Kinetics of the reduction of dialkyl peroxides. New insights into the dynamics of dissociative electron transfer

Article abstract of DOI:10.1021/ja9906148

The concerted dissociative reduction of di-tert-butyl peroxide (DTBP), dicumyl peroxide (DCP), and di-n-butyl peroxide (DNBP) is evaluated by both heterogeneous and homogeneous electron transfer using electrochemical methods. Electrochemical and thermochemical determination of the O-O bond energies and the standard potentials of the alkoxyl radicals allow the standard potentials for dissociative reduction of the three peroxides in N,N-dimethylformamide and acetonitrile to be evaluated. These values allowed the kinetics of homogeneous ET reduction of DTBP and DCP by a variety of radical anion donors to be evaluated as a function of overall driving force. Comparison of the heterogeneous ET kinetics of DTBP and DNBP as a function of driving force for ET allowed the distance dependence on the reduction kinetics of the former to be estimated. Results indicate that the kinetics of ET to DTBP is some 0.8 order of magnitude slower in reactivity than DNBP because of a steric effect imposed by the bulky tert-butyl groups. Experimental activation parameters were measured for the homogeneous reduction of DTBP with five mediators, covering a range of 0.4 eV in driving force over the temperature range -30 to 50°C in DMF. The temperature dependence of the kinetics leads to unusually low preexponential factors for this series. The low preexponential factor is interpreted in terms of a nonadiabatic effect resulting from weak electronic coupling between the reactant and product surfaces. Finally, the data are discussed in the context of recent advances of dissociative electron transfer reported by Saveant and by German and Kuznestov. In total the results suggest that these peroxides undergo a nonadiabatic dissociative electron transfer and represent the first reported class of compounds where this effect is reported.

Full text of DOI:10.1021/ja9906148

J. Am. Chem. Soc. 1999, 121, 7239-7248
7239
Kinetics of the Reduction of Dialkyl Peroxides. New Insights into the
Dynamics of Dissociative Electron Transfer1
Robert L. Donkers,† Flavio Maran,*,‡ Danial D. M. Wayner,*,§ and Mark S. Workentin*,†
Contribution from the Department of Chemistry, The UniVersity of Western Ontario,
London, ON Canada N6A 5B7, Dipartimento di Chimica Fisica, UniVersita` di PadoVa, Via Loredan 2,
35131 PadoVa, Italy, and Steacie Institute for Molecular Sciences, National Research Council of Canada,
Ottawa, ON Canada K1A 0R6
ReceiVed February 26, 1999
Abstract: The concerted dissociative reduction of di-tert-butyl peroxide (DTBP), dicumyl peroxide (DCP),
and di-n-butyl peroxide (DNBP) is evaluated by both heterogeneous and homogeneous electron transfer using
electrochemical methods. Electrochemical and thermochemical determination of the O-O bond energies and
the standard potentials of the alkoxyl radicals allow the standard potentials for dissociative reduction of the
three peroxides in N,N-dimethylformamide and acetonitrile to be evaluated. These values allowed the kinetics
of homogeneous ET reduction of DTBP and DCP by a variety of radical anion donors to be evaluated as a
function of overall driving force. Comparison of the heterogeneous ET kinetics of DTBP and DNBP as a
function of driving force for ET allowed the distance dependence on the reduction kinetics of the former to be
estimated. Results indicate that the kinetics of ET to DTBP is some 0.8 order of magnitude slower in reactivity
than DNBP because of a steric effect imposed by the bulky tert-butyl groups. Experimental activation parameters
were measured for the homogeneous reduction of DTBP with five mediators, covering a range of 0.4 eV in
driving force over the temperature range -30 to 50 °C in DMF. The temperature dependence of the kinetics
leads to unusually low preexponential factors for this series. The low preexponential factor is interpreted in
terms of a nonadiabatic effect resulting from weak electronic coupling between the reactant and product surfaces.
Finally, the data are discussed in the context of recent advances of dissociative electron transfer reported by
Save´ant and by German and Kuznestov. In total the results suggest that these peroxides undergo a nonadiabatic
dissociative electron transfer and represent the first reported class of compounds where this effect is reported.
Introduction
reaction free energy, ∆G°, (eq 4) that is equal to the well-known
Marcus equation7 with the exception that the intrinsic barrier
(∆Gq0) contains contributions from the bond dissociation en-
thalpy of the A-B bond (BDE) in addition to the reorganization
energy (λ), which is often separated into the solvent (λs) and
inner reorganization (λi) energies (where the latter term does
not include the contribution of the mode of the A-B bond).
Electron transfer (ET) to an organic molecule (A-B) is often
accompanied by fragmentation with the formation of a radical,
A•, and an anion, B-.2-4 This process can occur either via a
stepwise mechanism with an intermediate radical anion (eqs 1
and 2) or via a concerted pathway in which ET and bond
breaking occur in one step (eq 3). Work by Save´ant and co-
workers have laid the foundation of our understanding of the
concerted mechanism in comparison with the corresponding
stepwise process.5 The Save´ant model is based on a Morse
potential for the A-B bond and the assumption that the
dissociative potential for the product state is the same as the
repulsive part of the reactant potential.6 This leads to an
expression relating the activation free energy, ∆Gq, to the
A-B + e- h A-B•-
A-B•- f A• + B-
(1)
(2)
A-B + e- f A• + B-
(3)
(4)
2
† The University of Western Ontario.
∆G°
∆Gq ) ∆Gq0 1 +
‡ Universita` di Padova.
4∆Gq0
(
)
§ National Research Council of Canada.
(1) Issued as NRCC Publication No. 42182.
(2) Save´ant, J.-M. AdV. Phys. Org. Chem. 1990, 26, 1.
(3) Save´ant, J.-M. Acc. Chem. Res. 1993, 26, 455.
BDE + λ
∆Gq0 )
(5)
4
(4) (a) Saeva, F. D. In Topics in Current Chemistry; Mattay, J., Ed.;
Springer-Verlag: Berlin, 1990; Vol. 156, p 59. (b) Schuster, G. B. In
AdVances in Electron Transfer Chemistry; Mariano, P. S., Ed.; JAI Press:
Greenwich, CT, 1991; Vol. 1, p 163. (c) Maslak, P. In Topics in Current
Chemistry; Mattay, J., Ed.; Springer-Verlag: Berlin, 1993; Vol. 168, p 1.
(d) Gaillard, E. R.; Whitten, D. G. Acc. Chem. Res. 1996, 29, 292.
(5) Save´ant, J.-M. In AdVances in Electron Transfer Chemistry; Mariano,
P. S., Ed.; JAI Press: Greenwich, CT, 1994; Vol. 4, p 53.
(6) Save´ant, J.-M. J. Am. Chem. Soc. 1987, 109, 6788.
The model has been validated, in particular, by a number of
studies of both heterogeneous and homogeneous reduction of
carbon-halogen bonds.2,3 We applied this model in our study
of the dissociative reduction of oxygen-oxygen bonds of alkyl
(7) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265.
10.1021/ja9906148 CCC: $18.00 © 1999 American Chemical Society
Published on Web 07/23/1999

7240 J. Am. Chem. Soc., Vol. 121, No. 31, 1999
Donkers et al.
peroxides.8 In that study we showed that the electrochemical
reduction of alkyl peroxides is in agreement with a concerted
mechanism. By use of the potential dependence of the transfer
coefficient, R, both the intrinsic barriers and bond dissociation
energies for O-O bond cleavage could be derived. Values for
the heterogeneous intrinsic barrier and the BDE of the peroxide
of 10-13 and 34-37 kcal mol-1, respectively, were obtained
and depended to some extent on the structure. We applied the
same method to derive the standard potential for the concerted
reduction of biologically relevant endoperoxides.9
A-B + D•- f (A•B-D)sol
(6)
BDE + λS
∆G°
(T∆S°φ)2
2
C
F
∆Gq )
1 +
-
- HRP (7)
(
)
4
BDE + λS
4 BDE
∆G°
T∆S°φ
1
2
C
F
∆Sq ) 1 +
(∆S°φ + ∆S°) +
(8)
(9)
F
S
(
)
BDE + λS
2 BDE
∆G° ) ∆G° + T∆S°F(1 - φ)
C
We also reported rate constants for the homogeneous reduc-
tion of di-tert-butyl peroxide (DTBP) in acetonitrile (MeCN)
and N,N-dimethylformamide (DMF) in a previous study.10 At
that time we reported that the Save´ant model overestimated the
actual rate constants by almost 4 orders of magnitude. We
suggested that steric inhibition was partly responsible for this
discrepancy due to the exponential decrease of the electronic
coupling between reactant and product states. The bulky tert-
butyl groups block access of the reductants to the O-O bond.
The remainder of the discrepancy was attributed to a nonadia-
batic effect resulting from intrinsically poor electronic coupling
between the reactant and product surfaces.
∆G°
1
C
R ) 1 +
(10)
(
)
2
BDE + λS
In this paper we reexamine the concerted reduction of DTBP
in the context of the cage and nonadiabatic effects. By use of
available thermodynamic data, the activation parameters are
predicted using Save´ant’s most recent model.11 Experimental
activation parameters for the reduction of DTBP by five
mediators that cover a range of 0.4 eV in driving force are
obtained from the temperature dependence of the kinetics
between 50 and -30 °C in DMF. In addition, the role of steric
effects on the kinetics of these processes is evaluated by
comparison of DTBP with the heterogeneous reduction of di-
n-butyl peroxide (DNBP) and the homogeneous reduction of
dicumyl peroxide (DCP). Finally, these data are discussed with
respect to the more generalized quantum mechanical theory of
dissociative electron transfer proposed by German and Kuz-
netsov.12
A recent paper by Save´ant and co-workers points out that in
our original report we used the bond dissociation free energy
(BDFE) rather than the BDE in our estimate of the intrinsic
barrier.11 As we will see, this has the effect of decreasing the
rate constants predicted by the model by about 1.5 orders of
magnitude. Thus, the discrepancy between the model and the
experiment is now only 2.0-2.5 orders of magnitude. Save´ant
and co-workers go on to develop an extension of their model,
which takes cage and entropy effects into account. This paper
represents a key advance in how one should think about the
concerted processes. In essence, it points out that the available
thermodynamic driving force, -∆G°, provides information that
relates energies of solvent-separated reactants to solvent-
separated products (eq 3 where e- is either the electrode or a
homogeneous reductant). However, the reaction for which the
measured activation energy is relevant is one in which the
reactants are solvent-separated species while the products are
formed in a solvent cage (eq 6). The products diffuse apart and
become independently solvated in a separate step with an
activation barrier that is much less than the barrier for the ET.
To solve this complex problem, it was assumed that the entropy
change associated with the formation of the fragments in a cage,
∆S° , is a fraction (φ) of the overall entropy change, ∆S°. It
Experimental Section
Chemicals. N,N-Dimethylformamide (Janssen, 99%) was purified
as previously described.8 Acetonitrile (BDH) was distilled over CaH2
and stored under an argon atmosphere. The supporting electrolyte was
tetraethylammonium perchlorate, TEAP, (Fluka) that was recrystallized
twice from ethanol and dried at 60 °C under vacuum. Di-tert-
butylperoxide (Aldrich), dicumyl peroxide (Aldrich), acetanilide (Jan-
ssen), fluorene (Janssen), cumyl alcohol (Aldrich), chrysene (Aldrich),
7,8-benzoquinoline (Aldrich), pyrene (Fluka), anthracene (Erba), 9,-
10-diphenylanthracene (Aldrich), fluoranthene (Ega), perylene (Fluka),
acenaphthylene (Fluka), naphthacene (Fluka), naphthalene (Aldrich),
benzophenone (Erba), 2,2,2-trifluoroethanol (Aldrich), and 2,6-di-tert-
butyl phenol were of high purity and either used as received or purified
prior to use. 4-Methyl-azobenzene and 4-methyl-4′-ethoxyazobenzene
were synthesized as previously described.13 The synthesis of di-n-butyl
peroxide was carried out by slight modifications of a literature method.14
Electrochemistry. The glassy carbon (Tokai GC-20) electrode was
prepared and activated before each measurement as previously de-
scribed.8 The electrode area, necessary to calculate the diffusion
coefficients, was determined through the limiting convolution15 currents
of ferrocene; the diffusion coefficient of ferrocene is 1.13 × 10-5 and
2.38 × 10-5 cm2 s-1 in DMF and MeCN, respectively.16 The reference
electrode was Ag/AgCl, calibrated after each experiment against the
ferrocene/ferricenium couple. In the presence of 0.1 M TEAP, we
measured E°Fc/Fc+ to be 0.475 and 0.450 V versus the KCl saturated
calomel electrode (SCE) in DMF and in MeCN, respectively. All
potentials values are reported versus SCE. The counter electrode was
a 1 cm2 Pt plate.
F,C
F
was further assumed that the entropy changes linearly from
reactants to products leading to eqs 7-9, which can be fit
iteratively to the experimental data (HRP is the avoided crossing
energy and ∆S° is the change in solvation entropy associated
S
with the reaction). The overall entropy change is simply ∆S°
S
+ ∆S°. Finally, the transfer coefficient, R, at a given driving
F
force can be calculated (eq 10). In eqs 7, 8, and 10, the λi term
has been neglected; this seems to be a reasonable approximation
for strongly dissociative ETs, i.e., when dealing with aromatic
electron donors and with acceptors where the breaking bond
stretches along the reaction coordinate without significant
rearrangement of the rest of the molecular framework.
(8) Antonello, S.; Musumeci, M.; Wayner, D. D. M.; Maran, F. J. Am.
Chem. Soc. 1997, 119, 9541.
(9) (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.
(12) (a) German, E. D.; Kuznetsov, A. M. J. Phys. Chem. 1994, 98, 6120.
(b) German, E. D.; Kuznetsov, A. M.; Tikhomirov, V. A. J. Phys. Chem.
1995, 99, 9095.
(13) Severin, M. G.; Are´valo, M. C.; Maran, F.; Vianello, E. J. Phys.
Chem. 1993, 97, 150.
(10) Workentin, M. S.; Maran, F.; Wayner, D. D. M. J. Am. Chem. Soc.
1995, 117, 2120.
(11) Andrieux, C. P.; Save´ant, J.-M.; Tardy, C. J. Am. Chem. Soc. 1998,
120, 4167.
(14) Foglia, T. A.; Silbert, L. S. Synthesis 1992, 545.
(15) Imbeaux, J. C.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 44, 169.
(16) Curtis, N.; Donkers, R. L.; Leaist, D. G.; Maran, F.; Workentin,
M. S. Manuscript in preparation.

Reduction of Dialkyl Peroxides
J. Am. Chem. Soc., Vol. 121, No. 31, 1999 7241
Electrochemical measurements were conducted in an all-glass cell
thermostated at the required temperature. For the temperature depen-
dence studies the temperature was controlled using a VWR Scientific
model 1150A constant temperature circulator; the cell was allowed to
equilibrate for 30 min at each temperature. An EG&G-PARC 173/179
potentiostat-digital coulometer, EG&G-PARC 175 universal program-
mer, Nicolet 3091 12-bit resolution digital oscilloscope, and Amel 863
X/Y pen recorder or an EG&G-PARC 283 potentiostat interfaced to a
computer were used. In all cases, iR compensation was employed.
Convolution analyses were carried out on digitalized, background-
subtracted voltammetric curves as previously described.8 Digital
simulations of the cyclic voltammetry curves were performed by using
the DigiSim 2.1 software by Bioanalytical Systems Inc.
Table 1. Cyclic Voltammetric Data for the Reduction of DTBP,
DCP, and DNBP at the Glassy Carbon Electrode (0.2 V s-1, T ) 25
°C) and Electrolysis Data for the Same Peroxides, Both in the
Absence and Presence of Acids
n (F mol-1) n (F mol-1
)
compound solventa Ep (V) Rb
Rc
-2.50 0.254 0.231
MeCN -2.53 0.236 0.228
DMF -2.10 0.277 0.250
MeCN -2.07 0.261 0.258
DMF -2.09 0.244 0.210
MeCN -2.08 0.260 0.234
no acid
with acid
DTBP
DTBP
DCP
DMF
1.9
2.0
2.0
2.0
0.9
0.9
1.9d
2.0d
2.0d
2.0e
1.4d
2.0f
DCP
DNBP
DNBP
a 0.1 M TEAP. b From ∆Ep/2 ) 1.857RT/(FR) (ref 17). c From ∂Ep/
∂ log V ) 1.15RT/(FR) (ref 17). d Acetanilide. e 2,6-Di-tert-butyl-4-
methylphenol. f 2,2,2-Trifluoroethanol.
Controlled Potential Electrolysis and HPLC Analysis. Controlled
potential bulk electrolyses were performed in a divided cell using a
mercury pool cathode or a platinum grid as the working electrode.
Electrolyses were carried out at 25 °C in 10 mM solutions continuously
deoxygenated with argon at a constant potential just beyond the
voltammetric reduction peak. The electron consumption was determined
after the electrolysis current dropped to 1-2% of its original value.
Some electrolyses were carried out also in the presence of added weak
acids (trifluoroethanol, fluorene, acetanilide, or 2,6-di-tert-butylphenol).
The indirect controlled potential electrolyses were carried out by
reducing the mediator (1 mM perylene) in the presence of the peroxide
(2 mM). The extent of the catalyzed reduction was followed by cyclic
voltammetry and by taking aliquots of the partially electrolyzed solution
at given values of the charge consumed. Each aliquot was divided into
two samples one of which was acidified. In all cases, HPLC analysis
gave the same result. The indirect electrolyses were arbitrarily halted
after theoretical destruction of half of the peroxide, based on the
the peak current, ip. The ip values, or the limiting convolution
currents, are essentially independent of the solvent after cor-
rection for solvent viscosity.19,20
Electrolyses of DTBP, DCP, and DNBP were carried out at
a mercury pool cathode (or platinum grid), under magnetic
stirring, as described in the Experimental Section. The number
of electrons consumed, n, in the absence and presence of acid
is summarized in Table 1. With DCP these values were verified
by monitoring the formation (HPLC) of 2-phenyl-2-propanol:
1.9 (DMF, no acid), 1.8 (MeCN, no acid), 1.9 equiv (MeCN,
acid). For DNBP the low electron consumption in the absence
of acid is presumably due to the known slow base-induced
decomposition of the peroxide and other possible competing
reactions (vide infra) that are not significant on the cyclic
voltammetry (CV) time scale.21
The two-electron stoichiometry and the concerted nature of
the initial ET bond breaking step8 are in agreement with the
reaction sequence outlined in eqs 11 and 12, where the alkoxy
radical produced in the dissociative reduction is reduced,
providing an overall stoichiometry shown in eq 13.
consumption of 2 F mol-1
.
HPLC was performed using a Perkin-Elmer series 4 liquid chro-
matograph (column: Sperisorb ODS2 C18, 5 µm, 4.6 mm × 15 cm),
equipped with a UV LC-85 variable-wavelength detector and a Perkin-
Elmer 3700 data station for chromatogram analysis. The detection
wavelength was 220 nm. The eluting solution was programmed: 2 min
at 50% acetonitrile/50% water, 1 min to reach 90% acetonitrile/water,
and then the same eluent was maintained for 7 min. The flow rate was
2.0 mL/min. Quantitative analysis was based on peak areas that were
calibrated using authentic samples. Naphthalene was used as an internal
standard.
RO-OR + e- f RO• + RO-
(11)
RO• + e- f RO-
(12)
(13)
Results and Discussion
RO-OR + 2e- f 2 RO-
Voltammetric Behavior and Coulometry. The reduction of
DTBP and DCP (and other dialkyl peroxides) was previously
studied in DMF/0.1 M tetra-n-butylammonium perchlorate
(TBAP).8 In DMF or MeCN at either a glassy carbon or mercury
electrode, only one electrochemically irreversible reduction peak
is observed. Results for DNBP were qualitatively similar,
although the voltammetry at the mercury electrode for this
compound was not as well defined. The reduction of the
peroxides is essentially independent of the electrolyte, as verified
by changing TBAP with TEAP. The latter was the electrolyte
of choice in the present study. The peak potential (Ep) values
measured at 25 °C at a scan rate (V) of 0.2 V s-1 are given in
Table 1. For comparison, the values of the transfer coefficient
Two macroelectrolyses were carried out in both solvents by
making use of the principles of homogeneous electrocatalysis.22
The radical anion of an aromatic compound is generated by
electrolysis at a potential negative to the reduction peak of the
mediator itself but more positive than the reduction potential
(19) The limiting convolution current, Il, is defined as Il ) nFAD1/2C*,
where n is the overall electron consumption, D the diffusion coefficient,
and C* the substrate concentration. Il is the plateau value reached by the
convolution current I when the applied potential is negative enough. I is
related to the actual current i through the convolution integral15
t
i(u)
I ) π-1/2
1/2 du
∫
0 (t - u)
R, obtained from the corresponding peak width, ∆Ep/2
)
1.857RT/(F/R),17 and from the scan rate dependence of the
irreversible peak, ∂Ep/(∂ log V) ) 1.15 RT/(F/R),17 are also
reported. Weak acids capable of protonating the product
For example, the diffusion coefficient of DCP, determined by convolution
voltammetry, is 7.34 × 10-6 and 1.86 × 10-5 cm2 s-1 in DMF and MeCN,
respectively. This leads to a ratio of 2.53, in good agreement with the ratio
between the viscosity of DMF and that of MeCN, 0.796/0.344 ) 2.31,20
and thus with the Stokes-Einstein relation. Analogous results are obtained
with the other peroxides. This is relevant because it means that the number
of exchanged electrons is the same in both solvents, within error.
alkoxides8 (trifluoroethanol, fluorene, acetanilide, and 2,6-di-
DMF
tert-butylphenol with pKa
) 24.1, 23.3, 22.3, and 17.7,
respectively)18 had no effect in either solvent on both Ep and
(20) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic SolVents,
Physical Properties and Methods of Purification, 4th ed.; Weissberger, A.,
Ed.; Techniques of Chemistry II; John Wiley and Sons: New York, 1986.
(21) Organic Peroxides; Ando, W., Ed.; Wiley: New York, 1992.
(22) (a) Andrieux, C. P.; Blocman, C.; Dumas-Bouchiat, J. M.; M’Halla,
F.; Save´ant J.-M. J. Electroanal. Chem. 1980, 113, 19. (b) Andrieux, C.
P.; Save´ant J.-M. J. Electroanal. Chem. 1986, 205, 43.
(17) (a) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706. (b) Bard,
A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and
Applications; Wiley: New York, 1980.
(18) (a) Bordwell, F. G. Acc. Chem. Res. 1988, 21, 456. (b) Maran, F.;
Celadon, D.; Severin, M. G.; Vianello, E. J. Am. Chem. Soc. 1991, 113,
9320.

7242 J. Am. Chem. Soc., Vol. 121, No. 31, 1999
Donkers et al.
likely related to the fast H atom abstraction from DMF by
CumO•. Decay of the radical (lifetime is 60 ns in DMF
compared to 1.6 µs in MeCN) would have the consequence of
lowering the overall electron stoichiometry. H atom abstraction
would also be consistent with similar results obtained from the
mediated electroreduction of DTBP.24 The difference between
the direct and indirect electrolyses of DCP in DMF is related
to the dissociative nature of the initial ET. Thus, in the direct
electrolysis the cumyloxy radical is generated at the electrode
surface where it is immediately reduced. Likewise, the lower
electron stoichiometry for DNBP in DMF can be attributed to
H-abstraction reactions with solvent and the peroxide itself.
Dissociative Standard Potential of Peroxides. Dissociative
ETs (eq 3) are irreversible reactions, and therefore, their standard
•
potentials (E°AB/A ,B-) cannot be measured directly. However,
they can be estimated in two ways: (i) by thermochemical
calculations or (ii) by kinetic ET data coupled with the use of
the quadratic activation-driving force relationship 4, as shown
very recently for different dissociative-type compounds.8,9,25,26
The first approach is based on the thermochemical cycle outlined
below (eq 18).27
AB a A• + B•
B• + e- a B-
BDFE
Figure 1. Cyclic voltammetry curves taken during the macroreduction
of DCP (2 mM) mediated by perylene (1 mM) in MeCN/0.1 M TEAP,
at 0.2 V s-1. The curves (top to bottom) correspond to an electron
consumption of 0, 0.2, 0.4, 0.6, 0.8, 1.0, and 2.0 F mol-1. The last
curve is coincident to that of perylene in the absence of DCP. The
electrode was glassy carbon, and T ) 25 °C.
-FE°B /B-
•
net: AB + e- a A• + B-
E°AB/A ,B- ) E°B /B-
-FE°AB/A ,B-
•
-BDFE/F
(18)
•
•
of the substrate (in these cases the peroxide). For example, we
used perylene as the mediator and focused on DCP. The
evolution of the electrolysis was monitored by both cyclic
voltammetry and HPLC. The reduction peak of perylene in the
absence and in the presence of 2 equiv of DCP is shown in
Figure 1. The presence of the peroxide causes the peak current
of perylene (the donor, D) to increase because of the catalytic
cycle outlined in eqs 14-16. Figure 1 also illustrates how the
voltammetric wave changes progressively after the passage of
small quantities of charge, each wave corresponding to 0.2 F
mol-1. HPLC reflects the evolution toward the overall stoichi-
ometry of eq 13. For every equivalent of DCP consumed, 2
equiv of cumyl alcohol is produced. No change in the
concentration of the perylene mediator or the formation of other
species was observed, indicating that no coupling (such as the
reaction in eq 17) similar to that observed in the reduction of
alkyl and benzyl halides is observed. It is also noteworthy that
in the product study for the reduction of DCP no acetophenone
was observed. Acetophenone would be formed from the known
â-scission of the cumyloxy radical (CumO•), before its ET
reduction (eq 16),23 suggesting that the latter reaction must be
close to diffusion-controlled.
Peroxides are characterized by low bond dissociation enthal-
pies, BDE, of about 30-40 kcal mol-1 28
Some of the reported
.
data are obtained from the gas-phase kinetics and must be
converted to solution BDFEs by an appropriate entropy cor-
rection (vide infra).29 Alternatively, BDFEs can be calculated
from the solution homolysis equilibrium constant obtained from
the decomposition rate constant and the rate constant for the
dimerization of RO• radicals, kd. For t-BuO• or CumO•, kd ) 2
× 109 M-1 s-1 at 25 °C.30 For DTBP, reported BDE values are
37.4, 38.0, and 36.4 kcal mol-1, leading to an average BDFE
value of 28.8 kcal mol-1 (∆S° ) 28.5 cal mol-1 K-1 29), which
is close to the value based on the equilibrium constant of 28.7
kcal mol-1. The equilibrium constant K for the homolysis of
DTBP was determined from the extrapolated forward rate
constant, 1.66 × 10-12 s-1 32 and the kd value given above. For
DCP, a similar analysis leads to BDFE ) 27.2 kcal mol-1 33
,
which also agrees with the value of 27.7 kcal mol-1 obtained
by convolution.8 The latter value will be used in the following
discussion. The BDFE of DNBP is not known but can be
estimated by comparison with the BDE of di-n-propyl (37.1
and 36.5 kcal mol-1), diisopropyl (37.7 kcal mol-1 31b,34
and
)
D + e- a D•-
(14)
(15)
(24) Kjær, N. T.; Lund, H. Acta Chem. Scand. 1995, 49, 848.
(25) Antonello, S.; Maran, F. J. Am. Chem. Soc. 1997, 119, 12595.
(26) Antonello, S.; Maran, F. J. Am. Chem. Soc. 1998, 120, 5713.
(27) Wayner, D. D. M.; Parker, V. D. Acc. Chem. Res. 1993, 26, 287.
(28) Baldwin, A. C. In The Chemistry of Peroxides; Patai, S., Ed.;
Wiley: New York, 1983; p 97.
(29) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York,
1976.
(30) Wong, S. K. Int. J. Chem. Kinet. 1981, 13, 433.
(31) (a) Batt, L.; Benson, S. W. J. Chem. Phys. 1962, 36, 895. (b) Batt,
L.; Christie, K.; Milne, R. T.; Summers, A. Int. J. Chem. Kinet. 1974, 6,
877. (c) Lewis, D. K. Can. J. Chem. 1976, 54, 581.
(32) Matsugo, S.; Saito, I. In Organic Peroxides; Ando, W., Ed.;
Wiley: New York, 1992.
D
•- + RO-OR f RO• + RO- + D
D
•- + RO• f RO- + D
•- + R• f DR-
(16)
(17)
D
For DCP in MeCN, electrolysis requires 2 F mol-1, but only
1.4 F mol-1 is consumed in the corresponding indirect elec-
trolysis in DMF. The difference between these two values is
(33) Denisov, E. T. In Liquid Phase Reaction Rate Constants; Plenum:
New York, 1974.
(34) Benson, S. W. J. Chem. Phys. 1964, 40, 1007.
(23) Avila, D. V.; Brown, C. E.; Ingold, K. U.; Lusztyk, J. J. Am. Chem.
Soc. 1993, 115, 466.

Reduction of Dialkyl Peroxides
J. Am. Chem. Soc., Vol. 121, No. 31, 1999 7243
Table 2. Rate Constants for the Homogeneous Electron Transfer (khom) from Electrogenerated Radical Anion Donors to DTBP at 25 °C
E°D/D•- (V)
(DMF)
∆G° (eV)a
log khom
(DMF)
E°D/D•- (V)
(MeCN)
∆G° (eV)b
log khom
(MeCN)
donor (D)
chrysene
7,8-benzoquinoline
isoquinoline
pyrene
anthracene
9,10-diphenylanthracene
fluoranthene
perylene
acenaphthylene
naphthacene
(DMF)
(MeCN)
-2.245
-2.170
-2.092
-2.004
-1.928
-1.837
-1.729
-1.645
-1.633
-1.545
-0.765
-0.690
-0.612
-0.524
-0.448
-0.357
-0.249
-0.165
-0.153
-0.065
5.11
4.68
4.39
4.05
3.31
2.89
2.15
1.82
1.26
0.91
-2.266
-2.150
-0.716
-0.600
4.87
4.51
-2.008
-1.965
-1.873
-1.762
-1.670
-1.653
-0.458
-0.415
-0.323
-0.212
-0.120
-0.103
3.82
3.09
2.85
2.03
1.67
1.04
a E°t-BuOOBu-t/t-BuO•,t-BuO-(DMF) ) -1.48 V. b E°t-BuOOBu-t/t-BuO•,t-BuO-(MeCN) ) -1.55 V.
di-sec-butyl peroxide (36.4 kcal mol-1).35 The BDE of DNBP
can therefore be estimated to be about 36.8 kcal mol-1, which
leads to an estimate of 28.3 kcal mol-1 for the BDFE.
By contrast, the standard potential for the CumO•/CumO-
couple (E°B•/B-) can be calculated from voltammetric measure-
ments on the alkoxide (prepared separately or by reduction of
the DCP). This is because cumyl alcohol is more acidic than
water by 2-3 pKa units.8 In DMF, an irreversible oxidation
peak that can be attributed to the anion CumO- is detectable
for V > 0.5 V s-1 and is well defined for V g 2 V s-1. The scan
rate dependence of this peak was measured between 0.5 and
50 V s-1. The one-electron oxidation appears to be sufficiently
fast in DMF to analyze the peak in order to obtain the desired
E°B•/B- in this solvent. The voltammetric data are consistent
with a first-order reaction consuming the electrogenerated
species (i.e., direct hydrogen atom abstraction from the solvent
as the major reaction channel).17 The constant value of ip/V1/2
is consistent with having a steady concentration of CumO- in
the diffusion layer near the electrode. By use of literature values
for the rate constants of the followup reactions,17,27 a value of
E°CumO•/CumO- ) -0.12 ( 0.05 V was obtained. This value is
reasonable in comparison with the above thermochemical
calculations for the t-BuO•/t-BuO- and n-BuO•/n-BuO- couples
as well as the experimental E° for the Ph3CO•/Ph3CO- couple,
-0.03 V.8 In MeCN, the quality of the Ep data prevented a
quantitative calculation. Qualitatively, however, the experimental
data are consistent with a similar potential shift calculated for
t-BuO- (0.07 V on going from DMF to MeCN). Accordingly,
E°CumO•/CumO-(DMF) ) -0.12 V and E°CumO•/CumO-(MeCN) )
-0.19 V. By use of the above values, the corresponding
dissociative E° values can be calculated (( 0.05-0.1 V):
•
The value of E°B /B- can be obtained either from thermo-
chemical calculations or from voltammetry of RO• or RO-.36
The thermochemical approach was chosen for the t-BuO•/t-
BuO- and n-BuO•/n-BuO- couples, since the voltammetric
wave for the reduction of t-BuO• is ill-defined and the pKa’s of
n-BuO- and t-BuO- are too high to be produced in solution at
a sufficiently high concentration (even in carefully purified
solvents the concentration of water, a stronger proton donor than
butanol by about 1 pKa unit,18a is still at millimolar levels). The
standard potentials for the t-BuO•/t-BuO- and n-BuO•/n-BuO-
couples were calculated using eq 19, which is derived from the
thermochemical cycle below.
RO• + H• a ROH
ROH a RO- + H+
-BDFE
2.303RT(pKa)
H+ + e- a H•
-FE°H+/H
•
net:
RO• + e- a RO-
-FE°RO•/RO-
E°t-BuO•/t-BuO-
)
BDFE/F - 2.303(RT/F)pKa + E°H+/H• (19)
Values for the BDFE of RO-H can be estimated from gas-
phase data, correcting for solvation of the proton.27,37 pKa values
for tert-butyl alcohol were calculated using the value reported
for dimethyl sulfoxide, 32.2,18a and one of the two equations
pKa(DMF) ) 1.56 + 0.96 pKa(Me2SO) and pKa(MeCN) ) 7.10
+ 1.17 pKa(Me2SO).18b,10, Accordingly, the pKa values of
t-BuOH are estimated to be 32.5 and 44.8 and those of n-BuOH
are estimated to be and 30.4 and 42.3 in DMF and MeCN,
respectively. The E°H+/H• values are -2.69 and -2.01 V vs SCE
in DMF and MeCN, respectively,27 leading to the following
E°t-BuOOBu-t/t-BuO•,t-BuO-(DMF) ) -1.48 V
E°t-BuOOBu-t/t-BuO•,t-BuO-(MeCN) ) -1.55 V
E°n-BuOOBu-n/n-BuO•,n-BuO-(DMF) ) -1.38 V
E°n-BuOOBu-n/n-BuO•,n-BuO-(MeCN) ) -1.43 V
E°CumOOCum/CumO•,CumO-(DMF) ) -1.32 V
E°CumOOCum/CumO•,CumO-(MeCN) ) -1.39 V
standard potentials: E°t-BuO•/t-BuO-(DMF)
) -0.23 V;
E°t-BuO•/t-BuO-(MeCN) ) -0.30 V; E°n-BuO•/n-BuO-(DMF) )
-0.15 V; E°n-BuO•/n-BuO-(MeCN) ) -0.20 V.
(35) Walker, R. F.; Phillips, L. J. Chem. Soc. A 1968, 2103.
(36) In principle it is possible to generate a constant concentration of
these radicals and to study their reduction by photomodulated voltammetry,
as previously done with many other radicals (Wayner, D. D. M.; McPhee,
D. J.; Griller, D. J. Am. Chem. Soc. 1988, 110, 132), but the electrochemistry
is ill-defined.
(37) NIST Standard Reference Database 25; NIST Structures and
Properties Database and Estimation Program, U.S. Department of Com-
merce: Gaithersburg, MD, 1991.
Electron Transfer to DTBP and DCP. The homogeneous
ET to DTBP in both DMF and MeCN was previously reported,
and the rate (the khom values pertains to the dissociative ET of
eq 14) and driving force data are reported in Table 2. A similar
study was carried out for DCP, again in both solvents. The
indirect reduction was accomplished by homogeneous redox
catalysis using electrogenerated radical anions as homogeneous
electron donors.22 As already mentioned, the reversible reduction
peak of the mediator is transformed into a chemically irrevers-
(38) Izutzu, K. Acid-Base Dissociation Constants in Dipolar Aprotic
SolVents; Chemical Data Series 35; Blackwell Scientific Publications:
Oxford, 1990.

7244 J. Am. Chem. Soc., Vol. 121, No. 31, 1999
Donkers et al.
Table 3. Rate Constants for the Homogeneous Electron Transfer (khom) from Electrogenerated Radical Anion Donors to DCP at 25 °C
E°D/D•- (V)
(DMF)
∆G° (eV)a
(DMF)
log khom
(DMF)
E°D/D•- (V)
(MeCN)
∆G° (eV)b
(MeCN)
log khom
(MeCN)
donor
anthracene
9,10-diphenylanthracene
benzophenone
fluoranthene
perylene
acenaphthylene
naphthacene
terephthalonitrile
4-methyl-4′-ethoxyazobenzene
4-methylazobenzene
-1.928
-1.837
-1.755
-1.729
-1.645
-1.633
-1.545
-1.545
-1.485
-1.355
-0.608
-0.517
-0.435
-0.409
-0.325
-0.313
-0.225
-0.225
-0.165
-0.035
4.81
4.40
3.57
3.81
3.29
2.97
2.54
2.67
1.63
0.82
-1.965
-1.873
-0.575
-0.483
4.98
4.35
-1.762
-1.670
-1.653
-0.372
-0.280
-0.263
3.83
3.10
2.96
-1.580
-1.485
-1.385
-0.190
-0.095
+0.005
2.73
1.85
1.06
a E°CumOOCum/CumO•,CumO-(DMF) ) -1.32 V. b E°CumOOCum/CumO•,CumO-(MeCN) ) -1.39 V.
is formed by reaction of tert-butoxyl radical with the solvent;
eqs 20 and 21).24
RO• + Me2NCHO f ROH + Me2NC•O
•- + Me2NCO • f Me2NC(O)D-
(20)
(21)
D
In principle, it should be possible to detect these anions on the
positive scan after the catalytic reduction. Although anions of
this type are expected to undergo a relatively facile oxidation,40
no oxidation peak could be detected after indirect reduction of
DTBP. However, this does not rule out the possibility that these
reactions contribute on the longer electrolysis time scale. Indeed
the apparent electron consumption of less than 2 in DMF from
the indirect electrolysis of DCP is consistent with this scheme.
This effect is almost undetectable at low catalysis rates
(relatively high scan rates and/or low substrate concentrations)
and was taken into account in the determination of the
corresponding khom values.
Heterogeneous Kinetics for Electron Transfer to DNBP.
We were not able to obtain reproducible homogeneous rate
constants for the reduction of DNBP, so a comparison between
the homogeneous ET kinetics of DNBP and that of DTBP is
not possible. This is likely because of the base-catalyzed
chemistry induced by ET to DNBP and the complex radical
and base-induced peroxide decomposition chemistry that fol-
lows. However, equivalent information regarding the effect of
steric inhibition of ET to DTBP can be obtained from the
kinetics of the heterogeneous ET to the two peroxides.
Unfortunately, the reduction of DNBP at a mercury electrode
is not well behaved and precludes study on this material (in a
sense, this effect may be a result of an increased inner sphere
contribution to the less hindered peroxide). This would have
simplified the analysis because of the possibility of correcting
for the double layer effect, as recently described for the reduction
of a series of dialkyl peroxides, including DTBP and DCP.8
Nevertheless, as already described, the reductions of DNBP and
DTBP have standard potentials that differ by only 0.10-0.12
V, and thus, a comparison of the heterogeneous rates at the
same driving force (and thus where essentially the same double
layer effect pertains) is relevant. For both peroxides, the
heterogeneous rate was studied in MeCN/0.1 M TEAP at the
glassy carbon electrode by using the convolution analysis
approach.8,15 The convolution analysis relies on a series of steps
in which background-subtracted cyclic voltammograms are
treated to transform the real current i into a convoluted current
I.19 The two currents i and I, which are functions of the time
passed during the experiment, are then combined to obtain the
Figure 2. Plot showing the variation in the logarithm of the rate
constant for ET, log(khom), with the driving force, for the homogeneous
electron-transfer reactions of a number of aromatic radical anions with
(a) DTBP and (b) DCP in DMF (b) and MeCN (9) at 25 °C. The
curve is simply a fit to a second-order polynomial.
ible, catalytic peak upon addition of the peroxide (eqs 14-16).
The current of the catalytic peak depends on both the scan rate
and the concentration of the substrate. Rate constants (scan rate
of 0.2-2 V s-1 using at least three concentrations of the
substrate) were then determined using theoretical curves or by
simulation of the experimental voltammograms corresponding
to eqs 14-16. Data for DCP from cyclic voltammograms are
reported in Table 3. For both peroxides, the uncertainty of the
measured khom values is estimated to be (10-15%. The proton
donors were shown to be mild enough to protonate the alkoxide
ions but not the radical anion of the donor and had no effect on
the extracted log khom values.39 By use of the values of the
dissociative standard potentials determined above, log(khom) for
DTBP and DCP can be plotted as a function of the reaction
free energy (Figure 2).
One possible complication in the analysis is the consumption
of the catalyst by coupling with the DMF-derived radical (which
(39) Evidence for the occurrence of the proton transfer was gained
through the observation of the oxidation peak of the conjugate base of the
added acid during the positive-going scan following the catalytic reduction
(e.g., fluorene, Eox ) -0.64 V, or acetanilide, Eox ) 0.08 V).
(40) Parker, V. D.; Tilset, M.; Hammerich, O. J. Am. Chem. Soc. 1987,
109, 7905 and references therein.

Reduction of Dialkyl Peroxides
J. Am. Chem. Soc., Vol. 121, No. 31, 1999 7245
proposed.10 It also is interesting that the Arrhenius preexpo-
nential factor decreases as the driving force increases. A similar
trend was reported in the temperature study of the reduction of
tert-butyl bromide by aromatic radical anions;41 however, in
the reduction of the peroxides the trend is more pronounced.
While the low preexponential factors are consistent with our
original suggestion of a nonadiabatic process, other explanations
should be considered. First, it is possible that the separation
of entropy and enthalpy is not precise over the narrow
temperature range used in this study. The errors in the
determination of the rate constants leads to uncertainties in log A
and Ea of ca. 0.2 and 0.02, respectively; the former is smaller
than the observed variation of log A for the mediators used
in this study. Nevertheless, the largest log A in this study,
which is for the slowest mediated reaction, is still significantly
smaller than those measured for the tert-butyl bromides.41
Second, there may be subtle temperature changes in the overall
electrochemical mechanism that are not evident from macro-
scale electrolyses. While we do not completely understand the
reasons for the observed trend in log A, it is interesting to see
if taking account of the cage and entropy effects provides further
insights.
Figure 3. Free energy dependence of the logarithm of the heteroge-
neous rate constant, log(khet), for the reduction of (a) DNBP and (b)
DTBP in MeCN/0.1 M TEAP at the glassy carbon electrode. T ) 25
°C.
potential dependence of the heterogeneous electron-transfer rate
constant, khet. When the electrode process is irreversible, eq 22
applies.
ln khet ) ln D1/2 - ln[(Il - I(t))/i(t)]
(22)
To make use of eqs 7-10, values of λs, ∆S°, and ∆S° must
F
S
be determined or estimated. The λs value was determined by
using the equation λs ) 95[(2rD)-1 + (2rA)-1 - (rD + rA)-1],
where D and A are the donor and acceptor, respectively, and
the equation is derived from an extensive set of experimental
data.43 An average value of 3.8 Å for rD was chosen,43,44 while
for DTBP the effective radii approach was used,5,8 leading
to 2.7 Å. This provides λs ) 15.5 kcal mol-1. The value of
Although we encountered no problems in analyzing the volta-
mmetric curves of DNBP, the reduction of DTBP is close to
the solvent/electrolyte discharge with the consequence of
complicating the evaluation of Il. Therefore, we used an
approach in which,8,26 in order to estimate Il, the rising part of
the convolution curves pertaining to different scan rates was
fitted by a sigmoid equation. The Il values thus estimated agreed
with each other within 2%, and this was taken as a good
indication of the correctness of the procedure employed. The
data were finally corrected for the diffusion coefficients, which
are 2.45 × 10-5 and 2.47 × 10-5 cm2 s-1 for DNBP and DTBP
in MeCN, respectively. A comparison of the plots resulting from
the logarithmic analyses pertaining to the two peroxides is shown
in Figure 3. It is clear that the heterogeneous kinetics for ET to
DNBP is faster than to DTBP at the same driving force by ca.
0.8 log(khet) units. This difference represents the falloff of
the rate of reduction of DTBP that can be attributed to the
fact that ET must occur over a distance as a result of the O-O
σ* being shielded by the bulky tert-butyl groups in DTBP.
This effect accounts for only about half of the discrepancy
between the experimental results and theoretical prediction (vide
infra).
Activation Parameters for Reduction of DTBP. Arrhenius
plots of the rate constants for reduction of DTBP by a series of
aromatic radical anions (listed in Table 4) are shown in Figure
4. Rate constants were determined by homogeneous redox
catalysis in DMF/0.1 M TEAP solution, as described previously.
The activation parameters are given in Table 4. We have used
Z ) 3 × 1011 M-1 s-1 (Z ) d2[8πkBT/µ]1/2, where d is the
encounter distance and µ is the reduced mass) to extract the
activation enthalpy and apparent activation entropy from the
Arrhenius parameters.
∆S° can be estimated from data in the literature to be 34.6 cal
F
mol-1 K-1 in the gas phase. Following the suggestion that a
correction for the change in the standard state from the gas
phase to the liquid phase is required,11 decreasing the standard
entropy of each component by (R/F)ln(22.4) leads to a final
value of ∆S° ) 28.6 cal mol-1 K-1. As expected, this value is
F
close to the value used by Save´ant in his estimation of
parameters for tert-butyl bromide, since most of the entropy
change comes from increasing the number of fragments from
one to two.
The estimation of ∆S° (eq 23) is more difficult, since
S
thermodynamic data for the solvation of alkoxide ions are not
available. The last term in eq 23 is the entropy change associated
with the conversion of the homogeneous donor into its anion.
Save´ant has determined this value to be -46 cal mol-1 K-1 for
anthracene. We have assumed that this value is constant for all
of the polynuclear aromatic donors used in our study. The
entropy of the tert-butoxyl radical may be estimated from gas-
phase data (S°t-BuO•,DMF ) S°t-BuO•,g(75.6 cal mol-1 K-1) -
[(R/F)ln(22.4)](6.2 cal mol-1 K-1) ) 69.4 cal mol-1 K-1). It is
possible to obtain a rough estimate of S°t-BuO-,DMF from the
(42) A plot of ∆Gq versus ∆G° has a slope of RG ) 0.29 (r2 ) 0.991).
Although the plot is actually more parabolic (r2 ) 0.994), linearization does
not affect the significance of the following. Plots of ∆Hq and T∆Sq versus
∆G° lead to values of RH and RS of 0.53 (r2 ) 0.991) and 0.24 (r2 ) 0.961),
respectively (RG ) RH - RS). Although not discussed in detail in ref 41,
very similar trends were observed in the reaction of tert-butyl bromide with
some aromatic radical anions. In that case, values of RG, RH, and RS of
0.38 (r2 ) 0.976), 0.51 (r2 ) 0.955), and 0.12 (r2 ) 0.799), respectively,
can be derived from their reported data. It is striking that the enthalpic
dependence is ca. 0.5 in both cases and that the apparent transfer coefficients
(i.e., RG) are determined by different entropic dependencies. It seems
reasonable to expect that the overall entropy change in these reactions (i.e.,
∆S°F + ∆S°S) is relatively independent of the mediator; therefore, ∆∆G°
≈ ∆∆H° and ∆∆Hq/∆∆H° ≈ 0.5, as expected for any moderately driven
activated process.
One interesting aspect of the reduction of DTBP is the
unusually low Arrhenius preexponential factors, ca. 2.5 orders
of magnitude lower than in the reduction of tert-butyl bromide.41
The latter is generally agreed to be an adiabatic ET process. In
contrast, the low preexponential factors determined in this study
are consistent with a nonadiabatic process as we originally
(41) (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.
(43) Kojima, H.; Bard, A. J. J. Am. Chem. Soc. 1975, 97, 6317.
(44) Eberson, L. AdV. Phys. Org. Chem. 1982, 18, 79.

7246 J. Am. Chem. Soc., Vol. 121, No. 31, 1999
Donkers et al.
Table 4. Experimentally Determined Activation Parameters for the Reduction of DTBP by a Number of Aromatic Radical Anions
a
Ea
log(khom
)
∆Sqb
∆Hqc
∆Gqa,d
donor
log(A)
(kcal mol-1
)
(M-1 s-1
)
(cal mol-1 K-1
)
(kcal mol-1
)
(kcal mol-1
)
R
chrysene
isoquinoline
pyrene
anthracene
7.06
7.47
8.08
8.15
8.76
2.79
4.25
5.52
6.37
7.76
5.11
4.39
4.05
3.31
2.89
-21.2
-19.3
-16.5
-16.2
-13.4
2.49
3.95
5.22
6.07
7.48
8.81
9.72
10.15
10.91
11.47
0.226
0.271
0.297
0.319
0.346
9,10-diphenylanthracene
a At 298 K. b From ∆Sq ) R(ln A - ln Z - 0.5), Z ) 3 × 1011 M-1 s-1
.
c ∆Hq ) Ea - 0.5RT. d ∆Gq ) ∆Hq - T∆Sq.
this factor.
2
D + λ
4
∆G°
D + λ
∆Gq )
1 +
1 +
(25)
(26)
(
)(
)
2
BDFE + λ
∆G°
BDFE + λ
∆Gq )
(
)(
)
4
A few observations are obvious from Tables 4 and 5 and
Figure 5. About half of the discrepancy between the experi-
mental and predicted data as originally reported in ref 10 may
be attributed to the use of the BDFE rather than the BDE. At a
glance, it appears that the incorporation of the cage and entropy
effects accounts for the remainder of the difference.46 While
eqs 7-9 appear to correctly predict the activation free energy,
some discrepancies remain. In particular, the predicted activation
entropy is underestimated by a factor of 4, leading to an
overestimate of the preexponential factor (log A) by about 2.5
orders of magnitude. This is compensated by an overestimate
of the activation enthalpy. Furthermore, the model predicts an
average R value of ca. 0.42 that is in the gray area between the
concerted and stepwise mechanisms. The experimental value
of ca. 0.3 is clearly consistent with the concerted mechanism.
Finally, these models make no assumption concerning steric
effects on the ET. Since we have shown that this effect accounts
for a factor of about 100.8, we should in principle increase the
experimental log(khom) values by this amount in order to
compare theory and experiment. This places the experimental
points between the prediction based on the original Save´ant
theory and that from the latest revision including entropy
effects.
Figure 4. Arrhenius type plot showing the temperature dependence
of the logarithm of the homogeneous ET rate constant log(khom vs
1/T for the reaction of DTBP with the following homogeneous
donors: ([) diphenylanthracene, (b) anthracene, (9) pyrene, (+)
isoquinoline, and (2) chrysene.
)
298
relationship between the ionic radius (rX) of singly charged
anions and both the entropy in aqueous solution (S°X-,aq) and
the entropy change for the transfer of ions from water to DMF
(∆S°tr).45 In this case the value of S°t-BuO-,DMF is determined
from eq 24. We have assumed that ca. 60% of the surface of
tert-butoxide is solvated as if it were hydroxide ion (rX ) 140
pm) while the hindered side, ca. 40% of the surface, is solvated
as if it were an anion with rX ) 210 pm. This leads to values
of S°t-BuO-,aq and ∆S°tr of 16.8 and -24.2 cal mol-1 K-1
respectively, giving ∆S° ) -23.8 cal mol-1 K-1
,
.
S
∆S° ) (S°t-BuO-,DMF - S°t-BuO•,DMF) - ∆S°AfA-,DMF (23)
S
The evidence above seems to indicate, as we originally
suggested,10 that nonadiabaticity effects may play a role in ET
to dialkyl peroxides. This led us naturally to examine our
experimental data on the basis of a theory for nonadiabatic
dissociative ET recently published by German and Kuznetsov.12
An ET reaction is viewed as nonadiabatic when the electronic
S°t-BuO-,DMF ) S°t-BuO-,aq + ∆S°tr )
43.1 cal mol-1 K-1 (24)
The predicted activation parameters are given in Table 5.
Plots of the experimental and predicted rate constants as a
function of the driving force derived from eqs 7-9 and the
Eyring equation (log(Z) ) 11.5) are shown in Figure 5. This
figure shows the predicted rate constants calculated from
the dissociative ET theory as derived originally by Save´ant
(eq 25)6 and as originally reported by using the bond dissocia-
tion free energy (BDFE) rather than enthalpy10 in the determi-
nation of the intrinsic barrier (eq 26; BDFE ) 28.8 kcal mol-1).
For consistency, we have assumed that there is no contribu-
tion to the activation barrier from the avoided crossing energy
(i.e., HRP ) 0), since neither of the previous models consider
coupling energy between the reactant and product states, HRP
,
is distinctly below RT, i.e., 0.592 kcal mol-1 (200 cm-1).47 This
is the equivalent to saying that the electronic transmission
coefficient κel , 1 (k ) κelZ exp[-∆Gq/(RT)]) and that the
reactant and product potential surfaces do not interact signifi-
cantly. The calculation of HRP, however, is rather complicated
even for nondissociative type systems. For example, HRP is often
treated as an adjusting parameter to fit the experimental data
with theoretical calculations. Because of this premise, the
calculations to follow strictly allow a qualitative examination
of our results in the framework of the theories of ET. Although
the German and Kuznetsov (GK) theory has been developed to
take into account quantum effects, for consistency with the
(45) A correlation between the crystallographic ionic radius, rX, and the
entropy in aqueous solution, S°X-,aq, gives S°X-,aq ) -250.2 + 1.91rX (r
) 0.984, eight ions. Marcus, Y. In Ion SolVation; Chichester; Wiley:
Toronto, 1985.). A similar relationship is found for the entropy of transfer
from water to DMF: ∆S°tr ) -53.9 - 0.28rX (r ) 0.58). The poor
correlation coefficient for the second relationship is due to the dearth of
data (only five ions) and the relative insensitivity of ∆S°tr to the ionic radius
(the range of values is from -87 meV/K for fluoride to -107 meV/K for
thiocyanate).
(46) It should be noted that inclusion of the avoided crossing energy
increases the predicted rate constant. For example, a value of ΗRP ) 1.38
kcal mol-1, as used by Save´ant in his treatment of tert-butyl bromide,
increases the predicted rate constants by 1.5 orders of magnitude, so they
appear to overlap the closed circles in Figure 2.
(47) Newton, M. D.; Sutin, N. Annu. ReV. Phys. Chem. 1984, 35, 437.

Reduction of Dialkyl Peroxides
J. Am. Chem. Soc., Vol. 121, No. 31, 1999 7247
Table 5. Predicted Activation Parameters for the Homogeneous Reduction of DTBP by a Number of Aromatic Radical Anions
Ea
log(k)b
∆Sqc
∆Hq
∆Gqd
mediator (E° vs SCE)
log(A)a
(kcal mol-1
)
(M-1 s-1
)
(cal mol-1 K-1
)
(kcal mol-1
)
(kcal mol-1
)
R
chrysene
isoquinoline
pyrene
anthracene
9,10-diphenylanthracene
10.68
10.60
10.56
10.52
10.48
7.17
8.49
9.27
10.01
10.91
5.42
4.39
3.76
3.19
2.48
-3.39
-3.74
-3.94
-4.10
-4.31
6.57
7.89
8.69
9.41
10.31
7.59
8.99
9.87
10.63
11.60
0.38
0.41
0.43
0.45
0.47
a Assuming log Z ) 11.5. b 298 K. c Based on eq 8. d Based on eq 7.
transition state (eq 31). Note that the ∆G° of eq 32 also equals
-F(E°ROOR/RO•,RO- - E°D/D•-).
∆Gq ) (1 - zq)2{BDE + λs[1 - zq +
(B/BDE)m(zq)2m-1]-2} (31)
∆G° ) BDE(1 - zq)2 - Bz2m
-
(B/BDE)m(zq)2m-1 - 1 + zq
(B/BDE)m(zq)2m-1 + 1 - zq
λs
(32)
When the UP is simply taken as the repulsive part of the Morse
curve of the reagents,6 i.e., for B/BDE ) âP/âR ) 1, eq 29
simplifies to eq 33, where ∆Gq is as in eq 4. R (eq 30) then
transforms into eq 10 (where ∆G° ≡ ∆G°C).
Figure 5. Plot of log(k)298 vs driving force for the reaction of some
aromatic radical anions with DTBP. The open circles are the experi-
mental data. The open squares are derived using eqs 7-9. The closed
circles and closed squares are derived from eqs 25 and 26, respectively.
2π
kq ) (HRP)2(16πRT∆Gq0 exp[-âR(rq - r0)])-1/2
p
exp[-∆Gq/(RT)] (33)
Save´ant adiabatic theory we considered the semiclassic limit
of the nonadiabatic theory. In this limit, the harmonic ap-
proximation is used for the intramolecular vibrations and the
solvent polarization, and the breaking bond is viewed as ruled
by a Morse potential (eq 27), where r0 is the equilibrium length
of the breaking bond. In the analysis, an exponential is used
for the repulsion potential for the product state (eq 28). A
difference in this model compared with the Save´ant model is
that B and âP can be different from BDE and âR, respectively.
The experimental second-order rate constant khom can be
compared with the first-order rate constant kq by taking into
account the equilibrium constant for the diffusion-controlled
formation of the caged donor-acceptor couple, Kd; therefore,
khom ) Kdkq. Since the acceptor is an uncharged species and
thus no electric work is required to bring the donor D and the
acceptor A together, Kd can be calculated by using the equation
Kd ) [(4πNrrδr)/1000].49 The ET rate, khom, is viewed as having
no orientation preferences and occurring significantly only in a
range of r values between r and r + δr. Assuming close contact
of the ET couple, the separation distance r can be taken as rD
+ rA, i.e., the sum of the donor and acceptor radii. Reasonable
values of δr appear to be ∼2 and ∼0.3 Å for adiabatic and
nonadiabatic reactions, respectively.49
UR ) BDE{exp[-2âR(r - r0)] - 2 exp[-âR(r - r0)]} +
BDE (27)
UP ) B exp(-2âPr)
(28)
In the GK theory the first-order rate constant for ET within
the precursor complex, kq, has the form given in eq 29. Here,
the two second derivatives of the functions f and g48 are
calculated at the saddle point, where the transfer coefficient R
(eq 30, where z ) exp[-âR(r - r0)] and m ) âP/âR) and the
bond length r are given by Rq and rq, respectively.
We started by carrying out a test calculation on the dissocia-
tive ET to tert-butyl bromide, already discussed as an adiabatic
ET.41,50 To compare reaction free energies similar to those used
for the peroxides (see below), we focused on the data pertaining
to two donors, the radical anions of quinoxaline (E° ) -1.64
V, log khom ) 1.66) and azobenzene (E° ) -1.32 V, log khom
1/2
|d2UR/dr2|r
) -0.92).51 We used the following parameters: E°t-BuBr
)
2π
p
0
kq ) (HRP)2
2
2
2
2
-1.06 V,26 rD ) 3.8, effective rA ) 2.8 Å, â ) 1.43 Å-1, BDE
) 66 kcal/mol,50 B/BDE ) âP/âR ) 1, λs ) 15.1 kcal/mol. The
application of the GK approach led to the data reported in Table
6. It can be thus concluded that the ET to t-BuBr is indeed
essentially adiabatic. Whereas the calculations were carried out
for δr ) 0.3 Å, it should be noted that using δr ) 2 Å would
have decreased HRP by a factor (0.3/2)1/2 ) 0.39. In addition,
by using the experimental rate constants and the Eyring equation,
κel can be evaluated to be ca. 1 (with Z ) 1012 M-1 s-1), again
pointing to an adiabatic dissociative ET.
[
]
2πRT|∂ g/∂R |R |∂ f/∂r |r
q
q
exp[-∆Gq/(RT)] (29)
(B/BDE)z2m - z2 + 2z - 1
1
∆G°
R ) 1 +
+
(30)
(
)
2
λs
λs/BDE
The activation free energy ∆Gq (eq 31) and the free energy
∆G° (eq 32) are functions of the bond elongation, rq - r, at the
(48) The two functions and their second derivatives are the following:12
f ) (1 - R)UR(r) + RUP(r); g ) R∆G° + R(1 - R)λs + (1 - R)UR(r*) +
(49) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441.
(50) Save´ant, J.-M. J. Am. Chem. Soc. 1992, 114, 10595.
(51) Lund, T.; Lund, H. Acta Chem. Scand. 1986, B40, 470.
RUP(r*) - UR(r0); ∂2f/∂r2 ) 2(1 - R)(2z2 - z)âR(BDE) + R(2âP)2Bz2m
∂2g/∂R2 ) 2λs + [2âR(BDE)(z - z2) + 2âPBz2m] (dr/dR).
;

7248 J. Am. Chem. Soc., Vol. 121, No. 31, 1999
Donkers et al.
Table 6. Nonadiabaticity Calculations for the Homogeneous Electron Transfer to DTBP, DCP, and tert-Butyl Bromide (t-BuBr)
∆G°a,b
eV
log khom
(DMF)
r - r*
(Å)
HRP
(cm-1
)
c,d
acceptor
donor
R
DTBP
DTBP
DCP
DCP
t-BuBr
t-BuBr
pyrene
fluoranthene
9,10-diphenylanthracene
naphthacene
quinoxaline
-0.524
-0.249
-0.517
-0.225
-0.580
-0.260
4.05
2.15
4.40
2.54
1.66
0.190
0.230
0.186
0.229
0.378
0.435
0.386
0.445
0.383
0.449
0.418
0.463
6.0-15.4
5.8-15.1
6.2-16.1
7.3-18.9
82-212
azobenzene
-0.92
63-163
b
a E°DTBP ) -1.48 V, E°DCP ) -1.32 V. λsDTBP ) 15.5 kcal mol-1, λsDCP ) 14.7 kcal mol-1
.
c B/BDE ) âP/âR ) 1. d Lower and upper values
correspond to δr ) 2 and 0.2 Å, respectively.
The calculations were carried out using data pertaining to
the ET between either DTBP or DCP with donors selected to
provide similar free energy values (Table 6). Besides the DTBP
values given above, we used 2.9 Å and 14.7 kcal mol-1 for the
effective radius and λs of DCP. âR was calculated to be 2.56
and 2.97 Å-1 for DTBP and DCP, respectively, through the
O-O stretching frequency, ν0,52 and the relationship âR ) ν0-
(2π2µ/BDE)1/2, where µ is the reduced mass of the O-O atoms.
The data reported in Table 6 show that for both peroxides and
independently of the driving force, HRP lies in the range 6-19
cm-1 and thus suggests nonadiabaticity in the ET. The effect
of B/BDE was tested by using an arbitrarily selected value (0.5),
taking into account that B is expected to be smaller than
BDE.53,54 In all cases, HRP was found to decrease further by a
factor of 15-20. Finally, by contrast with t-BuBr, κel was found
to be significantly smaller than 1, namely, 0.01-0.02.
Finally, if one agrees that the actual preexponential factor Z
is 2 orders of magnitude lower than the adiabatic limit, then
the activation entropies reported in Table 4 should be adjusted
from a range -21 to -13 cal mol-1 K-1 to a range -11 to -3
cal mol-1 K-1. Of course, the activation ethalpies are not
affected. This reduces the activation free energies to a range
5.5-8.1 kcal mol-1. This points to the pitfall in converting the
Arrhenius preexponential factor (log A) into an activation
entropy, since in the absence of clear evidence the choice of
log Z may be arbitrary.
of magnitude, leaving the discrepancy between theory and
experiment as 2-2.5 orders of magnitude. The effect of steric
hindrance, estimated by comparison of the reduction of DTBP
with DNBP, was found to account for a factor of 6, still leaving
a discrepancy of 1.2-1.7 order of magnitude. The temperature
dependence of the reduction of DTBP leads to low preexpo-
nential factors. These unusually low preexponential factors are
not predicted by the Save´ant theory even after accounting for
cage and entropy effects.11 Although the free energy dependence
is not easily explained, their unusually low values are consistent
with a nonadiabatic effect. On the other hand, GK theory
predicts the low preexponential factors found for DTBP because
of a weak electronic coupling (HRP ≈ 15 cm-1). Thus, we
conclude that the concerted dissociative reduction of the
peroxides is nonadiabatic.
With this conclusion it is interesting to speculate why the
reduction of DTBP is nonadiabatic while the reduction of tert-
butyl bromide is apparently adiabatic. The stretching of the
C-Br bond results in a change in the dipole moment of the
bond because of electron redistribution. The bromine atom that
will eventually accept an electron becomes more electron-
deficient as the bond lengthens. This seems ideal for the
concerted dissociative reduction, since the molecular trajectory
along the reaction coordinate sets up the Br group to accept an
electron. On the other hand, the peroxides are completely
symmetrical, so while the stretching of the O-O bond may lead
to a change in polarizability of the bond, there is no change in
dipole moment. At the transition state it is not clear to which
fragment the electron will go; somehow the symmetry must be
broken. Under these conditions, perhaps it is not surprising that
there is poor electronic coupling between the reactant and the
product surfaces.
Summary and Conclusions
A clearer picture now emerges of the dynamics of the
concerted dissociative reduction of peroxides. In our original
communication we suggested that the discrepancy between the
experimentally determined rate constants and the Save´ant theory
was about 4 orders of magnitude, about half of which could be
attributed to a distance dependence on the ET caused by a steric
effect. The other half was attributed to an intrinsic nonadiabatic
effect.10 However, in our original report the BDFE and not the
BDE was used in the estimate of the intrinsic barrier. The use
of the BDE11 lowers the theoretical estimate by about 1.5 orders
Acknowledgment. We dedicated this to Dr. Keith Ingold
on his 70th birthday and in recognition of his outstanding
contributions to science. We thank Professor J.-M. Save´ant for
helpful comments. M.S.W. thanks the Natural Sciences and
Engineering Research Council of Canada and the University
of Western Ontario (ADF) for funding. F.M. thanks the
Consiglio Nazionale delle Ricerche for financial support (Short-
term Mobility Program).
(52) Lin-Vien, D.; Colthup, N. B.; Fateley, W. G.; Grasselli, J. G. The
Handbook of Infrared and Raman Characteristic Frequencies of Organic
Molecules; Academic Press: Toronto, 1991.
(53) Marcus, R. A. Acta Chem. Scand. 1998, 52, 858.
(54) Daasbjerg, K.; Jensen, H.; Benassi, R.; Taddei, F.; Antonello, S.;
Gennaro, A.; Maran, F. J. Am. Chem. Soc. 1999, 121, 1750.
JA9906148