Mechanism and reactivity parameters of the reduction of arylmethyl radicals from time-resolved electron-photoinjection experiments

Article abstract of DOI:10.1021/ja981801t

The 9-anthrylmethyl, diphenylmethyl, benzyl, and 4-methylbenzyl radicals are generated by reduction of the corresponding chlorides with electrons photoinjected in laser pulse experiments. The 'polarograms' derived from the variation of the charge flowing through the electrode with the dc potential of the electrode represent the reduction of these radicals to the corresponding anions. The meaning of the half-wave potentials is investigated through their variations with the measurement time and with the addition of acids in the solution, which accelerates the disappearance of the carbanion. Correcting the kinetic data for the effect of radical dimerization, the reduction kinetics appear to be mostly under the control of the follow-up reaction of the carbanion with acids present in the medium, although the effect of charge-transfer kinetics begins to interfere at the lower end of the time window. The results are compared with earlier data obtained by other techniques. The changes in reactivity observed in the series are discussed with the help of density functional quantum chemical calculations.

Full text of DOI:10.1021/ja981801t

J. Am. Chem. Soc. 1998, 120, 10171-10179
10171
Mechanism and Reactivity Parameters of the Reduction of Arylmethyl
Radicals from Time-Resolved Electron-Photoinjection Experiments
1
Jos e´ Gonzalez, Philippe Hapiot, Valery Konovalov, and Jean-Michel Sav e´ ant*
Contribution from the Laboratoire d’Electrochimie Mol e´ culaire de l’UniVersit e´ Denis Diderot, Unit e´ Mixte
de Recherche UniVersit e´ sCNRS No 7591, 2 place Jussieu, 75251 Paris Cedex 05, France
ReceiVed May 26, 1998
Abstract: The 9-anthrylmethyl, diphenylmethyl, benzyl, and 4-methylbenzyl radicals are generated by reduction
of the corresponding chlorides with electrons photoinjected in laser pulse experiments. The “polarograms”
derived from the variation of the charge flowing through the electrode with the dc potential of the electrode
represent the reduction of these radicals to the corresponding anions. The meaning of the half-wave potentials
is investigated through their variations with the measurement time and with the addition of acids in the solution,
which accelerates the disappearance of the carbanion. Correcting the kinetic data for the effect of radical
dimerization, the reduction kinetics appear to be mostly under the control of the follow-up reaction of the
carbanion with acids present in the medium, although the effect of charge-transfer kinetics begins to interfere
at the lower end of the time window. The results are compared with earlier data obtained by other techniques.
The changes in reactivity observed in the series are discussed with the help of density functional quantum
chemical calculations.
The redox properties of free radicals are essential parameters
for predicting whether electron transfer to molecules may trigger
a radical or an ionic chemistry. If these redox properties can
Direct reductive cyclic voltammetry may be used to inves-
•
tigate the reduction characteristics of transient free radicals, R ,
2
generated in situ by reduction of a cleaving RX molecule,2
be converted into standard potentials, they may then be used to
estimate other thermodynamic parameters, such as pKas and
bond dissociation free energies.3 Several direct or indirect
electrochemical methods have been proposed for investigating
the reduction characteristics of free radicals. However, none
of them provides the reduction standard potential in a straight-
forward manner.
-
•
-
RX + e (electrode) f R + X
in one step or in two steps)
(
•
-
-
R + e (electrode) h R
The effects of second-order self-reactions of the radical (e.g.,
dimerization and H atom disproportionation) and of charge-
transfer kinetics on the radical wave have been fully analyzed.2
These treatments can be easily adapted to other reactions in
which the radical and/or the anion would be engaged. One
limitation of the method is that the leaving group, X, has to be
selected so that the reduction potential of RX, at which the
radical is generated, is less negative than the reduction potential
of the radical.
The simplest of these methods involves the recording of the
oxidation wave of the anion in steady-state or cyclic voltam-
,6
4
metry. One drawback of this method is that it is limited to
cases where the anion is sufficiently stable in the assay solution.
The waves thus obtained are rarely reversible because of the
instability of the radical (which often undergoes a rapid
dimerization). Their half-wave or peak potentials, therefore,
do not lead directly to the standard potential. Possibilities for
circumventing this difficulty have been discussed.5
An indirect electrochemical method, based on redox cataly-
sis, has also been applied to the determination of the reduction
7
(1) Present address: Center for Materials for Information Technology,
8
•-
potential of transient radicals. The reduced form, Q , of a
University of Alabama, P.O. Box 870209, Room 205 Bevill Building,
Tuscaloosa, AL 35487.
reversible redox couple, P/Q (Q•- is usually an aromatic anion
radical in a nonacidic solvent), serves as mediator of the
electrochemical reduction of the radical generating substrate,
•-
(
2) Andrieux, C. P.; Gallardo, I.; Sav e´ ant, J.-M. J. Am. Chem. Soc. 1989,
11, 1620.
3) (a) Bordwell, F. G.; Zhang, X.-M. Acc. Chem. Res. 1993, 26, 510.
b) Wayner, D. M.; Parker, V. D. Acc. Chem. Res. 1993, 26, 287.
4) (a) Kern, J. M.; Federlin, P. Tetrahedron 1978, 34, 661. (b) Bordwell,
1
(
(
(8) (a) Fuhlendorf, R.; Occhialini, D.; Pedersen, S. U.; Lund, H. Acta
Chem. Scand. 1989, 43, 803. (b) Lund, H.; Daasbjerg, K.; Occhialini, D.;
Pedersen, S. U. Russ. J. Electrochem. 1995, 31, 865. (c) Lund, H.; Daasbjerg,
K.; Lund, T.; Occhialini, D.; Pedersen, S. U. Acta Chem. Scand. 1997, 51,
135.
(
F. G.; Bausch, M. J. J. Am. Chem. Soc. 1986, 108, 1979. (c) Bordwell, F.
G.; Bausch, M. J. J. Am. Chem. Soc. 1986, 108, 1985.
(5) (a) Andrieux, C. P.; Hapiot, P.; Pinson, J.; Sav e´ ant, J.-M. J. Am.
Chem. Soc. 1993, 115, 7783. (b) Lund, T.; Pedersen, S. U. J. Electroanal.
Chem. 1993, 362, 109.
(9) (a) Nadjo, L.; Sav e´ ant, J.-M.; Su, K. B. J. Electroanal. Chem. 1985,
196, 23. (b) Pedersen, S. U. Acta Chem. Scand. A 1987, 41, 391.
(10) (a) Wayner, D. D. M.; Griller, D. J. Am. Chem. Soc. 1985, 107,
7764. (b) (a) Wayner, D. D. M.; McPhee, D. J.; Griller, D. J. Am. Chem.
Soc. 1988, 110, 132. (c) Griller, D.; Wayner, D. D. M. Pure Appl. Chem.
1989, 61, 754. (d) Nagaoka, T.; Griller, D.; Wayner, D. D. M. J. Phys.
Chem. 1991, 95, 6264. (e) Wayner, D. D. M.; Houmam, A. Acta Chem.
Scand. 1998, 52, 377.
(6) (a) Andrieux, C. P.; Grzeszczuk, M.; Sav e´ ant, J.-M. J. Am. Chem.
Soc. 1991, 113, 8811. (b) Andrieux, C. P.; Grzeszczuk, M.; Sav e´ ant, J.-M.
J. Electroanal. Chem. 1991, 318, 369.
(7) (a) Andrieux, C. P.; Sav e´ ant, J.-M. In Electrochemical Reactions in
InVestigation of Rates and Mechanisms of Reactions, Techniques of
Chemistry; Bernasconi, C. F., Ed.; Wiley: New York, 1986; Vol. VI/4E,
Part 2, pp 305-390. (b) Andrieux, C. P.; Hapiot, P.; Sav e´ ant, J.-M. Chem.
ReV. 1990, 90, 723.
(11) Smith, K. D.; Strohben, W. E.; Evans, D. H. J. Electroanal. Chem.
1990, 288, 111.
S0002-7863(98)01801-0 CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/17/1998

10172 J. Am. Chem. Soc., Vol. 120, No. 39, 1998
Gonzalez et al.
tion of the order of 10- mol/ cm ) has built up at the electrode
surface. The variation of the photoinduced charge flowing
through the electrode with the electrode dc potential allows the
construction of a polarogram of the radical which represents
its reduction into the corresponding carbanion. The half-wave
potential is a measure of the reducibility of the radical, but,
here again, the standard potential of the radical/anion couple
cannot be equated with the half-wave potential in most cases.
We have established elsewhere the theoretical expressions
that relate the half-wave potential and shape of the radical
polarograms to the thermodynamics and kinetics of the various
reactions in which the radical and the anion resulting from its
13
2
RX, according to Scheme 1.
Scheme 1
-
•-
P + e (electrode) h Q
•
-
•
-
RX + Q f R + X + P
(in one step or in two steps)
kET
•
•-
-
R + Q
8 R + P
kcoupling
•
•-
-
R + Q
8 RQ
Using, for example, linear scan voltammetry, the cathodic
peak current (normalized to its value in the absence of RX) is
a function of the ratio kET/kcoupling.9 kET can be varied using a
series of more and more reducing mediators so as to reach
eventually the bimolecular diffusion limit. kcoupling seems to be
about constant in series of aromatic anion radicals and lower
than the bimolecular diffusion limit. Plotting of the ratio kET/
13
reduction may be engaged. In the work reported below, we
have applied the ensuing mechanism diagnostic criteria and
reactivity determination procedures to the reduction of a series
of arylmethyl radicals. The 9-anthrylmethyl, diphenylmethyl,
benzyl, and 4-methylbenzyl radicals were generated by reduction
of the corresponding chlorides by electrons photoinjected in laser
pulse experiments. The variation of the half-wave potential with
the measurement time was the main source of mechanism and
reactivity information, and the shape of the polarograms was
used as an additional diagnostic criterion. Addition of acids
into the solution, insofar as it accelerates the disappearance of
the carbanion, provided further insight into the reaction mech-
anism. The results are compared with earlier data obtained by
other techniques, when available, and the reactivity parameters
are discussed with the help of density functional quantum
chemical calculations.
(kET + kcoupling) leads to a “polarogram” of the radical whose
half-wave potential provides the potential where kET ) kcoupling
and, therefore, the value of kET for this value of the potential,
provided kcoupling is known independently (the various assump-
tions under which the rate data are analyzed and the necessity
of an independent estimation of kcoupling limit the applicability
and accuracy of the method). The derivation of the standard
potential from the value of kET thus obtained requires the
application of an activation/driving force relationship (derived,
e.g., from Marcus theory) and an independent estimation of the
intrinsic barrier.
Results
Two photoelectrochemical methods have been proposed for
investigating the reduction characteristics of transient free
Most experiments were carried out at 20 °C in N,N′-
dimethylformamide (DMF) with Et4NClO4 as supporting elec-
trolyte. The working electrode was a gold disk. These
experimental conditions appear to be the most satisfactory in
terms of reproducibility. A few test experiments were, never-
theless, performed with n-Bu4NPF6 as electrolyte and acetonitrile
as solvent for comparing our results with earlier data obtained
by application of the photolytic and redox catalysis techniques.
The polarograms, i.e., the plots of the apparent fraction of
electron, n, consumed in the reduction of the radical versus the
dc electrode potential, E, were extracted from the raw charge
injection data as described in section 1 of ref 13.
10
radicals. In one of them, the radical is generated by photolysis
of a labile substrate with modulated light. The reduction current
of the radical at a minigrid electrode, whose potential can be
controlled independently, varies periodically with time at the
frequency of the modulated light and can be recorded at any
value of the phase lag between light and current. Finite
difference simulation of the in-phase and out-of-phase current
potential curves with a reaction scheme involving, besides
electron transfer at the electrode, dimerization of the radical
and follow-up reactions of the anion (or cation in the case of
an oxidation) has allowed the determination of the various rate
parameters and of the radical standard potential, at least in the
9-Anthrylmethyl. We start with the reduction of 9-anthryl-
methyl chloride, for which the determination of all the ther-
modynamic and kinetic parameters is the easiest. Figure 1a
and b shows typical polarograms recorded at each end of the
time window (7 and 500 µs, respectively). Figure 1c displays
the variation of the half-wave potential, E1/2, with the measure-
ment time, t, over the whole time window. The shape of this
curve, particularly the presence of an inflection in the middle
of the time window, is typical of the kinetic influence of the
electron-transfer step and of a relatively slow follow-up reaction
(see Figure 7 in ref 13), most probably a reaction of the anion
with acids present in the medium. One should also take into
account the dimerization of the radical, which is expected to
be a fast reaction. As discussed earlier, the effect of this reaction
is to diminish the slope of the E1/2 vs log t plot, more for longer
times than for short times (see Figure 19 in ref 13). This picture
is confirmed by the changes observed upon addition of an acid,
phenol, into the solution (Figure 1c). The result is a general
positive shift of the half-wave potential, which is larger at long
times than at short times, while the inflection progressively
case of the reduction (and oxidation) of the diphenylmethyl
radical in acetonitrile.1
0d
One may also produce the radical by
continuous irradiation and use fast electrochemical techniques,
such as normal and reverse pulse voltammetry at an ultrami-
croelectrode, to obtain the radical standard potential, at least in
favorable cases, such as the oxidation of the diphenylmethyl
1
1
radical and the reduction of the diphenylcyanomethyl radical.
One limitation of the method is the possible superposition of
large photocurrents arising from the photoinjection of electrons
from the electrode into the solution.12
The exploitation of the latter phenomenon is the basis of the
electron photoinjection method.12b The radical-generating
molecule is photostable at the wavelength selected to photoeject
the electrons from the electrode by means of a laser pulse. The
radical is produced by reduction of a rapidly or concertedly
cleaving substrate RX by the thermalized photoinjected elec-
trons. Thus, shortly after the end of the laser pulse, a thin layer
(of the order of 30-100 Å thick) of radicals (surface concentra-
(12) (a) Hapiot, P.; Sav e´ ant, J.-M., unpublished results. (b) Hapiot, P.;
Konovalov, V. V.; Sav e´ ant, J.-M. J. Am. Chem. Soc. 1995, 117, 1428 and
references therein.
(13) Gonzalez, J.; Hapiot, P.; Konovalov, V. V.; Sav e´ ant, J.-M.,
submitted.

Parameters of the Reduction of Arylmethyl Radicals
J. Am. Chem. Soc., Vol. 120, No. 39, 1998 10173
Table 1. Thermodynamic and Kinetic Parametersa
kPhOHe
kd (×10 E0 c (V
b
9
k0
d
(×10
8
kSf
λelec
g
2
M
-
1
-1
vs SCE) (×10 s-1) M
4
-1
s
-1) (cm s ) (eV)
-1
radical
s
)
9-anthrylmethyl
3
-1.018
-1.107
-1.215
1
30
5
4
2.0 0.782
4.5 0.702
0.7 0.925
diphenylmethyl
benzyl
2
8
2
2
kR/(1-R)D1/(1-R)
b
9
0
0
2
kd (×10
E +
E +
-
1
-1
2/(1-R)
M
s
)
k
(RT/2F) ln k (RT/RF) ln kS
S
benzylh
8
6
∞
-1.467
-1.320
10-
5
-1.175
4-methylbenzyl
a
At 20 °C, in DMF + 0.1 M Et
4
NClO
4
, unless otherwise stated.
b
c
Dimerization rate constant. Standard potential of the radical/anion
couple. Rate constant of the follow-up reaction with no acid added.
Bimolecular rate constant of the reaction of the anion with phenol.
d
e
f
Electron-transfer standard rate constant, R ) 0.5 unless otherwise
stated. g Reorganization free energy of the electrochemical electron
transfer, computed from k = Zelec exp(-Fλelec/4RT), with Zelec ) (RT/
S
/2
3 -1 h
2
+
πM)1 ) 4.6-, 4.7-, and 6.6 × 10 cm s , respectively. In acetonitrile
4 6
0.1 M n-Bu NPF , R ) 0.4.
Figure 1. Reduction of 9-anthrylmethyl chloride (1 mM) by laser pulse
photoinjected electrons in DMF + 0.1 M Et NClO . (a, b) Polarograms
4 4
of the 9-anthrylmethyl radical at 7 and 500 µs, respectively. (c)
Variation of the half-wave potential with the measurement time in the
absence (O) and presence of 0.25 (3), 0.5 (0), and 2 (4) mM phenol.
The potentials are in volts vs SCE. The full lines are simulated curves
(see text).
disappears. These observations are consistent with Scheme 2,
0
where E , R, and kS are the standard potential, transfer
coefficient, and standard rate constant of electron transfer,
respectively, and k ) k0 + kPhOH[PhOH].
Figure 2. Neutralization of the 9-anthrylmethyl carbanion with phenol.
Variation of the pseudo-first-order rate constant with the phenol
concentration.
Scheme 2
2
kd
2R•
experimental points is necessary. When the inflection has
disappeared, after addition of enough phenol, the fitting curves
can be derived from a single working curve (see Figures 16
R-R 7
E0
•
-
-
R + e yR, kSz R
0
and 18 in section 6 of ref 13). The resulting values of E , 2kd,
k0
kS, and k0 (the rate constant of the follow-up reaction in the
absence of phenol) are gathered in Table 1. Simulation of the
whole individual polarogram confirms the assignment of the
reaction mechanism. Two typical examples are shown in Figure
R-
98 products
kPhOH
-
-
R + PhOH
8 RH + PhO
1
a and b, corresponding to each end of the time window.
The variation of the rate constant of the follow-up reaction
The fact that the positive shift of E1/2 is larger at long times
than at short times, where it vanishes, results from the tendency
for the follow-up reaction to control the kinetics in the former
conditions, whereas the forward electron-transfer step becomes
rate-determining in the latter conditions. Since, as seen below,
the reduction potential of the radical is not far from its standard
potential, we may assume that R ) 0.5. Finite difference
simulation of the polarograms according to the procedure
depicted in section 6 and Appendix IV of ref 13, allows the
with the concentration of phenol is displayed in Figure 2. As
expected, the variation is linear:
k ) k + kphenol[PhOH]
0
The slope of this linear plot provides the rate constant of the
second-order reaction of the anion with phenol (Table 1).
Diphenylmethyl. In this case, too, the half-wave potential
shifts positively upon addition of phenol (Figure 3), suggesting
a similar reduction mechanism. There are, however, significant
differences between the E1/2 vs log t plots in the diphenylmethyl
and 9-anthrylmethyl cases. The inflection observed in the
absence of phenol is less apparent than that with the 9-anthryl-
methyl radical, indicating that the follow-up reaction is faster.
It is also remarkable that, in the presence of phenol, the slopes
of the E1/2 vs log t curves indicate that the reduction is controlled
almost completely by the follow-up reaction, with only a modest
kinetic interference of the electron-transfer step. This observa-
tion falls in line with the fact that the vertical distance between
0
fitting of the E1/2 vs log t plots with the values of E , k, kS, and
2
kd reported in Table 1. The adjustment of the value for 2kd
is, in fact, better performed with the highest concentration of
phenol after the inflection has disappeared. The inclusion of
the dimerization reaction in the reaction scheme according to
which the simulations are carried out requires the value of Γ°,
the amount of radical initially generated from the capture of
the solvated electrons by 9-anthrylmethyl chloride. Γ° was
-14
-2
found to be equal to 8.7 × 10 mol cm using the procedure
described in section 1 of ref 13. As long as the E1/2 vs log t
plot exhibits an inflection, a full finite difference fitting of the

10174 J. Am. Chem. Soc., Vol. 120, No. 39, 1998
Gonzalez et al.
Figure 3. Reduction of diphenylmethyl chloride (30 mM) by laser
pulse photoinjected electrons in DMF + 0.1 M Et NClO . (a, b)
Polarograms of the diphenylmethyl radical at 7 and 500 µs, respectively.
c) Variation of the half-wave potential with the measurement time in
the absence (O) and presence of 10 (4) and 20 (3) mM phenol. The
Figure 4. Reduction of benzyl chloride (10 mM) by laser pulse
photoinjected electrons in DMF + 0.1 M Et NClO . (a, b) Polarograms
4
4
4
4
of the benzyl radical at 7 and 500 µs, respectively. (c) Variation of the
half-wave potential with the measurement time in the absence (O) and
(
0
presence of 5 (3) mM phenol. The potentials are in volts vs SCE. Γ
) 10 mol cm . The full lines are simulated curves (see text).
0
-13
-2
-13
-2
potentials are in volts vs SCE. Γ ) 10 mol cm . The full lines are
simulated curves (see text).
was made in acetonitrile in the absence of phenol, which can
be explained within the same framework, since acetonitrile,
being easier to reduce than DMF, may well capture the solvated
electrons concurrently with benzyl chloride. The values of the
various thermodynamic and rate parameters derived from the
fitting of the experimental points shown in Figure 4 are listed
in Table 1. We also checked that the slopes of the individual
polarograms agree with the reaction mechanism and the values
of the various parameters (two illustrative examples are given
in Figure 4a and b).
the curves is almost constant from the left to the right end of
the time window, being only slightly smaller in the first case
than in the second. Since the follow-up reaction is faster than
that with the 9-anthrylmethyl radical and, at the same time, the
kinetic interference of the electron-transfer step is weak, we
expect the standard rate constant to be larger. This is, indeed,
what appears from the fitting of the E1/2 vs log t plots. The
0
resulting values of E , k0, kS, and 2kd are listed in Table 1. The
variation of k with the phenol concentration is again linear,
leading to the value of kphenol reported in Table 1. The shapes
of the polarograms again provide a satisfactory confirmation
of the reaction mechanism. There is, indeed, a good agreement
between the experimental and simulated polarograms, as il-
lustrated by the two examples, taken at each end of the time
window, which are represented in Figure 3a and b.
Although we currently carried out most experiments with Et4-
NClO as supporting electrolyte, we performed a test experiment
4
with n-Bu NPF for comparison with earlier data derived from
4
6
10
8
the photolytic and redox catalysis techniques. No significant
differences were found between the two electrolytes.
Acetonitrile, rather than DMF, was used in previous pho-
1
0
Benzyl. Typical polarograms and E1/2 vs log t plots are
shown in Figure 4. They exhibit the same general feature as
in the preceding cases. The right-hand side of the E1/2 vs log
t plot is, however, flatter, indicating that the dimerization of
the radical is faster. The inflection is much less apparent than
that with the 9-anthrylmethyl radical, indicating that the follow-
up reaction is faster. The fact that the E1/2 vs log t plot obtained
upon addition of phenol converges with the plot obtained
without phenol at the lower end of the time window indicates
that the electron-transfer step becomes rate-determining under
these conditions. In the presence of phenol, meaningful results
cannot be obtained at the upper end of the time window. This
is presumably due to the fact that some phenol is reduced by
the solvated electrons simultaneously with benzyl chloride. That
this phenomenon is not observed with anthrylmethyl and
diphenylmethyl chlorides, which are reduced at more positive
potentials than benzyl chloride (the cyclic voltammetric peak
potentials of the chlorides, on a gold disk electrode at 0.2 V/s,
are -1.38, -1.89, and -2.19 V vs SCE respectively), confirms
this interpretation. As seen further on, the same observation
tolytic studies. Acetonitrile gives rise to larger background
currents in EPI experiments because it is a better scavenger of
the photoinjected electrons. At the price of some limitation of
the time window toward its upper end, we carried out an
experiment in acetonitrile in order to unravel the intriguing
observation that the reduction potential of benzyl radical is
reported to be ca. 200 mV more negative than what we find in
DMF (Figure 4). Rather than benzyl chloride, we used the more
reducible benzyl bromide to improve the fraction of photoin-
jected electrons captured by the substrate rather than by the
solvent. Figure 5 shows our results. It appears that the
reduction potential is about 200 mV more negative in acetonitrile
than in DMF, thus reaching values that are in agreement with
the value found by the photolytic technique. Another differ-
ence with DMF is that electron transfer is the rate-determining
step over the whole available time window, thus masking the
effect of the follow-up reaction. This observation indicates that
the electron transfer is slower and/or the follow-up reaction faster
in acetonitrile than in DMF. Under these conditions, the
standard potential cannot be rigorously derived from the E1/2
1
0

Parameters of the Reduction of Arylmethyl Radicals
J. Am. Chem. Soc., Vol. 120, No. 39, 1998 10175
Figure 5. Reduction of benzyl bromide (30 mM) by laser pulse
Figure 6. Reduction of 4-methylbenzyl chloride (10 mM) by laser
pulse photoinjected electrons in DMF + 0.1 M Et NClO . Variation
photoinjected electrons in acetonitrile + 0.1 M n-Bu
of the half-wave potential with the measurement time. Γ ) 2.2 ×
mol cm
4 6
NNPF . Variation
4
4
0
of the half-wave potential with the measurement time in the absence
-
13
-2
0
-13
-2
1
0
.
(O) and presence of 5 (3) mM phenol. Γ ) 1.13 × 10 mol cm
.
place in the absence of phenol is not known. It seems likely to
involve Lewis and/or Br o¨ nsted acids present in the reaction
medium. A test experiment where the concentration of sup-
porting electrolyte was increased from 20 mM to 0.2 M did
not show any significant variation of the E1/2 vs log t plot, thus
ruling out the involvement of the Br o¨ nsted acid properties of
the tetraalkylammonium. We may, therefore, conclude that the
solvent itself is involved as a Lewis acid. Because acetonitrile
is more acidic than DMF, we expect the standard potential to
be more positive, the follow-up reaction to be faster, and the
standard rate constant of electron transfer to be smaller in
vs log t plot. What can be obtained is a reduction potential
combining the standard potential, the transfer coefficient, and
the standard rate constant. Fitting of the experimental points
with the appropriate working curve (Figure 15 and eq 143 in
ref 13), as shown in Figure 5, leads to the determination of 2kd,
0
R, and E + (RT/RF) ln kS (Table 1).
4
-Methylbenzyl. Figure 6 shows the E1/2 vs log t plots
obtained in the absence of and in the presence of phenol. In
the latter case, we observe the same inaccessibility of the long
measurement times as with benzyl chloride (4-methylbenzyl
chloride is even more difficult to reduce than benzyl chloride,
with a peak potential of -2.21 V vs SCE, on a gold disk
electrode at 0.2 V/s). The follow-up reaction is now so fast
that no trace of inflection can be detected in the E1/2 vs log t
plot. The slope of the plots and their small separation indicate
that electron transfer almost completely controls the reduction
reaction of the radical, in competition with dimerization. Thus,
the electron transfer is slower and/or the follow-up reaction faster
with the 4-methylbenzyl radical than with the benzyl radical.
Fitting of the experimental points, as shown in Figure 6, leads
1
4
acetonitrile than in DMF. The combination of the latter two
factors explains why electron transfer is the rate-determining
step in acetonitrile, whereas electron transfer and the follow-
up reaction jointly govern the kinetics in DMF.
If we compare our results with those of the redox catalysis
technique in DMF, it appears that the standard potential we find
for the benzyl radical, -1.215 V vs SCE, is significantly more
positive than the value derived from redox catalysis, -1.40 V
8
vs SCE, which is, itself, close to the photolytic half-wave
1
0
to the determination of 2kd, R, kR/(1-R)D1/(1-R)/kS
2/(1-R)
0
potential in acetonitrile. The significant differences in half-
wave potentials and kinetic control we have found between the
two solvents suggest that the standard potentials should also be
different. The redox catalysis data were analyzed in the
framework of Scheme 1, where the forward electron-transfer
step is irreversible, assuming a rather small value of the self-
exchange reorganization free energy, λse (0.433 eV). As shown
below, our results and the redox catalysis data may be reconciled
using a larger value of λse, which seems more likely in view of
, E +
0
(
RT/2F) ln k, and E + (RT/RF) ln kS (Table 1).
For each compound, the constants in Table 1 were derived
from the consistent analysis of all the E1/2 vs log t plots obtained
in the absence of and in the presence of phenol, with the same
values of the standard potential, transfer coefficient, and standard
rate constant of electron transfer. Repeated simulations then
showed that the uncertainty on rate constants is less than 50%
and is about (5 mV on the potentials.
the electrochemical kinetic data and of a quantum chemical
0
P/Q
estimate. With the mediator (E
) - 1.42 V vs SCE)
Discussion
corresponding to the redox catalysis “half-wave potential”, ke
Among the results gathered in Table 1, the values of the
radical dimerization rate constants are consistent with literature
data.1 Concerning the characteristics of the electron-transfer
9
-1 -1
)
kcoupling ) 10 M s . Our value of the standard potential
implies that the cross-exchange reorganization free energy λ is
equal to 0.94 eV, as results from the application of the following
equations.
0d
step, we may first compare our results to those previously
obtained by the photolytic technique in acetonitrile.1
0b-d
The
half-wave potentials we find in DMF for the benzyl radical are
0
P/Q
0 2
q
E
- E
λ
F∆Ge
q
λ
4
about 200 mV more positive than the half-wave potential found
∆G ) 1 +
, k ) Z exp -
e
(
)
e
(
)
in acetonitrile by the photolytic technique.10 However, the
RT
checking EPI experiment we carried out in acetonitrile gave
half-wave potentials that are in agreement with the latter value.
Thus, there is no real discrepancy between the two techniques.
In acetonitrile, the EPI experiments have shown that the rate-
determining step is the forward electron transfer (in competition
with radical dimerization), while, in DMF, there is a mixed
kinetic control involving both the electron transfer and the
follow-up reaction. The same should be true with the photolytic
technique. The exact nature of the follow-up reaction taking
q
where ∆Ge is the activation free energy of electron transfer,
1
1
-1 -1
and Z ) 6.6 × 10
M
s
is the bimolecular collision
frequency. Since λ ) (λse + λed)/2 , (λed are the self-exchange
reorganization free energies of the electron donor), λse may be
(14) (a) It has previously been observed that solvent reorganization is
larger in acetonitrile than in DMF in the reduction of stable organic
compounds1 and, more generally, that it increases with the acceptor number
4b
14c
of the solvent. (b) Sav e´ ant, J.-M.; Tessier, D. J. Electroanal. Chem. 1975,
65, 57.(c) Fawcett, W. R.; Jaworski, J. S. J. Phys. Chem. 1983, 87, 2972.

10176 J. Am. Chem. Soc., Vol. 120, No. 39, 1998
Gonzalez et al.
estimated as equal to 1.24 eV.15 As will be shown further on,
the latter value is close to what quantum chemical calculations
predict. This value of λse is significantly larger than the value
previously assumed.8 For the reasons given below, it is also
consistent with the kinetics of the electrochemical reduction of
the radical. The electrochemical reorganization free energy is
estimated as λelec ) 0.925 eV from the standard rate constant
of electron transfer, uncorrected for double-layer effects. From
previous data on the electrochemical reduction of a series of
aromatic molecules in DMF,1 it appears that the solvent
reorganization free energy derived from double-layer corrected
data falls between the predictions of Marcus’s model (where
Table 2. Quantum Chemical Estimationsa
diphenyl- anthryl-
radical
benzyl
methyl
methyl
0
solv
b
-
•
R
R
-2.43
-2.15
-2.10
solvation G
-0.08
-0.08
0.17
-0.13
-0.15
0.84
-0.13
-0.13
0.95
RH
-∆U
•
-
-
0
el
0
el
R + e h R
c
0
solv
2
.51
2.86
2.92
-
-
(∆U + ∆G
∆G
)
0 d
2.58
1.21
0.07
5b
λ
λ
0,elec
1.07
0.08
-0.86
1.05
0.05
-0.88
1
8
i,elec
-
0
R + PhOH h
RH + PhO-
c
-1.94
∆U
el
1
6a,b
0
0
image effects are taken into account)
and Hush’s model
-2.06
-2.01
-1.32
-1.32
-1.36
∆
U + ∆G
el
0 d
solv
(
where they are not).16c,d The latter model thus predicts that
∆G
the electrochemical and homogeneous self-exchange reorganiza-
tion free energies are the same. Starting from data that are
uncorrected for double-layer effects, λelec is found to be slightly
a
Energies in eV. b Solvation free energy. c Variation of the electronic
energy. d Includes the electronic, zero-point, and thermal energies and
the entropic term (at 20 °C).
smaller than Hush’s predictions, thus leading to λelec )
5c
0
.89λse.1 If we assume that the double-layer effect is about
the same at a mercury electrode where the aromatic molecule
data were gathered and at the gold electrode with which we
obtained the benzyl radical data, it follows that λse should be
-
1
of the order of 1.04 eV (24 kcal mol ), more than twice the
value used in the previous analysis of the redox catalysis data.
An additional confirmation of the above analysis stems from
the consideration of the role of the follow-up reaction in the
kinetics of the redox-catalyzed reaction, replacing the irreversible
electron-transfer step in Scheme 1 by the following two
reactions.
Figure 7. Correlation of the variation in electronic energy (a) and the
variation of the sum of the electronic energy and the solvation free
energy (b) with the experimental standard potential. Energies in
electronvolts, potential in volts vs SCE.
ke
k0
9
R + Q y z R + P, R-
•
•-
-
8 products
k-e
With a value of λse as small as 0.433 eV, the follow-up
reaction is expected to be the rate-determining step, whereas
with λse) 1.24 eV, the rate-determining step is the forward
electron transfer.17
functional approach as a compromise between accuracy and
calculation time. This approach is expected to provide more
reliable results than semiempirical and simple Hartree-Fock
techniques, especially with open-shell molecules, while it
remains tractable with the relatively large molecules we are
dealing with. The results thus obtained are summarized in Table
2.
Both the benzyl radical and the benzyl anion are planar, while
the diphenylmethyl and anthrylmethyl radicals and anions are
slightly distorted. The geometry, charge distribution, and energy
data for these species and the corresponding hydrocarbons are
given in the Supporting Information.
For the diphenylmethyl radical, the standard potential we find,
-1.107 V vs SCE, is much closer to the value derived from
redox catalysis experiments, -1.07 V vs SCE. The electro-
chemical electron transfer is very fast, corresponding to a small
electrochemical reorganization free energy, 0.7 eV. Rough
estimates of λse and λ are 0.8 and 0.7 eV, respectively, pointing
to a possible involvement of the follow-up reaction in the
kinetics of the redox catalytic reduction besides the electron-
0
P
transfer step (k C /k0 is of the order of 2).
-e
In agreement with experiments and intuition, the calculations
indicate that the standard potential shifts positively from the
benzyl to the diphenylmethyl and anthrylmethyl radicals. Figure
To help chemical intuition in interpreting the thermodynamic
and kinetic data summarized in Table 1, we performed a series
of quantum mechanical calculations. We selected a density
7
a shows the correlation between the experimental standard
0
1
5b
potential and the variation of the electronic energy, -∆U ,
(
15) (a) Taking λed ) 0.64 eV. (b) Kojima, H.; Bard, A. J. J. Am.
el
Chem. Soc. 1975, 97, 6317. (c) Andrieux, C. P.; Sav e´ ant, J.-M.; Tardy, C.
J. Am. Chem. Soc. 1998, 120, 4167.
from the anion to the radical. The variations of the two
quantities are parallel, but the variation of the electronic energy
term is much more rapid than the variation of the experimental
(
16) (a) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (b) Marcus, R. A.
J. Chem. Phys. 1956, 24, 979. (c) Hush, N. S. J. Chem. Phys. 1958, 28,
62. (d) Hush, N. S. Trans Faraday Soc. 1961, 57, 557. (e) Marcus, R. A.
J. Chem. Phys. 1965, 43, 679.
17) The kinetic competition between electron transfer and follow-up
0
9
E (the slope is close to 4). In Figure 7b, the correlation takes
into account the solvation free energy upon passing from the
anion to the radical. This term was calculated according to the
(
0
P
0
P
reaction is a function of the dimensionless parameter k-eC /k , where C is
0
the concentration of mediator. From the standard potential of the mediator
corresponding to the “half-wave” potential, -1.42 V vs SCE, and a value
of the standard potential of the radical equal to -1.40 V vs SCE
(
18) (a) λi is obtained from the difference in energy between the radical
at its equilibrium geometry and at the equilibrium geometry of the anion
and, conversely, from the difference in energy between the anion at its
equilibrium geometry and at the equilibrium geometry of the radical. For
homogeneous self-exchange reactions, λi is the sum of these two energies,
while it is the half-sum for electrochemical reactions. The two energies
thus obtained were found to be almost the same for all three radicals, 0.075
and 0.078 for benzyl, 0.075 and 0.084 for diphenylmethyl, 0.051 and 0.052
for anthrylmethyl. (b) Klimkans, A.; Larsson, S. Chem. Phys. 1994, 189,
25.
8
-1 -1
(
corresponding to λse) 0.433 eV), one obtains k-e ) 5 × 10 M
s
.
0
P
-3
0
P
With C ) 2 × 10 M, and k0 from Table 1, it is found that k C /k )
17b
-e
0
2
0 (.1), indicating that the follow-up reaction is the rate-determining step.
16
The standard potential of the radical is equal to -1.215 V vs SCE
5
-1 -1
(
k
corresponding to λse) 1.24 eV), k-e ) 3 × 10
M
s , and thus
0
C /k ) 0.01 (,1), indicating that the redox-catalyzed reduction is
-e
P
0
under the kinetic control of the forward electron transfer.

Parameters of the Reduction of Arylmethyl Radicals
J. Am. Chem. Soc., Vol. 120, No. 39, 1998 10177
charge isodensity method, optimization of the geometry being
performed in the gas phase.19 The variations are again parallel,
but, although improved, the slope of the correlation, 2, is still
well above 1. Possible causes of this overestimation of the
variation of the standard potential are as follows. It may result
from the optimization of the geometry being performed in the
gas-phase rather than in the solvent. Another reason may be
the neglect of the discreteness of the solvent. A third factor is
the stabilizing interaction of the anion with the cation of the
supporting electrolyte, which is expected to decrease with the
concentration of the negative charge, i.e., from the benzyl to
the diphenylmethyl and anthrylmethyl radicals.
Figure 8. Kinetics of electron transfer. Correlation between the
theoretical and experimental (see text) reorganization free energies (in
eV).
It is noteworthy that the diphenylmethyl data point stands
above the correlation lines (Figure 7), suggesting that the
diphenylmethyl anion is relatively less solvated (and interacts
relatively less with the countercation) that the two other anions.
A possible reason for this behavior is a lesser accessibility,
caused by steric hindrance, of the negative charge borne by the
benzylic carbon (see the molecular structures in the Supporting
Information).
Regarding electrochemical kinetics, the Marcus-Hush model16
divides the attending reorganization free energy into a solvent
reorganization term, λ0,elec, and an intramolecular reorganization
term, λi,elec. Estimation of λi,elec18 shows that it is much smaller
than λ0,elec (Table 2). The solvent reorganization free energy
Figure 9. Correlation between the theoretical (see text) and experi-
mental pK
a
s of the benzyl, diphenylmethyl, and anthrylmethyl anion,
of phenol (18.8) in DMF.
referenced to the pK
a
for the homogeneous self-exchange reaction, λ0,se may be
by the benzylic carbon in the diphenylmethyl anion as compared
to the two other radicals.
0
derived from -∆G by multiplication by (1/Dop - 1/DS)/(1
solv
-
1/DS), where Dop ) 2.04 is the optical dielectric constant,
We now discuss the kinetics of protonation of the benzyl,
diphenylmethyl, and anthrylmethyl anions. It is remarkable that
the protonation rate constants of the three anion are practically
2
0
and DS ) 36.7 is the static dielectric constant in DMF. In
Hush’s model, the reaction site is assumed to be far enough
from the electrode surface for the image force and double layer
effects to be neglected. It is thus expected that λelec ) λ0,se +
λi,elec, where λelec is directly derived from the raw kinetic data
with no correction of the double-layer effect. In Marcus’s
model, the reaction is assumed to take place when the reactant
is in close contact with the electrode surface. Thus, λelec )
λ0,se/2 + λi,elec, where λelec is derived from the kinetic data after
correction of the double-layer effect, which, in the case of the
formation of an anion from a neutral molecule, is expected to
increase the rate constant by ca. 1 order of magnitude and thus
to decrease λ0,elec by ca. 0.24 eV. As discussed earlier, data
pertaining to the reduction of an extended set of aromatic
molecules on mercury are close to the prediction of Hush’s
model, namely λelec ) 0.89λse. It thus seems natural to attempt,
in the present case, a correlation between the theoretical values
of λtheor ) λ0,se λi,elec and the experimental values of λelec, λexp,
derived from the raw kinetic data with no correction of the
double-layer effect. Figure 8 shows the correlation between
these two quantities. For the benzyl and anthrylmethyl radicals,
there is a good correlation corresponding to λelec ) 0.72λse,
which seems reasonable taking into account the uncertainty in
the estimation of double-layer effects on gold, as compared to
mercury, and the fact that the location of the reaction site for
the present radicals is not necessarily the same as for aromatic
molecules. In contrast, the reduction of the diphenylmethyl
radical is significantly faster than predicted theoretically. This
anomaly, which we have already observed with the standard
potentials, may be explained along the same lines, namely, a
lesser accessibility of the solvent to the negative charge borne
8
-1 -1
the same ((2-5) × 10 M s ), while being clearly below
10
-1 -1
the diffusion limit (10
M
s ). The pKas of the diphenyl-
methyl and anthrylmethyl anions have been measured in
dimethyl sulfoxide (DMSO) and found to be 32.25 and 31.1,
21a
21b
respectively, which translate into 32.5 and 31.4 in DMF.
For toluene, the value given previously in DMSO converts into
9 when the standard potential we have found in the present
work is introduced into the thermodynamic cycle. The pKa of
3
21b,d
phenol may be estimated as 18.8 in DMF.
Figure 9 shows
the correlation between the experimental and theoretical ∆pKas
(
pKa(hydrocarbon) - pKa(phenol)). The theoretical ∆pKas were
obtained from the variation of the electronic energy and of the
free energy of solvation (Table 2). The slope of the correlation
22
is significantly larger than 1 for the same reasons as already
given in the discussion of the electron-transfer thermodynamics.
It is noteworthy that the pKa of the diphenylmethyl anion
exhibits the same anomaly as the standard potential of the
diphenylmethyl radical/diphenylmethyl anion couple, although
the two quantities derive from independent measurements. The
0
pK is larger, and the E more negative, than expected from the
a
comparison with the two other anions because the diphenyl-
methyl anion is less accessible to solvation and interaction with
the countercation.
The driving forces for the protonation of the three anions by
phenol are very large, ranging from 12 to 20 in terms of pKa
(Figure 9). Despite this, the protonation rate constants are
(21) (a) Bordwell, F. G.; Cheng, J.-P.; Harrelson, J. A. J. Am. Chem.
Soc. 1988, 110, 1229. (b) According to pKa(DMF) ) 1.5 + 0.96
pKa(DMSO). 2 (c) Maran, F.; Celadon, D.; Severin, M. G.; Vianello, E.
J. Am. Chem. Soc. 1991, 113, 9320. (d) Bordwell, F. G. Acc. Chem. Res.
1c
(19) (a) Foresman, J. B.; Frisch, A. Exploring Chemistry with Electronic
1
988, 21, 456.
Structure Methods; Gaussian Inc.: Pittsburgh, PA, 1996. (b) Foresman, J.
B.; Keith, T. A.; Wiberg, K. B. Snoonian, J.; Frisch, M. J. J. Phys. Chem.
0
0
(
22) For the phenol-phenate couple, we found U
- U
-
)
-
el,PhO
el,PhO
0
0
0
0
0
-
G
15.62, (U + G )PhOH - (U + G )PhO- ) -13.16, and G
1
996, 100, 16098.
20) Marcus, Y. Ion SolVation; Wiley: New York, 1985.
el solv el solv PhOH
0
(
-
) -12.81 eV.
PhO

10178 J. Am. Chem. Soc., Vol. 120, No. 39, 1998
Gonzalez et al.
Table 3. Half-wave and Standard Potentials
a
E
1/2
radical
3 µs
1 ms
E0 a
9
-anthrylmethyl
-1.035
-1.115
-1.270
-1.005
-1.050
-1.220
-1.018
-1.107
-1.215
diphenylmethyl
benzyl
a
In volts vs SCE.
clearly below the diffusion limit. If the reaction is under
activation control, the values of the rate constant imply large
reorganization energies, 2.5, 2.0, and 1.8 eV for the benzyl,
diphenylmethyl, and anthrylmethyl anions, respectively, assum-
ing a Marcus-type quadratic activation-driving force relation-
ship. It is noteworthy that the reorganization energy increases
as the pKa increases, unlike what is generally found with carbon
2
3
acids bearing activating electron-withdrawing groups. One
may also envisage, as rate-determining step, the diffusion-
controlled formation of a precursor complex in which the anion
and the acid would adopt precisely defined relative positions.
Further insights into the problem should await the determination
of Br o¨ nsted plots over a reasonable range of pKas.
Although the components of the half-wave potential could
not be dissected in the case of the 4-methylbenzyl radical, the
EPI results indicate that the follow-up deactivation of the anion
is faster and the electron transfer slower than with the benzyl
radical. Both effects fall in line with the electron-donating
properties of the 4-methyl substituent.
Figure 10. Instrument for the electron photoinjection experiments. WE,
RE, CE, working, reference, counter electrodes, respectively; M,
semitransparent mirror; L, lens; F, filter.
series). Intuition is confirmed by density functional calculations.
Electron transfer to the radicals is relatively fast, but not as fast
as it is with aromatic hydrocarbons of similar conjugation. More
precisely, reorganization free energies for the electrochemical
reaction uncorrected from double-layer effects range from 0.7
to 0.9 eV. Analysis of earlier redox catalysis data and density
functional estimations agree and indicate homogeneous self-
exchange reorganization free energies ranging from 1.1 to 1.3
eV. Solvent reorganization is amply predominant (the intramo-
lecular reorganization free energy represents about 5% of the
total). The relatively large solvent reorganization free energy,
as compared to those of anion radicals, is caused by the presence
of a large fraction of the negative charge on the benzylic carbon,
even if a significant fraction is delocalized over the aromatic
ring (more in the case of diphenylmethyl and anthrylmethyl
anions that with the benzyl anion, which explains the corre-
sponding increase of the solvent reorganization free energy).
Protonation of the anions by phenol is highly exergonic (from
Conclusions
Application of the EPI technique has allowed the determi-
nation of the reduction mechanism of benzyl, diphenylmethyl,
and anthrylmethyl radicals in DMF and the dissection of the
half-wave potential into its various components. Besides
dimerization of the radical, the reduction is jointly controlled
by the kinetics of the electron-transfer step and of a follow-up
deactivation of the anion involving acids present or purposely
added. The determination of the standard potential and of the
rate constants of the electron transfer and follow-up reaction in
DMF is made possible by the fact that the latter step is not too
fast and the former not too slow. The situation is less favorable
in acetonitrile, where the follow-up reaction is faster and the
electron transfer slower. There is thus an increased tendency
for the reduction to be under the sole kinetic control of the
electron-transfer step, as is the case with the benzyl radical.
Under such conditions, the half-wave potential represents an
irreversible reduction potential from which the contribution of
the standard potential and the standard rate constant of electron
transfer cannot be separately extracted unless the attending
reorganization free energy could be independently estimated.
A similar situation is expected in DMF for slower reducing
radicals and more reactive anions (4-methylbenzyl radical is
one example).
12 to 20 pK units). It is remarkable that, despite this large
a
driving force, the protonation rate constant is 1.5 orders of
magnitude below the diffusion limit. It is also noteworthy that
the protonation rate constant does not vary significantly when
the driving force varies from 12 to 20 pK units.
a
As compared to the two other anions, diphenylmethyl anion
exhibits an anomalous behavior as far as the thermodynamics
and kinetics of electron transfer and also its basicity are
concerned, which can be explained by some steric hindrance
to solvation of its benzylic carbon position.
In DMF, the neglect of the kinetic factors in the estimation
of the standard potential of the benzyl, diphenylmethyl, and
anthrylmethyl radicals, simply equating its value with the value
of the half-wave potential, leads to an error which ranges from
negligible to ca. 60 mV (1 order of magnitude in terms of
equilibrium constants) according to the measurement time (Table
Experimental Section
Chemicals. The solvents, DMF (Fluka, puriss. 0.01% H
2
O) and
4
(Fluka,
acetonitrile (Merk-Uvasol) were used as received. Et NClO
4
purum), used as supporting electrolyte, was recrystallized from a 1-2
NPF (Fluka, purum) was re-
3).
ethyl acetate-ethanol mixture. n-Bu
4
6
The standard potential of the radicals varies in the order
benzyl < diphenylmethyl < anthrylmethyl, as expected intu-
itively (the π orbital of the radical gets lower and lower in the
crystallized from a water-ethanol mixture. Phenol and benzyl chloride
were purchased from Fluka and diphenylmethyl, 4-methylbenzyl, and
9
-anthrylmethyl chlorides from Aldrich. They were used as received.
Instrumentation and Procedures for Electron Photoinjection
(23) Bernasconi, C. F. AdV. Phys. Org. Chem. 1992, 27, 119.
Experiments. The instrument (Figure 10) includes three elements: an

Parameters of the Reduction of Arylmethyl Radicals
J. Am. Chem. Soc., Vol. 120, No. 39, 1998 10179
electrochemical cell equipped with three electrodes, a excimer laser
delivering a short light pulse onto the working electrode, and an
electronic setup which imposes the dc potential of the working electrode
and allows the recording and integration of the transient photopotential.
The whole system is triggered and controlled by a personal computer.
The working electrode is a 0.5-mm-diameter gold disk, frequently
polished with diamond pastes, rinsed with acetone, and ultrasonicated
in methylene chloride. The counter electrode is a platinum wire. The
reference electrode is an aqueous saturated calomel electrode. Its
potential is checked against the ferrocene-ferrocenium couple at the
end of each experiment. All potentials given in the text are thus referred
the same aqueous SCE. The cell is equipped with a double jacket,
allowing it to be thermostated (the temperature was fixed at 20 °C
throughout the present study). The bottom of the cell is a quartz
window allowing the passage of the light beam, and the tip of the
working electrode is positioned 1 mm above the window.
Γ° is the amount of solvated electrons per unit surface area that will
-
13
2
be eventually captured (0.9 × 10 mol/ cm in the present case), k
d
10
-1
() 2 × 10 M s ) is the diffusion-limited rate constant, and D
e
()15
-
5
2
-1
× 10 cm s ) is the diffusion coefficient of the solvated electrons.
It is thus seen that the carbanions formed in this way during the capture
process are less than 3% of the radicals formed and have, therefore,
no detectable influence on the polarograms and on their variations with
time.
Theoretical Modeling. The calculations were performed using the
PC-Spartan software 1.1 (Wavefunction Inc., Irvine, CA) and the
Gaussian 9424 package for HF calculations and Gaussian 94 package
for density functional and solvation calculations. Gas-phase geometries
and electronic energies were calculated by full optimization of the
25
conformations using the B3LYP density functional with the 6-31G*
basis set,26 starting from preliminary optimizations at the HF/6-31G*
level. Solvation free energies were calculated on the gas-phase
optimized conformations according to the SCRF (self-consistent reaction
field) method using the IPCM model19 and the B3LYP density
functional. In this method, the solvent is treated as a continuum of
uniform dielectric constant in which the solute is placed into a cavity
defined as an isodensity surface of the molecules. The free enthalpies
were obtained after appropriate frequency calculations in the case of
the benzyl radical and anion.
The laser was a Questek 2054 filled with a XeCl mixture (wavelength
3
08 nm, pulse duration 20-50 µs, pulse stability (5%). The laser
beam is directed toward the cell by semitransparent mirrors and focused
onto the surface of the electrode so as to covered a slightly larger area.
Filters are used to attenuate the beam when necessary so as to shine an
energy of ca. 100 µJ on the electrode surface.
A more detailed sketch of the potentiostat and photopotential
measuring device is given in Figure 2 of ref 12b. The sampling
resistance R was set equal to 100 kΩ in all experiments. The function
generator and the digital oscilloscope were Schlumberger 4431 and
Tektronix TDS 430A instruments, respectively.
S
Supporting Information Available: Drawings of the op-
timized geometries at the B3LYP/6-31G* level with the
corresponding Cartesian coordinates and the distance matrix,
followed by the total atomic charges or total spin densities for
open-shell calculations in the case of radicals, the values of
energies in hartrees, and S**2 showing the spin contamination
for the radicals, anions, and hydrocarbons of benzyl, diphenyl,
and 9-methylanthryl compounds (24 pages, print/PDF). See any
current masthead pages for ordering information and Web access
instructions.
The electrode dc potential is varied incrementally, each 5 mV, so
as to cover a potential range of (200 mV around the half-wave
potential. After each of a series of 5-10 laser shots, the photopotential
is sampled in the digital oscilloscope at 22 preselected times from 3
µs to 1 ms along a logarithmic incrementation. The resulting
photopotential/time curves are averaged, and the averaged curve is
transferred to the PC. The same cycle of operations is repeated at each
value of the dc potential, and the whole set of data, stored in the PC,
is treated so as to display one polarogram for each preselected time.
The substrate concentration was 10-30 mM, with the exception of
JA981801T
9
-anthrylmethyl chloride, where a concentration of only 1 mM was
(24) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
used in order to avoid significant absorption of light by the substrate.
Even with such a low concentration, the possible generation of the
carbanion from the reduction of the radical by solvated electrons remains
negligible for the following reasons. Since solvated electrons are potent
reductants, the reduction of the radical should proceed at a rate constant
close to the diffusion limit, as for their capture by the substrate. As
Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G.
A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski,
V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Revision E.1; Gaussian,
Inc.: Pittsburgh, PA, 1995.
13
shown elsewhere, the ratio of the average concentrations of carbanions
and radicals formed at the end of the capture process is given by the
(25) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
(26) Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 16, 217.
0
1/2
0
1/2
expression Γ (k
d
/D
e
[RX]) /{1 - exp(-Γ (k
d
/D
e
[RX]) )} - 1, where