Butyl-1-
methylcyclohexyl bromide (4) served as a model to estimate
the dissociative E° of the acceptor, using the convolution
voltammetry approach. Information on the intermolecular
counterpart of eq 6 was obtained by studying the ET between
4 and the radical anions electrogenerated from the esters
Y-PhC(O)OMe (5), in comparison with the literature data on
tert-butyl bromide.13
R )
) 0.5 +
8∆G#0
∂R
∂∆G°
∂2∆G#
1
)
)
∂(∆G°)2 8∆G#0
derivative of eq 3 provides the transfer coefficient (or symmetry
factor) R of the reaction (eq 4), the second derivative (eq 5)
yields the curvature of the parabola. Since the curvature is
inversely proportional to ∆G#0, it follows that it might be
difficult to detect the expected quadratic activation-driving
force relationship for reactions characterized by large ∆G0#
values. Conversely, when the latter values are not too large,
as it is for peroxides as a result of their small bond dissociation
energy values,16 the expected parabolic pattern is detectable
beyond experimental error.10,12,17,18 Therefore, if a quadratic
rate-free energy law is in general better at describing dissociative
Experimental Section
Chemicals. N,N-Dimethylformamide (Janssen, 99%) and tetrabu-
tylammonium perchlorate (TBAP, 99%, Fluka) were purified as
previously described.12 The following compounds were used as
received: 4-tert-butylcyclohexanone (Fluka), methyl iodide (Acros),
hydrobromic acid (48% aqueous, Fluka), 1,4-cyclohexanone monoet-
hylene acetal (Fluka), sodium borohydride (Janssen), benzoyl chloride
(Fluka), 3-fluorobenzoyl chloride (Aldrich), 3-phenoxybenzoic acid
(Janssen), 1-naphthoyl chloride (Aldrich), 4-(methylsulfonyl)benzoic
acid (Aldrich), 4-cyanobenzoyl chloride (Aldrich), thionyl chloride
(Fluka), methyl benzoate (Janssen), methyl 4-cyanobenzoate (Aldrich).
4-Methylcyclohexanol was obtained by NaBH4 reduction of 4-meth-
ylcyclohexanone (Aldrich). 3-Phenoxybenzoyl chloride and 4-(methyl-
sulfonyl)benzoyl chloride were obtained by reaction of the acid with
thionyl chloride. Compounds 3 were obtained by reacting 4-methyl-
cyclohexanol with the pertinent aroyl chloride, in pyridine. The methyl
esters 5b-e were obtained by acid-catalyzed reaction of the aroyl acid
with methanol. 4-tert-Butyl-1-methylcyclohexanol was obtained by
(11) Wayner, D. D. M.; Parker, V. D. Acc. Chem. Res. 1993, 26, 287.
(12) Antonello, S.; Musumeci, M.; Wayner, D. D. M.; Maran, F. J. Am.
Chem. Soc. 1997, 119, 9541.
(13) (a) Lund, T.; Lund, H. Acta Chem. Scand. 1986, B40, 470. (b)
Pedersen, S. U.; Svensmark, B. Acta Chem. Scand. 1986, A40, 607. (c)
Andrieux, C. P.; Gallardo, I.; Save´ant, J.-M.; Su, K. B. J. Am. Chem. Soc.
1986, 108, 638. (d) Grimshaw, J.; Langan, J. R.; Salmon, G. A. J. Chem.
Soc., Faraday Trans. 1994, 90, 75.
(14) Save´ant, J.-M. J. Am. Chem. Soc. 1992, 114, 10595.
(15) Lund, H.; Daasbjerg, K.; Lund, T.; Pedersen, S. U. Acc. Chem. Res.
1995, 28, 313.
(16) The intrinsic barrier ∆G#0, i.e., the activation free energy at zero
driving force, is related4 to the bond dissociation energy (BDE) and to the
(18) Workentin, M. S.; Donkers, R. L. J. Am. Chem. Soc. 1998, 120,
2664. We are grateful to Prof. Workentin for providing us a copy of the
manuscript prior to publication.
solvent reorganization energy λo by equation ∆G# ) (BDE + λo)/4.
0
(17) Antonello, S.; Maran, F. J. Am. Chem. Soc. 1997, 119, 12595.

Intramolecular DissociatiVe ET Rates
J. Am. Chem. Soc., Vol. 120, No. 23, 1998 5715
Grignard reaction of 4-tert-butylclohexanone with methyl iodide. 4-tert-
Butyl-1-methylcyclohexyl bromide19 (4) was obtained as a 20:1 mixture
of isomers by reaction of 4-tert-butyl-1-methylcyclohexanol with
aqueous HBr: 1H NMR (200 MHz, CDCl3, TMS) δ 0.84 and 0.88
(3H, 2s, t-Bu), 1.61 and 1.63 (1H, 2s, Me).
The general synthetic scheme used to obtain the compounds 1 is as
follows. Grignard reaction of 1,4-cyclohexanedione monoethylene
acetal (Fluka) with methyl iodide gave 4-hydroxy-4-methylcyclohex-
anone monoethylene acetal20 in about 80% yield. The ketone was then
deprotected in acetone-aqueous 0.1 N HCl (5:1), at reflux for 1 h;
after neutralization and extraction, 4-methyl-4-hydroxycyclohexanone21
was obtained (about 85% yield). The latter was reduced with NaBH4
in methanol to a mixture (ca. 80% yield) of isomeric diols.22 The donor
side of the system was introduced by reacting the diol mixture with
the selected aroyl chloride in pyridine.23 This reaction proceeded
regioselectively onto the secondary alcohol group to give a mixture of
stereoisomeric esters 2, in 50-80% yield. The tertiary bromides 1a-f
were obtained by mixing the corresponding 2 with aqueous HBr (48%)
and stirring the resulting slurry for ca. 12 h. The reaction usually gave
similar amounts of two stereoisomers (75-85% overall yield) that were
easily separated by chromatography. NMR {1H}-1H nuclear over-
hauser effect measurements and X-ray crystallography indicated that
compounds 1a-f have a cis equatorial-axial configuration, the bromine
atom being axial. Full details of the spectroscopic and the structural
analyses of both series of compounds will be published elsewhere.24
Figure 1. Cyclic voltammetry of bromide 4 (3 mM) in DMF/0.1 M
TBAP obtained at a glassy carbon electrode, V ) 0.2 V s-1, T ) 25
°C.
transferred to a PC. The background-subtracted curves were analyzed
by the conventional voltammetric criteria26-28 or the convolution
approach,12,29 using our own laboratory software. Digital simulations
of the cyclic voltammetry curves were performed by using the DigiSim
2.1 software by Bioanalytical Systems Inc.
1
The melting points (uncorrected) and H NMR spectroscopy (400
MHz, CDCl3, TMS) of bromides 1 are as follows. 1-Methyl-4-
1
benzoyloxycyclohexyl bromide 1a: mp 94-95 °C; H NMR δ 1.89
Results and Discussion
(3H, s, Me), 4.97 (1H, m, CHO), 7.45-8.06 (5H, m, C6H5). 1-Methyl-
4-(3′-phenoxybenzoyloxy)cyclohexyl bromide 1b: mp 101-102 °C;
1H NMR δ 1.88 (3H, s, Me), 4.94 (1H, m, CHO), 7.01-7.80 (9H, m,
C6H5 and C6H4). 1-Methyl-4-(3′-fluorobenzoyloxy)cyclohexyl bro-
Standard Potentials and Heterogeneous ET Kinetics. The
free energy of the intramolecular dissociative ET between the
donor and the acceptor (eq 6) is related to the difference between
the two relevant E°s (eq 2). Whereas the E° values for the
donor side of compounds 1 can be easily determined (see
1
mide 1c: mp 56-57 °C; H NMR δ 1.89 (3H, s, Me), 4.96 (1H, m,
CHO), 7.26-7.85 (4H, m, C6H4). 1-Methyl-4-(1′-naphthoyloxy)-
cyclohexyl bromide 1d: mp 92-94 °C; 1H NMR δ 1.90 (3H, s, Me),
5.08 (1H, m, CHO), 7.51-8.90 (7H, m, C10H7). 1-Methyl-4-(4′-
methylsulfonylbenzoyloxy)cyclohexyl bromide 1e: mp 152-153 °C;
1H NMR δ 1.90 (3H, s, Me), 3.08 (3H, s, MeSO2), 5.00 (1H, m, CHO),
8.04-8.25 (4H, m, C6H4). 1-Methyl-4-(4′-cyanobenzoyloxy)cyclo-
•
-
below), the estimation of E°DSpA/DSp ,A is complicated because
dissociative ETs are highly irreversible reactions. In fact, it
has been shown that the direct reduction of alkyl halides suffer
a large activation overpotential;13c for example, although the
voltammetric peak potential (Ep) for the reduction of tert-butyl
bromide is -2.51 V (0.1 V s-1, glassy carbon, DMF, 10 °C),
thermochemical calculations bracket the dissociative ET E°
ranging from -0.93 to -1.05 V (eq 7, R ) t-Bu).3,4b,30 Since
1
hexyl bromide 1f: mp 133-135 °C; H NMR δ 1.89 (3H, s, Me),
4.99 (1H, m, CHO), 7.74-8.15 (4H, m, C6H4).
Electrochemistry. The glassy carbon (Tokai GC-20) electrode was
prepared and activated before each measurement as previously de-
scribed.12 The reference electrode was a homemade Ag/AgCl,25
calibrated after each experiment against the ferrocene/ferricinium couple
and then against the KCl-saturated calomel electrode, SCE (in DMF/
RBr + e- f R• + Br-
(7)
+
0.1 M TBAP, E°Fc/Fc ) 0.464 V vs SCE). In the following, all of the
tert-butyl bromide mimics satisfactorily the acceptor side of
compounds 1, such E° values could be used in eq 2. However,
although thermochemical calculations can provide, under favor-
able conditions, remarkably precise data, we tried to obtain an
potential values will be reported against SCE. The standard potentials
given in the text are actually formal potentials because concentrations
were used instead of activities.26 The counter electrode was a 1 cm2
Pt plate. Electrochemical measurements were conducted in an all glass
cell, thermostated at 25 ( 0.2 °C, and under an argon atmosphere.
The voltammetric curves were obtained by using an EG&G-PARC 173
potentiostat, an EG&G-PARC 175 universal programmer, and a Nicolet
3091 12-bit resolution digital oscilloscope, using special precautions
to reduce the electrical noise.12 The feedback correction was applied
in order to minimize the ohmic drop between the working and reference
electrodes. In most of the experiments, the cyclic voltammograms were
recorded in a selected potential range and for scan rates ranging from
0.1 to 200 V s-1 (first in the absence and then in the presence of the
substrate) by the digital oscilloscope (digitalized 1 point/mV) and then
•
-
independent check of E°DSpA/DSp ,A and studied the direct
reduction of 4-tert-butyl-1-methylcyclohexyl bromide 4 by
cyclic voltammetry, using a glassy carbon electrode. Compound
4 has the advantage of being structurally similar to the actual
D-Sp-A systems and possesses the tertiary halide character
of tert-butyl bromide.
The irreversible, dissociative electroreduction of 4 (eq 7, RBr
) 4) leads to a voltammetric peak (Figure 1) located at -2.47
V (0.2 V s-1), i.e., at essentially the same Ep observed with
t-BuBr.13c When the scan rate is increased, the peak shifts
toward more negative values by 116 mV/log V, leading to an
average value of R of 0.255;26 correspondingly, the peak width
(19) Kirk, D. N.; Shaw, P. M. J. Chem. Soc. C 1970, 182.
(20) Courtot, P. Bull. Soc. Chim. Fr. 1962, 1493.
(21) Bushweller, J. H.; Anzalone, L.; Spencer, T. A. Synth. Commun.
1989, 19, 745.
(22) Brown, D.; Davies, B. T.; Halsall, T. G. J. Chem. Soc. 1963, 1095.
(23) Jones, R. H.; Sondheimer, F. J. Chem. Soc. 1949, 615.
(24) Antonello, S.; Gennaro, A.; Maran, F.; Venzo, A. To be published.
(25) Farnia, G.; Maran, F.; Sandona`, G.; Severin, M. G. J. Chem. Soc.,
Perkin Trans. 2 1982, 1153.
(26) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals
and Applications; Wiley: New York, 1980.
(27) (a) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706. (b)
Nicholson, R. S. Anal. Chem. 1965, 37, 1351.
(28) Nadjo, L.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 48, 113.
(29) (a) Imbeaux, J. C.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 44,
169. (b) Save´ant, J.-M.; Tessier, D. J. Electroanal. Chem. 1975, 65, 57.
(30) The two limiting values arise by either neglecting or by taking into
account in the calculation a different solvation of the halide relative to the
corresponding radical. For details, see refs 3 and 4b.

5716 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Antonello and Maran
into account the double-layer effect, the E° of 4 was finally
estimated to be about -1.06 V.31 Although reliable experi-
mental data could only be collected in a limited potential range
(0.5 V), causing the error on E° to be about (0.1 V, the
agreement with the thermochemical estimates pertaining to
t-BuBr3,4b is very good and thus strengthens the reliability of
the electrochemical estimate.32 Consequently, the value -1.06
V will be used in the following discussion.
•-
The standard potentials of the candidate donors (E°D/D ) were
selected to have no competition between the direct reduction
of the donor and of the bromide.33 A homogeneous series of
substituted benzoates was chosen as the pro-donors, i.e., as those
groups able to provide the active form of the donor upon one-
electron reduction. The resulting radical anions are convenient
donors in that their formation is often reversible on the time
scale of cyclic voltammetry, which means that their lifetimes
are longer than a few seconds. This was checked with the series
of the cyclohexyl benzoates, 2 and 3, and the methyl benzoates,
5.34 Table 1 shows the E° values of compounds 2, 3, and 5,
obtained from the reversible reduction peaks. In general, the
E° undergoes a slightly negative shift upon varying the alkyl
substituent from methyl to cyclohexyl and this shift tends to
vanish when going to more easily reducible substrates. On the
other hand, comparison between the E° values of 2 and 3
indicates that the remote cyclohexyl susbtituent does not affect
the reduction of the benzoate aryl moiety, within experimental
error. Conversely, the ease of the reduction is strongly affected
by the substituents on the aryl ring. In the last column of Table
1, the diffusion coefficients of 2, calculated from the peak
current values obtained at low scan rates, are also reported. As
Figure 2. Convolution curves of the background-subtracted voltam-
metric curves for the reduction of 4 (3 mM) in DMF/0.1 M TBAP at
the glassy carbon electrode, T ) 25 °C. The dotted lines were obtained
by sigmoidal fitting of the experimental data, according to equation12
I ) a0 + a1/{1 + exp[-(E - a2)/a3]}.
(31) According to the dissociative ET theory,4 the electrochemical transfer
coefficient R should be given by eq 4, where ∆G° ) F(E - E°) and thus
R ) (∂∆G#/∂E)/F. Accordingly, R ) 0.5 when E ) E°. However, when
the electron donor is an electrode instead of a soluble species, ∆G° is best
written as F(E - E°- φ#), where φ# is the difference between the potential
at the reaction site (average distance from the electrode at which the substrate
is located when the ET takes place) and the potential of the bulk solution.
Therefore, R is related to Rapp through equation R ) Rapp/(1 - ∂φ#/∂E).
The problem is that the reduction of halides is best performed by using
glassy carbon, the double-layer properties of which are unknown. On the
other hand, by using a mercury electrode (for which the double-layer
correction is feasible), we have recently shown that when Rapp is used in
place of R, a negative error of 60-70 mV in the estimate of E° ensues.12
In the hypothesis that the double-layer effects of glassy carbon and mercury
are similar, we applied the same correction to the results obtained with 4
(the uncorrected E° is -1.13 V). We believe, however, that the error
estimated for E° ((0.1 V) takes into account also possible double-layer
differences.
Figure 3. Potential dependence of the logarithm of the heterogeneous
rate constant for the reduction of 4 in DMF/0.1 M TBAP at the glassy
carbon electrode, T ) 25 °C.
∆Ep/2 (difference between the potential measured at half-peak
height and Ep) increases, in agreement with a potential
dependence of R.12 To obtain an estimate of the E° for the
dissociative ET to 4, we carried out the convolution analysis.12,29
The background-subtracted curves obtained in different experi-
ments and for scan rates in the 0.2-2 V s-1 range were subjected
to convolution followed by logarithmic analysis to obtain the
heterogeneous ET rate constant (k) as a function of the potential
E. The logarithmic equation valid for an irreversible electrode
process is ln k ) ln D1/2 - ln[(Il - I(t))/i(t)], where real (i) and
convoluted (I) current values are combined; a limiting convolu-
tion current (Il) is reached when the electrode process becomes
diffusion controlled.29 Only low scan rates could be employed
because of the proximity of the solvent-electrolyte discharge.
In addition, since Il was reachable only at potentials too close
to the cathodic discharge, therefore leading to unacceptable
uncertainty in its evaluation, we used an approach in which the
rising part of the convolution curves was fitted by a sigmoid
equation.12 Il values were thus estimated for each scan rate and
found to agree with each other within 3%. While Figure 2
shows typical examples of convolution curves and fitting, Figure
3 provides the final results of the logarithmic analysis. The
(32) Taking into account that the dissociative ET E° can be expressed11,12
•
-
as E°A /A - BDFE/F, our results would suggest that differences in the
BDFEs of the two bromides are essentially undetectable. Our analysis would
also support the correctness of the solvation free energy correction,30 which
led to ca. -1.05 V.3,4b
(33) Since the peaks of the donors in 1 were expected to appear at more
positive potentials than the reversible Ep value, owing to the kinetic effect
of the intramolecular follow-up reaction,26-28 and also because the bromide
peak shifts consistently toward more negative potentials upon increasing V
•-
(116 mV/log V), the condition E°D/D - Ep(4) > 0.2 V proved to be ade-
quate.
(34) We tried other benzoate-type donors and found that the presence
of certain substituents led to labile radical anions, as indicated by either
the absence or the reduced height of the anodic peak corresponding to the
reoxidation of the radical anion during the backward voltammetric scan.
For example, we encountered this situation with the methyl esters of
pyrazinecarboxylic acid (E° ) -1.58 V) or nicotinic acid (E° ) -1.98 V)
and, with compounds 2, for Y ) 2-CF3 (E° ) -1.95 V), 4-CF3 (E° )
-1.84 V), 2-C(O)OMe (E° ) -1.98 V), or 3-CN (E° ) -1.89 V). The
decay rate of the radical anion can be rather high, such as for the latter
compound where a first-order rate constant of 26 s-1 was determined by
studying the anodic-to-cathodic peak current ratio as a function of the scan
rate.27a Since it is not completely clear how these decays take place
(Wagenknecht, J. H.; Goodin, R. D.; Kinlen, P. J.; Woodard, F. E. J.
Electrochem. Soc. 1984, 131, 1559), the above radical anions were discarded
as candidate electron donors.
potential dependence of the apparent value of R, i.e., Rapp
)
-(RT/F) d(ln k)/dE, was obtained by quadratic fitting of the
whole series of ln k data followed by derivatization. By taking

Intramolecular DissociatiVe ET Rates
J. Am. Chem. Soc., Vol. 120, No. 23, 1998 5717
Table 1. Voltammetric Data for the Reduction of Substituted Benzoates in DMF/0.1 M TBAP at T ) 25 °C
Y in Y-PhC(O)OR
E°(2)a (V)
E°(3)a (V)
E°(5)a (V)
k°(2)b (cm s-1
)
D(2)b,c (cm2 s-1
)
H (a)
3-OPh (b)
3-F (c)
2,3-benzo (d)
4-SO2Me (e)
4-CN (f)
-2.27
-2.15
-2.09
-1.91
-1.66
-1.61
-2.26
-2.14
-2.08
-1.92
n.d.d
-2.22
-2.12
-2.06
-1.89
-1.65
-1.60
0.12 ( 0.01
5.5 × 10-6
4.2 × 10-6
4.5 × 10-6
4.3 × 10-6
3.9 × 10-6
4.8 × 10-6
0.081 ( 0.007
0.11 ( 0.01
0.15 ( 0.015
0.057 ( 0.006
0.088 ( 0.006
-1.61
a Potentials are against SCE; uncertainty is 5-10 mV. b Average of two or three independent experiments. c The uncertainty is (0.2 × 10-6 cm2
s-1 d Not determined.
.
Table 2. Rate-Driving Force Data for the Indirect Dissociative ET
to 4 in DMF at 25 °C
Pro-donor Y in
Y-PhC(O)OMe or ArH
log kET
(M-1 s-1
)
•-
E°D/D (V)
∆G° (eV)
H (5a)
3-OPh (5b)
3-F (5c)
2,3-benzo (5d)
1-cyanonaphthalene
4-CN (5f)
-2.22
-2.12
-2.06
-1.89
-1.85
-1.60
-1.16
-1.06
-1.01
-0.83
-0.79
-0.54
5.1
4.6
4.4
3.0
2.9
0.8
of 4 was accomplished by using electrogenerated radical anions
as homogeneous electron donors (mostly obtained from com-
pounds 5), according to the homogeneous redox catalysis
approach.35 The reversible reduction peak of the mediator is
transformed into an irreversible peak upon addition of suitable
amounts of 4; the peak is catalytic because in the exergonic ET
to 4 the neutral form of the donor is regenerated and thus can
be reduced again at the electrode. The corresponding ET rate
constant values were determined by simulation of the experi-
mental curves, using the DigiSim 2.1 software. The cyclic
voltammograms were obtained by using a glassy carbon
electrode, different potential scan rates (in the 0.02-20 V s-1
range), and three molar ratios between mediator and substrate.
In the simulation, the ET and coupling reactions already focused
in studies on the intermolecular dissociative ET to alkyl halides
were taken into account.36 Because of the selected donor-
acceptor systems, we carried out measurements for reactions
characterized by driving forces in the 0.5-1.2 eV range. Table
2 shows the kET values resulting from this analysis. The
uncertainty of the measured kET values is estimated to be 10-
15%, as found in analogous studies.13,37
Electroreduction of 1 and Intramolecular ET Rates. The
voltammetric reduction of 1a-e is characterized by an irrevers-
ible peak, followed by a reversible component for 1a-c (Figure
5). The splitting of the peaks becomes progressively less evident
by increasing V or going to more easily reducible substrates.
At 0.1 V s-1, only the reduction peak of 1f is partially reversible,
indicating that the chemical reaction of the ensuing radical anion
is rather slow. A similar situation holds for 1e, for which an
anodic peak corresponding to the main reduction peak appears
Figure 4. Scan rate dependence of the separation between the cathodic
and the anodic peak potentials for the reduction of 1.4 mM 2f (0) or
1f (4) in DMF/0.1 M TBAP at the glassy carbon electrode, T ) 25
°C. The plot is the best fit (k° ) 0.088 cm s-1) of the data to the
theoretical curve describing the competition between diffusion and
electron transfer (R ) 0.5).28 The same D value (4.8 × 10-6 cm2 s-1
)
has been used for substrates and radical anions.
expected because of the negligible difference between the radii
of the corresponding 2 and 3, the D values of the corresponding
benzoates 3 were found to be equal within experimental
uncertainty.
An important parameter to study chemical reactions following
an heterogeneous ET is the apparent standard rate constant (k°).
Accordingly, the k° values of 2a-f were determined by studying
the scan rate dependence of the separation between the cathodic
and the anodic peak potentials (∆Ep).27b Figure 4 illustrates a
typical plot showing how, upon increasing the scan rate V, ∆Ep
increases relative to its reversible value (59 mV at 25 °C26). In
the figure, ∆Ep is plotted against a kinetic parameter describing
the competition between diffusion and electron transfer. For
each compound, an excellent fit to the Nicholson theoretical
curve27b was achieved in the whole scan rate range investigated
(0.1 to 100 V s-1). This outcome, and also because quasi-
reversible behavior was detectable starting from relatively low
scan rates (see Figure 4), led to good determinations of k° (Table
1). The rather small values of k° reported in Table 1 are
comparable with the values obtained with other carbonyl
compounds in the presence of a tetrabutylammonium salt as
the supporting electrolyte, using glassy carbon electrodes.5e It
is also relevant to add that differences in the heterogeneous
behavior among compounds 1-3 were not detectable. For
example, as shown by Figure 4, the ∆Ep values of 1f (whose
reduction is chemically reversible for V > 1 V s-1; see below)
cannot be distinguished from those of 2f within experimental
error.
(35) (a) Andrieux, C. P.; Blocman, C.; Dumas-Bouchiat, J. M.; M’Halla,
F.; Save´ant J.-M. J. Electroanal. Chem. 1980, 113, 19. (b) Andrieux, C.
P.; Save´ant J.-M. J. Electroanal. Chem. 1986, 205, 43.
(36) The reactions between electrogenerated electron donors (D•-) and
alkyl halides (RX) are given by following equations13,15
where the last two reactions describe the competition reactions (ET and
coupling with the radical anion donor) destroying the radical R•.
(37) Daasbjerg, K.; Pedersen, S. U.; Lund, H. Acta Chem. Scand. 1991,
45, 424.
Intermolecular ET. The homogeneous ET to 4 was studied
to gain information on the effect of intermolecular processes
on the electroreduction of compounds 1. The indirect reduction

5718 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Antonello and Maran
Figure 6. Multiscan (4 cycles) voltammetry of 1.8 mM 1a obtained
in DMF/0.1 M TBAP. Glassy carbon electrode, V ) 0.2 V s-1, T ) 25
°C.
Scheme 1
Figure 5. Comparison of the cyclic voltammograms of 1.8-2.0 mM
1a-f in DMF/0.1 M TBAP obtained at the glassy carbon electrode, V
) 0.1 V s-1, T ) 25 °C.
due to the reduction of the product accumulating near the
electrode, in the diffusion layer, and is coincident to that of an
authentic sample of 3. Although the above experiments were
carried out in DMF by using a glassy carbon electrode, which
is known to provide an inert electrode surface for halogen-
containing substrates, we observed a similar voltammetric
behavior (compound 1a) either by using a mercury electrode,
provided that V was higher than 2 V s-1, or in acetonitrile. Also,
in both DMF and acetonitrile, the addition of either a weak acid,
such as N-benzylisobutyramide or formanilide (pKDa MF ) 25.8
and 20.3, respectively38), or an H-atom donor (2-propanol,
60 equiv) did not change significantly the voltammetric pat-
tern.
The voltammetric behavior can be interpreted by the mech-
anism shown in Scheme 1. The first step involves the reduction
of the benzoate moiety (reaction a). In fact, although the direct
reduction of the alkyl bromide is more facile on a thermody-
namic ground, it suffers a large activation overpotential. The
electron is then transferred dissociatively to the accepting
bromide function in a second step (reaction b ) eq 6), with a
kET value that is a function of the reducing power of the
for V > 0.2 V s-1. Some reversibility is detectable also for
compounds 1d and 1c when V is increased to ca. 10 and 200 V
s-1, respectively, whereas the lifetimes of the radical anions of
1a and 1b is too short relative to our experimental time window.
By using sufficiently high scan rates, the E° of 1f, 1e, and 1d
were thus calculated to be -1.60, -1.66, and -1.92 V,
respectively, and that of 1c estimated to be ca. -2.08 V. In
line with the above conclusions, these values are equal to the
E° values of 2 and 3 (Table 1), within experimental error. Peak
current measurements showed that the apparent number of
electrons characterizing the irreversible reduction of 1a-d is
greater than 1.5 at low scan rate and tends to 2 upon increasing
V. This was verified by comparison of the irreversible peaks
with the reversible peaks of 2a-d. Only the peaks of compound
1f and 1e correspond to a one-electron process, at relatively
low scan rates. Further information on the overall process was
gained by multiscan voltammetry experiments, in which the
disappearance of the irreversible reduction peak and the ap-
pearance of a well-defined steady voltammogram was observed
(for example, see Figure 6). The resulting reversible peak is
(38) Maran, F.; Celadon, D.; Severin, M. G.; Vianello, E. J. Am. Chem.
Soc. 1991, 113, 9320.

Intramolecular DissociatiVe ET Rates
J. Am. Chem. Soc., Vol. 120, No. 23, 1998 5719
Table 3. Rate-Driving Force Data for the Intramolecular
Dissociative ET in Compounds 1 in DMF at 25 °C
benzoate, i.e., 1a > 1b > 1c > 1d > 1e > 1f. Therefore, the
benzoate function acts as an ET antenna shuttling the electron
from the electrode to the bromide in the same way, though now
intramolecularly, as in the above intermolecular reactions. Once
the intramolecular ET takes place, the radical formed can accept
an electron from the electrode, the benzoate moiety acting again
as the antenna (reaction c). This is in fact the most likely
heterogeneous pathway because, although the E° for the
reduction of a tertiary carbon radical is per se not very negative
(its value can be bracketed between -1.5 and -1.8 V),39,40 it
has been shown that the direct reduction of alkyl radicals is
controlled by a significant activation overpotential (the direct
reduction of the tert-butyl radical takes place at ca. -2.6 V).39
As a result, the electrode reduction tends to become a two-
electron process, provided kET is large enough. A second
intramolecular ET then takes place (reaction d), and the ensuing
carbanion is protonated to form 3, which is the species to which
the reversible component of the cyclic voltammetry curves can
be assigned (reactions e-f). This sequence for the direct
reduction is paralleled by intermolecular reactions in which the
radical anions of 1 and 3 can act as electron donors toward 1
(reactions g, X ) Br or H). The second electrode reduction
(reaction c) has no direct homogeneous counterpart. However,
the ET and coupling reactions between D-Sp• and the radical
anions of 1 and 3 must be considered (reactions h and i, X )
Br or H), in analogy to that found in mediated ET processes.15,36
The protonation of the carbanion (reaction e) is probably by a
parent molecule undergoing a 1,2-elimination to form a cyclo-
hexene derivative (self-protonation mechanism). This reaction
might be the origin of the scan rate dependence of the apparent
number of exchanged electrons.41 Hydrogen atom abstraction
by D-Sp• can be regarded as negligible in the overall electrode
process because no appreciable effects were brought about on
the cyclic voltammetry by addition of a good H-atom donor
(2-propanol) or by changing DMF with acetonitrile (a poorer
H-atom donor than DMF).
Kinetic analysis of the reduction peaks of compounds 1 was
carried out along similar lines as recently described for the
similar mechanisms occurring in the electroreduction of a-
substituted acetophenones.5d,e,6 In general, except for those
compounds where it is possible to outrun the intramolecular
ET by increasing the scan rate until reversible behavior is
reached, the knowledge of the E° corresponding to the initial
heterogeneous ET often requires assumptions and estimates.
Whereas this holds, e.g., for many R-substituted aceto-
phenones,5d,e,6 the accepting bromide in compounds 1 is located
at an appreciable distance from the ET antenna that the E° values
of donor and acceptor are not coupled. In fact, we observed
that the E° of the corresponding 1, 3 (equations a,f) and 2 are
equal (Table 1), leading us to use the same value also for the
reduction of the donor side of D-Sp• (Scheme 1, equation c).
The same holds for k°, which is insensitive of the remote
substitution at the cyclohexyl spacer, although it depends to
some extent on the substituent on the aryl group (Table 1).
•-
D-Sp-Br
E°D/D (V)
∆G° (eV)
log kET (s-1
)
1a
1b
1c
1d
1e
1f
-2.27
-2.15
-2.09
-1.91
-1.66
-1.61
-1.21
-1.09
-1.03
-0.85
-0.60
-0.55
5.5
4.7
3.8
2.4
0.3
-0.2
The reduction of compounds undergoing relatively fast
follow-up reactions and characterized by not very high k° values
is known to be to a large extent under mixed kinetic control by
the heterogeneous ET and the follow-up chemical reaction.6b,28,42,43
Under these circumstances, ∆Ep/2 and Ep - E° constitute the
parameters of choice to determine the rate constant of the
chemical step (e.g., kET). Also, of great help to the analysis is
the knowledge of both E° and k°, as it is for the compounds
here investigated. Therefore, the scan rate dependence of ∆Ep/2
and Ep - E° was used to obtain kET values for compounds 1a-
c. The analysis was accomplished by fitting working curves,
obtained from tabulated data28 using kET as a parameter and E°
and k° as the known inputs, to the experimental data. The effect
of the reversible peak following the main reduction peak was
taken into account (the presence of the second peak causes the
first peak potential to be slightly more negative than in its
absence), and thus, more weight was given to the data points
obtained at the lowest scan rates, where the peak separation is
larger. Since the use of tabulated data28 involves a simplification
of the mechanism of Scheme 1, the kET results were checked
by simulation (DigiSim 2.1) of the cyclic voltammetry curves.
However, no relevant differences were obtained. Finally, by
simulation, it was possible to determine the kET value of 1d-f
and to have an idea of the relative contribution of the
intermolecular reactions corresponding to the above scheme.
Table 3 shows the final results of the voltammetric analysis.
Because of the complexity of the analysis, the error in log kET
depends on the actual experimental case, as indicated by the
error bars in the semilogarithmic plot of Figure 7. In particular,
the error reduces to ca. (0.15 when either the two peaks are
sufficiently separated (1a) or the radical anions are relatively
stable (1e and 1f).
Comparison of Tables 2 and 3 shows that, at a given
concentration (voltammetric experiments were run with 1-2
mM substrate concentrations), the intermolecular ET rates are
slower than the corresponding intramolecular rates by at least
2 orders of magnitude. During the voltammetric scan, however,
the concentrations of substrate and electrogenerated species
change in the layer adjacent to the electrode surface.26 While
the concentration of DSpBr decreases, that of DSpH builds up.
Simulation of the mechanism of Scheme 1 indicates that when
the concentration of DSpBr in the reaction layer is low enough
relative to that of DSpH and for potentials more negative than
Ep, the effect of the intermolecular reactions becomes evident.
Also, it results that the intermolecular reactions of the DSpBr
radical anion are less important than those of the DSpH radical
anion. Although the intermolecular reactions have no relevant
(39) Andrieux, C. P.; Gallardo, I.; Save´ant, J.-M. J. Am. Chem. Soc. 1989,
111, 1620.
(40) Occhialini, D.; Pedersen, S. U.; Lund, H. Acta Chem. Scand. 1990,
44, 715.
(41) (a) Maran, F.; Vianello, E.; D’Angeli, F.; Cavicchioni, G.; Vecchiati,
G. J. Chem. Soc., Perkin Trans. 2 1987, 33. (b) Maran, F.; Roffia, S.;
Severin, M. G.; Vianello, E. Electrochim. Acta 1990, 35, 81. (c) By acting
as a proton donor, part of the starting material is transformed into a species
that is not reducible at the working potentials. Accordingly, the number of
exchanged electrons is less than expected. An increase of V tends to outrun
the effect of self-protonation reactions. We are currently investigating the
relevance of this reaction and of radical coupling reactions in the overall
process.24.
(42) Evans, D. H. J. Phys. Chem. 1972, 76, 1160.
(43) When an electrode process is affected by a follow-up reaction, the
two limiting cases are when the heterogeneous ET is in equilibrium
(nernstian ET) and the follow-up reaction is the rate-determining step or
when the kinetic control is by the heterogeneous charge transfer.28, 42 For
example, ∂Ep/∂log V varies form 29.6 mV/log V to 59.1 mV/log V (25 °C,
R ) 0.5) when the system passes from the former to the latter kinetic control.
In the intermediate situation (ca. 6 orders of magnitude in V), a nonlinear
peak potential shift connects the two limiting zones.

5720 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Antonello and Maran
sions.3,4,10,13-15,37 Instead, a value for R of 0.51 is obtained by
linear regression of the intramolecular data, a result which would
be expected only if ∆G° ≈ 0 (see eq 4), i.e., at a driving force
significantly smaller than those in the investigated range (0.5-
1.2 eV). As a first hypothesis, the reasons for such a difference
may come from the definition of R (eq 4); an intrinsic barrier
for the intramolecular ET much larger than that pertaining to
the intermolecular process could indeed account for the above
difference between the R values. In particular, because of the
compounds considered, differences in ∆G#0 must be related
essentially to differences in the solvent reorganization energies;
a bond energy of 66 kcal mol-1 4b can be used as a common
value for the C-Br bond of the above tertiary bromides.16,32 It
is known that the solvent (or outer) reorganization energy (λo),
is a function of the donor-acceptor distance.45,46 Equation 8
can be used to evaluate the λo values of both the intermolecular
ET, at van der Waals contact in the solvent cage, and the
intramolecular ET within the radical anion of 1, where donor
and acceptor further separated by the spacer. In eq 8, NA is
Figure 7. Plot of the logarithm of the first-order intramolecular (9)
and the second-order intermolecular (0), this work; 4, ref 13a,b; 3,
ref 13c; O, ref 13d) ET rate constants for the reduction of tertiary
bromides against the reaction free energy. For the sake of better
comparison, the free energy window has been restricted to ca. 1.1 eV.
The dashed line is that obtained by nonlinear least-squares fitting of
the intermolecular data; the dotted line is the linear fitting of the
intramolecular data.
NAe2
1
1
1
1
1
λo )
-
+
-
(8)
(
)(
)
4πꢀ0 ꢀop ꢀs 2rD 2rA RDA
Avogadro’s number, e is the charge of the electron, ꢀ0 is the
permittivity of vacuum, ꢀop and ꢀs are the optical and static
dielectric constants of the solvent, rD and rA are the radii of the
donor and the acceptor (assumed as spherical), and RDA is the
distance between their centers; RDA is equal to rD + rA, for the
intermolecular ET, or to rD + rA + rSp, for the intramolecular
ET, where rSp is the edge-to-edge distance of the spacer (3.88
Å, for 1,4-cyclohexanedyil). For DMF and considering radii
of the donors in the 3.6-3.9 Å range and an effective radius of
the acceptor of 2.83 Å,4b λo can be estimated to be 24-25 and
32-33 kcal mol-1 for the inter- and intramolecular processes,
respectively. Equation 8, however, tends to overestimate λo,47,48
and the distance-independent term in the right-hand side of eq
8 should be adjusted according to experimental data.47 An
alternative and probably4b better way to estimate λo is to make
use of a correlation based on self-exchange data in DMF.48 This
procedure leads to values of λo of ca. 15 and 20-21 kcal mol-1
for the inter- and intramolecular processes, respectively. Which-
ever way is adopted to calculate λo, the presence of the spacer
causes the intramolecular λo to increase by 30-40% relative to
the intermolecular values while the intrinsic barrier increases
by no more than 10%. This is not as much as would be required
to obtain R ≈ 0.5, within error, at the negative ∆G° explored:
In fact, even if one uses the largest of the intramolecular λo
estimates, for the investigated range of driving forces (0.5-1.2
eV) an R increase of only 0.01 would be expected as a
consequence of the presence of the spacer.
influence on either ∆Ep/2 or Ep - E°, they affect markedly the
shape of the cyclic voltammetry past the reduction peak, in
particular during the backward scan.24
Activation-Free Energy Relationships. Figure 7 shows the
intermolecular and intramolecular dissociative ET rate constants
as a function of the driving force; for the sake of comparison,
the literature data pertaining to the homogeneous reduction of
t-BuBr13 are also shown. Two aspects are worth noting in
Figure 7. First, there is no difference, within error, between
the activation driving force relationships describing the reduction
of the tertiary bromide 4 and that of t-BuBr. This is in
agreement with a common E° for these tertiary bromides and
with similar preexponential factors and sensitivities on ∆G°
variations. On the other hand, the second outcome is that the
inter- and the intramolecular kinetic results display different
sensitivities to the driving force, as illustrated by the independent
fittings we carried out on the two series of experimental values.
It is not our intent to discuss the difference between the intra-
and the intermolecular log ket data; in fact, in addition to the
distance effect, the pertinent frequency factors are expected to
play a role in determining such a difference. We wish to focus
here on the intriguing difference between the local slopes of
the two semilogarithmic plots. In this context, a point that
should be stressed is the remarkable consistency of the
intermolecular data shown in Figure 7 although the intermo-
lecular ET is the result of random distance and orientation
distributions between donors and acceptor. On the other hand,
for the intramolecular ET data the distance factor is controlled
in well-defined way, and therefore, by comparison, there are
good reasons to believe that the trend of the resulting log kET
- ∆G° contains elements of particular interest.
These arguments may lead to the attractive hypothesis that
the observed intramolecular R value is actually the result of an
increase of the effectiVe distance between the two redox sites
on going progressively along the series from 1a to 1f. This
hypothesis derives from the following considerations. The
intramolecular dissociative ET consists of the transfer of one
electron from the π* orbital of the donor to the σ* orbital
localized on the acceptor side of the D-Sp-A molecule. While
the latter is kept constant along the investigated series, the orbital
The best way to compare the data is via the corresponding
values of the ET coefficient R (eq 4). Concerning the
intermolecular data, R values in the range of 0.38-0.41 can be
calculated by assuming either a linear13d,37 or a quadratic4,44
log kET - ∆G° relationship. These R values are in agreement
with exergonic dissociative ETs, as discussed on many occa-
(45) Marcus, R. A. J. Chem. Phys. 1956, 24, 966.
(46) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller,
J. R. J. Phys. Chem. 1986, 80, 3673.
(44) R was calculated by the derivative of both the quadratic fit to the
experimental data and the parabola deriving from the theoretical treatment,4
both derivatives being calculated at the midpoint of the explored ∆G° range.
(47) Paulson, J. R.; Pramod, K.; Eaton, P.; Closs, G. L.; Miller, J. R. J.
Phys. Chem. 1993, 97, 13042.
(48) Kojima, H.; Bard, A. J. J. Am. Chem. Soc. 1975, 97, 6317.

Intramolecular DissociatiVe ET Rates
J. Am. Chem. Soc., Vol. 120, No. 23, 1998 5721
Conclusions
initially occupied by the unpaired electron strongly depends on
the substitution on the aryl group. A less negative E° is also
associated with a shift of the center of the π* orbital of the
donor away from the acceptor and is predictable if we go from,
e.g., 1a to 1f and consider the effect of the electron-withdrawing
competition between CN and COOR in the latter. This is also
supported by the decrease of the sensitivity of the benzoate E°
on the alkyl substituent at oxygen on going from 1a to 1f (Table
1). The shift can be detectable only in the intramolecular ET,
because of the geometric constrains of the D-Sp-A framework.
According to the apparent value of R (or by comparison with
the plot of the intermolecular data), it appears that the kET value
pertaining to 1f is lower than expected on the basis of the value
of 1a and of a “normal” R value by about 1 order of magnitude.
Taking into account the exponential decrease of the coupling
energy between the electronic wave functions of donor and
acceptor with the distance, the activated process ET rate constant
kET can be described in a classical form by eq 949
The reduction of the compounds 1 has been investigated by
electrochemical methods to obtain information on the distance
effect in dissociative ETs within well-defined D-Sp-A mo-
lecular systems. To define the reaction free energy of the
intramolecular dissociative ET from benzoate radical anions to
the tertiary bromide acceptor group, the standard potential for
the reduction of the bromide has been estimated by convolution
analysis. The E° was found to be about -1.06 V, in very good
agreement with literature thermochemical calculations pertaining
to tert-butyl bromide. The standard potential for the reduction
of the benzoate-type function to the corresponding radical anion
was easily determined by cyclic voltammetry and shown to be
independent of the substitution at the other side of the spacer.
This led to a free-energy picture more easily defined than in
previous investigations on intramolecular dissociative ETs. The
rate constants for the intramolecular ET between the donors
and the tertiary bromide moieties have been determined by
cyclic voltammetry analysis for an overall variation of the free
energy of ca. 0.7 eV. The analogous intermolecular ETs have
been determined by homogeneous redox catalysis and found to
be indistinguishable from the available literature data on the
reduction of tert-butyl bromide.
∆G#
RT
kET ) ν κ exp[-â(r - r )] exp -
(9)
(
)
n
el
0
where νn is the effective frequency for motion along the reaction
coordinate, κel is the electron transmission coefficient at the van
der Waals separation r0 between the donor and acceptor centers,
r is the actual distance at which ET takes place, and â is the
exponential decay parameter. The second exponential is
distance dependent through the link between ∆G# and the
intrinsic barrier (eq 3) and thus λo.16 A simple calculation can
be carried out through eq 9 by using â values in the range 0.8-
1.2 Å-1, as found with several non dissociative-type systems.1a,47,50
Accordingly, a rate drop of ca. 80-90% is accounted for by an
increase of, e.g., 1.4 Å (half the distance of a benzene ring) in
the effective distance between the two centers exchanging the
electron, an increase that is not unlikely on the basis of the
electron-withdrawing properties of the p-cyano group in 1f. The
rate drop is mainly due (60-80%) to the effect of λo on the
nuclear factor, through ∆G#0.51,53
The comparison of the intramolecular and the intermolecular
kinetic data reveals that for the latter ETs the transfer coefficient
R is distinctly smaller than 0.5 (namely, 0.38-0.41), as expected
for such exergonic processes (comparison is made for driving
forces of 0.5-1.2 eV), and the intramolecular rates are
significantly more sensitive to driving force changes. The
intramolecular R value is 0.51, although such a value would be
expected at ∆G° ≈ 0. The experimental outcome can be
explained by considering that the effective distance at which
the intramolecular ET takes place changes in the D-Sp-A
series when the driving force is varied. An increase of the
effective distance when the reaction becomes less exergonic is
accounted for by a shift of the π* orbital away from the acceptor.
As a consequence, the intramolecular ET rate is also decreased.
Simple calculations aimed to evaluate the rate drop expected
for an increase of the effective distance at which the ET takes
place, in comparison with the experimental results, support this
hypothesis.
Even though a quantitative understanding of this problem
requires further experimental and theoretical work, the signifi-
cance of these intramolecular results would be useful in a more
detailed interpretation of the distance effect on ETs. This is
particularly true when relatively short spacers are considered
and thus when differences in the shape of the donor orbital are
significant compared with the spacer length. This is consistent
with the fact that previous kinetic studies, aimed to determine
the activation driving force relationships of (stable) D-Sp-A
systems (in which the spacer was kept constant), could not reveal
the secondary distance effect suggested here most likely because
of the length of the spacer and, also, the very large driving force
increments considered.1a
(49) (a) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441. (b) Sutin, N. In
Electron Transfer in Inorganic, Organic, and Biological Systems; Bolton,
J. R., Mataga, N., McLendon, G., Eds.; Advances in Chemistry Series 228;
American Chemical Society: Washington, DC, 1991; p 25.
(50) (a) Newton, M. D. Chem. ReV. 1991, 91, 767. (b) Barbara, P. F.;
Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100, 13148.
(51) The adiabaticity degree of the ET is expected to have a role in this
framework. For example, if the intramolecular dissociative ET process is
best described as nonadiabatic (κel , 1), the preexponential factor becomes
a function of both λo and the elongation of the C-Br bond at the transition
state.52 On the other hand, if the dissociative ET is adiabatic (κel ≈ 1), the
preexponential factor might be determined by solvent relaxation in a similar
way as in nondissociative ETs (for example, see: Bixon, M.; Jortner, J.
Chem. Phys. 1993, 176, 467) and thus, again, might depend on λo, although
in a different way. At this stage, it is impossible to settle this issue for the
investigated reactions, and in fact, there is no doubt that in general the
problem of adiabaticity vs nonadiabaticity in dissociative ETs awaits further
investigation. Some research in this direction is currently underway with
dialkyl peroxides.10b.
(52) (a) German, E. D.; Kuznetsov, A. M. J. Phys. Chem. 1994, 98, 6120.
(b) German, E. D.; Kuznetsov, A. M.; Tikhomirov, V. A. J. Phys. Chem.
1995, 99, 9095.
(53) Interesting improvements of the adiabatic dissociative ET are
underway (Andrieux, C. P.; Save´ant, J.-M.; Tardy, C. J. Am. Chem. Soc.
1998, 120, 4167; we are grateful to Prof. Save´ant for providing us an
advanced copy of the manuscript). One of them is that λo is described as
dependent on the stretching of the breaking bond at the transition state. In
particular, λo would increase when the driving force is decreased (the tran-
sition state is now relatively more product-like), with the consequence that
Our data do not provide an answer to the problem14,15 of the
shape of the activation driving force relationship describing the
dissociative ET to alkyl halides. However, the observed linear
dependence of the intramolecular rates on ∆G° can be explained
(mostly) on the basis of the effect of λo on ∆G#, using the
quadratic relationship of eq 3. An interesting aspect is that the
ET mechanism proposed here involves the concept that an
intramolecular ET system contains useful features that can be
revealed thanks to a more controlled molecular framework. At
the same time this may lead to anomalous driving force
kET decreases more rapidly than expected. However, this is common to both
the inter- and the intramolecular ETs and thus cannot be considered as a
relevant factor in determining the difference between the observed R values.

5722 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Antonello and Maran
dependencies (in a not too large ∆G° range) relative to inter-
molecular ETs, where random distance and orientation distribu-
tions in the encounter complex yield an average ET rate con-
stant. We are now exploring different D-Sp-A systems in order
to verify these conclusions together with other aspects of the
intramolecular dissociative ET in well-defined molecular sys-
tems. At this stage, however, it is relevant to add that pre-
liminary experiments carried out with the trans isomers of 1
led to an experimental sensitivity to driving force analogous to
that described above, although the rates are significantly dif-
ferent.24
Acknowledgment. Dedicated to Prof. Ferruccio D’Angeli
on the occasion of his retirement. This work was financially
supported by the Consiglio Nazionale delle Ricerche (CNR) and
the Ministero dell’Universita` e della Ricerca Scientifica e
Tecnologica (MURST).
JA9741180