Evidence for the transition between concerted and stepwise heterogeneous electron transfer-bond fragmentation mechanisms

Article abstract of DOI:10.1021/ja971649f

The electrochemical reduction of tert-butyl p-cyanoperbenzoate in DMF leads to the cleavage of the oxygen-oxygen bond. A subsequent reaction yielding tert-butyl p-cyanobenzoate could be avoided by the addition of a mild acid, with the result that the main

Full text of DOI:10.1021/ja971649f

J. Am. Chem. Soc. 1997, 119, 12595-12600
12595
Evidence for the Transition between Concerted and Stepwise
Heterogeneous Electron Transfer-Bond Fragmentation
Mechanisms
Sabrina Antonello and Flavio Maran*
Contribution from the Dipartimento di Chimica Fisica, UniVersita` di PadoVa, Via Loredan 2,
35131 PadoVa, Italy
ReceiVed May 21, 1997. ReVised Manuscript ReceiVed October 3, 1997X
Abstract: The electrochemical reduction of tert-butyl p-cyanoperbenzoate in DMF leads to the cleavage of the oxygen-
oxygen bond. A subsequent reaction yielding tert-butyl p-cyanobenzoate could be avoided by the addition of a mild
acid, with the result that the main reduction peak was affected only by the kinetics of the electron transfer bond
fragmentation process. Unusual features of the heterogeneous electron transfer mechanism were evidenced by the
conventional voltammetric criteria, which pointed to a nonlinear potential dependence of the transfer coefficient R.
The fine details of the electron transfer mechanism were obtained by convolution analysis of the voltammetric curves,
a procedure that led to a bell-shaped potential dependence of R. The observed behavior is explained by the assumption
that when the electrode potential is decreased, the process changes from a concerted electron transfer bond cleavage
to a partially stepwise mechanism. The observed potential dependence of R is in agreement with the results from
simple calculations aimed to obtain the potential dependences of R expected for the two pure mechanisms.
Introduction
negative than Eo
AB/A•,B-
, the activation free energies of the two
processes [(∆G#)1 and (∆G#)3] may provide the actual discrimi-
nating factor. According to the current theories of outersphere
ET5 and dissociative ET,3 the ET 1 (n ) 1) and ET 3 (n ) 3)
can be expressed by a formally identical activation-driving
force relationship (eq 5), the only difference being the nature
A relevant amount of recent studies has been devoted to the
study of thermally-induced1 or photoinitiated2 electron transfer
(ET) processes that are associated with bond fragmentation. It
is now reasonably well established that the mechanism by which
an acceptor molecule (AB) is dissociatively reduced to form a
radical (A•) and an anion (B-) can be either stepwise (eqs 1
and 2) or concerted (eq 3).3 The fact that one mechanism may
of the intrinsic barrier (∆G#)n, i.e., the activation free energy at
0
zero driving force. In fact, (∆G#)1 and (∆G#)3 are given by
0
0
2
A-B + e h A-B•-
A-B•- f A• + B-
A-B + e f A• + B-
(1)
(2)
(3)
(∆G°)n
(∆G#)n ) (∆G#0)n 1 +
(5)
#
[
]
4(∆G0)n
λ/4 and (λ + BDE)/4, respectively, where λ is the sum of the
internal and the solvent reorganization energies and BDE is the
bond dissociation energy.3,5 From a practical point of view,
this leads to a quite relevant difference, because if we consider
typical dissociative-type systems such as halides1a,3 and perox-
ides,4,6,7 the contribution of the BDE term to the intrinsic barrier
amounts to 70-80%. As a consequence, ET 1 and ET 3
respond to changes in the reaction free energy in a very different
way and this may result in a smaller (∆G#)1 relative to (∆G#)3,
in spite of a less favorable reaction free energy for ET 1 than
for ET 3.8
prevail over the other depends on several factors. The difference
in the reaction free energy (∆G°) between ET 1 and ET 3 is
given by the difference between the corresponding standard
•-
•
-
potentials E°AB/AB and E°AB/A ,B . Since the latter potential
can be expressed, thanks to a thermochemical cycle,4 through
eq 4, it follows that when the A-B bond dissociation free energy
E°AB/A ,B- ) E° - - BDFE/F
(4)
•
•
B /B
•
-
(BDFE) is small and/or E°B /B is positive enough, the chances
for a dissociative ET to provide the preferred reaction path are
enhanced. This is, however, a necessary but not sufficient
The adiabatic dissociative ET theory has been proposed by
Save´ant only a few years ago,9 and although different experi-
mental systems have provided positive feedback, further tests
•-
condition because even if E°AB/AB is significantly more
(5) For example, see: Marcus, R. A.; Sutin, N. Biochem. Biophys. Acta
1985, 811, 265.
(6) Workentin, M. S.; Maran, F.; Wayner, D. D. M. J. Am. Chem. Soc.
1995, 117, 2120.
X Abstract published in AdVance ACS Abstracts, December 1, 1997.
(1) (a) Save´ant, J.-M. AdV. Phys. Org. Chem. 1990, 26, 1. (b) Save´ant,
J.-M. Acc. Chem. Res. 1993, 26, 455.
(2) (a) Saeva, F. D. In Topics in Current Chemistry; Mattay, J., Ed.;
Springer-Verlag: Berlin, 1990; Vol. 156, p 59. (b) Schuster, G. B. In
AdVances in Electron Transfer Chemistry; Mariano, P. S., Ed.; JAI Press:
Greenwich, CT, 1991; Vol. 1, p 163. (c) Maslak, P. In Topics in Current
Chemistry; Mattay, J., Ed.; Springer-Verlag: Berlin, 1993; Vol. 168, p 1.
(d) Gaillard, E. R.; Whitten, D. G. Acc. Chem. Res. 1996, 29, 292.
(3) Save´ant, J.-M. In AdVances in Electron Transfer Chemistry; Mariano,
P. S., Ed.; JAI Press: Greenwich, CT, 1994; Vol. 4, p 53.
(7) Maran, F.; Wayner, D. D. M.; Workentin, M. S.; et al. Manuscript
in preparation.
(8) Differences may arise also because of different preexponential terms
in the rate expression for ET 1 and ET 3. Although the formation of the
radical anion is likely an essentially adiabatic ET process, there are reasons
to believe that the concerted ET to peroxides can be nonadiabatic.6,7 This
would result in a smaller preexponential factor for ET 3 and thus, at a given
potential, to a less relevant weight of the rate of ET 3 relative to that of ET
1.
(4) Antonello, S.; Musumeci, M.; Wayner, D. D. M.; Maran, F. J. Am.
Chem. Soc. 1997, 119, 9541.
(9) Save´ant, J.-M. J. Am. Chem. Soc. 1987, 109, 6788.
S0002-7863(97)01649-1 CCC: $14.00 © 1997 American Chemical Society

12596 J. Am. Chem. Soc., Vol. 119, No. 51, 1997
Antonello and Maran
are still necessary to better define its scope and limitations. In
general, a very good way to test the dissociative ET theory is
to find well-behaved experimental systems in which the
transition between a stepwise and a concerted mechanism can
be observed. In this context and as can be argued on the basis
of the above discussion, the energy of the donor and thus the
free energy of the reactant system is quite important, indepen-
dent of the fact that one deals with a solution ET or a
heterogeneous ET. When the standard potential for the forma-
tion of the electron donor (homogeneous ET) or the electrode
potential E is changed to more positive values, it may be
possible, in principle, to obtain a transition from a stepwise to
a concerted mechanism. As described above, such a transition
is expected to be mainly8 due to the different ways by which
(∆G#)1 and (∆G#)3 respond to free energy changes. In the
borderline situation, the system is in an energy range in which
the acceptor molecule AB can be reduced through both
mechanisms, although with different rates.
has not been used often for kinetic purposes in recent years,
with the result of being very little known. This method,
however, is very precise, and we believe it to be particularly
useful in the study of ET reaction associated with fast bond
cleavage reactions. It should be emphasized that, unlike the
conventional voltammetric approach, all of the data points
composing the voltammetric curve are used in the kinetic
analysis and, moreover, that no a priori assumption on the ET
rate law has to be assumed in the analysis of the experimental
data. Very recently, we applied this experimental approach to
the study of the dissociative ET to a series of dialkyl peroxides,
and by analysis of the irreversible voltammetric peaks, we were
•
-
able to obtain thermodynamic results, such as the E°AB/A ,B
values and the corresponding BDFEs, in good agreement with
available thermochemical information.4 With such a support,
we were therefore confident that, since it is possible to collect
a considerable amount of rate-driving force data through
convolution of (good) experimental voltammetric curves, this
method would have provided a very good choice in detecting
possible changes in the ET mechanism.
In this paper, the results we obtained on the electrochemical
reduction of tert-butyl p-cyanoperbenzoate (CP) in DMF, in
comparison with those of the corresponding ester, tert-butyl
p-cyanobenzoate (CB), are described. The reduction was
studied by cyclic voltammetry followed by convolution analysis
of the data. Due to the particular experimental system selected
and the quality of the data, we obtained evidence for a well-
behaved case of a borderline ET bond fragmentation mechanism.
This is in good agreement with what is expected on the basis
of the above discussion and therefore in line with the concepts
and consequences underlying the dissociative ET theory.
The C-S bond cleavage induced upon ET to triphenylmethyl
phenyl sulfide by a series of aromatic electron donors provides
the only experimental observation of such a transition under
homogeneous conditions.10 When the reaction free energy was
varied by 0.5 eV, it was in fact possible to observe the
predicted,11 S-shaped activation-driving force relationship.
However, the homogeneous approach is intrinsically less
sensitive than the corresponding heterogeneous one. Whereas
in the heterogeneous case the reorganization energy λ depends
essentially only on the acceptor molecule, the homogeneous λ
and, therefore, the intrinsic barrier (∆G#)n depend also on the
0
dimension and the structure of the one-electron donor. More-
over, and quite important for practical reasons, whereas in the
homogeneous case the number of electron donors is forcefully
limited, in the heterogeneous approach the free energy of the
reaction can be varied continuously by simply changing the
applied potential E; as a result, the quantity of data that can be
collected is significantly larger, with obvious consequences in
terms of precision and reliability of the data. Indeed, voltam-
metric effects coherent with a transition behavior have been
recently reported for the reduction of two sulfonium cations;12
however, since the conventional voltammetric analysis13 was
applied, only an approximate, though indicative, picture of the
ET mechanism could be obtained. In terms of sensitivity to
ET rate changes, an initial problem associated with the
conventional voltammetric approach is that although an ir-
reversible peak such as those observed for mechanisms 1 and
2 or mechanism 3 develops over a potential range of some
hundred millivolts, only two points of the voltammetric curve
are actually analyzed, i.e., those corresponding to the peak
potential (Ep) and the potential at mid-peak height (Ep/2). A
second drawback is that if one uses the conventional voltam-
metric equations, a linear activation-driving force relationship
is implicity assumed;13 therefore, the results are forcefully
approximated if a rate law such as that given in eq 5 is better
at describing the actual experimental system.
Experimental Section
Chemicals. N,N-Dimethylformamide (Janssen, 99%) and tetrabu-
tylammonium perchlorate (TBAP, 99%, Fluka) were purified as
previously described.4 tert-Butyl p-cyanoperbenzoate15 was prepared
from tert-butyl hydroperoxide and p-cyanobenzoyl chloride: 1H NMR
(200 MHz, CDCl3, TMS) δ 1.42 (9H, s, t-Bu), 7.7-8.1 (4H, AA′BB′,
C4H4). tert-Butyl p-cyanobenzoate16 was prepared from tert-butyl
alchool and p-cyanobenzoyl chloride. p-Cyanobenzoic acid (Aldrich,
99%) and tetrabutylammonium hydroxide 30-Hydrate (Fluka, 99%)
were used as received.
Electrochemical Apparatus and Procedures. The glassy carbon
electrode was built from a glassy carbon rod (Tokai GC-20), treated,
and stored as previously described.4 Before each measurement, the
electrode was polished with a 0.25 µm diamond paste (Struers),
ultrasonically rinsed with ethanol for 5 min, and electrochemically
activated in the background solution by means of several cycles at 0.5
V s-1 between 0 and -2.8 V against the KCl saturated calomel electrode
(SCE). The reference electrode was a homemade Ag/AgCl, its potential
being calibrated after each experiment against the ferrocene/ferricinium
+
couple (in DMF/0.1 M TBAP, E°Fc/Fc ) 0.464 V vs SCE). In the
following, all of the potential values will be reported against SCE. The
counterelectrode was a 1 cm2 Pt plate. The electrochemical instru-
mentation employed for cyclic voltammetry was the same as recently
described.4 The feedback correction was applied to minimize the ohmic
drop between the working and reference electrodes. The confidence
in the positive feedback was judged as already described, i.e., by
checking the voltammetric behavior of a couple of known ET kinetics;4
in addition, the agreement between the different sets of kinetic data
provided an a posteriori test of it, as described in the Results and
Discussion.
The convolution analysis of the voltammetric curves provides
a powerful tool to study fine details of electrode processes.
Although this method has been presented many years ago,14 it
(10) Severin, M. G.; Farnia, G.; Vianello, E.; Are´valo, M. C. J.
Electroanal. Chem. 1988, 251, 369.
(11) Andrieux, C. P.; Save´ant J.-M. J. Electroanal. Chem. 1986, 205,
43.
(12) Andrieux, C. P.; Robert, M.; Saeva, F. D.; Save´ant J.-M. J. Am.
Chem. Soc. 1994, 116, 7864.
(13) (a) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706. (b) Nadjo,
L.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 48, 113. (c) Bard, A. J.;
Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications;
Wiley: New York, 1980.
Electrochemical measurements were conducted in an all glass cell,
thermostated at 25 ( 0.2 °C. The solution was carefully deoxygenated
(14) Imbeaux, J. C.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 44, 169.
(15) (a) Herwig, K.; Lorenz, P.; Ru¨chardt, C. Chem. Ber. 1975, 108,
1421. (b) Filliatre, C.; Maillard, B.; Villenave, J. J. Thermochim. Acta 1980,
39, 195.
(16) McMahon, K.; Arnold, D. R. Can. J. Chem. 1993, 71, 450.

Electron Transfer-Bond Fragmentation
J. Am. Chem. Soc., Vol. 119, No. 51, 1997 12597
carboxylate ArCOO-; the same anion is also responsible for
an irreversible oxidation peak at 1.56 V that can be detected in
the positive-going scan after reduction of CP. Information on
both the reductive and oxidative behavior of ArCOO- was
obtained by studying the electrochemical behavior of an
authentic sample of the carboxylate, obtained in situ by reaction
of p-cyanobenzoic acid with tetrabutylammonium hydroxide.
In analogy with the behavior that we are observing with other
perbenzoates,18 the reduction of CP leads to the cleavage of
the O-O bond, according to the overall reaction in eq 6. The
leaving group B- in eqs 2 and 3 is easily identified as ArCOO-,
which better accommodates the negative charge; on the other
hand, eq 6 takes into account that, at the potentials of the peak,
the reduction of the radical fragment t-BuO• (E° ) -0.23 V)6
also occurs. The electrogeneration of the anion t-BuO- causes
ArCOOO-t-Bu + 2e f t-BuO- + ArCOO-
(6)
ArCOOO-t-Bu + t-BuO- f ArCOO-t-Bu + t-BuOO- (7)
the formation of the ester CB through substitution (eq 7). The
latter reaction is very sensitive to the presence of water traces,
since t-BuOH (pKa ) 32.5) is less acidic than H2O by 0.8 pKa
unit;19 accordingly, the height of the CB peak and, therefore,
the amount of CP which is formed are a function of the
concentration of the still-surviving t-BuO- anion.20 The decay
of CP by chemical means, however, can be efficiently hampered
by protonation of t-BuO- with a weak, nonreducible acid such
as acetanilide (pKa ) 22.3).19b As a result, the reduction of
CP gives rise to a two-electron peak (eq 6), the potential of the
first peak is slightly more negative (-1.26 V), and the peak of
CB disappears (see Figure 1). This overall behavior is coherent
with what expected when the starting material undergoes a
reaction with an electrogenerated intermediate (parent-child
reaction).21 Since the focus of the present work was to obtain
the rate law by which the uptake of the first electron takes place,
all of the data described below were collected in the presence
of acetanilide, to ensure a constant electron consumption in the
overall time scale required by the voltammetry experiments.
Figure 1. Cyclic voltammetries for the reduction of (top to bottom)
CP, CP in the presence of an equivalent amount of acetanilide,
p-cyanobenzoic acid in the presence of an equivalent amount of
tetrabutylammonium hydroxide, and CB. The curves were obtained in
DMF/0.1 M TBAP at the glassy carbon electrode; T ) 25 °C.
with Argon (SIAD, 99.9995%), and a blanket of gas was then mantained
over the liquid. For quantitative measurements, the behavior of the
glassy carbon electrode was first studied in the background solution,
in a selected potential range and for scan rates ranging from 0.1 to 200
The conventional voltammetric analysis of the reduction peak
of CP revealed anomalous features (Figures 2 and 3). When V
was increased, the absolute slope of the Ep vs log V plot was
found to decrease in the 0.1-20 V s-1 range and then increase
for higher V values (Figure 2). The peak width, ∆Ep/2, i.e., the
difference between Ep/2 and Ep, decreases upon increasing V,
reaches the minimum value of 150 mV at 20 V s-1, and then
increases for higher scan rates (Figure 2). Figure 3 shows a
typical series of the V-normalized voltammograms where it can
be seen that ip/V1/2 initially increases with V, reaches a maximum
at 10-20 V s-1, and decreases thereafter. Such an overall
behavior not only indicates that the transfer coefficient R is
V-dependent, as found with other peroxides,4,18 but also and most
important that such a dependence is far from being linear. For
example, the average value of the apparent transfer coefficient
V s-1
. The cyclic voltammograms were recorded by the digital
oscilloscope, using the necessary expedients to reduce the electrical
noise,4 and then transferred to a PC. The substrate was then added to
the solution, and the same procedure was repeated. The corresponding
background curves were subtracted from the cyclic voltammograms to
eliminate the contribution of the capacitive current. The resulting curves
were then analyzed by the conventional voltammetric criteria13 and the
convolution approach,14,17 using specially designed laboratory software.
Digital simulations of some of the cyclic voltammetry curves were
performed by using the DigiSim 2.0 software by Bioanalytical Systems
Inc.
Results and Discussion
The voltammetric reduction of CP in DMF/0.1 M TBAP gives
rise to three reduction peaks (Figure 1). The main reduction
peak is irreversible, and its peak potential is -1.21 V when the
scan rate (V) is 0.2 V s-1. The second peak, Ep ) -1.63 V, is
detectable only at low V and is due to the reversible reduction
of CB, as verified by comparison with the cyclic voltammetry
of an authentic sample of it. The third reduction peak at -2.30
V is reversible and corresponds to the reduction of the
(18) Antonello, S.; Maran, F.; et al. Work in progress.
(19) The pKa(DMF) of t-BuOH and that of water can be obtained from
the corresponding DMSO data19a using the correlation pKa(DMF) ) 1.56
+ 0.96 pKa(DMSO).19b (a) Olmstead, W. N.; Margolin, Z.; Bordwell, F.
G. J. Org. Chem. 1980, 45, 3295. (b) Maran, F.; Celadon, D.; Severin, M.
G.; Vianello, E. J. Am. Chem. Soc. 1991, 113, 9320.
(20) When t-BuO- is protonated, the so-formed OH- is liable to attack
CP with formation of the corresponding acid, whose main action is to act
as a proton donor.
(21) For example, see: Maran, F.; Roffia, S.; Severin, M. G.; Vianello,
E. Electrochim. Acta 1990, 35, 81.
(17) Save´ant, J.-M.; Tessier, D. J. Electroanal. Chem. 1975, 65, 57.

12598 J. Am. Chem. Soc., Vol. 119, No. 51, 1997
Antonello and Maran
Figure 2. Scan rate dependence of the voltammetric peak potential
(9) and peak width (0) for the reduction of 1.47 mM CP in DMF/0.1
M TBAP at the glassy carbon electrode. The measurements were carried
out at 25 °C in the presence of an equivalent amount of acetanilide.
Figure 4. Potential dependence of the logarithm of the heterogeneous
rate constant for the reduction of CP in DMF/0.1 M TBAP at 25 °C.
The plot is formed from a collection of curves obtained in four separate
experiments.
point/mV, were subjected to the convolution procedure followed
by logarithmic analysis, using the equation which holds for an
irreversible process.25 The corresponding log k(E) - E plots
are shown in Figure 4. For each scan rate and four separate
experiments carried out with different samples of CP, the
logarithmic analysis led to the potential dependence of the
heterogeneous rate constant k(E) in a range of 0.35-0.40 V.
Taking into account that when V is increased, the peak shifts
toward more negative potentials, it should be stressed that in
this way 12-36 k(E) determinations per millivolt were eventu-
ally carried out in the -1.0 to -1.5 V range. Two main features
can be noticed in the figure, namely, the satisfactory agreement
between the different sets of data (the average standard deviation
is 7%) and an unusual but definite upward curvature in a
potential range from ca. -1.1 to -1.4 V in the overall plot.26
Each logarithmic plot was treated separately to obtain the
corresponding derivative plot, which is linked to Rapp through
eq 8. The experimental Rapp values were obtained by linear
Figure 3. Background-subtracted linear scan voltammetries for the
reduction of 1.47 mM CP in DMF/0.1 M TBAP at the glassy carbon
electrode. For the sake of comparison, the faradaic current is reported
in the usual V-normalized form. The scan rates were (left to right):
0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200 V s-1. T ) 25 °C.
Rapp (i.e., double-layer uncorrected)22 that can be calculated23
from ∂Ep/∂ log V is 0.26 at V < 2 V s-1, 0.35 at 2 e V e 20 V
s-1, and 0.20 at V > 20 V s-1; similarly, the average Rapp values
RT d ln k
Rapp ) -
(8)
(
)
F
dE
23
calculated from the ∆Ep/2 are 0.25, 0.28, 0.32, and 0.28 at
0.2, 2, 20, and 200 V s-1, respectively.24
regression of the ln k(E) data within 20-30 mV E intervals.
Since the only inert electrode for the reduction of perbenzoates
is glassy carbon,18 the double-layer properties of which are yet
unknown, the Rapp data could not be corrected for the double
layer. However, we have previously observed that in the
explored E range even uncorrected transfer coefficient data
provide a reasonable representation of the process,4,22 and
As recently shown for the reduction of dialkyl peroxides,4
the convolution analysis of the voltammetric data provides a
more powerful way than the direct voltammetric analysis to
observe the details of the electrode process. Accordingly, the
background-subtracted voltammograms, obtained at nine dif-
ferent scan rates in the 0.1-50 V s-1 range and digitalized 1
accordingly, we assume in the following that R ≈ Rapp
.
(22) The difference between R and Rapp is given by the equation4,22a
R
) Rapp/(1 - ∂φ#/∂E), were φ#(E) is the difference between the potential at
the average distance at which the substrate is located when the electron
transfer takes place and the potential of the bulk solution. For mercury, for
example, in the same solvent/electrolyte and potential range and under the
usual hypothesis that the reaction site can be identified with the outer
To exemplify the results of such a procedure, Figure 5 shows
both the voltammetric curve and the R analysis obtained in one
of the experiments for scan rates of 0.2 and 20 V s-1. Both
graphs provide an example of the remarkably good agreement
we found between each set of convolution R data and the R
Helmholtz plane,13c,22b app is systematically smaller than R by only 3%.22c
R
(a) Save´ant J.-M.; Tessier, D. Faraday Discuss. Chem. Soc. 1982, 74, 57.
(b) Severin, M. G.; Are´valo, M. C.; Maran, F.; Vianello, E. J. Phys. Chem.
1993, 97, 150. (c) Are´valo, M. C.; Rodriguez, J. L.; Severin, M. G., Vianello,
E. Unpublished results.
(25) The equation is17 ln k ) ln D1/2 - ln[(Il - I(t))/i(t)], where real (i)
and convoluted (I) current values are combined; a limiting convolution
current (Il) is reached when the electrode process becomes diffusion
controlled.14 For CP, a diffusion coefficient D of 4.9 × 10-6 cm2 s-1 was
calculated from Il by using an electrode of known area.4
(23) Rapp can be calculated from the equations |∂Ep/∂ log V| ) 1.15RT/
13
FRapp and ∆Ep/2 ) 1.857RT/FRapp
.
(24) When the cyclic voltammetries are simulated, assuming that a linear
activation-driving force relationship holds in the potential range spanned
by each peak up to Ep and by using the R values obtained from the
experimental ∆Ep/2 values, it is possible to obtain an ip/V1/2 vs log V pattern
that matches the experimental values pretty well, the average difference
being 2% in the 0.1-100 V s-1 range.
(26) This outcome provides an a posteriori indication that the ohmic drop
correction was properly adjusted in the digital acquisition of the experimental
curves. It is well-known that unproper ohmic-drop compensation leads to
both a negative shift and a broadening of the voltammetric curves; in terms
of the convolution output this would result in a poor overlapping of the log
k(E) - E plots obtained in the same potential range at different scan rates.

Electron Transfer-Bond Fragmentation
J. Am. Chem. Soc., Vol. 119, No. 51, 1997 12599
from ca. 2 V s-1). This means that the observed behavior
reflects a real potential dependence of R, beyond experimental
error or artifacts.
Such a nonlinear behavior can be explained by hypothesizing
that the electrode mechanism changes as a function of the
potential. To test this hypothesis, some simple calculations can
be performed to check whether the experimental R trend of
Figure 6 is in agreement with that expected for a concerted-
to-stepwise transition upon decreasing E. Since the theoretical
analyses3,5 pertaining to ET 1 and ET 3 result in the same
quadratic activation-driving force relationship (eq 5), the
corresponding transfer coefficients Rn (eq 9) have the potential
dependence shown in eq 10. Provided that the ET mechanism
∂(∆G#)n ∂(∆G#)n
Rn )
)
(9)
F∂E
∂(∆G°)n
∂Rn
∂E
F
)
(10)
8(∆G#0)n
does not change with the potential, ∂R/∂E is constant within
the approximation for the double-layer effect. As mentioned
in the Introduction, (∆G#)1 and (∆G#)3 are given by λ/4 and (λ
0
0
+ BDE)/4, respectively. On the basis of the results obtained
very recently with other peroxides,4 a likely estimate of the
heterogeneous reorganization energy λ can be bracketed between
the Marcus value and the λ that can be calculated by using an
empirical correlation deriving from data pertaining to the
reduction of aromatic compounds.27 For both calculations, an
effective radius for CP was calculated from the diffusion
coefficients of CP (obtained by convolution) and ArCOO-
(through the ip values for its reduction), using the Stokes-
Einstein equation and r ) rB(2rAB - rB)/rAB, where rAB and rB
are the radii of CP and ArCOO-, respectively.3,4 Concerning
the BDE, we used the value of 36.0 ( 0.7 kcal/mol, which
Figure 5. Background-subtracted cyclic voltammetries for the reduction
of 1.47 mM CP in DMF/0.1 M TBAP at the glassy carbon electrode,
T ) 25 °C. The curves were obtained at (a) 0.2 V s-1 and (b) 20 V
s-1. Also reported in the graphs are the convolution R data (O) and the
peak-width R datum (9).
derives from thermolysis data.15b Accordingly, (∆G#)1 ) 3.4
0
( 0.6 and (∆G#)3 ) 12.4 ( 0.8 kcal/mol.
0
The E° values of ET 1 and ET 3 are also required to complete
the picture. Whereas, due to the strong delocalizing properties
of the ArCO moiety, the E° for the formation of the radical
anion of CP can be safely taken as to be equal within ∼50 mV
to that of CB (-1.60 V), the E° of the dissociative ET can
•
-
be calculated through eq 4. The estimation of E°ArCOO /ArCOO
is not straightforward but can be carried out in an approximate
way by studying the oxidation peak of ArCOO-, which can be
conveniently generated in the DMF solution by reaction of
p-cyanobenzoic acid with tetrabutylammonium hydroxide. The
scan rate dependence indicates that such an oxidation peak is
controlled by slow ET kinetics at low to high scan rates,
although at a very low scan rate the process falls under mixed
kinetic control with a following chemical reaction, most likely
H-atom abstraction from DMF by the ensuing aroyloxyl
radical.28 Taking into account reasonable potential shifts from
the reversible value, we arrived to the prudential estimate
Figure 6. Potential dependence of the transfer coefficient R for the
reduction of CP in DMF/0.1 M TBAP at the glassy carbon electrode,
T ) 25 °C. The data pertain to experiments carried out at scan rates in
the 0.1-50 Vs-1 range and substrate concentrations in the 1.4-2.8
mM range. The left and right dashed lines correspond to the behavior
expected for the concerted and the stepwise mechanisms, respectively;
the dotted lines represent the correponding uncertainties.
value calculated from the peak width and reported against the
mid-potential of the range pertaining to the peak width. The
sharpening of the peak on going from 0.2 to 20 V s-1 is also
worth noting. The result of the R analysis carried out over the
whole series of data is plotted in Figure 6, definitely showing
that the electrode process is not ruled by a simple ET
mechanism; the plot is in fact characterized by a maximum at
ca. -1.38 V, corresponding to an average R value of 0.32.
Although not evidenced in Figure 6, which is composed by ca.
600 R values, it is worth noting that the same maximum was
obtained within only 20 mV at any of the scan rates capable of
providing R data in the appropriate potential range (i.e., starting
29,30
•
-
E°ArCOO /ArCOO ) 1.69 ( 0.1 V.
Finally, from the reported
activation parameters,15b the BDFE of CP can be calculated to
be 32.2 kcal/mol. Although the reported error on the activation
(27) The solvent reorganization energy can be calculated by using the
Marcus approach and thus by equation λ ) e2(ꢀop - ꢀs-1)/4r, where
-1
e is the charge of the exchanged electron, ꢀop and ꢀs are the high frequency
and static dielectric constants of the solvent, respectively, and r is the
molecular radius: Marcus, R. A. J. Chem. Phys. 1965, 43, 679. The
correlation, λ(kcal/mol) ) 55.7/r(Å), is obtained using selected values from
previously reported data: Kojima, H.; Bard, A. J. J. Am. Chem. Soc. 1975,
97, 6317.

12600 J. Am. Chem. Soc., Vol. 119, No. 51, 1997
Antonello and Maran
enthalpy is 0.7 kcal/mol, the error on the free energy is believed
to be larger owing to the entropy change, with a much less polar
solvent than DMF used in the thermolysis study;15b a more
reasonable error is likely within (2 kcal/mol. On these grounds,
the E° of the dissociative ET is calculated to be 0.29 ( 0.18 V.
Although the error on this E° value is much larger than that
expected for the formation of CP radical anion, we can
nevertheless conclude that the dissociative ET is thermodinami-
cally favored over the stepwise ET by a free energy difference
of no less than 1.7 eV.
In the hypothesis that the above barriers and corresponding
E° values represent satisfactorily the two limiting situations, it
is now possible to estimate the potential dependence of R for
both the concerted and the stepwise reduction of CP; the
predicted patterns are shown by the dashed lines in Figure 6,
the dotted lines accounting for the errors on both the slopes
and E° values. In spite of the roughness of the calculations,
the experimental R data indeed seem to tend to such lines,
therefore supporting the hypothesis of a concerted-to-stepwise
mechanism transition caused by the different sensitivity of
(∆G#)1 and (∆G#)3 to changes in the driving force. The
reduction of CP seems to proceed mostly through a concerted
mechanism as long as
E
is more positive than
•-
E°ArCOOO-t-Bu/ArCOOO-t-Bu by ∼0.7 V. On the other hand,
when E is changed to more negative values, the rate of the
stepwise process starts becoming more competitive to the
concerted, one-step process. Although a complete transition
was not observed in the potential range in which the R data
could be collected (due to the experimental limitations), the R
pattern of Figure 6 seems to provide a well-behaved case of a
borderline ET bond fragmentation mechanism, beyond the
experimental error. It is also worth noting the result shown in
Figure 5: since the R values that can be collected for each V
value span a typical E range of 0.3-0.35 V, the convolution
analysis allowed us to detect a partial mechanism transition even
within a single voltammetric curve, a possibility that is obviously
precluded when only one average R value per curve is
determined by the conventional voltammetry approach.
(28) That the main reaction underwent by the (4-cyanobenzoyl)oxyl
radical is most likely H-atom abstraction from DMF is suggested, for
example, by the flash photolysis experiments carried out with di-p-
methoxybenzoyl peroxide (Maran, F.; Wayner, D. D. M., Unpublished
results) that led to the observation that the lifetime of the (4-methoxyben-
zoyl)oxyl radical decreases by ca. 1.8 orders of magnitude on going from
MeCN to DMF, where it reaches the value of 69 ns; by taking into account
the possible substituent effects on the lifetime of aroyloxyl radicals
(Chateauneuf, J.; Lusztyk, J.; Ingold, K. U. J. Am. Chem. Soc. 1988, 110,
2886), the lifetime of the (4-cyanobenzoyl)oxyl radical is not expected to
be significantly different from the above value.
(29) Concerning the voltammetric analysis, we found that the ∂Ep/∂ log
V value for the oxidation of ArCOO- is about 45-50 mV/decade at the
slowest scan rates, although it increases to about 60 mV/decade when V )
2-5 V s-1. The calculation of the standard potential was carried out by
both classical methods13b and by using the DigiSim software. Whereas a
rate constant of 1 × 107 s-1 was assumed for the decay of the radical,28 the
heterogeneous standard rate constant was bracketed in the 0.1-0.2 cm s-1
range to fit the experimental peak potentials well within the experimental
error. It is relevant to note that, due to the kinetic zone in which the
experimental system is,13b even by allowing the chemical rate constant to
be in error by as much as 1 order of magnitude, the uncertainty in the
standard potential is within 50 mV. A larger error, however, was prudently
assumed due to the problems associated to voltammetric measurements in
DMF at such positive potentials.
The reduction of CP thus provides another convincing support
to the Save´ant theory of dissociative electron transfer3 and
relative implications. Considering the state of the art for
research on dissociative ETs, at least one final observation
should be made: since one of the most important requirements
to detect a borderline ET bond fragmentation mechanism is the
difference beween the standard potentials of ET 1 and ET 3,
one might also expect that within families of related compounds
(similar BDE and λ values) experimental outcomes analogous
•
-
to that of CP should be observed once the difference E°AB/A ,B
•-
- E°AB/AB is kept to similar values by proper selection of the
ring substituent. Further studies are currently underway in our
laboratory to verify this expectation.
Acknowledgment. This work was financially supported by
the Consiglio Nazionale delle Ricerche (CNR) and the Ministero
dell’Universita` e della Ricerca Scientifica e Tecnologica
(MURST).
(30) It should be added that we arrived in a similar way to 1.5 V as a
preliminary estimate of the standard potential of the corresponding PhCOO•/
PhCOO- couple,18 in reasonable agreement with a recent, nonelectrochemi-
cal estimate of it, 1.24 V: Andrieux, C. P.; Save´ant, J.-M.; Tallec, A.;
Tardivel, R.; Tardy, C. J. Am. Chem. Soc. 1996, 118, 9788.
JA971649F