Theoretical and electrochemical analysis of dissociative electron transfers proceeding through formation of loose radical anion species: Reduction of symmetrical and unsymmetrical disulfides

Article abstract of DOI:10.1021/ja012545e

The dissociative reduction of a series of symmetrical (RSSR, R = H, Me, t-Bu, Ph) and unsymmetrical disulfides (RSSR′, R = H, R′ = Me and R = Ph, R′ = Me, t-Bu) was studied theoretically, by MO ab initio calculations and, for five of them, also experimentally, by convolution voltammetry in N,N-dimethylformamide. The reduction is dissociative but proceeds by a stepwise mechanism entailing the formation of the radical anion species. The electrochemical data led to estimated large intrinsic barriers, in agreement with an unusually large structural modification undergone by the disulfide molecules upon electron transfer. The theoretical results refer to MP2/3-21G*//MP2/3-21G*, MP2/3-21*G*//MP2/3-21G*, CBS-4M, and G2(MP2), the latter approach being used only for the molecules of small molecular complexity. A loose radical-anion intermediate was localized and the dissociation pattern for the relevant bonds analyzed. For all compounds, the best fragmentation pathway in solution is cleavage of the S-S bond. In addition, S-S bond elongation is the major structural modification undergone by the disulfide molecule on its way to the radical anion and eventually to the fragmentation products. The calculated energy of activation for the initial electron transfer was estimated from the crossing of the energy profiles of the neutral molecule and its radical anion (in the form of Morse-like potentials) as a function of the S-S bond length coordinate. The inner intrinsic barrier obtained in this way is in good agreement with that determined by convolution voltammetry, once the solvent effect is taken into account.

Full text of DOI:10.1021/ja012545e

Published on Web 05/31/2002
Theoretical and Electrochemical Analysis of Dissociative
Electron Transfers Proceeding through Formation of Loose
Radical Anion Species: Reduction of Symmetrical and
Unsymmetrical Disulfides
Sabrina Antonello,† Rois Benassi,‡ Giovanna Gavioli,‡ Ferdinando Taddei,*,‡ and
Flavio Maran*,†
Contribution from the Dipartimento di Chimica Fisica, UniVersita` di PadoVa, Via Loredan 2,
35131 PadoVa, Italy, and Dipartimento di Chimica, UniVersita` di Modena e Reggio Emilia,
Via Campi 183, 41100 Modena, Italy
Received November 15, 2001. Revised Manuscript Received February 19, 2002
Abstract: The dissociative reduction of a series of symmetrical (RSSR, R ) H, Me, t-Bu, Ph) and
unsymmetrical disulfides (RSSR′, R ) H, R′ ) Me and R ) Ph, R′ ) Me, t-Bu) was studied theoretically,
by MO ab initio calculations and, for five of them, also experimentally, by convolution voltammetry in N,N-
dimethylformamide. The reduction is dissociative but proceeds by a stepwise mechanism entailing the
formation of the radical anion species. The electrochemical data led to estimated large intrinsic barriers, in
agreement with an unusually large structural modification undergone by the disulfide molecules upon electron
transfer. The theoretical results refer to MP2/3-21G*//MP2/3-21G*, MP2/3-21*G*//MP2/3-21G*, CBS-4M,
and G2(MP2), the latter approach being used only for the molecules of small molecular complexity. A
loose radical-anion intermediate was localized and the dissociation pattern for the relevant bonds analyzed.
For all compounds, the best fragmentation pathway in solution is cleavage of the S-S bond. In addition,
S-S bond elongation is the major structural modification undergone by the disulfide molecule on its way
to the radical anion and eventually to the fragmentation products. The calculated energy of activation for
the initial electron transfer was estimated from the crossing of the energy profiles of the neutral molecule
and its radical anion (in the form of Morse-like potentials) as a function of the S-S bond length coordinate.
The inner intrinsic barrier obtained in this way is in good agreement with that determined by convolution
voltammetry, once the solvent effect is taken into account.
Introduction
a neutral molecule (AB), a stepwise dissociative reduction
mechanism entails the formation of an intermediate radical anion
Dissociative electron transfers are processes in which electron
transfer (ET) causes the cleavage of a σ bond.1 The mechanism
of these reactions depends strongly on the structure of the
electron acceptor or electron donor undergoing the cleavage.
Although there are systems in which ET and bond fragmentation
may be concerted, such as in the dissociative reduction of most
alkyl halides2,3 and peroxides,4-7 the majority of compounds
react by a stepwise mechanism.2b,7,8 If the electron acceptor is
(AB•-), which only subsequently undergoes the cleavage to yield
a radical (A•) and an anion (B-). There are two major aspects
associated with these processes. The first has been investigated
by several research groups and concerns the understanding of
the cleavage step and thus issues such as the rate/driving force
relationship ruling the cleavage, the problem of homolytic versus
heterolytic fragmentation, the solvent effect, the role of the
leaving group, and the stereochemical effect on the intramo-
lecular ET.8-13 The second aspect, which has been much less
investigated, refers to the nature of the intrinsic barrier involved
in the formation of the radical anion itself. The intrinsic ET
* Corresponding author. E-mail: f.maran@chfi.unipd.it. Phone: +39
(049) 827-5147. Fax: +39 (049) 827-5135.
† Universita` di Padova.
‡ Universita` di Modena e Reggio Emilia.
(1) Save´ant, J.-M. In AdVances in Electron-Transfer Chemistry; Mariano, P.
S., Ed.; JAI Press: Greenwich, CT, 1994; Vol. 4, p 53.
(2) (a) Save´ant, J.-M. Acc. Chem. Res. 1993, 26, 455. (b) Save´ant, J.-M. AdV.
Phys. Org. Chem. 2000, 35, 117.
(6) (a) Workentin, M. S.; Donkers, R. L. J. Am. Chem. Soc. 1998, 120, 2664.
(b) Donkers, R. L.; Workentin, M. S. J. Phys. Chem. B 1998, 102, 4061.
(c) Magri, D. C.; Donkers, R. L.; Workentin, M. S. J. Photochem. Photobiol.
A: Chemistry 2001, 138, 29. (d) Donkers, R. L.; Workentin, M. S. Chem.
Eur. J. 2001, 7, 4012.
(3) (a) Lund, H.; Daasbjerg, K.; Lund, T.; Pedersen, S. U. Acc. Chem. Res.
1995, 28, 313. (b) Lund, H.; Daasbjerg, K.; Lund, T.; Occhialini, D.;
Pedersen, S. U. Acta Chem. Scand. 1997, 51, 135.
(4) (a) Workentin, M. S.; Maran, F.; Wayner, D. D. M. J. Am. Chem. Soc.
1995, 117, 2120. (b) Donkers, R. L.; Maran, F.; Wayner, D. D. M.;
Workentin, M. S. J. Am. Chem. Soc. 1999, 121, 7239.
(5) (a) Antonello, S.; Musumeci, M.; Wayner, D. D. M.; Maran, F. J. Am.
Chem. Soc. 1997, 119, 9541. (b) Antonello, S.; Maran, F. J. Am. Chem.
Soc. 1997, 119, 12595. (c) Antonello, S.; Maran, F. J. Am. Chem. Soc.
1999, 121, 9668. (d) Antonello, S.; Formaggio, F.; Moretto, A.; Toniolo,
C.; Maran, F. J. Am. Chem. Soc. 2001, 123, 9577.
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2001, 36, 85.
(8) (a) Eberson, L. Electron-Transfer Reactions in Organic Chemistry; Springer-
Verlag: New York, 1987. (b) Maslak, P. In Topics in Current Chemistry;
Mattay, J., Ed.; Springer-Verlag: Berlin, Germany, 1993; Vol. 168, p 1.
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Scand. 1999, 53, 751.
9
10.1021/ja012545e CCC: $22.00 © 2002 American Chemical Society
J. AM. CHEM. SOC. 2002, 124, 7529-7538
7529

A R T I C L E S
Antonello et al.
q
barrier, ∆G0 , which is defined as the activation free energy
tion is neglected. On the other hand, as mentioned above, it is
reasonable to expect that in the formation of the radical anion
the breaking bond will weaken and stretch to some extent.
Although the possibility of significant internal reorganization
in stepwise processes should not, as a rule, be ignored with
other classes of compounds, the majority of the data supporting
this expectation comes from recent studies on the cleavage of
C-S or S-S bonds.7 The first detailed studies in this field dealt
with the heterogeneous and homogeneous reduction of benzyl
aryl sulfides.18-20 These studies, particularly that on the reduc-
tion of triphenylmethyl p-cyanophenylsulfide,19 provided evi-
(∆Gq) at zero reaction free energy (∆G°), is a measure of the
overall ET reorganization energy and provides essential infor-
mation on the intrinsic kinetic facility of the ET step. In general,
the initial electron uptake is expected to cause some change of
both bond lengths and angles. According to the commonly
accepted ET models, these factors determine the magnitude of
the inner reorganization energy (∆G0,iq) of the reacting system.
∆G0q is obtained by summing such a reorganization term with
that pertaining to the reorganization of the solvent molecules
(∆G0,sq), which accompanies the ET step.14 Obtaining an
accurate description of the ET step and thus of how the intrinsic
barrier is partitioned into these two terms is important not only
per se but also because it provides the basis to understand how
the dynamics of the following ion-radical fragmentation devel-
ops.7 For example, the bond dissociation energy (BDE) of the
scissile bond should decrease because of the antibonding nature
of the orbital that hosts the unpaired electron. In addition,
knowing how the negative charge is localized or delocalized in
the radical anion allows one to better understand the extent of
solvent reorganization accompanying the cleavage. Both factors
are responsible for the intrinsic barrier of the cleavage itself.
q
dence that ∆G0,i may be even larger than ∆G0,sq. Some
indication that ∆G0,iq may be large for other molecular systems
was obtained by studying the homogeneous reduction of three
disulfides.21
A specific study of the relevance of the inner reorganization
energy, however, was not available until very recently, thanks
to the comparative study that we carried out on the homogeneous
and heterogeneous dissociative reduction of a series of diaryl
disulfides.22 The reduction of diaryl disulfides has provided
convincing examples of dissociative ETs in which significant
inner reorganization is involved. However, the presence of
strongly electron-withdrawing substituents capable of keeping
the unpaired electron away from the breaking bond (particularly,
If the ET product is a delocalized radical anion, such as with
q
aromatic compounds, ∆G0,i is rather small (because little
q
molecular deformation occurs), usually within 1 kcal mol-1
.
by nitro-group substitution on the aryl ring) may decrease ∆G0,i
substantially, pointing to the relevance of the π* versus σ*
nature of the radical anion. The overall picture, however, is far
from complete and more experimental examples and theoretical
information are required to better understand stepwise dissocia-
tive electron transfers. It is particularly important to understand
why there are molecular systems undergoing stepwise reduction
in which the ET step is fast because little intramolecular
reorganization occurs, such as ethers,7 and others in which the
ET is significantly slow, as for disulfides and sulfides.
The reduction of disulfides seemed to us a particularly
convenient model to shed some light onto this general problem,
also in view of the relevance of the S-S bond in biological
molecules.23 Disulfides are easily activated by reductive cleavage
of the S-S bond, both chemically and electrochemically.24 In
aprotic solvents, the homogeneous or heterogeneous dissociative
reduction of disulfides RSSR is irreversible and occurs by a
stepwise mechanism, in which ET and S-S bond breaking occur
sequentially (eqs 1 and 2).7,21,22 Given the strength of the
reductants (solution electron donors or applied electrode po-
tential, E) necessary to carry out the RSSR reduction, the
Because of this, the inner component has been regarded as being
most often negligible. For these processes, the most important
q 8a,15,16
contribution to the intrinsic barrier is thus ∆G0,s
,
the
values being typically in the 2.5-3.5 kcal mol-1 range. On the
other hand, ∆G0,i is expected to increase when the ET
q
eventually provokes the cleavage of a σ bond and thus the
fragmentation of the radical anion. In the limiting case of the
q
concerted dissociative ET mechanism, in particular, ∆G0,i
becomes as large as one-forth of the BDE of the breaking
bond.17 It is not clear, however, to which extent ∆G0,i affects
q
the intrinsic barrier of those dissociative ETs involving the
transient formation of a radical anion. Most often, this contribu-
(9) (a) Maslak, P.; Vallombroso, T. M.; Chapman, W. H., Jr.; Narvaez, J. N.
Angew. Chem., Int. Ed. Engl. 1994, 33, 73. (b) Kimura, N.; Takamuku, S.
J. Am. Chem. Soc. 1994, 116, 4087. (c) Kimura, N.; Takamuku, S. J. Am.
Chem. Soc. 1995, 117, 8023. (d) Phillips, J. P.; Gillmore, J. G.; Schwartz,
P.; Brammer, L. E., Jr.; Berger, D. J.; Tanko, J. M. J. Am. Chem. Soc.
1998, 120, 195. (e) Tanko, J. M.; Phillips, J. P. J. Am. Chem. Soc. 1999,
121, 6078. (f) Zheng, Z.-R.; Evans, D. H.; Chan-Shing, E. S.; Lessard, J.
J. Am. Chem. Soc. 1999, 121, 9429. (g) Kimura, N. J. Am. Chem. Soc.
2001, 123, 3824.
(10) (a) Addock, W.; Andrieux, C. P.; Clark, C. I.; Neudeck, A.; Save´ant, J.-
M.; Tardy, C. J. Am. Chem. Soc. 1995, 117, 8285. (b) Andrieux, C. P.;
Robert, M.; Save´ant, J.-M. J. Am. Chem. Soc. 1995, 117, 9340. (c) Andrieux,
C. P.; Save´ant, J.-M.; Tallec, A.; Tardivel, R.; Tardy, C. J. Am. Chem.
Soc. 1997, 119, 2420. (d) Andrieux, C. P.; Combellas, C.; Kanoufi, F.;
Save´ant, J.-M.; Thie´bault, A. J. Am. Chem. Soc. 1997, 119, 9527.
(11) (a) Andersen, M. L.; Mathivanan, N.; Wayner, D. D. M. J. Am. Chem.
Soc. 1996, 118, 4871. (b) Andersen, M. L.; Long, W. N.; Wayner, D. D.
M. J. Am. Chem. Soc. 1997, 119, 6590. (c) Andersen, M. L.; Wayner, D.
D. M. Acta Chem. Scand. 1999, 53, 830.
(18) (a) Are´valo, M. C.; Farnia, G.; Severin, M. G.; Vianello, E. J. Electroanal.
Chem. 1987, 220, 201. (b) Severin, M. G.; Are´valo, M. C.; Farnia, G.;
Vianello, E. J. Phys. Chem. 1987, 91, 466. (c) Severin, M. G.; Farnia, G.;
Vianello, E.; Are´valo, M. C. J. Electroanal. Chem. 1988, 251, 369.
(19) Severin, M. G.; Are´valo, M. C.; Maran, F.; Vianello, E. J. Phys. Chem.
1993, 97, 150.
(20) Jakobsen, S.; Jensen, H.; Pedersen, S. U.; Daasbjerg, K. J. Phys. Chem. A
1999, 103, 4141.
(21) Christensen, T. B.; Daasbjerg, K. Acta Chem. Scand. 1997, 51, 307.
(22) Daasbjerg, K.; Jensen, H.; Benassi, R.; Taddei, F.; Antonello, S.; Gennaro,
A.; Maran, F. J. Am. Chem. Soc. 1999, 121, 1750.
(12) Antonello, S.; Maran, F. J. Am. Chem. Soc. 1998, 120, 5713.
(13) (a) Jensen, H.; Daasbjerg, K. Acta Chem. Scand. 1998, 52, 1151. (b)
Enemærke, R. J.; Christensen, T. B.; Jensen, H.; Daasbjerg, K. J. Chem.
Soc., Perkin Trans. 2 2001, 1620.
(14) (a) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (b)
For reasons that will become clearer later, it is more practical to use intrinsic
barriers instead of the perhaps more familiar reorganization energy (λ)
terminology. It should be reminded that, provided the harmonic approxima-
tion can be used to describe both the solvent and the inner reorganization
(23) (a) Valentine, S. J.; Anderson, J. G.; Ellington, A. D.; Clemmer, D. E.
J. Phys. Chem. B 1997, 101, 3891. (b) Zubarev, R. A.; Kruger, N. A.;
Fridriksson, E. K.; Lewis, M. A.; Horn, D. H.; Carpenter, B. K.; McLafferty,
F. W. J. Am. Chem. Soc. 1999, 121, 2857. (c) Vela´zquez, I.; Riemann, C.
T.; Tapia, O. J. Phys. Chem. B 2000, 104, 2546. (d) Dai, S.; Schwendmayer,
C.; Schu¨rmann, P.; Ramaswamy, S.; Eklund, H. Science 2000, 287, 655.
(24) (a) The Chemistry of Sulphur-Containing Functional Groups, Suppl. S;
Patai, S., Rappoport, Z., Eds.; Wiley: New York, 1993. (b) Simonet, J. In
The Chemistry of Sulphur-Containing Functional Groups, Suppl. S; Patai,
S., Rappoport, Z., Eds.; Wiley: New York, 1993; Chapter 10, p 439. (c)
S-Centered Radicals; Alfassi, Z. B., Ed.; Wiley: Chichester, 1999.
q
modes, ∆G0 ) λ/4.
(15) Kojima, H.; Bard, A. J. J. Am. Chem. Soc. 1975, 97, 6317.
(16) (a) Larsen, H.; Pedersen, S. U.; Pedersen, J. A.; Lund, H. J. Electroanal.
Chem. 1992, 331, 971. (b) Ju¨rgen, D.; Pedersen, S. U.; Pedersen, J. A.;
Lund, H. Acta Chem. Scand. 1997, 51, 767.
(17) Save´ant, J.-M. J. Am. Chem. Soc. 1987, 109, 6788.
9
7530 J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002

Disulfide Radical Anions
A R T I C L E S
ensuing radicals are also reduced (eq 3). In fact, the standard
potential of the RS•/RS- couple is generally at least 1 V more
positive than the potential at which the disulfide is reduced.7
Therefore, in the absence of side reactions, the process is an
overall 2-electron reduction (eq 4).
In this paper, we examine the dissociative reduction of a series
of symmetrical and unsymmetrical disulfides 1-7 having the
general formula RSSR′, where R and R′ are H, alkyl, or phenyl
groups. The reduction was studied both experimentally, by cyclic
voltammetry in N,N-dimethylformamide (DMF) containing 0.1
M tetrabutylammonium perchlorate (TBAP), and theoretically.
By using the convolution analysis approach,7,33 we could
RSSR + e a RSSR•-
RSSR•- f RS• + RS-
RS• + e f RS-
(1)
(2)
(3)
•-
estimate the E°RSSR/RSSR values of 3-7 and the corresponding
heterogeneous standard rate constants (khet°), i.e., the value of
khet for E ) E°. From the khet° values, we obtained the intrinsic
barrier of the heterogeneous process. The experimental outcome
was then compared with the results of theoretical calculations,
carried out at different levels and aimed at studying the
homolytic cleavage in both the neutral molecules 1-7 and the
corresponding radical anions 1a-7a.34 The calculations deter-
RSSR + 2e f 2RS-
(4)
There are several pieces of evidence pointing to the existence
of a discrete radical anion RSSR•-. The lifetime of the RSSR•-
radical anions is usually very short, being on the microsecond
time scale in water.25 However, they have been detected and
characterized by time-resolved optical methods. In one early
study, γ irradiation of matrices containing alkyl and aryl
disulfides provided spectroscopic evidence for the formation
of the corresponding radical anions.26 Subsequently, the forma-
tion of RSSR•- radical anions has been well documented,
particularly by EPR, flash photolysis, and pulse radiolysis. The
RSSR•- radical anions may be obtained from different ap-
proaches. One is of course by one-electron reduction of
disulfides (eq 1), such as by pulse radiolysis or electrochem-
istry.7,25,27,28 However, the most common approach is by
association of RS• and RS- (eq 5).28-30
mined the relative stability of these species and also the energy
changes associated with the variation of selected coordinates
of the ET and the cleavage reaction. All compounds form 2σ/
1σ* radical anions undergoing endergonic cleavages. The results
are rationalized by introducing a model that may be called as
the “almost-dissociative” stepwise ET-bond breaking mecha-
nism, i.e., a mechanism in which the initial electron uptake has
an intrinsic barrier that is closer to that of a concerted
dissociative ET than to that of the ET step of common stepwise
processes.
RS• + RS- a RS-SR•-
(5)
The formation of RSSR•- from RS• and RS- species is
particularly relevant in the present context because it is the
reverse of the electroinduced radical anion cleavage (eq 2).
Equilibrium constants in the range 102-104 M-1 for the
association reaction (eq 5) were determined for some alkyl-
type systems in water.30,31 The rate constants for the formation
of RSSR•-, determined in aqueous solution, are nearly diffusion
controlled [(3-5) × 109 M-1 s-1].31 It is thus clear that a
concerted ET-bond fragmentation mechanism, leading directly
to the fragmented products (eq 6), should be, as a rule, discarded.
Experimental Section
Chemicals. Dimethyl disulfide, di-tert-butyl disulfide, diphenyl
disulfide, phenylmethyl disulfide, and tert-butylphenyl disulfide were
commercial products (Acros or Fluka, >99%). Their purity was checked
before electrochemical measurements by GC-mass spectrometry, using
a Hewlett-Packard 5898A spectrometer. N,N-Dimethylformamide (Acros,
99%) and tetrabutylammonium perchlorate (Fluka, 99%) were treated
as previously described.5a
Electrochemistry. The electrochemical experiments were carried
out in DMF/0.1 M TBAP, using glassy carbon electrodes. The
experimental setup and procedures were as previously described in
detail.5 Potentials were measured relative to ferrocene oxidation and
are given against the KCl saturated calomel electrode (SCE); in our
hands, the E° of the ferrocene/ferricenium couple is 0.464 V vs SCE.
Electrochemical measurements were carried out at 25 °C, unless
otherwise stated. For the temperature studies, however, the reference
electrode was always kept at 25 °C, using a nonisothermal salt bridge
arrangement.35 The convolution analysis was carried out on background-
subtracted cyclic voltammetry curves by using our own laboratory
software. Digital simulations were carried out by using the DigiSim
3.03 software (Bioanalytical Systems Inc).
RSSR + e f RS• + RS-
(6)
Concerning the thermodynamics of formation of RSSR•- species
in nonaqueous solvent,32 a few estimates of the corresponding
•-
standard potential (E°RSSR/RSSR ) could be obtained by studying
the kinetics of the reduction of symmetrical diaryl disulfides as
a function of the driving force.21,22
(25) Hoffman, M. Z.; Hayon, E. J. Am. Chem. Soc. 1972, 94, 7950.
(26) Shida, T. J. Phys. Chem. 1968, 72, 2597.
(27) Asmus, K.-D.; Bonifacˇic´, M. In S-Centered Radicals; Alfassi, Z. B., Ed.;
Wiley: Chichester, 1999; p 141.
(28) See, e.g.: Griller, D.; Martinho Simo˜es, J. A. In Sulfur-Centered ReactiVe
Intermediates in Chemistry and Biology; Chatgilialoglu, C., Asmus, K.-
D., Eds.; Plenum Press: New York, 1990; p 327 and references therein.
(29) (a) Cremonini, M. A.; Lunazzi, L.; Placucci, G. J. Chem. Soc., Perkin Trans.
2 1992, 451. (b) Cremonini, M. A.; Lunazzi, L.; Placucci, G. J. Org. Chem.
1993, 58, 3805.
(30) Mezyk, S. P.; Armstrong, D. A. J. Chem. Soc., Perkin Trans. 2 1999, 1411.
(31) In particular, see: Armstrong, D. A. In Sulfur-Centerd ReactiVe Intermedi-
ates in Chemistry and Biology; Chatgilialoglu, C., Asmus, K.-D., Eds.;
Plenum Press: New York, 1990; p 121 and references therein.
(32) For thermochemical estimates of E° values in water, see: (a) Armstrong,
D. A. In S-Centered Radicals; Alfassi, Z. B., Ed.; Wiley: Chichester, 1999;
p 27.
(33) (a) Imbeaux, J. C.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 44, 169.
(b) Save´ant, J.-M.; Tessier, D. J. Electroanal. Chem. 1975, 65, 57.
(34) The theoretical analysis of the dissociative reduction of 1 has been reported
previously: (a) Benassi, R.; Taddei, F. J. Phys. Chem. A 1998, 102, 6173.
(35) Anxolabe´he`re, E.; Lexa, D.; Momenteau, M.; Save´ant, J.-M. J. Phys. Chem.
1992, 96, 9348.
9
J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002 7531

A R T I C L E S
Antonello et al.
Table 1. Electrochemical and Kinetic Parameters for the
Computational Details. Calculations were performed on compounds
1-7 and their radical anions 1a-7a at the MO ab initio level with the
GAUSSIAN-94 and GAUSSIAN-98 series of programs,36,37 run on a
Silicon Graphics 4CPU MIPS R10000 calculator and on a IBM AIX/
6000 workstation. The molecules were studied at the MP2/3-21G*//
MP2/3-21G* frozen core level38,39 and the effect of diffuse augmented
functions was tested at the MP2/3-21+G*//MP2/3-21G* level. Station-
ary points were located through full geometry relaxation. UHF wave
functions were employed for the open shell systems and the spin
projection operator40 was applied to remove contamination from higher
spin states. The value of s2 was nevertheless greater than 0.75 for
radicals and radical anions containing the phenyl ring. The CBS-4M41
and G2(MP2)42 methods were also employed, the latter being applied
only to the molecules of smaller molecular size 1-3 and 1a-3a, to
compare the results obtained at a low level of theory with those obtained
with more sophisticated methods. A further parametrization was
introduced43 in the CBS-4M method to minimize the accumulation of
errors in molecules of increasing size. Thermodynamic data refer to
298.15 K. For the radical anions, real minima were located in the energy
hypersurface. The solvent effect was calculated with the SM5-42R
solvation model44 and the GAMESOL program.45
Reduction of Disulfides in DMF/0.1 M TBAP at 25 °C
d,f
log k°het
(cm s-1
∆G0q g
disulfide
Epa (V)
Rb
Ra,c
Rd,e
E° d,f (V)
)
(kcal mol-1
)
3
4
5
6
7
-2.43 0.322 0.350 0.337 -1.88 -5.45
-2.72 0.319 0.376 0.375 -2.34 -4.53
12.6
11.2
10.7
11.1
12.1
-1.65 0.325 0.432 0.430 -1.37 -4.22h
-1.97 0.324 0.398 0.373 -1.62 -4.45
-2.19 0.324 0.366 0.359 -1.71 -5.20
a V ) 0.2 V s-1
.
b Calculated from |∂Ep/∂logV| ) 1.15RT/FR.47
c Calculated from the peak width ∆Ep/2 ) 1.857RT/FR.47 d Convolution data.
e Calculated for the mid-potential of the peak width range, i.e., for Ep
-
0.5∆Ep/2, where Ep ) Ep(0.2 V s-1).5b f Within the assumptions explained
in the text, the experimental uncertainty is 30-40 mV and 0.2-0.3 log
units for the double-layer uncorrected E° and log k°het, respectively. g Values
q
obtained by using k°het ) Z exp[-∆G0 /RT]. h From ref 22.
Results and Discussion
Electrochemical Analysis. The voltammetric reduction of
disulfides 3-7 was studied in DMF/0.1 M TBAP at the glassy
carbon electrode. The reduction proceeds irreversibly, as
described in eqs 1-3. Since the focus of the present investigation
is on the initial ET step (eq 1), only the most relevant and
pertinent features of the voltammetric pattern will be consid-
ered.46 The irreversible reduction peak is broad and its position
(36) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. W.; Wong, M.
W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Repogle,
E. S.; Gomberts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.;
Gonzales, C. R.; Martin, L.; Fox, D. J.; Defrees, D. J.; Baker, J. T.; Keith,
A.; Petersson, G. A.; Montgomery, J. A.; Al-Laham, M. A.; Zakrzewski,
V. G.; Ortiz, J. V.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.;
Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Stewart, J. J. P.;
Pople, J. A. GAUSSIAN 94, Revision A.1; Gaussian Inc.: Pittsburgh, PA,
1995.
(37) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M.
A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann,
R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin,
K. N.; Strain, M.; Farkas, C. O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi,
R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.;
Petersson, G. A.; Ayala, P.; Cui, Y. Q.; Morokuma, K. D.; Malick, K.;
Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz,
J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.;
Komaromi, I.; Gomperts, R.; Martin, L. R.; Fox, D. J.; Keith, T.; Al-Laham,
M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.;
Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian
98, Revision A.7: Gaussian, Inc.: Pittsburgh, PA, 1998.
Figure 1. Reduction of 7 (2.1 mM) in DMF/0.1 M TBAP at the glassy
carbon electrode. The upper graph shows a series of background-subtracted
cyclic voltammograms as a function of scan rate (left to right: 0.2, 0.5, 1,
2, 5 V s-1). The lower graph shows the plots of the corresponding potential
dependence of log khet (left scale) and transfer coefficient R (right scale).
(peak potential, Ep) depends markedly on the R and R′
substituents (Table 1). Upon increasing the scan rate (V), Ep
shifts toward more negative potentials by 91-93 mV/log V.
From these values as well as from the peak width, ∆Ep/2 (∆Ep/2
is the difference between the potential at mid-peak height and
Ep), it is possible to calculate the transfer coefficient R. R
describes the sensitivity of the activation free energy on the
reaction free energy, i.e., R ) ∂∆Gq/∂∆G°. The low values of
R, which are gathered in Table 1, indicate that for all compounds
the initial ET controls the electrode kinetics.47 In addition, when
V increases, the peak broadens while the ratio between the peak
current ip and the square root of V (a quantity that should be
independent of V according to the classical Butler-Volmer
kinetic model47) decreases (Figure 1). This behavior indicates
that the transfer coefficient R depends on the applied potential
(E).5 The kinetics of the heterogeneous ET was thus studied in
detail by convolution voltammetry,7,33 which we believe to be
the most powerful electrochemical method to study the fine
details of heterogeneous ET processes. The graphs correspond-
ing to some steps of the convolution analysis are illustrated in
(38) (a) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102,
939. (b) Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre,
W. J. J. Am. Chem. Soc. 1982, 104, 2797. (c) Pietro, W. J.; Franck, M. M.;
Hehre, W. J.; Defrees, D. J.; Pople, J. A.; Binkley, J. S. J. Am. Chem. Soc.
1982, 104, 5039.
(39) Frisch, M. J.; Pople, J. A. J. Chem. Phys. 1980, 72, 4244 and references
therein.
(40) (a) Schlegel, H. B. J. Chem. Phys. 1986, 84, 4530. (b) Schlegel, H. B. J.
Phys. Chem. 1988, 92, 3075. (c) Sosa, C.; Schlegel, H. B. Int. J. Quantum
Chem. 1986, 30, 55.
(41) Petersson, G. A.; Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W. J.
Chem. Phys. 2000, 112, 6532.
(42) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem.
Phys. 1991, 94, 7221.
(43) (a) Benassi R.; Taddei, F. J. Comput. Chem. 2000, 21, 1405. (b) Benassi
R. Theor. Chem. Acc. 2001, 106, 259.
(44) Li, J.; Hawkins, G. D.; Cramer, C. J.; Truhlar, D. G. Chem. Phys. Lett.
1998, 288, 293.
(45) Xidos, J. D.; Li, J.; Zhu, T.; Hawkins, G. D.; Chuang, Y.-Y.; Fast, P. L.;
Liotard, D. A.; Rinaldi, D.; Cramer, C. J.; Truhlar, D. G. GAMESOL,
version 3.0; University of Minnesota: Minneapolis, MN, 2001, based on
the General Atomic and Molecular Electronic Structure System (GAMESS)
as described in: Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S.
T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, K. A.; Nguyen,
K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput.
Chem. 1993, 14, 1347.
(46) Some reductions required the addition of acetic acid to avoid the interference
of side reactions involving starting material and electrogenerated bases
(father-son reactions).7
(47) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and
Applications, 2nd ed.; Wiley: New York, 2001.
9
7532 J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002

Disulfide Radical Anions
A R T I C L E S
Table 2. Bond Dissociation Energies (BDE and ∆H°, kcal mol-1) from Different Theoretical Approaches for Organic Disulfides
level of theory
MP2/3-21G*//
MP2/3-21G*
MP2/3-21+G*//
MP2/3-21G*
G2(MP2)
∆H° a
CBS-4M
∆H° a
MP2/3-1G*//MP2/3-21G*
CBS-4M
(ꢀ ) 37)b,c
compd
bond broken
(ꢀ ) 37)b,c
exptld
1
S-S
54.07
64.74
53.50
64.68
64.72
74.64
62.20
73.82
52.53
64.80
60.66
73.88
66 ( 2e
64.5
H-S
70 ( 1.5f
76.2
2
3
S-S
C-S
H-S
S-S
55.4
59.5
62.1
56.7
55.5
58.3
61.7
57.8
65.62
63.46
71.74
66.49
62.90
62.25
70.71
63.47
53.75
61.13
61.62
55.00
61.25
63.88
70.23
61.77
65.2
64.1
79.0
74 ( 2g
65.6
C-S
56.9
55.7
59.29
58.98
58.06
60.14
57 ( 1.5g
66.6
4
5
S-S
C-S
S-S
61.2
59.2
46.8
62.4
60.5
56.9
65.96
57.72
47.90
59.51
58.45
46.24
64.27
56.97
47.34
67.7
53.9
55.0h
49.2
C-S
77.3
51.6
74.1
69.5
55.5
78.8
79.09
55.48
76.05
76.89
50.46
73.20
78.68
54.34
75.15
75.0h
71.8
6
7
S-S
65.0h
59.6
C(aryl)-S
69.6h
82.7
C(alkyl)-S
S-S
C(aryl)-S
C(alkyl)-S
59.6
55.0
73.7
64.7
58.7
60.1
79.5
67.4
61.61
57.88
75.53
63.18
61.24
53.65
72.64
64.14
63.25
56.53
74.47
59.92
60.1
58.4
70.9
54.7
a Bond dissociation enthalpy. b In solution. c Solvent effect at the HF/3-21G*//HF/3-21G* level, GAMESOL method. d Experimental or calculated from
literature ∆fH° data (see Supporting Information). e From: Benson, S. W. Chem. ReV. 1978, 78, 23. f Nourbakhsh, S.; Liao, C.-L.; Ng, C. Y. J. Chem. Phys.
1990, 92, 6587. g Reference 54. h From: Plaza, S.; Gruzinski, R. Wear 1996, 194, 212.
Figure 1 for compound 7. The background-subtracted voltam-
mograms, obtained at several scan rates in the 0.1-20 V s-1
range, were transformed into the corresponding convolution
current (I) versus E curves. The heterogeneous rate constant
s-1). In fact, concerted dissociative ETs take place at potentials
which are normally much more negative than E° (usually, by
at least 0.8-1 V). The results obtained with 3-7 are also in
line with the results previously obtained with some substituted
diaryl disulfides22 and with the evidence collected from other
experimental sources for the existence of disulfide radical anions
(see Introduction). A simple calculation can be carried out to
verify that the concerted mechanism cannot be competitive to
the stepwise one. The E° corresponding to eq 6 can be expressed
k
het was then obtained by logarithmic analysis of the I-E data
as a function of E.48,49 The apparent values of R were obtained
as a function of E from the ln khet - E plots, being R )
-(RT/F)(d ln khet/dE). For 3-7, the ensuing R vs E plots
are linear. Some representative values of R obtained by the
convolution approach are reported in Table 1. The latter shows
that regardless of how R is calculated, the R values are rather
small, although on the average they are slightly larger than the
R values corresponding to typical concerted dissociative ETs.1,7
Usually, provided the R vs E plot is linear within error,
the standard potential E° of the electrode reaction can be
estimated as the E value at which R ) 0.5.5a,7 This is because
most theoretical models for outer-sphere or dissociative ETs
share the result that R should be about 0.5 at zero driving
force.14a,17 Under the assumption that this may approximately
hold also for the systems under investigation (we will return
to that point later), the E° values of disulfide reduction (eq 1)
were estimated through extrapolation of the experimental R vs
E plots. By using these E° estimates, the apparent values of
the standard rate constant, k°het, were obtained by parabolic fit
to the log khet - E plots. Both the E° and k°het values are reported
in Table 1. The consistency of the E° and k°het values was finally
checked by digital simulation of the cyclic voltammograms,
which led to good reproduction of the experimental curves by
using the convolution results.
•
-
•
-
as E°RSSR/RS ,RS ) E°RS /RS - BDFE/F, where BDFE is the
S-S bond dissociation free energy. By using the result of the
calculations carried out at the MP2/3-21G*//MP2/3-21G* level
(see below), the standard potentials of the PhS•/PhS- (E° )
0.07 V) couple,50 and an entropy correction of 8.5 kcal mol-1
(for T ) 298.15 K),4b the following E°RSSR′/RS′ ,RS values can
be estimated: 5, -1.59 V; 6, -1.80 V; 7, -1.95 V. These values
are ∼0.2 V more negative than the experimental results. By
•
-
(48) The convolution analysis allows one to obtain the convoluted current I,
which is related to the actual current i through the convolution integral,
t
I ) π-1/2 ∫0 i(u)/[(t - u)1/2] du, as a function of E. The I-E plots display
a plateau corresponding to diffusion-controlled conditions. The limiting
value of I is Il ) nFAD1/2C*, where n is the overall electron consumption,
A the electrode area, D the diffusion coefficient, and C* the substrate
concentration. When the back electrode reaction is absent (because the
dissociative ET is concerted) or negligible (thanks to the occurrence of
a fast reaction destroying the reduction product, such as in the step-
wise mechanism under consideration), the heterogeneous rate constant
khet is related to i and I by the following equation: ln khet ) ln D1/2 - ln
n{[Il - I(t)]/i(t)t}.
(49) The reduction of 4 is near the solvent-electrolyte discharge and thus, since
the peak shifts toward more negative potentials by increasing V, the
maximum scan rate was 10 V s-1. In addition, because of the proximity of
the discharge, the convolution analysis was carried out as previously
described for di-tert-butyl peroxide5a or a tertiary bromide.12
The electrochemical results obtained with disulfides 3-7 are
thus in agreement with the formation of discrete radical anion
species at moderate overpotentials (the E° values are 0.28-
0.55 more positive than the corresponding Ep values at 0.2 V
(50) The standard potentials of the RS•/RS- couple was determined by studying
the scan-rate dependence of the oxidation peak of the RS- anion, generated
by electroreduction of the corresponding disulfide in DMF. Both cyclic
voltammetry analysis and digital simulation of the experimental curves were
employed, as described elsewhere.7
9
J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002 7533

A R T I C L E S
Antonello et al.
Table 3. Bond Dissociation Energies (BDE and ∆H°, kcal mol-1) from Different Theoretical Approaches for Radical Anions of Organic
Disulfides.
level of theory
bond-cleavage
process
MP2/3-21G*//
MP2/3-21G*
MP2/3-21+G*//
MP2/3-21G*
G2(MP2)
∆H°a
CBS-4M
∆H°a
MP2/3-21G*// MP2/3-21G*
CBS-4M
(ꢀ ) 37)b,c
compd
(ꢀ ) 37)b,c
1a
HS• + -SH
28.7
41.3
23.6
31.7
29.6
36.0
26.9
24.1
29.8
29.1
15.0
45.1
19.4
33.2
53.3
26.7
22.3
31.3
51.2
31.4
24.1
42.3
19.0
29.1
28.9
35.5
24.1
22.1
27.3
31.1
21.9
54.0
19.1
32.4
55.8
25.9
23.4
30.6
55.7
34.2
24.8
44.0
19.3
29.4
26.4
37.8
23.7
20.0
25.9
47.5
20.0
30.3
29.3
41.0
25.1
23.5
26.4
26.7
22.4
54.7
16.8
26.6
50.0
24.1
22.8
25.5
51.8
29.3
8.9
35.3
4.4
18.6
25.9
30.6
9.9
16.5
12.5
15.9
1.8
34.6
7.6
10.5
37.3
20.2
7.9
13.9
37.2
20.3
6.1
41.5
0.8
17.2
25.6
35.6
8.1
15.9
9.1
13.5
9.2
44.2
5.0
3.9
34.0
17.6
8.4
H• + -SSH
2a
MeS• + -SH
MeS- + •SH
Me• + -SSH
MeSS- + •H
MeS• + -SMe
Me• + -SSMe
tBuS + -StBu
tBu• + -SStBu
PhS• + -SPh
Ph• + -SSPh
PhS- + •SMe
PhS• + -SMe
Ph• + -SSMe
PhSS- + •Me
PhS- + •StBu
PhS• + -StBu
Ph• + -SStBu
PhSS- + •tBu
3a
4a
5a
6a
7a
8.1
37.8
18.2
a Bond dissociation enthalpy. b In solution. c Solvent effect at the HF/3-21G*//HF/3-21G* level, GAMESOL method.
•
-
taking also into account that even more negative E°RSSR/RS ,RS
Theoretical Calculations. The CBS-4M41 and the G2(MP2)42
methods were employed to calculate the heats of formation
(∆fH°) of molecules, radical anions, and fragments. The latter
method was applied only to the molecules of smaller molecular
size. The ∆fH° values (CBS-4M) of the various species were
found to be in reasonable agreement with experimental values32a,53
also for large molecules such as 4-7 (see Supporting Informa-
tion). The bond energy values were calculated as the difference
between the total molecular energy of the neutral molecules
1-7 or their radical anions 1a-7a and that of the fragments
obtained upon homolytic fragmentation. The results are shown
in Tables 2 and 3. For the neutral molecules, the BDEs obtained
at the MP2/3-21G*//MP2/3-21G* level are, as a rule, slightly
smaller than the corresponding experimental values (Table 2).
No significant improvement was obtained by including diffuse
functions. The dissociation energies of the S-S bond were found
to be more underestimated than those of the C-S and H-S
bonds. The systematic underestimation of the calculated BDE
values of the S-S bond of disulfides and the existence of a
fairly linear relationship between calculated and experimental
values were previously discussed.54 The ∆H° values calculated
for 1-3 and their radical anions 1a-3a at the G2(MP2) and
CBS-4M levels, which include both electronic and vibrational
energies, are in rather good agreement with experimental BDE
values.
values are estimated by using experimental BDE values (Table
2), we can confidently conclude that the concerted mechanism
cannot be operative.
It is worth noting that the values of the calculated hetero-
geneous standard rate constants are remarkably small, pointing
q
to a large intrinsic barrier for radical anion formation. ∆G0
was calculated by using the rate constant expression k°het
)
Z exp[-∆G0 /RT], with Z ) (RT/2πM)1/2, where M is the molar
mass, assuming that the investigated processes are adiabatic.
That these ETs are adiabatic was checked by carrying out a
temperature study on compound 5. The reduction was studied
by convolution voltammetry at temperatures ranging from -25
to 50 °C. From the corresponding log khet vs E plots, the khet
values measured at selected potentials were then used to
calculate the Arrhenius prefactor A. The average value was
found to be log A ) 3.7 ( 0.1, which is in agreement with an
adiabatic heterogeneous outer-sphere ET (for 5, log Z ) 3.6).51
q
q
The ∆G0 values of 3-7 are reported in Table 1. Since the
solvent contribution accompanying the heterogeneous ET,
∆G0,sq, can be calculated for the investigated compounds to be
in the range 3.8-6.3 or 2.6-4.4 kcal mol-1, depending on the
method adopted,52 the inner reorganization term can be finally
extracted from ∆G0 . For 3-7, the ∆G0,iq result is particularly
q
large, its value being typically 50-64% or 65-75%, respec-
tively, of the total. These results are in full agreement with the
occurrence of major molecular reorganization during the reduc-
tion step.
In compounds 1 and 2, H-S is the strongest bond at all levels
of theory employed. Concerning disulfides 2 and 3, the C-S
and S-S bonds have similar gas-phase bond energy values.
Although the C-S bonds of 2 and 3 appear to be weaker than
the S-S bond at the G2(MP2) and CBS-4M levels, the trend is
inverted for 2 at a lower level of calculation. The C(alkyl)-S
bond is weaker than the C(aryl)-S bond (disulfides 6 and 7) at
any level of calculation. Concerning specifically the S-S bond,
(51) Analogous conclusion can be reached by using literature values on the
homogeneous ET to disulfides 3, 4, and 521 to estimate the homogeneous
Z value, expected to be ∼log Zhom ) 11.5. By using a simple quadratic
activation/driving force relationship and the experimental intrinsic barriers
(Table 1), log Zhom can be estimated to range from 11.9 to 12.8. Lowering
the intrinsic barrier by about 1 kcal mol-1 would lead to an even closer
agreement with the above log Zhom. Nonadiabaticity, i.e., much smaller
apparent Zhom values, would require much smaller intrinsic barriers, leading,
however, to very poor agreement with the experimental results.
(53) Afeefy, H. Y.; Liebman, J. F.; Stein, S. E. Neutral Thermochemical Data
in NIST Chemistry WebBook, NIST Standard Reference Database Number
69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards
and Technology: Gaithersburg, MD, July 2001 (http://webbook.nist.gov).
(54) Benassi, R.; Fiandri, G. L.; Taddei, F. J. Mol. Struct. (THEOCHEM) 1997,
418, 127.
q
(52) The two sets of ∆G0,s values were calculated by using the empirical
equation λS ) 4∆G0,s ) 55.7/r,5a,15 where λS is given in kcal mol-1 and the
q
molecular radius r is in Å, and the Marcus approach,14a respectively. The
radii were obtained from molecular models, the experimental diffusion
coefficients, and the Stokes-Einstein equation.
9
7534 J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002

Disulfide Radical Anions
A R T I C L E S
that of diphenyl disulfide 5 is, as a general rule, weaker than
that of the other disulfides. The S-S bond becomes stronger
as the alkyl character of the substituent increases, as can be
seen along the series 1 f 4 and 6 f 7.
The above results refer to the gas phase. The strength of the
relevant bonds was examined also in solution by simulating the
presence of a medium having the dielectric constant of the
solvent employed for the electrochemical measurements (DMF,
ꢀ ) 37). Calculations were performed at the HF/3-21G*//HF/
3-21G* level. The results are reported in Table 2. Solvent effect
at this level was also employed to correct the bond dissociation
enthalpies at the CBS-4M level. The results do not differ
significantly from those obtained for the isolated molecules and
thus the same trends described above hold.
Figure 2. Energy profiles for the C-S (dashed lines) and S-S (solid lines)
bond cleavage of the neutral molecule 3 and radical anion 3a at the MP2/
3-21G*//MP2/3-21G* level. The data points (S-S bond: O, 3; b, 3a; C-S
bond: 4, 3; 2, 3a) refer to the corresponding stationary-point calculations
(see text).
A selection of the most relevant (i.e., weakest) bond energies
of the radical anions 1a-7a is reported in Table 3; full data
are provided in the Supporting Information. All values are
positive, pointing to homolytic fragmentation of the investigated
disulfide radical anions. The bond energies calculated for the
cleavage of the different bonds of 1a-3a do not depend
significantly on the calculation level employed.55,56 Although
different levels of theory provide different absolute values, for
radical anions 1a, 2a, and 5a-7a the common trend for the
relative dissociation of the examined bonds is that S-S bond
cleavage is the favored process. Only for 3a and 4a the gas-
phase cleavage of the S-S and the C-S bonds seems to be
equally favored, although it should be noted that for 2a, 6a,
and 7a the BDEs of the C(alkyl)-S bonds are only slightly
larger than those of the S-S bond. The effect of implementing
the 3-21G* basis set with diffuse functions did not lead to
significant changes in the calculated BDE values of 1a-7a,
except for the reaction paths leading to carbanions or H-. As
expected, the solvent has a much larger effect on the radical
anions than on the neutral molecules and, consequently, the
calculated BDE and ∆H° values are generally significantly
smaller in solution. Some details of the computational results
are particularly worth noting. Although in the gas phase the
BDEs of the S-S and C(alkyl)-S bonds may have similar or
even equal values, the dissociation of the S-S bond always
becomes the preferred path for the cleavage of 3a-7a in
solution.56
carried out also at different geometries along the nuclear
coordinate. These values were found to be in very good
agreement with the corresponding values obtained from the
above Morse curves. Whereas crossing of the energy profiles
of 3 and its radical anion 3a requires ∼44 kcal mol-1 along the
C-S coordinate, the much lower value of ∼19 kcal mol-1 is
found along the S-S bond coordinate.
For the unsymmetrical radical anions 6a and 7a, S-S bond
cleavage with formation of the PhS- anion is the favored process
in the gas phase. At higher energies, there are two processes
having similar energy requirements: whereas one yields the
PhSS- anion and the alkyl radical, the other yields the PhS•
radical and the RS- anion. In solution, however, the two modes
of S-S bond cleavage are the most favored processes at both
levels of theory. Slightly different energy contributions, how-
ever, are required for these two reaction patterns: at the CBS-
4M level, the formation of the PhS• radical is the favored
process, whereas the PhS- anion should form according to the
lowest level of theory. Indeed, the calculated BDEs for these
two patterns are rather similar. The path leading to the solvated
PhS- anion, however, seems to be more realistic on the basis
of the standard potentials of the t-BuS•/t-BuS- (E° ) -0.07 V)
and PhS•/PhS- (E° ) 0.07 V) couples that we estimated by
electrochemical methods.50
In Figure 2, the gas-phase energy profiles corresponding to
the S-S bond and the C-S bond reaction coordinates of 3 and
3a are compared. The energy profiles were constructed as
Morse-like potential energy functions of the S-S or C-S
coordinate by using the second derivative of the molecular
energy with respect to the specific reaction coordinate, as
previously reported.34a A series of calculations, however, were
Kinetics of the ET Reaction. The theoretical results obtained
on the ET reaction are in keeping with the outcome of the
electrochemical analysis, pointing to the transient formation of
radical anion species.57 To become a radical anion, the original
molecule must reach a structure that allows the ET to take place
without any further structural modification, according to the
Franck-Condon principle. In general terms, the energy of the
system increases as a consequence of internal and solvent
reorganizations. However, if we consider molecules in the gas
phase, only internal rearrangements are relevant and thus only
modifications of bond lengths and angles are required. On the
basis of the results and evidence described in the previous
section on the type of bond cleavage, we will focus on the
minima having the S-S bond distance elongated with respect
to the neutral molecule. In general, we found that the S-S bond
increases considerably, going from 2.04-2.07 Å in the neutral
(55) The gas-phase BDE values of 1 and 3 and their radical anions 1a and 3a
are comparable with those obtained very recently by using different levels
of calculation.55a,b (a) Berge`s, J.; Kassab, E.; Conte, D.; Adjadj, E.; Houe´e-
Levin, C. J. Phys. Chem. A 1997, 101, 7809. (b) Carles, S.; Lecomte, F.;
Schermann, J. P.; Desfranc¸ois, C.; Xu, S.; Nilles, J. M.; Bowen, K. H.;
Berge`s, J.; Houe´e-Levin, C. J. Phys. Chem. A 2001, 105, 5622.
(56) The energies required for fragmentation leading to carbanions or H- are
significantly much lower at the G2(MP2) and CBS-4M levels of calculation.
This outcome, however, is not influent in the context of the following
discussion because independently of the adopted approach the dissociation
modes that are more dependent on the calculation level are also those
requiring the highest energy and thus are those representing the least
probable reaction paths. Large negative bond energies are calculated at
the CBS-4M level when the anion H- is formed due to the extremely large
solvation energy calculated for this anion by the GAMESOL method. At
the same level of theory, also the fragmentation paths leading to carbanions
have substantially smaller energies than those calculated at the lowest level
employed.
(57) It is also worth mentioning that the differences between the energies or
the enthalpies of formation of the radical anion and the neutral molecule
are fairly well correlated with the electrochemical E° values, particularly
when the solvent effect is taken into account (see Supporting Information).
9
J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002 7535

A R T I C L E S
Antonello et al.
Table 4. Most Significant Structural Changes of Molecules 1-7
on Passing from the Neutral Species to the Radical Anion at the
MP2/3-21G*//MP2/3-21G* Levela
To gain more insight into the ET step and to better compare
theory and experiment, it is now useful to analyze the relation-
ship between the Morse parameter â and the BDEs of disulfides.
By carrying out an extensive analysis of the uncoupled stretching
frequencies (ν) of several bonds, Zavitsas concluded that there
is a linear correlation between ν and the square root of BDE.60a
By using the equation â ) ν(2π2µ/BDE)1/2, where µ is the
reduced mass of the S-S bond, â can be related to ν and thus
to BDE. The same concept was subsequently extended to other
bonds, including the S-S bond.60b By using the same approach,
we arrived at the correlation â ) 4.43 - 22.4/(BDE)1/2 (see
Supporting Information), which shows that a decrease of BDE
is matched by a significant decrease of â. Since it has been
shown that these correlations are valid for different types of
bond and bond order,60 we may assume that disulfide radical
anions obey similar rules. From a qualitative standpoint, this is
in agreement with the results shown in Table 5. Conversely, it
has been recently proposed that while radical anion formation
entails a decrease of the BDE, â(•-) may be kept equal to the
Morse factor of the neutral molecule.8c This model has been
used to describe the reactivity of some classes of compound.2b,13b
Although acceptable for more rigid radical molecular frame-
works, this seems to be too severe an assumption to describe
the formation of the disulfide radical anions and, more generally,
loose radical anion species. As a matter of fact, simple
application of the equation that was derived for ∆G0,iq, i.e.,
compd d(S−S)b
∆d c
d(C−S)b
∆d c
d(S−H) or d(C′−S)b
∆d c
1
2
3
4
5
6
7
2.058 0.766
1.341
1.343
-0.001
-0.003
2.050 0.756 1.830
2.042 0.759 1.832
2.049 0.807 1.865
2.069 0.765 1.788
2.052 0.768 1.828d
0.003
-0.001
-0.019
-0.022
0.004
1.793e
1.798e
-0.043
-0.031
2.040 0.757 1.862d -0.014
a Bond lengths (d) in Å. b Values referring to the neutral molecule.
c Change of bond length in the radical anion with respect to the neutral
molecule: positive values indicate higher values in the radical anion.
d S-C(alkyl) bond. e S-C(phenyl) bond.
molecules to 2.80-2.86 Å in the radical anions (Table 4). As
a further check, the local minima corresponding to elongation
of the C-S bond also were localized for 3 and its radical anion
3a (Figure 2), using the MP2/3-21G*//MP2/3-21G* approach.
We found, however, that the C-S bond length of 3a becomes
exceptionally large, ca. 3.8 Å, compared to the value in the
neutral molecule, 1.83 Å, which once again points to the small
relevance of this fragmentation mode.
Comparative analysis of the calculated structures of 1-7 and
1a-7a shows that the most significant structural change brought
about by the ET is, by far, stretching of the S-S bond. For
example, while the S-S bond stretches, the other bonds do not
change appreciably, as shown for the different C-S (or S-H)
bonds in Table 4. Although the C-S-S and H-S-S bond
angles do undergo some significant changes (see Supporting
Information), the energy associated with these structural modi-
fications is believed to be generally smaller than that necessary
to stretch the S-S bond to reach the structure of the ET
transition state. This assumption was tested in detail for
compound 3. The results showed that while decreasing the
C-S-S bond angle by as much as 20° requires only 5.3 kcal
mol-1, more than 18 kcal mol-1 are required to stretch the S-S
bond by 0.5 Å. The length of the cleaving S-S bond can thus
be taken as the main coordinate describing the energy profile
of the inner reorganization of both ET (eq 1) and bond breaking
(eq 2). The values of the activation energy, ∆Eq, and of the
elongation of the bond length at the intersection of the Morse
curves, ∆dq, are reported in Table 5 together with the Morse
parameters. The ∆Eq values are corrected for the zero-point
vibrational energy and Franck-Condon vibrational effects,58
referred to the mode associated with the reaction coordinate,
and were computed by setting the two energy minima at the
same level (for the sake of comparison with the electrochemical
intrinsic barriers). The calculated ∆Eq values, which measure
the inner component of the activation energy, now can be
compared with the corresponding electrochemical information,
∆G0,i ) (BDE1/2 - BDE(•-)1/2)2/4,8c together with the use of
q
our theoretical BDE values of the neutral and radical anion
q
disulfides, at the various levels employed, would lead to ∆G0,i
values in the range 1.2-2.8 kcal mol-1 and thus to values that
are too small compared to both the theoretical and the
electrochemical evidence.
Table 5 shows that the experimental barriers are systemati-
cally smaller than suggested by the gas-phase calculations. On
the other hand, although the Morse curve of the neutral disulfide
is left almost unchanged by the presence of a dielectric, we
have seen that the BDE of the radical anion decreases
significantly, leading to a shallower potential energy curve with
respect to the gas phase. The solvent effect should lead to an
earlier and less energetic transition state and thus the actual ∆dq
and ∆Eq values should be smaller than those reported in Table
5. For example, by using the BDE values obtained for ꢀ ) 37
at the lower level of calculation and the â factors of Table 5
we calculate that the “solution” ∆dq and ∆Eq values decrease
to an average of 0.23 Å and 6.9 kcal mol-1. Therefore,
computation of the solvent effect is indeed necessary to obtain
a closer agreement between theory and experiment. It should
be noted that use of the same BDE values in the equation
q
developed for â ) â(•-) leads to average ∆G0,i values of 5.2
and 5.6 kcal mol-1 at the MP2/3-21G*//MP2/3-21G* and CBS-
4M levels, respectively. These values also, although still a bit
small, point to the need of including the solvent effect in any
comparison between theory and experiment.
q
i.e., ∆G0,i (Table 5).59 Despite the approximate nature of the
theory employed in the calculations and the fact that ∆Eq is
uncorrected for resonance stabilization, the trend displayed by
the ∆Eq values is consistent with the electrochemical results,
particularly those corrected for the solvent reorganization energy
by using the Marcus approach.
The agreement between calculations and electrochemical
analysis supports the view that the ET to disulfides is associated
with significant S-S bond elongation. Thus, unless very special
geometrical or environmental constraints hamper S-S bond
stretching, the harmonic approximation should not provide an
(58) King, G. W. Spectroscopy and Molecular Structure; Holt, Rinehart and
Winston, Inc.: New York, 1964.
(59) The average entropy change associated with the formation of the loose
radical anions 3a-7a was calculated to be T∆S° ) 2.5 kcal mol-1 (at 298.15
K). Only a fraction of it, depending on the position of the transition state,
would conceivably affect the barrier (for related arguments, see: Andrieux,
C. P.; Save´ant, J.-M.; Tardy, C. J. Am. Chem. Soc. 1998, 120, 4167).
(60) (a) Zavitsas, A. A. J. Phys. Chem. 1987, 91, 5573. (b) Zavitsas, A. A.;
Chatgilialoglu, C J. Am. Chem. Soc. 1995, 117, 10645.
9
7536 J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002

Disulfide Radical Anions
A R T I C L E S
Table 5. Kinetic Parameters for the Reduction of Compounds 3-7 to Their Radical Anions 3a-7a (Calculations Refer to the Gas Phase)
∆Eq a
∆d q a,b
(Å)
∆Eq c
∆d q b,c
(Å)
âd
(Å
â(•-)
(Å
∆G0,i
(kcal mol-1
∆G0,i
(kcal mol-1
)
e
q f
q g
-1
-1
compd
(kcal mol-1
)
(kcal mol-1
)
)
)
)
3
4
5
6
7
11.8
12.5
11.7
13.1
12.1
0.322
0.321
0.359
0.363
0.332
12.2
12.2
13.6
12.9
12.6
0.305
0.301
0.395
0.342
0.329
1.896
1.873
1.930
1.929
1.906
1.164
1.025
1.558
1.478
1.297
6.3
5.9
6.9
6.4
7.8
8.3
7.5
8.1
7.9
9.1
a From the total molecular energy (MP2/3-21G*//MP2/3-21G* level) of the neutral molecule and radical anion at the crossing point, assuming the same
energy for the minima and after zero-vibrational and Franck-Condon corrections. b Elongation of the S-S bond distance at the crossing point. c From
CBS-4M enthalpies, â values of columns 6 and 7 and assuming the same energy for the minima. d Coefficient of the Morse function (MP2/3-21G*//MP2/
3-21G* energies) for the neutral molecule. e Coefficient of the Morse function (MP2/3-21G*//MP2/3-21G* energies) for the radical anion. f Calculated from
the convolution analysis data, using an empirical equation (see ref 52). g Calculated from the convolution analysis data, using the Marcus approach (see
ref 52).
accurate description of the inner reorganization energy. Again,
as for concerted dissociative ETs,17,61 Morse functions may be
used to obtain a more realistic analytical description of the
potential energy changes along the most important contribution
to the reaction coordinate. The problem is that when the two
Morse curves describing the neutral and the radical anion are
different because of different â and BDE values, the ensuing
rate-driving force relationship is not parabolic,62 unless very
special assumptions are explicitly made.8c On the other hand,
our experimental R-E plots are pretty linear, which is in
agreement with an approximately parabolic ∆Gq-∆G° relation-
ship. Therefore, in the absence of a general (and simple) ∆Gq-
∆G° relationship, we used our theoretical Morse curves to
simulate the driving force dependence of the crossing between
Figure 3. Comparison between the heterogeneous standard rate constants
the reactant and product curves. Indeed, we found that for all
compounds the ensuing relationship can be nicely fit by a
second-order equation, leading to linear R-∆G° plots. However,
for 3-7 the R value corresponding to ∆G° ) 0 is now smaller
than 0.5, being on the average 0.41. A similar result was
obtained by studying the formation of the radical anion of Cl2.62
As previously discussed, however, the solvent effect must be
necessarily included to obtain a more realistic description of
the system and thus a better comparison between experimental
and theoretical data. Noteworthy, when the above analysis is
carried out for 3-7 by taking into account the solvent effect,
the average R value corresponding to ∆G° ) 0 is now very
close to 0.5 (0.52 ( 0.03). These differences would not affect
significantly the electrochemically determined quantities (E°,
of the reduction of disulfides. The data are plotted as a function of E° and
were obtained in DMF/0.1 M TBAP at 25 °C, using the glassy carbon
electrode. The legends correspond to either (b) the name of the dialkyl or
alkyl-aryl disulfides (this work), including dibenzyl disulfide,63a or (O)
the para substituent of a series of disubstituted diaryl disulfides.22 The solid
line is meant to underline the experimental trend.
result point to a stepwise dissociative reduction involving the
intermediacy of a transient radical anion followed by cleavage
of the S-S bond. With respect to most compounds undergoing
similar reductive cleavages, the mechanism of the stepwise
dissociative ET to disulfides is peculiar in that a loose radical
anion species forms. Although during the formation of the
radical anion some bond angle deformation occurs, the most
relevant inner reorganization has been clearly identified as the
stretching of the cleaving S-S bond, which increases by as
much as 0.8 Å in the radical anion. Noteworthy, this remarkably
large structural reorganization is essentially independent of the
R and R′ substituents in RS-SR′. The extent of this inner
reorganization puts this class of dissociative ETs at the border
between classical stepwise mechanisms (with little reorganiza-
tion associated with the ET step) and purely dissociative
reductions (where the BDE of the cleaving bond is the major
parameter determining the intrinsic barrier).
The large inner reorganization is responsible for the low value
of the heterogeneous standard rate constant observed for the
investigated compounds. This is illustrated in Figure 3 in
comparison with the electrochemical results pertaining to diaryl
disulfides.23,63 The trend is that almost no differences show up
for the least easily reducible compounds (which implies that
the intrinsic barriers are very similar) and that only for diaryl
disulfides containing good electron-withdrawing groups is the
q
log k°het, ∆G0 ) obtained by using R ) 0.5 and thus the
substance of our conclusions. In fact, the E° values would be
slightly more positive, the log k°het smaller by ca. 1 unit, and
consequently the ∆G0 larger by ca. 1 kcal mol-1. Therefore,
q
our analysis suggests that although different Morse curves (and
Morse parameters) must be used to describe the initial step of
this “almost-dissociative” stepwise ET bond breaking mecha-
nism, reasonable estimates of relevant electrochemical quantities
still may be obtained along similar lines as previously applied
to concerted dissociative ETs and to the ET step of “cassical”
stepwise dissociative processes.
Conclusions and Final Remarks. The reductive cleavage
of a series of symmetrical and unsymmetrical disulfides has
been investigated by convolution analysis and carrying out
specific calculations at different levels of theory. Both types of
(61) (a) Wentworth, W. E.; Becker, R. S.; Tung, R. J. Phys. Chem. 1967, 71,
1652. (b) Wentworth, W. E.; George, R.; Keith, H. J. Chem. Phys. 1969,
51, 1791. (c) Steelhammer, J. C.; Wentworth, W. E. J. Chem. Phys. 1969,
51, 1802. (d) German, E. D.; Kuznetsov, A. M. J. Phys. Chem. 1994, 98,
6120.
(63) The electroreduction of diaryl disulfides22 and dibenzyl disulfide63a was
carried out along the same lines described for 3-7. (a) Antonello, S.; Maran,
F. Unpublished work.
(62) German, E. D.; Kuznetsov, A. M. J. Phys. Chem. A 1998, 102, 3668.
9
J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002 7537

A R T I C L E S
Antonello et al.
display significant differences. This is nicely illustrated in Figure
4 in which the SOMOs of 3a, 5a, and 6a are depicted.
Because of the nature of the antibonding orbital hosting the
unpaired electron, the BDE of these radical anions is much
smaller than that of the neutral molecule. This is particularly
true in solution because of the extensive solvation experienced
by the small anionic fragments formed in the dissociation. For
the neutral molecules and their radical anions, we could estimate
the shape of the corresponding Morse curves, which allowed
us to calculate the energy change required to reach the transition
state of the ET step. Once the solvent effect is taken into
account, the calculated inner barriers are in reasonable agreement
with the electrochemical results. Concerning the fragmentation
of the radical anions, the reaction is an endergonic, homolytic
cleavage. For example, by using our experimental results, it is
possible to calculate the free energy change for the fragmenta-
tion of 5a-7a through the following equation:7 ∆GRSSR
)
•-
•-
•
-
BDFERSSR + F(E°RSSR/RSSR - E°RS /RS ). By using the solution
bond energies of Table 2 and some entropy contribution, we
•-
estimate ∆GRSSR to be approximately in the range 5-10 kcal
mol-1, pointing to radical anions having lifetimes not shorter
than 1 ns.
In conclusion, the mechanism of the stepwise dissociative
reduction of disulfides now seems to be reasonably well
understood. We believe this result to be important in the context
of future studies on these and other functional groups liable to
form loose radical anion species, particularly for application in
more complex molecular systems, such as in biologically
relevant macromolecules.
Acknowledgment. Dedicated to Professor Hans J. Scha¨fer
on the occasion of his 65th birthday. This work was financially
supported by the University of Padova (research project
A.0EE00.97) and the Ministero dell’Istruzione, dell’Universita`
e della Ricerca (MIUR).
Supporting Information Available: Descriptions of the
geometries of the stationary points and the absolute energies
of each stationary point, additional tables of calculated data
and illustrations of relevant orbitals, and data on the reaction
energy for the formation of the radical anion (PDF). This
material is available free of charge via the Internet at
http://pubs.acs.org.
Figure 4. SOMOs of the radical anions 3a (top), 5a (middle), and 6a
(bottom).
π* character of the singly occupied molecular orbital (SOMO)
able to reduce the extent of the inner reorganization component.
In turn, this comparison also indicates that the reduction of most
nonactivated disulfides, such as the ones investigated here, does
entail the formation of σ* radical anions. In fact, when the
disulfide sets up to accept the electron at the transition state,
the necessary elongation of the S-S bond provokes the lowering
of the energy of an antibonding orbital that, once the final radical
anion equilibrium structure is reached, localizes onto the loose
S-S bond.64 In this respect, phenyl or alkyl substituents do not
JA012545E
(64) The LUMO of compounds 3 and 4 is the S-S σ* orbital and thus
essentially equal to the corresponding SOMO. On the other hand, the
LUMO of 5-7 display a significant π* character (examples are provided
in the Supporting Information), which, however, disappears upon S-S bond
elongation.
9
7538 J. AM. CHEM. SOC. VOL. 124, NO. 25, 2002