Electron transfer to sulfides and disulfides: Intrinsic barriers and relationship between heterogeneous and homogeneous electron-transfer kinetics

Article abstract of DOI:10.1002/chem.200700382

The electron-acceptor properties of series of related sulfides and disulfides were investigated in N,N-dimethylformamide with homogeneous (redox catalysis) and/or heterogeneous (cyclic voltammetry and convolution analysis) electrochemical techniques. The electron-transfer rate constants were determined as a function of the reaction free energy and the corresponding intrinsic barriers were determined. The dependence of relevant thermodynamic and kinetic parameters on substituents was assessed. The kinetic data were also analyzed in relation to corresponding data pertaining to reduction of diaryl disulfides. All investigated reductions take place by stepwise dissociative electron transfer (DET) which causes cleavage of the C_alkyl^-S or S-S bond. A generalized picture of how the intrinsic electron-transfer barrier depends on molecular features, ring substituents, and the presence of spacers between the frangible bond and aromatic groups was established. The reduction mechanism was found to undergo a progressive (and now predictable) transition between common stepwise DET and DET proceeding through formation of loose radical anions. The intrinsic barriers were compared with available results for ET to several classes of dissociative- and nondissociative-type acceptors, and this led to verification that the heterogeneous and the homogeneous data correlate as predicted by the Hush theory.

Full text of DOI:10.1002/chem.200700382

FULL PAPER
DOI: 10.1002/chem.200700382
Electron Transfer to Sulfides and Disulfides: Intrinsic Barriers and
Relationship between Heterogeneous and Homogeneous Electron-Transfer
Kinetics
Ana Bel›n Meneses,[a, b] Sabrina Antonello,[a] Maria Carmen ArØvalo,*[b]
Concepcion Carmen Gonzµlez,[c] Jadab Sharma,[a] Andrea N. Wallette,[d]
Mark S. Workentin,*[d] and Flavio Maran*[a]
In memory of Professor Sergio Roffia
Abstract: The electron-acceptor prop-
erties of series of related sulfides and
disulfides were investigated in N,N-di-
methylformamide with homogeneous
(redox catalysis) and/or heterogeneous
(cyclic voltammetry and convolution
analysis) electrochemical techniques.
The electron-transfer rate constants
were determined as a function of the
reaction free energy and the corre-
sponding intrinsic barriers were deter-
mined. The dependence of relevant
thermodynamic and kinetic parameters
on substituents was assessed. The ki-
netic data were also analyzed in rela-
tion to corresponding data pertaining
to reduction of diaryl disulfides. All in-
vestigated reductions take place by
stepwise dissociative electron transfer
(DET) which causes cleavage of the
ble bond and aromatic groups was es-
tablished. The reduction mechanism
was found to undergo a progressive
(and now predictable) transition be-
tween common stepwise DET and
DET proceeding through formation of
loose radical anions. The intrinsic barri-
ers were compared with available re-
sults for ET to several classes of disso-
ciative- and nondissociative-type ac-
ceptors, and this led to verification that
the heterogeneous and the homogene-
ous data correlate as predicted by the
Hush theory.
ꢀ
ꢀ
Calkyl S or S S bond. A generalized
picture of how the intrinsic electron-
transfer barrier depends on molecular
features, ring substituents, and the
presence of spacers between the frangi-
Keywords: electrochemistry · elec-
tron transfer · reduction · substitu-
ent effects · sulfur
Introduction
[a] A. B. Meneses, Dr. S. Antonello, Dr. J. Sharma, Prof. Dr. F. Maran
Dipartimento di Scienze Chimiche
Università di Padova
During the last two decades, substantial knowledge of the
thermodynamics, kinetics, and mechanisms of electron-trans-
fer (ET) reactions associated with cleavage of a s bond (dis-
sociative ET, DET) has been accumulated. Several aspects
of reductive DET, particularly with regard to carbon–halo-
Via Marzolo 1, 35131 Padova (Italy)
Fax (+39)049-827-5239
E-mail: flavio.maran@unipd.it
[b] A. B. Meneses, Prof. Dr. M. C. ArØvalo
Departamento de Química Fisíca
Universidad de la Laguna
ꢀ
gen and O O bonds, have been investigated and re-
viewed.[1–3] Dissociative reduction of a neutral species A B
ꢀ
Avda. Astrofísico Fco Sµnchez s/n, 38071 La Laguna (Spain)
Fax : (+34)922-318-002
E-mail: carevalo@ull.es
ꢀ
C
to form a radical A and an anion B may proceed either
through formation of a discrete radical anion intermediate
A B [stepwise DET, Eq. (1)] or concertedly [Eq. (2)].
[c] Dr. C. C. Gonzµlez
Cꢀ
ꢀ
Instituto de Productos Naturales y Agrobiologia del CSIC
Universidad de la Laguna
Avda. Astrofísico Fco Sµnchez s/n, 38071 La Laguna (Spain)
AꢀB þ e Ð AꢀBCꢀ ! AC þ Bꢀ
ð1Þ
ð2Þ
[d] A. N. Wallette, Prof. Dr. M. S. Workentin
Department of Chemistry
AꢀB þ e ! AC þ Bꢀ
The University of Western Ontario
N6A5B7 London, Ontario (Canada)
Fax : (+1)519-661-3022
The reaction pathway followed by the reduction is a func-
tion of parameters that may be directly associated with the
acceptor molecule, such as the nature of the cleaving bond,
the properties of substituents, and the redox potential of the
E-mail: mworkent@uwo.ca
Supporting information for this article is available on the WWW
under http://www.chemeurj.org/ or from the author.
Chem. Eur. J. 2007, 13, 7983 –7995
ꢀ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
7983

leaving group, or externally driven, such as temperature, sol-
vent, and the electrode potential (for heterogeneous reduc-
tions) or the standard potential of the solution one-electron
donor (for homogeneous reductions). In fact, it has been
found that even for a single acceptor molecule, the DET
mechanism can be changed by modifying one or more of
such parameters.[4–7] The transition between the two limiting
mechanisms of thermal DET can be detected by using ho-
mogeneous redox catalysis[8] or direct electrochemical meth-
ods,[4c] and these approaches have been thoroughly analyzed
and discussed.
An important factor that differs between the ET steps of
the two mechanisms is the intrinsic barrier DGꢀ0 ,[9] that is,
the activation free energy DGꢀ when the reaction free
energy (DG8) is 0, which characterizes the kinetic facility of
the ET reaction. The DGꢀ0 value is composed of an outer
component, namely, the solvent reorganization energy
(DGꢀ0,s), and an inner component (DG0ꢀ,i), which describes
the molecular deformation (of bond lengths and bond
angles) of the reacting system.[9] The DG0ꢀ,s is the most im-
portant factor determining the kinetics of ET proceeding
through the formation of rigid transient radical anions,
where reduction causes little molecular deformation and the
singly occupied molecular orbital (SOMO) is very weakly
coupled to the s* orbital of the cleaving bond; this behavior
is typical of most ethers and aryl halides.[1,3] In this mecha-
nism, the bond-cleavage step is an intramolecular DET
actantlike, and the activation energy decreases accordingly.
The DGꢀ0 value can become significantly smaller than that
of uncomplicated concerted dissociative processes and thus
its magnitude may be comparable to that of the loose radi-
cal anion DET mechanism. Clear-cut examples of this bor-
derline DET mechanism are provided by the reduction of
substituted benzyl halides[13] and halo acetonitriles.[14]
Because of specific features of the acceptor molecule and,
to some extent, the dielectric and molecular properties of
the solvent, different DET mechanisms may occur whose
detection requires determination of relevant parameters,
particularly the DGꢀ0 value. Among the various classes of
DET acceptor molecules, an unifying understanding of the
ꢀ
reductive cleavage of the C S bond of sulfides is still lack-
ing. This is partly because these DET reactions appear to be
particularly suited to give rise to mixed mechanistic behav-
iors, as already observed and/or discussed.[1,4a,15,16] For exam-
ple, certain sulfides are reduced with substantial inner reor-
ꢀ
ganization caused by C S bond elongation on radical-anion
formation.[15c,d] In one case, some evidence for a concerted-
to-stepwise mechanistic transition induced by driving force
was obtained by studying the dissociative reduction of tri-
phenylmethyl phenyl sulfide by a series of solution one-elec-
tron donors,[4a] though a different selection of mediators did
not reveal the same activation/driving force trend.[16] Con-
cerning disulfides, more qualitative and quantitative infor-
mation is available,[11,12] but factors remain that are unex-
ꢀ
ꢀ
from the p* SOMO to the A B s* orbital. The cleavage
plored. Understanding the reductive cleavage of C S and
ꢀ
ꢀ
step is accompanied by stretching of the A B bond and sig-
S S bonds in terms of both their kinetics and thermodynam-
nificant solvent reorganization (as the charge is eventually
localized on the leaving group). In the limiting case of con-
certed DETs, DGꢀ0 is much larger because the inner reor-
ganization contains as much as one-fourth of the dissocia-
tion energy of the cleaving bond[10] and is thus much larger
than the DGꢀ0,s term.
ics is essential to improve our knowledge of important or-
ganic and biological systems.[17] In particular, a main goal of
current research in the field is to establish a sufficiently ac-
curate model to predict the reactivity of these bonds toward
electron uptake in complex systems such as proteins and po-
lymer networks.
The recent observation of the occurrence of borderline
mechanisms makes the distinction between the two DET re-
actions less straightforward.[1b,2] There are stepwise process-
es in which the initial ET has a significant inner reorganiza-
tion energy. This happens when the SOMO involves the
To systematically address the issue of understanding how
different molecular features affect the ET step and the
cleavage dynamics, the dissociative reduction of series of re-
lated acceptors is studied by using direct (heterogeneous
DET) and/or indirect (homogeneous DET) electrochemical
methods.[1–3] Here we describe the dynamics of radical-anion
formation in the reduction of series of diphenylmethyl para-
substituted phenyl sulfides Ph2CHSAr (1), triphenylmethyl
para-substituted phenyl sulfides Ph3CSAr (2), and symmetri-
cal para- or meta-substituted benzyl disulfides, (ArCH2S)2
(3); for comparison, direct reduction of the disulfide of di-
phenylethanethiol (PhCH2CH2S)2 (4), in which the cleaving
bond is farther from the aryl groups, was also studied
(Table 1). The DET reactions were studied in N,N-dimethyl-
formamide (DMF) containing tetrabutylammonium perchlo-
rate (TBAP) by using a combination of homogeneous
(redox catalysis) and/or heterogeneous (cyclic voltammetry
and convolution analysis) approaches. The ET standard rate
constants and intrinsic barriers were determined, and the
dependence of the relevant thermodynamic and kinetic pa-
rameters on substituents assessed. The data were analyzed
by using information previously obtained for the reduction
ꢀ
ꢀ
frangible bond, whereby the A B bond length (the A B
bond order decreases), and thus DGꢀ0,i increases. For some
compounds, such as most disulfides,[11,12] the SOMO is more
ꢀ
localized on the S S bond so that it essentially corresponds
to the s* orbital. The ET intermediate now is a loose s*
radical anion, as opposed to the more rigid framework of
the p* radical anions that form in common stepwise DET
processes. The DGꢀ0 for formation of the loose radical anion
is thus quite large, but still not as large as that of concerted
DET. Concerted DET reactions can form caged fragmenta-
tion products that can undergo ion–dipole interactions, in
which the anionic leaving group, Bꢀ, electrostatically inter-
acts with the dipole moment present in the radical fragment
C [2,3]
ꢀ
A .
In concerted DETs, the A B bond length is an impor-
tant component of the reaction coordinate. In the case of
ꢀ
ion–dipole interactions, this A B bond elongation is less
pronounced, the resulting transition state becomes more re-
7984
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Chem. Eur. J. 2007, 13, 7983 –7995

Electron Transfer to Sulfides and Disulfides
FULL PAPER
Table 1. Identification of substituents X of 1–3 and 5 by labels a–i (or-
dered according to their Hammett s values).
Faraday cage. The cage and all instruments were connected to a common
ground. To minimize the ohmic drop between the working and reference
electrodes, feedback correction was employed.
The electrochemical experiments were performed by using homemade
glassy carbon (GC, Tokai GC-20) electrodes 1 mm in diameter that were
prepared as previously reported.[21] The GC electrodes were stored in
ethanol and were polished before experiments with a 0.25 mm diamond
paste (Struers) and ultrasonically rinsed with ethanol for 5 min. The elec-
trodes were electrochemically activated in the background solution by
means of several voltammetric cycles at 0.5 Vsꢀ1 between the anodic and
cathodic solvent/electrolyte discharges, until the quality features de-
scribed in reference [22] were obtained. The electrode area was deter-
mined by measuring the limiting convoluted current of ferrocene, whose
diffusion coefficient in DMF is 1.13”10ꢀ5 cm2 sꢀ1 [23]
The Ag/AgCl or Ag/
.
AgI reference electrode was calibrated at the end of each experiment
against the ferrocene/ferricenium couple, whose formal potential is
0.464 V against the KCl saturated calomel electrode (SCE); in the follow-
ing, all potentials are reported against SCE. A platinum ring or plate
served as the counterelectrode.
p-MeO
(a)
H
p-F p-Cl p-CO2Et p-COMe m-CN p-CN p-NO2
(b) (c) (d)
(d)
(f)
(g)
(h)
(i)
s
1
2
3
4
ꢀ0.27
+
0
0.06 0.23
0.45
0.50
0.56
066
+
0.78
+
+
+
+
+
+
+
+
+
+
The behavior of the working electrode was first studied in the back-
ground solution, in a selected potential range, and for scan rates ranging
from 0.1 to 100 Vsꢀ1. The same procedure was repeated after addition of
the electroactive species; another series of CVs was acquired after addi-
tion of 1 equiv of a weak acid (depending on the type of acceptor: acetic
acid, phenol, acetanilide, or trifluoroethanol). For the redox catalysis ex-
periments (which, given the range of ET rate constants investigated, were
carried out by CV), the latter procedure was repeated after addition of
increasing amounts of the acceptor (twice). A corresponding amount of a
weak acid (acetanilide) was always present in solution. Convolution anal-
ysis was carried out on digitalized (1 point per mV) background-subtract-
ed CV curves by using our own laboratory software and all necessary
precautions required to minimize the electrical noise.[21] To double check
the heterogeneous or homogeneous parameters obtained by convolution
or redox catalysis, the experimental CV curves were also digitally simu-
lated with the DigiSim 3.03 package by using a step size of 1 mV and an
exponential expansion factor of 0.5. The reproducibility of the homoge-
neous (single donor/acceptor system) and heterogeneous kinetic data (k
determination at any investigated E value, as obtained from different ex-
periments and scan rates) was in the range of 5–15%.
+
+
+
+
+
+
+
+
+
+
+
+
+
of diaryl disulfides 5,[11] which led to a consistent picture of
how molecular features (in different classes of compound)
and substitution (within the same family of compounds)
affect the ET step, particularly its inner barrier, and cause
the mechanism to undergo a progressive transition between
common stepwise DET and DET proceeding through for-
mation of loose radical anions. Finally, the intrinsic barriers
determined were compared with similar data for a variety of
other ET and DET acceptors. Thus, it was established for
the first time for such a range of compounds that the corre-
lation between the heterogeneous and the homogeneous
DGꢀ0 values agrees very well with the Hush model.[18]
Results and Discussion
Experimental Section
Direct reduction of sulfides 1: The cyclic voltammograms of
sulfides 1a–d in DMF/0.1m TBAP display single irreversible
peaks at very negative potentials, as previously reported for
1a[15d] and 1b;[15b] for example, at 0.2 Vsꢀ1 the peak poten-
tials Ep are in the range ꢀ2.35 to ꢀ2.52 V (Table 2). These
peaks are irreversible at all scan rates v investigated and
broaden as v increases. The electroreduction of 1h occurs at
a more positive potential (ꢀ1.86 V) and exhibits a second
reversible peak (Figure 1). The formal potential E8 of the
latter (half-sum between the cathodic and anodic peak po-
tentials) is ꢀ2.44 V. In the v range explored, the first peak
of 1h remains irreversible, that is, the ET step is followed
by a fast and irreversible chemical reaction. The reduction
peak of 1i is sharper and located at a much more positive
potential (ꢀ1.08 V), which corresponds to the typical behav-
ior expected for a nitro derivative. As previously repor-
ted,[20c] the peak of 1i already shows some reversibility (ap-
pearance of the corresponding anodic peak) at about
1.5 Vsꢀ1, that is, the chemical reaction affecting the initially
formed ET intermediate roughly occurs on the 0.1 s time-
Chemicals: DMF (Acros Organics, 99%) was treated with anhydrous
Na2CO3 and doubly distilled at reduced pressure under a nitrogen atmos-
phere. Tetra-n-butylammonium perchlorate (TBAP, 99%, Fluka) was re-
crystallized from ethanol/water (2/1) and dried at 608C under vacuum.
The ET mediators were commercially available, except for methyl 3-phe-
noxybenzoate and phthaloyl-a-aminoisobutyric acid methyl ester, which
were available from previous studies.[4d,19]
Sulfides 1 and 2 were synthesized from the appropriate thiophenol and
diphenylmethanol or triphenylmethanol in acetic acid with H2SO4, and
recrystallized from ethanol.[4a, 15c,16,20] Dibenzyl disulfides 3 were prepared
by the following steps: reaction of the appropriate benzyl bromide with
potassium acetate to yield an acetylsulfanyl methylbenzene derivative,
transformation of the latter into the thiol under acidic conditions, and ox-
idation of the thiol to the disulfide with iodine. Full details of the synthe-
ses of sulfide 1h and disulfides 3 are provided in the Supporting Informa-
tion. The synthesis of disulfide 4h will be described elsewhere.
Electrochemistry: For the electrochemical experiments, an EG&G-
PARC 173/179 potentiostat/digital coulometer, an EG&G-PARC 175 uni-
versal programmer, and a Nicolet 3091 digital oscilloscope with 12-bit
resolution were used. The electrochemical experiments were conducted
under an Ar atmosphere in an all-glass cell that was thermostated at
258C. The experiments were carried out inside a double-wall copper
Chem. Eur. J. 2007, 13, 7983 –7995
ꢀ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
7985

F. Maran, M. C. ArØvalo, M. S. Workentin et al.
Table 2. Electrochemical and kinetic parameters for the direct reduction of sulfides 1 in DMF/0.1m TBAP at
258C.
wide and/or the molecule car-
ries good electron-withdrawing
groups, reduction of the conju-
gate base of the starting mole-
cule can be detected at more
negative potentials.
In line with the general be-
havior of this type of com-
pound, the voltammetric pat-
tern of sulfides 1 is accounted
for by the reduction sequence
given by [Eqs. (3)–(6)], in
which radical anion formation
[a]
[a]
[c]
1
Ep
DEp/2
a[b]
106 D
E8[c]
[V]
logkꢁhet
(DGꢀ0 )het
(DGꢀ0,i)het
[V]
[mV]
[cm2 sꢀ1
]
[cmsꢀ1
]
[kcalmolꢀ1
]
[kcalmolꢀ1
]
a[d]
b
c
d
h
i
ꢀ2.52
ꢀ2.47
ꢀ2.47
ꢀ2.35
ꢀ1.87
ꢀ1.08
95
94
98
92
78
58
0.502
0.507
0.487
0.526
0.612
0.823
7.0
7.6
7.7
6.3
6.6
6.5
ꢀ2.45
ꢀ2.39
ꢀ2.32
ꢀ2.30
ꢀ1.94
ꢀ1.05
ꢀ2.80
ꢀ2.64
ꢀ2.96
ꢀ2.66
ꢀ1.38
ꢀ0.77
8.7
8.5
8.9
8.5
6.7
5.9
5.1
4.6
5.0
5.3
3.3
2.6
[a] At 0.2 Vsꢀ1. [b] Measured from DEp/2. [c] The experimental uncertainty associated with the parameters ob-
tained at a=0.5 is 20 mV (E8) and 0.2lg units (lgkꢁhet). [d] From ref [15d].
ꢀ
[Eq. (3)] is followed by C S bond cleavage [Eq. (4)], reduc-
C
tion of Ph2CH [Eq. (5)], and self-protonation [Eq. (6)].
Ph2CHSAr þ e Ð Ph2CHSArCꢀ
Ph2CHSArCꢀ Ð Ph2CHC þ ArSꢀ
Ph2CHC þ e ! Ph2CHꢀ
ð3Þ
ð4Þ
ð5Þ
ð6Þ
Ph2CHꢀ þ Ph2CHSAr Ð Ph2CH2 þ Ph2CSArꢀ
The reversible second peaks observed in the reduction of
1h and 1i are attributed to reduction of the corresponding
conjugate base Ph2CSArꢀ. On the positive-going scan, the
thiolate anions are oxidized at their characteristic potentials
(for the substituents of 1a–i, the E8 values range from ꢀ0.07
to 0.53 V)[11b] and so are the carbanions Ph2CSArꢀ (the E8
values are in the range ꢀ0.7 to ꢀ0.8 V). On the other hand,
if the water content in the solvent/electrolyte system is not
negligible, the latter peak disappears, and this suggests that
the self-protonation reaction [Eq. (6)] does not take place
(the pKDa MF of water is 31.7,[25a,d] but H2O is an OH acid and
thus protonation is kinetically faster than with common CH
acids). As previously done for 1a and 1b,[15b,d] we applied
the appropriate theory[15b] and found very similar values of
the self-protonation rate constants of (1–5)”10ꢀ4 mꢀ1 sꢀ1 that
suggest a mild substituent effect on the CH acidity; this also
Figure 1. Cyclic voltammetry curves of 5 mm 1h in DMF/0.1m TBAP in
the absence (dashed line) and presence (solid line) of 1 equiv of acetani-
lide. GC electrode, 258C, 0.02 Vsꢀ1
.
scale. As in the case of 1h, a second reduction peak for 1i
that is reversible even at low scan rate (E8=ꢀ1.52 V) is ob-
served. Finally, for all sulfides oxidation peaks are detecta-
ble during the backward positive-going scan for E>ꢀ0.8 V;
they are associated with oxidation of the carbanionic and/or
thiolate species (vide infra) formed in the reduction process.
Previous investigations[15b,d] showed that reduction of this
ꢀ
type of sulfide proceeds by cleavage of the C S bond to
form a thiolate ion (ArSꢀ) and the diphenylmethyl radical
C
(Ph2CH ); for both thermodynamic (the formal potential E8
C
is confirmed by the mild sensitivity of E8 of the Ph2CSAr /
Ph2CSArꢀ couple to the substituent. Addition of a proton
donor mild enough to protonate Ph2CHꢀ but not the radical
C
of Ph2CH is ꢀ1.1 V) and kinetic reasons (reduction is ac-
companied by little reorganization energy),[24] the radical is
rapidly reduced to the corresponding carbanion Ph2CHꢀ.
Since the latter is very basic (the pKDa MF of Ph2CH2 can be
estimated to be 32.6)[25a,b] and the original sulfide is the
strongest acid in solution (the pKDa MF of Ph2CHSPh is
27.2,[25a,c] and that of 1a was estimated to be only slightly
larger;[15d] similarly, the pKDa MF values of the other sulfides
should not be significantly smaller than 27), a self-protona-
tion reaction occurs. By this mechanism,[15b,26] part of the re-
ducible molecule is transformed into its conjugate base and
becomes electroinactive at the applied potentials. The over-
all electron consumption is thus less than the expected two
electrons per molecule (if the self-protonation reaction is
sufficiently fast, one electron per molecule is consu-
med).[15b,26] In previous self-protonation studies,[26b] we ob-
served that if the available potential window is sufficiently
anion formed in Equation (3), such as acetanilide (pKaDMF
=
22.3),[25a] efficiently hampers the self-protonation reaction
[Eq. (7)].
Ph2CHꢀ þ HA ! Ph2CH2 þ Aꢀ
ð7Þ
Consequently, all electroactive compounds can now be re-
duced at the working potentials, and thus the current of the
first peak increases to reach the expected two-electron stoi-
chiometry. This is illustrated in Figure 1 for compound 1h
(solid line as opposed to the dashed curve). Whereas both
the reduction and the oxidation peaks of Ph2CSArꢀ disap-
pear, the oxidation peak of ArSꢀ remains (not shown in the
figure), as thiophenols are the strongest acids in solution
(pKDa MF =12.3 and 6.8 for 1a and 1h, respectively).[25a,e]
7986
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Chem. Eur. J. 2007, 13, 7983 –7995

Electron Transfer to Sulfides and Disulfides
FULL PAPER
Because the main goal of this part of the study was the
determination of the heterogeneous ET parameters, all re-
sults described below and gathered in Table 2 were obtained
in the presence of acetanilide (and thus under conditions in
which the self-protonation reaction does not take place and
the electrode reaction is a two-electron process). Besides
the substituent effect on Ep, the results show that the peak
widths (DEp/2, which is the absolute difference between Ep
and the potential at mid-peak height) and consequently the
The dependences on potential of the apparent (uncor-
rected for double-layer effects) heterogeneous rate con-
stants khet were obtained from the i, I, and D values,[29] as ex-
emplified in Figure 2 for compound 1h. The apparent
values of a were obtained as a function of E by derivatiza-
tion of the corresponding lnkhet versus E plots as a=ꢀ
A
F)(dlnkhet/dE). For all sulfides, the a versus E plots were
linear within error, and thus point to an ET process control-
led by a quadratic activation/driving force relationship and
to the absence of ET-mechanism transitions.[4c] With these
conditions attained, the E8 of the electrode reaction can
usually be estimated as the E value at which a=0.5, as most
models or calculations for outer-sphere or dissociative ET
share the result that a should be about 0.5 at zero driving
force.[9,10,12,14,30] The E8 values of sulfides 1 were thus esti-
mated from the linear fit to the pertinent set of a versus E
data. By using these E8 estimates, the apparent values of the
standard rate constant kꢁhet were obtained by parabolic fitting
to the logkhet versus E plots. The consistency of the E8 and
kꢁhet values obtained by convolution analysis was also
checked by digital simulation of the cyclic voltammograms,
which led to very good reproduction of the experimental
curves obtained by varying v by about 2.5 orders of magni-
tude. From the kꢁhet values, using an Eyring-type equation
(lnkꢁhet =lnZhetꢀDGꢀ0 /RT) and the pertinent heterogeneous
frequency factors Zhet (Zhet =(RT/2pM)1/2, where M is the
molar mass of the electroactive species), the heterogeneous
intrinsic barriers (DGꢀ0 )het were calculated. The inner com-
ponents (DGꢀ0,i)het were obtained by subtracting the (DG0ꢀ,s)het
component from (DGꢀ0 )het; the (DG0ꢀ,s)het values were calcu-
lated from the empirical equation (DGꢀ0,s)het =13.9/r,[21]
where r [Š] is the sulfide radius obtained from the Stokes–
Einstein equation and the experimental D value.
corresponding values of the transfer coefficient a (DEp/2
=
1.857RT/Fa)[27] do not significantly vary for 1a–d; the peaks
of 1h and 1i, however, yield larger a values. All a values
are sufficiently large to ensure that the DET mechanism is
stepwise.[1–3] For all compounds, when v increases DEp/2 also
increases and thus a decreases. This is a general behavior in-
dicating that reduction is controlled by a nonlinear depend-
ence of the heterogeneous ET kinetics on E (i.e., the reac-
tion thermodynamics). The reductions were thus studied by
convolution analysis,[1a,21,28] which is an efficient tool for ob-
taining information on activation/driving force relationships
and mechanistic transitions of DET reactions. By this ap-
proach the convoluted current I was calculated from back-
ground-subtracted voltammograms obtained at several scan
rates (Figure 2). Convoluted current I is related to the real
As shown in Table 2, the main outcome of this analysis is
that the inner reorganization accompanying the reduction of
1a–d accounts for about 60% of the intrinsic barrier (with
no detectable substituent effect), whereas less inner reorgan-
ization affects the reduction of 1h and 1i. As already discus-
sed,[15e] there are good reasons to believe that the (DG0ꢀ,i)het
behavior observed for 1a–d is caused by a significant degree
ꢀ
of spreading of the SOMO onto the cleaving C S bond, and
thus to an elongation of the latter on radical-anion forma-
tion. Finally, we employed the calculated intrinsic barriers
and E8 values to simulate the CV behavior of 1h and could
Figure 2. Cyclic voltammetry curves for the reduction of 2.0 mm 1h in
DMF/0.1m TBAP at the GC electrode. The upper graph shows a series
of background-subtracted curves at different scan rates (left to right: 0.1,
0.2, 0.5, 1, 2, 5, 10, 20, 50 Vsꢀ1). The voltammetric current i is reported in
its v-normalized form. The lower graph shows plots of the corresponding
potential dependence of logkhet and a (full circles). T=258C.
ꢀ
estimate the C S bond cleavage rate constant kc to be 6”
105 sꢀ1. For 1i, kc was also calculated from the CV analysis
to be 11 sꢀ1.
The values discussed above were obtained by neglecting
double-layer effects. In fact, the characterization of the
double-layer properties of GC was carried out only very re-
cently, by applying the Gouy–Chapman–Stern double-layer
theory.[22] Application of such a correction, whose effect de-
pends on the explored potential range and the potential
region to which the experimental a or khet data need to be
extrapolated, does not change substantially the estimates of
Table 2: typically, the E8 values become slightly more posi-
tive (the experimental error in the estimated E8 of “slow”
current i through the convolution integral[30] and thus dis-
plays a sigmoidal dependence on the applied potential E
(see Figure S1 in the Supporting Information). For each ex-
periment and sulfide, the I–E curves were characterized by
the same limiting value Il[29] within 2%. From the Il values
and by using electrodes of known area, the diffusion coeffi-
cients D of compounds 1 were calculated (Table 2).
Chem. Eur. J. 2007, 13, 7983 –7995
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7987

F. Maran, M. C. ArØvalo, M. S. Workentin et al.
DET acceptors is already on the order of 0.1 V), the logkhꢁet
values increase by 0.4–0.6 units and the intrinsic barriers de-
crease by 0.6–0.8 kcalmolꢀ1, but the contribution of
(DGꢀ0,i)het to the latter decreases by no more than 5%. In the
following, for consistency with previous work carried out on
the reduction of other sulfides and disulfides at GC electro-
des, double-layer effects will be neglected. In fact, our dis-
cussion will specifically focus on a comparison of the general
trends displayed by the different series of compounds as a
function of the substituents.
Indirect reduction of sulfides 1: The indirect reduction of 1
was accomplished by homogeneous redox catalysis with
electrogenerated radical anions as homogeneous electron
donors (D).[8] The mechanism of the ET reaction is analo-
gous to that of the heterogeneous reduction, but the re-
Cꢀ
duced form of the donor (D ) replaces the electrode. The
reaction sequence pertaining to sulfides 1 is shown in
[Eqs. (8)–(11)], followed by carbanion protonation by the
added acid, acetanilide [Eq. (7)].
D þ e Ð DCꢀ
ð8Þ
ð9Þ
Figure 3. Cyclic voltammetry curves for the reduction of 0.1 mm 1h in
DMF/0.1m TBAP at two scan rates. The CVs were obtained in the ab-
sence (dashed lines) and presence of 1.0 mm anthracene (solid lines).
Simulations of the catalyzed reductions are shown by open circles. GC
electrode, T=258C.
DCꢀ þ Ph2CHSAr Ð D þ Ph2CHSArCꢀ
Ph2CHSArCꢀ Ð Ph2CHC þ ArSꢀ
DCꢀ þ Ph2CHC ! D þ Ph2CHꢀ
ð10Þ
ð11Þ
In homogeneous redox catalysis experiments, the reversi-
ble CV peak of the mediator is transformed into a chemical-
ly irreversible, catalytic peak on addition of the acceptor.
The current of the catalytic peak depends on the scan rate
and the concentration of the acceptor: the ET rate constant
khom [Eq. (9), forward reaction] is obtained by studying such
dependences. Because of the presence of 1 equiv of acetani-
lide, required to hamper the self-protonation reaction, we
avoided using mediators displaying some basicity, such as
azobenzene derivatives. It is common protocol to choose
mediators having E8 values (EꢁD) at least 200 mV more posi-
tive than the acceptor Ep at low scan rate, but in this study
we also aimed at verifying whether it could have been possi-
ble to “push” the experimental system by using mediators
with E8 values similar to or even more negative than the ac-
ceptor Ep. Figure 3, which pertains to 1h and to a mediator
(anthracene) with an E8 that is 70 mV more negative than
the acceptor Ep at 0.2 Vsꢀ1, nicely illustrates the outcome of
such experiments. The catalytic (and complete) reduction of
the acceptor occurs at potentials (prepeak to the mediator
peak) that are more positive than either the donor or ac-
ceptor peak. We could verify that this is indeed a possible
experimental strategy, as the experimental curves could be
simulated very well; for the case shown in Figure 3, we
could calculate a homogeneous ET rate constant as large as
5”107 mꢀ1 sꢀ1. With sulfides 1a and 1c, we could use media-
tors with E8 values almost as negative (30–40 mV) as the ac-
ceptor Ep. A typical logkhom versus EꢁD plot (sulfide 1h) is
shown in Figure 4, while the other plots are provided in Fig-
ures S2–S5 in the Supporting Information, together with all
ET rate constants (see Table S1).
According to the steady-state treatment of the kinetic
Scheme illustrated above, the forward rate constant of reac-
tion (9) khom can be expressed as in Equation (12).
1
1
1
1
¼
þ
þ
ð12Þ
ꢀ
Zhom expðꢀ DG =RTÞ kd expðꢀ DGꢁ=RTÞ
khom kd
Figure 4. Plot of the logarithm of the homogeneous ET rate constant
against EꢁD for the reduction of 1h by aromatic radical anions in DMF/
0.1m TBAP at 258C. The peak shows where the direct reduction of 1h
takes place at 0.2 Vsꢀ1. The dashed lines illustrate the three regions,
while the solid line is the fit to Equation (12).
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Chem. Eur. J. 2007, 13, 7983 –7995

Electron Transfer to Sulfides and Disulfides
FULL PAPER
Here kd is the diffusion-controlled rate constant in DMF
(8.7”109 mꢀ1 sꢀ1)[15c] and Zhom the collision frequency (aver-
expense of the onset of the counterdiffusion-controlled
zone. In both cases, we can take the most positive logkhom
value (most endergonic ET reaction) and impose a counter-
diffusion line with appropriate slope [i.e., ꢀF/(RTln10)]. If
kꢁhom is indeed small, minimum (i.e., more negative) values
of E8 (of 1a–d) can be estimated by extrapolation of the
line to the diffusion-controlled region.[8,11b] If the counterdif-
fusion zone is positively shifted by the occurrence of fast
cleavage in the solvent cage, the estimated E8 values pro-
vide maximum values (i.e., less negative), and the maximum
positive deviation from the “true” E8 value is about
0.12 V.[8] Interestingly, (Table 3) these E8 estimates are
indeed quite similar (but consistently more positive) to the
heterogeneous ET estimates (Table 2): this is in agreement
age value 3”1011 mꢀ1 sꢀ1), given by Z=d2[8pkBT/m]1/2, where
A
d is the encounter distance, kB the Boltzman constant, and m
the reduced mass);[9a] the solution ET is considered adiabat-
ic. DGꢀ can be expressed either as in the Marcus equation
[Eq. (13), where one of the two reactants is neutral] or as a
linear function of DG8 (neglecting the variation of the ET
coefficient with the driving force near E8).[31]
ꢀ
ꢁ
2
DGꢁ
4 DGꢀ0
DGꢀ ¼ DGꢀ0 1 þ
ð13Þ
Because of the form of the right-hand side of Equa-
tion (12), logkhom versus EꢁD can be partitioned into three re-
gions that are controlled by the diffusion of the reactants,
the actual ET within the solvent cage, and product escape
from the solvent cage (counterdiffusion); for the first and
the last regions, the acceptor E8 can be estimated.[8,31]
Analysis of the data pertaining to ET to sulfides 1a–d,h
by a series of mediators led to the results gathered in
Table 3. For 1a–d plots with a slope corresponding to the ac-
ꢀ
with either the occurrence of very fast C S bond cleavages
or small kꢁhom values and the fact that the heterogeneous E8
data of Table 2 are not corrected for the double layer
(which would cause a positive shift of the apparent E8
values). Indeed, the cleavage rates of compounds 1–3 (see
below) would suggest that the second hypothesis is more
likely.
For 1h, we used the same procedure that was previously
applied to study homogeneous ET to the similar sulfide
2h.[15c] Thus, a Marcusian form of the DG8 dependence of
the activation-controlled process [Eqs. (12) and (13)] was
employed. As shown in Figure 4, 1h displays both activation
and the counterdiffusion regions, and this allowed us to
safely (kc is sufficiently small, i.e., 6”105 sꢀ1) calculate the
homogeneous E8 from fitting of the logkhom versus EDꢁ =DCꢀ
data. The (DGꢀ0 )hom value was also obtained as a fitting pa-
rameter; in another analysis of the data, however, we em-
ployed the heterogeneous E8 and recalculated (DGꢀ0 )hom
(both values are shown in Table 3). As for the heterogene-
ous processes, the (DGꢀ0,i)hom values were obtained by sub-
tracting from the (DGꢀ0 )hom values the (DGꢀ0,s)hom that were
Table 3. Electrochemical and kinetic parameters for the homogeneous
reduction of sulfides 1 in DMF/0.1m TBAP at 258C.
[a]
[b]
[b]
[b]
[b]
1
Eꢁhom
[V]
ahom
lgkꢁhom
(DGꢀ0 )hom
(DGꢀ0,i)hom
[mꢀ1 sꢀ1
]
[kcalmolꢀ1
]
[kcalmolꢀ1
]
a
b
c
d
h
ꢀ2.40
ꢀ2.35
ꢀ2.27
ꢀ2.21
ꢀ1.97
0.55, 0.56
n.a., 0.53
0.53, 0.52
0.53, 0.53
0.77, 0.58
6.1, 5.7
5.9, 5.4
5.9, 5.5
6.2, 5.2
8.1, 8.1
7.3, 7.9
7.6, 8.3
7.6, 8.2
7.2, 8.3
4.7, 4.6
4.2, 4.8
4.4, 5.0
4.3, 4.9
4.3, 5.4
1.6, 1.5
[a] Determined from best fit of the redox catalysis data to Equation (12);
for details and uncertainties, see text. [b] The first and second figures
refer to the values obtained by using the convolution and redox-catalysis
E8 values, respectively.
calculated from the empirical equation (DGꢀ0,s)hom
=
24[(2rD)ꢀ1 +(2r)ꢀ1ꢀ(rD +r)ꢀ1],[33] in which we used rD =
tivation-controlled region (Supporting Information) were
obtained. The experimental data were linearly fitted to
Equation (12) by using ahom and logkꢁhom (the homogeneous
ET coefficient and standard rate constant, respectively) as
adjustable parameters[31] and the heterogeneous ET esti-
mates of the E8 values. As shown in Table 3, the ahom values
were slightly larger than 0.5, while the corresponding a
values obtained from CV measurements at low scan rate
(Table 2) were generally smaller. This is in keeping with the
fact that the homogeneous reductions are generally carried
out at lower driving forces than the corresponding heteroge-
neous processes (the mediators have less negative E8 values
than the applied potentials in direct electroreductions).
From the logkꢁhom results, the corresponding intrinsic barriers
could be obtained by using the above Zhom value and the
Eyring-type equation lnkꢁhom =lnZhomꢀ(DGꢀ0 )hom/RT.
3.8 Š as the average donor radius.
ꢀ
Concerning the C S bond cleavage reaction, as already
mentioned, the kc values could be determined by CV analy-
sis of the reduction peaks of 1h and 1i. By using the redox-
catalysis approach, the kc value for 1b could be calculated.
The method requires that the catalysis rate decreases as the
concentration of D increases.[34] By using 9-phenylanthra-
cene and varying its concentration in the range of 1–20 mm,
results were obtained (the catalytic efficiency as a function
of the pertinent kinetic parameter is shown in Figure S6 in
the Supporting Information) that allowed the calculation of
kc =9”107 sꢀ1.
Direct reduction of sulfides 2: The CVs of sulfides 2a,b,d
are quite similar and show single irreversible peaks located
at progressively more positive potentials. The peaks are
more positive by 0.23–0.26 V than those of the correspond-
ing sulfides 1. Addition of weak acids to the solution does
not affect these reduction peaks. The reduction of 2 f shows
an irreversible peak followed by a reversible peak with E8=
That the logkhom versus EDꢁ plots of 1a–d showed no indi-
cation of a counterdiffusion region can be related either to a
small value of khꢁom or to a very fast cleavage reaction,[32]
which would extend the activation-controlled region at the
Chem. Eur. J. 2007, 13, 7983 –7995
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7989

F. Maran, M. C. ArØvalo, M. S. Workentin et al.
Table 4. Electrochemical and kinetic parameters for the heterogeneous
reduction of 2 in DMF/0.1m TBAP at 258C.
ꢀ2.53 V. This is attributed to reduction of the corresponding
thiolate formed in the DET reaction [Eqs. (14)–(16)]. In
fact, and analogously to the behavior observed for the other
sulfides, an oxidation peak (the Ep of which correlates well
with the potentials of other para-substituted phenyl thio-
lates; by using the equation E8=0.069+0.619s, its E8 is es-
timated to be +0.38 V)[11b] attributable to thiolate oxidation
was detected during the backward positive-going scan. Both
the reduction and the oxidation peaks do not disappear on
addition of weak acids, as the thiolate is the conjugate base
of a relatively strong SH acid. However, the current of the
first peak increases (by a factor of 0.5 at 0.2 Vsꢀ1) when
1 equiv of acetanilide is added to the solution. The CV anal-
ysis indicates that a father–son reaction (such as self-proto-
nation: whereas the pKDa MF of acetophenone is 25.3, that of
the exogenous acid, acetanilide, is 22.3),[25a,c] affects the elec-
troreduction mechanism, as already discussed for sulfides 1.
The first irreversible peak of 2h is followed by a small
peak at low scan rates (v<1 Vsꢀ1) caused by the basic hy-
drolysis of the cyano group, as already discussed in de-
tail;[15c,35] addition of a mild proton donor (N-cyclohexyl iso-
butyramide, pKaDMF =27.9)[25a,26b] is sufficient to hamper this
reaction. Addition of stronger acids does not affect the cur-
rent of the reduction peak. The CV behavior of compound
2i has been already described in detail.[20d] The first peak is
irreversible, even at ꢀ308C and up to 1000 Vsꢀ1, but its E8
could be estimated from redox-catalysis data to be ꢀ1.00 V.
As for 2 f, the reversible reduction of the corresponding thi-
olate is observed at more negative potentials (E8=
ꢀ1.52 V).
[a]
[a]
[c]
2
Ep
[V]
DEp/2
a[b]
E8[c]
[V]
lgkꢁhet
(DGꢀ0 )het
(DGꢀ0,i)het
[mV]
[cmsꢀ1
]
[kcalmolꢀ1
]
[kcalmolꢀ1
]
a
b
d
f
h
i
ꢀ2.26 125
ꢀ2.21 113
ꢀ2.12 120
ꢀ1.61 82
ꢀ1.73 89
ꢀ0.88
0.382 ꢀ1.97 ꢀ3.94
0.423 ꢀ1.96 ꢀ3.84
0.399 ꢀ1.89 ꢀ3.60
0.582 ꢀ1.62 ꢀ2.08
0.536 ꢀ1.72 ꢀ2.06
ꢀ1.00
10.2
10.1
9.7
7.6
7.6
6.9
6.7
6.6
4.5
4.4
[a] Measured at 0.2 Vsꢀ1. [b] Measured from DEp/2. [c] The experimental
uncertainty associated with the parameters obtained at a=0.5 is 40 mV
(E8) and 0.3–0.4 lg units (lgkꢁhet).
(DGꢀ0,i)het becomes less pronounced, but it is still noticeable.
As already discussed for sulfides 1 and 2h,[15c] the substitu-
ent-dependent sluggishness of the heterogeneous reduction
of 2 is attributed to a more or less pronounced elongation of
ꢀ
the C S bond on radical-anion formation.
Direct reduction of disulfides 3 and 4b: With the exception
of 3i, reduction of dibenzyl disulfides 3 occurs at much
more negative potentials (0.6–0.7 V) than for the corre-
sponding para-substituted diaryl disulfides 5;[11b] this points
to a very large effect brought about by the presence of a
single methylene spacer between the aryl portion and the
ꢀ
S S bond. Figure 5 compares the CV curves (first peak) of
the unsubstituted compounds 1b, 2b, 3b, 4b, and 5b, togeth-
er with the range spanned by each series from p-OMe to p-
CN. The nitro derivatives were not included because these
compounds must be considered to be substituted nitro com-
pounds rather than nitro-substituted disulfides or sulfides.
Figure 5 also displays the reduction peak of disulfide 4b,
which shows that addition of a further methylene spacer to
3b does not modify the pattern significantly; the difference
in Ep is only 0.06 V.
For compounds 2a,b,d,f,h, if sufficiently anhydrous con-
ditions are attained,[15a] the oxidation peak of Ph3Cꢀ can be
observed; for 2i, the peak related to the triphenylmethyl
fragment is detected during the negative-going scan and is
C
due to the reduction of Ph3C . At sufficiently high scan rates
or in the presence of activated alumina, the peak of the
ꢀ
C
redox couple Ph3C /Ph3C
becomes reversible (E8=
The voltammetric patterns of disulfides 3 are generally
more complex than those of compounds 1, 2, and 5. The
CVs of 3a, 3b, and 3d, however, are quite similar and thus
can be discussed together. A typical CV shows a single irre-
versible reduction peak and, on the positive-going scan, the
ꢀ1.10 V).[4a,20d] For 2b,[4a] 2h,[15c] and 2i,[20d] the rate con-
ꢀ
stants for C S bond cleavage kc were previously calculated
from redox-catalysis data to be 8”1011, 1.2”108, and 4.1”
105 sꢀ1, respectively.
Ph3CSAr þ e Ð Ph3CSArCꢀ
Ph3CSArCꢀ Ð Ph3CC þ ArSꢀ
Ph3CC þ e ! Ph3Cꢀ
ð14Þ
ð15Þ
ð16Þ
The heterogeneous ET kinetics of sulfides 2 were studied
by convolution analysis at the GC electrode. The corre-
sponding E8, logkꢁhet, (DGꢀ0 )het, and (DG0ꢀ,i)het values were cal-
culated as explained for sulfides 1. The results (Table 4)
show that the trend already discussed for sulfides 1 is even
more pronounced. In particular, the inner reorganization ac-
companying the reduction of 2a,b,d now accounts for as
much as 65–70% of the intrinsic barrier (as opposed to
about 60% for 2a–d). For larger s values, the role of
Figure 5. Comparison between the CV curves (0.2 Vsꢀ1) of (left to right)
5b, 2b, 3b, 4b, and 1b in DMF/0.1m TBAP at 258C. The horizontal lines
show the range spanned for series 5, 2, 3, and 1 from the para-methoxy
to the para-cyano derivatives.
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Chem. Eur. J. 2007, 13, 7983 –7995

Electron Transfer to Sulfides and Disulfides
FULL PAPER
oxidation peak associated with thiolate oxidation. On addi-
tion of acetic acid (weaker acids such as phenol and trifluor-
oethanol do not affect the CV behavior), the reduction peak
does not change its shape and current, but a second peak
develops at more negative potentials (0.39–0.64 V, depend-
ing on the substituent). Increasing the amount of acid in the
disulfide solution does not affect the first peak, but the peak
current of the second peak progressively increases. This
second peak is coincident with the peak that can be ob-
served by reducing the corresponding thiol in the presence
of the same acid (independent experiments carried out with
the thiols). When the amount of acid in the thiol solution in-
creases, the peak current also increases, as already men-
tioned for the disulfides: this outcome indicates that thiol
reduction entails hydrogen evolution and thiolate formation,
followed by regeneration of the thiol through protonation.
In the case of the thiol of 3d, however, reduction occurs in
two steps. The first peak, which is weakly acid dependent,
duction entails thiolate formation (and thus hydrogen evolu-
tion) followed by thiol regeneration by protonation. The thi-
olate, obtained on addition of a base to the thiol solution, is
also reducible and its peak displays some reversibility at low
scan rates (E8=ꢀ1.30 V). With this information, the reduc-
tion behavior of 3i can be easily accounted for. The reduc-
tion of 3i (at 0.2 Vsꢀ1, Ep =ꢀ1.09 V) occurs at the same po-
tential as that of the thiol; at low scan rates, the peak is
chemically irreversible and a second reduction peak, with
same Ep as the thiolate, is observed. On acid addition, essen-
tially the same CV pattern as for the thiol is observed: the
current, however, is twice as large as that of the thiol. By
overlapping the CVs of 3i, thiol, and para-nitrotoluene, it is
evident that the latter does not form and thus that the re-
ꢀ
duction of 3i does not involve C S bond cleavage (see
below). To conclude, the reduction of 3i involves radical-
anion formation, and the SOMO is located at the nitro
ꢀ
group; intramolecular DET and then S S bond cleavage
ꢀ
appears to correspond to reductive cleavage of the C Cl
follow. The peak of 3i starts displaying reversibility as the
scan rate increases (at ca. 1 Vsꢀ1), while the peak attributed
to the thiolate disappears. The reversible peak, however, is
broad. This is because reduction may occur on both nitro
groups and this makes injection of a second electron into
the second nitro group slightly less favorable.[27c] Digital sim-
ulation of the CV curves obtained at different scan rates al-
lowed E8 values of ꢀ1.05 and ꢀ1.11 V to be estimated, and
the difference in E8 was indeed on the order of the expected
value (36 mV).[27c] The khꢁet of the initial ET is essentially the
same as that of the nitro derivatives described above.
bond (at 0.2 Vsꢀ1, Ep =ꢀ2.55 V) to form PhCH2SH; in fact,
the current of the second peak is dependent on the amount
of acid and the peak has the same Ep as PhCH2SH, that is,
the thiol of 3b.
ꢀ
Therefore, the reduction of 3a, 3b, and 3d occurs by S S
bond cleavage to form the thiolate and the thiyl radical; at
the working potentials, the latter is rapidly reduced to form
another thiolate ion. The peaks of 3a, 3b, and 3d obtained
in the absence of acid (but similar results were obtained in
the presence of phenol) were analyzed by convolution anal-
ysis, which led to the E8 and kꢁhet data shown in Table 5. The
same analysis was applied to 4b, which undergoes reduction
along similar lines as its shorter homologue 3b. It is note-
worthy that the kꢁhet values of these disulfides are very small,
much smaller than those of the corresponding sulfides. The
values are very similar to those previously obtained for a
series of dialkyl disulfides.[12] Because of the present find-
ings, and in line with the conclusions of the last-named in-
vestigation, the electroreduction of 3a, 3b, and 3d is ascri-
The CV patterns of the cyano derivatives 3g and 3h (first
reduction peak at ꢀ1.98 and ꢀ1.85 V, respectively) are com-
plicated by the presence of several peaks that are dependent
on the presence or absence of a weak acid. We describe
here the results obtained for 3h (cf. Figure S7 in the Sup-
porting Information); the main features of the CV behavior
of 3g are similar. A first indication of more complexity
comes from the fact that the peak for para-cyanotoluene is
ꢀ
present in the CV pattern. This implies that C S bond
ꢀ
ꢀ
bed to a dissociative S S bond cleavage proceeding through
cleavage occurs rather than S S bond cleavage. A possible
formation of a loose radical anion, the SOMO of which is
mechanism is thus initial formation of a p* radical anion
(the thiol of 3h is reducible at slightly more negative poten-
ꢀ
essentially coincident with the S S s* antibonding orbital.
ꢀ
The electroreduction of the thiol corresponding to disul-
fide 3i already shows some chemical reversibility at
0.2 Vsꢀ1; its E8 value of ꢀ1.11 V is more positive than that
of para-nitrotoluene (ꢀ1.16 V). On acid addition, the peak
current progressively increases, which indicates that the re-
tials) followed by intramolecular DET. Cleavage of a C S
bond forms the corresponding hydrodisulfide anion and the
para-cyanobenzyl radical, which is rapidly reduced to the
carbanion (its reduction potential in CH3CN is ꢀ0.77 V).[36]
Depending on the availability of protons in solution or by
addition of a weak acid, such as
acetanilide, the carbanion is
Table 5. Electrochemical and kinetic parameters for the heterogeneous reduction of 3 and 4b in DMF/0.1m
TBAP at 258C.
protonated to form para-cyano-
toluene (E8=2.39 V). Other
peaks related to the hydrodisul-
fide anion (ꢀ2.25 V at 0.2 Vsꢀ1)
and products derived from its
irreversible reduction are also
present. Interestingly, the thiol
of 3h undergoes a similar re-
duction mechanism that yields
[a]
[a]
Disulfide
Ep
DEp/2
a[b]
Eꢁhet
[V]
lgkꢁhet
(DGꢀ0 )het
(DGꢀ0,i)het
[V]
[mV]
[cmsꢀ1
]
[kcalmolꢀ1
]
[kcalmolꢀ1
]
3a
3b
4b
3d
3i
ꢀ2.39
ꢀ2.36
ꢀ2.42
ꢀ2.15
ꢀ1.09
127
129
132
124
55
0.376
0.370
0.361
0.385
0.852
ꢀ1.88
ꢀ1.84
ꢀ1.91
ꢀ1.75
ꢀ1.05
ꢀ5.70
ꢀ5.53
ꢀ5.58
ꢀ4.90
ꢀ1.10
12.6
12.5
12.5
11.5
6.3
9.5
8.7
9.2
7.9
3.1
[a] Measured at 0.2 Vsꢀ1. [b] Measured from DEp/2
.
Chem. Eur. J. 2007, 13, 7983 –7995
ꢀ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
7991

F. Maran, M. C. ArØvalo, M. S. Workentin et al.
ꢀ
para-cyanotoluene by C S bond cleavage. Because of the
bond, as typically found for dialkyl disulfides. Similar con-
siderations apply to 4b, which shows that, addition of a fur-
ther methylene unit does not modify the picture significant-
ly.
complexity of the reductions of 3g and 3h and particularly
the fact that the mechanism is different from that of the
other disulfides of series 3 (and 4b) and 5, we prefer not to
include the data of these compounds in the following discus-
sion.
Relation between heterogeneous and homogeneous reduc-
tions: The heterogeneous kinetic data can be compared to
the corresponding homogeneous kinetic data through the
pertinent intrinsic barriers (DGꢀ0 )het and (DG0ꢀ)hom. Whereas
the former needs no corrections, the (DGꢀ0 )hom values refer
to the standard rate constant kꢁhom and thus to the ET rate
constant from a hypothetical donor with the same E8.
(DGꢀ0 )hom can be transformed into the homogeneous self-ex-
change value (DGꢀ0 )hom,ex by using the cross-relation shown
in Equation (17).
DET mechanisms and intrinsic barriers: The heterogeneous
and homogeneous kinetic data of sulfides and disulfides
point to a common reduction mechanism for the acceptors
with electron-donating or mildly electron-withdrawing ring
substituents. As the Hammett s value becomes larger than
0.1–0.2, the intrinsic barriers decrease until, with the nitro
derivative, the typical values of nondissociative-type nitro
compounds is attained. Figure 6 illustrates the progressive
ðDGꢀ0 Þhom ¼ ½ðDGꢀ0 Þhom,ex þ ðDGꢀ0 Þhom,ex,D=DCꢀꢂ=2
ð17Þ
For the homogeneous self-exchange value of the donor
(DGꢀ0 )hom,ex,D/D ꢀ, which can be considered to be approxi-
C
mately constant for the donors commonly employed, we
used 3.6 kcalmolꢀ1.[37] For consistency, we used the (DG0ꢀ)hom
values corresponding to the E8 determined by convolution
analysis. The resulting (DGꢀ0 )het and (DGꢀ0 )hom,ex data of com-
pounds 1, 2 and 5 are plotted in Figure 7; the (DGꢀ0 )hom,ex
Figure 6. Hammett plot of the logarithm of the heterogeneous ET rate
&
*
constant for the reduction of sulfides 1 ( ), sulfides 2 ( ), disulfides 5
!
~
(
), disulfides 3 ( ), and 4b ( ) in DMF/0.1m TBAP at 258C. The
*
dashed lines are only intended to emphasize the experimental trends.
variation of logkhꢁet of compounds 1, 2, 3, and 5[11] as a func-
tion of s. Subtraction of the solvent-reorganization energies
from the (DG0ꢀ)het and (DG0ꢀ)hom values shows that the de-
crease in the standard rate constants at low s values is
caused by a progressive increase in DGꢀ0,i. The larger the
value of DGꢀ0,i the larger the extent of localization of the
SOMO onto the region of the cleaving bond.
Figure 7. Correlation between heterogeneous and homogeneous intrinsic
barriers for different classes of ET acceptors: aromatic compounds (ˆ),
As illustrated in Figure 6, the decrease is more marked as
one goes from compounds 1, to 2, to 5, to 3. For sulfides 1,
inner reorganization is relatively small, even at low s values.
On the other hand, sulfides 2 and diaryl disulfides 5 show
similar values and larger DGꢀ0,i values. Whereas for disulfides
!
*
benzyl aryl ethers and haloaromatic compounds ( ), sulfides ( ), disul-
~
&
^
fides ( ), peroxides ( ), haloacetonitriles (N), and alkyl halides ( ). The
solid line is the best linear fit to the data, while the dotted lines show the
99% confidence intervals. The two dash-dotted lines illustrate the Hush
(upper line) and Marcus (lower line) behaviors. The dashed curve repre-
sents the Hush prediction with a steady increase in inner reorganization
(see text).
5 we already showed both experimentally and through cal-
ꢀ
ꢀ
culations that DG0,i is related to elongation of the S S bond
on radical-anion formation, we have no specific information
on the causes making DGꢀ0,i of sulfides 2 almost as large as
that of disulfides 5. However, because calculations previous-
ly carried out for 2h provide evidence of some elongation of
values of sulfides 2 and disulfides 5 were obtained from
refs. [4a], [11b], [15c], and [16]. Figure 7 also displays a
number of additional ET data, also obtained in DMF and
treated as above. In particular, we added DGꢀ0 values per-
taining to: 1) outer-sphere aromatic acceptors forming
stable radical anions;[37] 2) stepwise-DET acceptors such as
benzyl aryl ethers,[1a] halobenzenes, and halopyridines;[38]
3) other cases of stepwise DET involving formation of loose
[15c]
ꢀ
the C S bond on radical-anion formation,
we expect that
also for 2 elongation of the cleaving bond is the most impor-
tant ingredient making DGꢀ0,i large. The very large values of
DGꢀ0,i and thus very small values of logk8 of disulfides 3, in
which a methylene spacer separates the cleaving bond from
[15a]
[39]
ꢀ
ꢀ
ꢀ
the aryl moieties, point to a SOMO localized on the S S
radical anions and cleavage of the C S
or S S bond;
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Chem. Eur. J. 2007, 13, 7983 –7995

Electron Transfer to Sulfides and Disulfides
FULL PAPER
ꢀ
ꢁꢀ
ꢁ
4) concerted-DET acceptors involving ion–dipole interac-
tions, such as haloacetonitriles;[14,40] 5) adiabatic concerted
DET acceptors such as alkyl halides,[19,41] benzyl bro-
mide,[13,42] benzyl chloride,[41b,43] and perfluoroalkyl hal-
ides;[44] 6) nonadiabatic concerted DET acceptors such as di-
alkyl peroxides,[21,33] endoperoxides,[45] and peresters.[4d,46]
Figure 7 shows the important result that, independent of
the actual ET or DET mechanism and despite the different
sources, the (DGꢀ0 )het/(DG0ꢀ)hom,ex data correlate very well.[47]
The figure also shows the trends expected according to the
Marcus[48] and Hush[18] models for outer-sphere ET. From
the point of view of the intrinsic barriers, the two models
differ in the magnitude of the solvent-reorganization energy
for heterogeneous ET: whereas in the Hush treatment the
acceptor (located at the reaction site) is viewed as sufficient-
ly distant from the electrode surface that the effect of the
image charge can be neglected, this effect is included in the
Marcus model. We also note that these models are inde-
pendent of whether the acceptor undergoes reductive cleav-
age of a s bond, and thus similar arguments can be applied
to DET. The heterogeneous and homogeneous solvent-reor-
ganization barriers are thus related by the following Marcus
[Eq. (18), where the acceptor–electrode distance is half the
donor–acceptor separation in the homogeneous case] and
Hush [Eq. (19)] expressions.
NAe2
16 pe0 eop eS
1
1
1
1
1
ðDGꢀ0,sÞhom,ex
¼
ꢀ
þ
ꢀ
ð23Þ
2 rD 2 r rD þ r
Here e is the charge of the electron, e0 is the permittivity
of vacuum, and eop and es are the optical and static dielectric
constants of the solvent. By using this (DGꢀ0,s)hom,ex value and
increasing the inner component, the Hush relationship
[Eq. (22)] takes the form shown in Figure 7 (dashed line).
Therefore, for sufficiently large DGꢀ0 values ((DG0ꢀ)hom,ex
>
6–7 kcalmolꢀ1) the two equations describe lines with the
same slope. In the Hush formulation, however, the intercept
has a nonzero value of 2.5 kcalmolꢀ1 ((DGꢀ0,s)hom,ex/2).
This is exactly, within error, what we observe in the exper-
imental plot of Figure 7. Linear fit of the data (solid line)
yields Equation (24).
ðDGꢀ0 Þhet ¼ 2:391 þ 0:528 ðDG0ꢀÞhom,ex
ð24Þ
The quality of the correlation, which is based on a collec-
tion of 68 data points (r2 =0.980) encompassing a (DGꢀ0 )hom,ex
range of 2–42 kcalmolꢀ1, is worth stressing because it now is
possible to predict (99% confidence) the values of (DGꢀ0 )het
and (DGꢀ0 )hom,ex to within 0.5–1 and 1–2 kcalmolꢀ1, respec-
tively. According to our extrapolation the average
(DGꢀ0,s)hom,ex is thus 4.8 kcalmolꢀ1, which is slightly smaller
than the value calculated from Equation (23) but larger than
that obtained with the above-mentioned empirical approach.
The ETs of Figure 7 can be roughly classified into four
groups. First, there is outer-sphere ETs forming either stable
radical anions or, for stepwise DETs, “stiff” radical anions.
For these acceptors DGꢀ0,s is the most important contribution
to DGꢀ0 . Because for common molecules (r=3–4 Š) the
(DG0ꢀ,s)hom,ex value is in the range of 3–5 kcalmolꢀ1 ((DG0ꢀ,s)het
are similar), typical values of (DGꢀ0 )hom,ex [transposition to
the corresponding heterogeneous values can be made
through Eq. (24)] for simple outer-sphere acceptors can be
taken as those within about 5 kcalmolꢀ1. The values slightly
increase for stepwise DET forming rigid radical anions
(benzyl aryl ethers and haloaromatic compounds) and, in
fact, some aryl halides undergo non-negligible inner reor-
ganization. When the SOMO partially involves the cleaving
bond, as for several sulfides and, particularly, disulfides,
bond elongation results in a large inner contribution, and
(DGꢀ0 )hom,ex values can be as large as 17–19 kcalmolꢀ1. For
concerted DETs, we collected values ranging from 16 to
42 kcalmolꢀ1. In fact, the intrinsic barrier of concerted DET
is DGꢀ0 =BDE/4+DG0ꢀ,s +DG0ꢀ,i’, where the latter term does
ðDGꢀ0,sÞhet ¼ 0:5 ðDG0ꢀ,sÞhom,ex
ðDGꢀ0,sÞhet ¼ ðDG0ꢀ,sÞhom,ex
ð18Þ
ð19Þ
Both models describe the inner component in the same
way, that is, the homogeneous value is twice the heterogene-
ous value, as in the latter case only one molecule reorganiz-
es [Eq. (20)].
ðDGꢀ0,iÞhet ¼ 0:5 ðDG0ꢀ,iÞhom,ex
ð20Þ
By using Equations (18)–(20) it follows that the relation-
ship between the heterogeneous and homogeneous intrinsic
barriers is different: in the Marcus case Equation (21) ap-
plies, but Equation (22) holds in the Hush treatment.
ðDGꢀ0 Þhet ¼ 0:5 ðDG0ꢀÞhom,ex
ð21Þ
ð22Þ
ðDGꢀ0 Þhet ¼ 0:5 ðDGꢀ0,iÞhom,ex þ ðDGꢀ0,sÞhom,ex
¼ 0:5 ðDGꢀ0 Þhom,ex þ 0:5 ðDG0ꢀ,sÞhom,ex
In the Marcus case, (DGꢀ0 )het is a linear function of
(DGꢀ0 )hom,ex (Figure 7, lower dash-dotted line, slope 0.5). The
same is true in Equation (21) for low barriers (simple outer-
sphere ET) in which solvent reorganization is the only term
contributing to the barrier. Under these conditions the Hush
slope is unity (Figure 7, upper dash-dotted line). If we con-
sider that the radii of common acceptors and donors are
about 3.8 Š, a reasonable limiting value of (DGꢀ0,s)hom,ex is
5.1 kcalmolꢀ1, as obtained from Equation (23)[18,48] (van der
Waals contact in the solvent cage).
not include the contribution of the mode corresponding to
[10]
ꢀ
the breaking A B bond. The BDE is the bond dissocia-
tion energy and is the dominant term. It may vary substan-
tially: while peroxides have typical BDE values of 30–
40 kcalmolꢀ1, alkyl halides have BDEs of 50–70 kcalmolꢀ1.
Because of this, while the experimental (DGꢀ0 )hom,ex values of
peroxides are 16–21 kcalmolꢀ1, those of halides are 26–
42 kcalmolꢀ1. Ion–dipole interactions in the cage, however,
may lower the barrier significantly: for example, halo aceto-
nitriles have values of 23–29 kcalmolꢀ1
.
Chem. Eur. J. 2007, 13, 7983 –7995
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7993

F. Maran, M. C. ArØvalo, M. S. Workentin et al.
[13] A. Cardinale, A. Gennaro, A. A. Isse, F. Maran in New Directions in
Organic Electrochemistry, Vol. 2000-15(Eds.: A. J. Fry, Y. Matsu-
mura), The Electrochemical Society, New Jersey, 2000, pp. 136–140.
[14] A. Cardinale, A. A. Isse, A. Gennaro, M. Robert, J.-M. SavØant, J.
Am. Chem. Soc. 2002, 124, 13533–13539.
[15] a) M. G. Severin, M. C. ArØvalo, G. Farnia, E. Vianello, J. Phys.
Chem. 1987, 91, 466–472; b) M. C. ArØvalo, G. Farnia, M. G. Sever-
in, E. Vianello, J. Electroanal. Chem. 1987, 220, 201–221; c) M. G.
Severin, M. C. ArØvalo, F. Maran, E. Vianello, J. Phys. Chem. 1993,
97, 150–157; d) A. B. Meneses, S. Antonello, M. C. ArØvalo, F.
Maran, Electrochim. Acta 2005, 50, 1207–1215.
To conclude, thanks to reliable and well-tested electro-
chemical protocols (for convolution analysis and homogene-
ous redox catalysis) and the variety of ET data accumulated
since the 1980s (particularly by SavØantꢁs group, the Aarhus
school, and us), it now is possible to observe that the law
governing the difference between the heterogeneous and
homogeneous data is common to different types of ET,
ranging from simple outer-sphere ETs to concerted DETs.
These processes are ruled by a quadratic activation/driving
force relationship of the Marcus or SavØant form. The corre-
lation of Figure 7 also shows progressive variation of the in-
trinsic barriers: the barriers of the two borderline DET
cases are similar, and those of peroxides (concerted DET)
are even smaller than those of disulfides forming s* radical
anions. A significance of Equation (24) validating the Hush
model is its predictability, because in many cases one of the
intrinsic barriers is often difficult or impractical to obtain.
[16] S. Jakobsen, H. Jensen, S. U. Pedersen, K. Daasbjerg, J. Phys. Chem.
A 1999, 103, 4141–4143.
[17] a) The Chemistry of Sulphur-Containing Functional Groups,
Suppl. S, (Eds.: S. Patai, Z. Rappoport), Wiley, New York, 1993;
b) S-centered Radicals (Ed.: Z. B. Alfassi), Wiley, Chichester, 1999;
c) R. A. Rossi, A. B. Pierini, A. B. PeÇØÇory, Chem. Rev. 2003, 103,
71–167.
[18] N. S. Hush, Electrochim. Acta 1968, 13, 1005–1023.
[19] S. Antonello, F. Maran, J. Am. Chem. Soc. 1998, 120, 5713–5722.
[20] a) C. Finzi, V. Bellavista, Gazzetta Chimica Italiana 1932, 62, 699–
709; b) G. Farnia, A. Ceccon, P. Ceselli, J. Chem. Soc. Perkin Trans.
2 1972, 1016–1021; c) G. Farnia, M. G. Severin, E. Vianello, J.
Chem. Soc. Perkin Trans. 2 1978, 1–8; d) G. Capobianco, G. Farnia,
M. G. Severin, E. Vianello, J. Electroanal. Chem. 1984, 165, 251–
263; e) S. Tognato, Laurea thesis, University of Padova, Italy, 1991.
[21] S. Antonello, M. Musumeci, D. D. M. Wayner, F. Maran, J. Am.
Chem. Soc. 1997, 119, 9541–9549.
Acknowledgements
This work was financially supported by the Ministero dell’Istruzione, del-
l’Università e della Ricerca (MIUR, Italy), the Integrated Action Italy-
Spain between the University of Padova and the Universidad de La
Laguna, and the Natural Science and Engineering Research Council
(NSERC) of Canada. A.B.M. is thankful to the Universidad de La
Laguna y Caja Canarias for a PhD grant.
[22] A. B. Meneses, S. Antonello, M. C. ArØvalo, F. Maran, Electroanaly-
sis 2006, 17, 363–370.
[23] F. Maran, M. S. Workentin, unpublished results.
[24] a) R. Fuhlendorff, D. Occhialini, S. U. Pedersen, H. Lund, Acta
Chem. Scand. 1989, 43, 803–806; b) D. D. M. Wayner, D. J. McPhee,
D. Griller, J. Am. Chem. Soc. 1988, 110, 132–137; c) J. Gamby, P.
Hapiot, J.-M. SavØant, J. Am. Chem. Soc. 2002, 124, 8798–8799.
[25] When not available, the pKDa MF values can be obtained from the cor-
[1] a) F. Maran, D. D. M. Wayner, M. S. Workentin, Adv. Phys. Org.
Chem. 2001, 36, 85–166; b) F. Maran, M. S. Workentin, Interface
2002, 31, 44–49.
responding data in DMSO[25b–e] by using the correlation pKDa MF
1.56+0.96pKaDMSO [25a]
a) F. Maran, D. Celadon, M. G. Severin, E.
=
[2] S. Antonello, F. Maran, Chem. Soc. Rev. 2005, 34, 418–428.
[3] J.-M. SavØant, Adv. Phys. Org. Chem. 2000, 35, 117–192.
[4] a) M. G. Severin, G. Farnia, E. Vianello, M. C. ArØvalo, J. Electroa-
nal. Chem. 1988, 251, 369–382; b) S. Antonello, F. Maran, J. Am.
Chem. Soc. 1997, 119, 12595–12600; c) S. Antonello, F. Maran, J.
Am. Chem. Soc. 1999, 121, 9668–9676; d) S. Antonello, F. Formag-
gio, A. Moretto, C. Toniolo, F. Maran, J. Am. Chem. Soc. 2001, 123,
9577–9584; e) F. Najjar, C. AndrØ-Barr›s, M. Baltas, C. Lacaze-Du-
faure, D. C. Magri, M. S. Workentin, T. TzØdakis, Chem. Eur. J.
2007, 13, 1174–1179.
[5] a) C. P. Andrieux, M. Robert, F. D. Saeva, J.-M. SavØant, J. Am.
Chem. Soc. 1994, 116, 7864–7871; b) C. P. Andrieux, J.-M. SavØant,
C. Tardy, J. Am. Chem. Soc. 1997, 119, 11546–11547; c) L. Pause,
M. Robert, J.-M. SavØant, J. Am. Chem. Soc. 1999, 121, 7158–7159;
d) C. Costentin, P. Hapiot, M. MØdebielle, J.-M. SavØant, J. Am.
Chem. Soc. 1999, 121, 4451–4460; e) C. Costentin, M. Robert, J.-M.
SavØant, J. Am. Chem. Soc. 2004, 126, 16834–16840.
[6] A. Houmam, E. M. Hamed, I. W. Still, J. Am. Chem. Soc. 2003, 125,
7258–7265.
.
Vianello, J. Am. Chem. Soc. 1991, 113, 9320–9329; b) F. G. Bord-
well, W. S. Matthews, N. R. Vanier, J. Am. Chem. Soc. 1975, 97, 442–
443; c) F. G. Bordwell, J. E. Bares, J. E. Bartmess, G. E. Drucker, J.
Gerhold, G. J. McCollum, M. Van Der Puy, N. R. Vanier, W. S. Mat-
thews, J. Org. Chem. 1977, 42, 326–332; d) W. N. Olmstead, Z. Mar-
golin, F. G. Bordwell, J. Org. Chem. 1980, 45, 3295–3299; e) F. G.
Bordwell, D. L. Hughes, J. Org. Chem. 1982, 47, 3224–3232.
[26] a) F. Maran, S. Roffia, M. G. Severin, E. Vianello, Electrochim. Acta
1990, 35, 81–88; b) F. Maran, J. Am. Chem. Soc. 1993, 115, 6557–
6563.
[27] a) R. S. Nicholson, I. Shain, Anal. Chem. 1964, 36, 706–723; b) L.
Nadjo, J.-M. SavØant, J. Electroanal. Chem. 1973, 48, 113–145;
c) A. J. Bard, L. R. Faulkner, Electrochemical Methods, Fundamen-
tals and Applications, 2nd ed., Wiley, New York, 2001.
[28] J.-M. SavØant, D. Tessier, J. Electroanal. Chem. 1975, 65, 57–66.
[29] The convolution integral (J. C. Imbeaux, J.-M. SavØant, J. Electro-
iðuÞ
anal. Chem. 1973, 44, 169–187) is: I=p1/2
"
1=2 du
0
ðtꢀuÞ
The I–E plot has a sigmoidal shape, and the limiting value is Il =
nFAD1/2C*, where n is the overall electron consumption, A the elec-
trode area, D the diffusion coefficient, and C* the substrate concen-
tration. For a slow heterogeneous ET or when the latter becomes ir-
reversible because of a fast follow-up reaction, such as bond cleav-
[7] M. A. Prasad, M. V. Sangaranarayanan, Chem. Phys. Lett. 2005, 414,
55–60.
[8] C. P. Andrieux, J.-M. SavØant, J. Electroanal. Chem. 1986, 205, 43–
58.
[9] a) R. A. Marcus, Ann. Pharm. Belg. Ann. Rev. Phys. Chem. 1964, 15,
155–196; b) R. A. Marcus, N. Sutin, Biochim. Biophys. Acta 1985,
811, 265–322.
[10] J.-M. SavØant, J. Am. Chem. Soc. 1987, 109, 6788–6795.
[11] a) K. Daasbjerg, H. Jensen, R. Benassi, F. Taddei, S. Antonello, A.
Gennaro, F. Maran, J. Am. Chem. Soc. 1999, 121, 1750–1751; b) S.
Antonello, K. Daasbjerg, H. Jensen, F. Taddei, F. Maran, J. Am.
Chem. Soc. 2003, 125, 14905–14916.
age, the potential-dependent heterogeneous rate constant khet
=
khet(E) is obtained as a function of E through equation lnkhet(E)=
lnD1/2ꢀln[(IlꢀI)/i].
[30] J.-M. SavØant, J. Phys. Chem. 1994, 98, 3716–3724.
[31] By assuming a linear activation/driving force relationship for the ET
reaction, Equation (12) takes the following form:[8]
ꢂ
ꢃ
1
1
kd
1
1
kd
1
1
=
þ
+
+
khom
kꢁhom expðꢀahom DGꢁ=RTÞ
Zhom expðꢀDGꢁ=RTÞ
[12] S. Antonello, R. Benassi, G. Gavioli, F. Taddei, F. Maran, J. Am.
Chem. Soc. 2002, 124, 7529–7538.
where kꢁhom is the homogeneous standard rate constant (correspond-
ing to the value of the ET rate constant by a generic donor matching
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Chem. Eur. J. 2007, 13, 7983 –7995

Electron Transfer to Sulfides and Disulfides
FULL PAPER
the condition DG8=0), and ahom is the average homogeneous trans-
fer coefficient.
[36] B. A. Sim, P. H. Milne, D. Griller, D. D. M. Wayner, J. Am. Chem.
Soc. 1990, 112, 6635–6638.
[37] H. Kojima, A. J. Bard, J. Am. Chem. Soc. 1975, 97, 6317–6324.
[38] The DGꢀ0 values were calculated from: C. P. Andrieux, C. Blocman,
J.-M. Dumas-Bouchiat, J.-M. SavØant, J. Am. Chem. Soc. 1979, 101,
3431–3441.
[32] When the cleavage occurs within the timescale of the solvent cage
(ca. 10ꢀ10 s), the third term of Equation (12) (counterdiffusion
region) is more complex.[8] Therefore, for fast-cleaving radical
anions (kc >1010 sꢀ1) the use of Equation (12) introduces further un-
certainty in the determination of the acceptor E8; in particular, a
lower limit of E8 can only be assessed. Among the investigated sul-
fides, only for 1h (radical-anion lifetimeꢃ1 ms) were rate-constant
data clearly obtained in the counterdiffusion region.
[39] T. B. Christensen, K. Daasbjerg, Acta. Chem. Scand. 1997, 51, 307–
317.
[40] The DGꢀ0
values were calculated from: A. A. Isse, A. Gennaro, J.
hom
Phys. Chem. A 2004, 108, 4180–4186.
[41] a) C. P. Andrieux, I. Gallardo, J.-M. SavØant, K.-B. Su, J. Am. Chem.
Soc. 1986, 108, 638–647; b) J.-M. SavØant, J. Am. Chem. Soc. 1992,
114, 10595–10602.
[33] R. L. Donkers, F. Maran, D. D. M. Wayner, M. S. Workentin, J. Am.
Chem. Soc. 1999, 121, 7239–7248.
[34] The method relies on the following reasoning. If the cleavage reac-
[42] The (DGꢀ0 )hom values were calculated from: a) K. Daasbjerg, H.
Lund, Acta Chem. Scand. 1993, 597–604; b) Y. Huang, D. D. M.
Wayner, J. Am. Chem. Soc. 1994, 116, 2157–2158.
Cꢀ
tion can be considered as irreversible, the disappearance of D
(which is involved in reactions (9) and (11) is ruled by the following
rate law, where khom and kꢀhom refer to reaction (9):
[43] The (DGꢀ0 )hom values were calculated[41b] from: T. Lund, H. Lund,
Acta Chem. Scand. 1987, 41, 93–102.
d½DC ꢀꢂ
dt
2kckhom ½Ph2CHSArꢂ
Cꢀ
ꢀ
=
[D ]
kcþk
½Dꢂ
ꢀhom
If kc @kꢀhom[D], the rate-determining step is the forward ET step
(9), but if the two terms in the denominator are comparable an in-
crease of the concentration of D inhibits the reaction. If kc !
kꢀhom[D], the ET step is a pre-equilibrium reaction. In practice,
when the kꢀhom[D] term is not negligible the catalytic increase R
(ratio between the ip values of the donor peak in the presence and
in the absence of sulfide in solution) decreases as [D] increases: for
any given combination of [D]/v the value of R, which is plotted
against the kinetic parameter logRT[D]/Fv, decreases when [D] is
made sufficiently large. Typical plots are shown in the Supporting
Information.
[44] C. P. Andrieux, L. GØlis, M. Medebielle, J. Pinson, J.-M. SavØant, J.
Am. Chem. Soc. 1990, 112, 3509–3520.
[45] R. L. Donkers, M. S. Workentin, Chem. Eur. J. 2001, 7, 4012–4020.
[46] S. Antonello, M. Crisma, F. Formaggio, A. Moretto, F. Taddei, C.
Toniolo, F. Maran, J. Am. Chem. Soc. 2003, 125, 11503–11513.
[47] Inclusion of the double-layer correction for the heterogeneous data
or using the E8 obtained from redox catalysis measurements does
not change the trend appreciably, also because the comparison con-
cerns a very extended range of DGꢀ0 values.
[48] a) R. A. Marcus, J. Chem. Phys. 1956, 24, 966–978; b) R. A. Marcus,
J. Chem. Phys. 1965, 43, 679–701.
[35] M. C. ArØvalo, F. Maran, M. G. Severin, E. Vianello, J. Electroanal.
Chem. 1996, 418, 47–52.
Received: March 8, 2007
Published online: July 6, 2007
Chem. Eur. J. 2007, 13, 7983 –7995
ꢀ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
7995