Thermodynamic control in ion radical cleavages through out-of-cage diffusion of products. Dynamics of C-C fragmentation in cation radicals of tert-butylated NADH analogues and other ion radicals

Article abstract of DOI:10.1021/ja9542294

According to the nature of the alkyl group, cation radicals of NADH analogues alkylated para to the nitrogen atom (AHR), generated by direct or indirect electrochemical means, may undergo C-C fragmentation or deprotonation. The former reaction is dominant

Full text of DOI:10.1021/ja9542294

3938
J. Am. Chem. Soc. 1996, 118, 3938-3945
Thermodynamic Control in Ion Radical Cleavages through
Out-of-Cage Diffusion of Products. Dynamics of C-C
Fragmentation in Cation Radicals of tert-Butylated NADH
Analogues and Other Ion Radicals
Agne`s Anne, Sylvie Fraoua, Jacques Moiroux,* and Jean-Michel Save´ant*
Contribution from the Laboratoire d’Electrochimie Mole´culaire de l’UniVersite´ Denis Diderot
(Paris 7), 2 place Jussieu, 75251 Paris Cedex 05, France
ReceiVed December 18, 1995X
Abstract: According to the nature of the alkyl group, cation radicals of NADH analogues alkylated para to the
nitrogen atom (AHR), generated by direct or indirect electrochemical means, may undergo C-C fragmentation or
deprotonation. The former reaction is dominant with the tert-butyl substituent and the latter with methyl and phenyl
substituents. It is shown that the cleavage reaction produces AH+ and the tert-butyl radical which is then rapidly
oxidized to form the tert-butyl cation. Changing the A group allows a variation of the C-C fragmentation rate
constant (determined by cyclic voltammetry or redox catalysis) by ca. six orders of magnitude for a change of ca.
0.4 eV in the standard free energy of the reaction. The logarithm of the rate constant varies linearly with the standard
free energy of the reaction with a slope of 1/(60 meV) showing that fragmentation is kinetically controlled by the
diffusion of the two fragments out of the solvent cage rather than by activation. The kinetic data thus allow an easy
determination of the thermodynamics of the fragmentation. Analysis of previous rate data concerning an extended
series of bibenzylic cation and anion radicals shows that they follow the same behavior.
The chemistry of cation radicals often involves deprotonation
protonation (reaction 2) even in the presence of strong bases.14
and carbon-carbon fragmentation.1 However, relatively few
time-resolved studies have been reported for deprotonation2-11
and even fewer for carbon-carbon fragmentation.12,13
AHR•+ h AH+ + R•
AHR•+ + B h AR• + BH+
(1)
(2)
One goal of the work described below was to investigate the
dynamics of carbon-carbon fragmentation in cation radicals
of alkylated NADH analogues attempting to relate kinetic reac-
tivity to the thermodynamic driving force. It has been previ-
Conversely, with MAHCH3‚+, MAHPh‚+ (as well as with
‚+
their deuterated analogues),9d and with MAHC2H5 and
‚+ 10b
MAHCH2CO2C2H5
deprotonation (dedeuteration) always
‚+
appeared faster than C-C fragmentation. With MAHCH2-
Ph,‚+ 9d,10b MAHCHPh2‚+, MAHCH(CH3)2‚+, and MAHCH-
(CH3)CO2C2H5‚+ 10b both deprotonation and C-C fragmentation
were observed, while with MAHC(CH3)3‚+, the latter reaction
predominated.15
ously shown that BNAHC(CH3)3 (see Chart 1) undergoes
expulsion of the tert-butyl radical (reaction 1) rather than de-
X Abstract published in AdVance ACS Abstracts, April 1, 1996.
(1) (a) For a recent review, see: ref 1b. (b) Albini, A.; Mella, M.;
Freccero, M. Tetrahedron 1994, 50, 575.
(2) (a) Schlesener, C. J.; Amatore, C.; Kochi, J. K. J. Am. Chem. Soc.
1984, 106, 7472. (b) Schlesener, C. J.; Amatore, C.; Kochi, J. K. J. Phys.
Chem. 1986, 90, 3747. (c) Masnovi, J. M.; Sankararaman, S.; Kochi, J. K.
J. Am. Chem. Soc. 1989, 111, 2263.
(3) Bacciochi, E.; Del Giacco, T.; Elisei, F. J. Am. Chem. Soc. 1993,
115, 12290.
(4) Dinnocenzo, J. P.; Banach, T. E. J. Am. Chem. Soc. 1989, 111, 8646.
(5) (a) Xu, W.; Mariano, P. S. J. Am. Chem. Soc. 1991, 113, 1431. (b)
Xu, W.; Zhang, X.; Mariano, P. S. J. Am. Chem. Soc. 1991, 113, 8863. (c)
Zhang, X.; Yeh, S. R.; Hong, S.; Freccero, M.; Albini, A.; Mariano, P. S.
J. Am. Chem. Soc. 1994, 116, 4211.
(6) (a) Reitsto¨en, B.; Parker, V. D. J. Am. Chem. Soc. 1990, 112, 4968.
(b) Parker, V. D.; Chao, Y.; Reitsto¨en, B. J. Am. Chem. Soc. 1991, 113,
2336. (c) Parker, V. D.; Tilset, M. J. Am. Chem. Soc. 1991, 113, 8778.
(7) (a) Ci, X.; Kellett, M. A.; Whitten, D. G. J. Am. Chem. Soc. 1991,
113, 3893. (b) Leon, J. W.; Whitten, D. G. J. Am. Chem. Soc. 1993, 115,
8038.
In the present work, we took as illustrative examples the four
tert-butyl derivatives shown in Chart 1 to investigate the
dynamics of C-C fragmentation in cation radicals.
Results
C-C Fragmentation vs Deprotonation. Cyclic voltam-
‚+
metric and preparative-scale evidence that BNAHC(CH3)3
undergoes C-C fragmentation rather than deprotonation has
been provided in a previous publication.14a Figure 1 shows the
cyclic voltammograms of BQAHC(CH3)3, BQCNHC(CH3)3, and
MAHC(CH3)3 at low scan rate where the oxidation wave is
irreversible. In all three cases, a one-electron irreversible peak
(8) For deprotonation of cation radicals of NADH analogues see refs.
9-11.
(13) (a) Maslak, P.; Asel, S. L. J. Am. Chem. Soc. 1988, 110, 8260. (b)
Maslak, P.; Chapman, W. H. J. Chem. Soc., Chem. Commun. 1989, 1810.
(c) Maslak, P.; Chapman, W. H. Tetrahedron 1990, 46, 2715. (d) Maslak,
P.; Narvaez, J. N. Angew. Chem., Int. Ed. Engl. 1990, 29, 283. (e) Maslak,
P.; Chapman, W. H. J. Org. Chem.. 1990, 55, 6334. (f) Maslak, P.;
Vallombroso, T. M.; Chapman, W. H.; Narvaez, J. N. Angew. Chem., Int.
Ed. Engl. 1994, 33, 73.
(14) (a) Anne, A.; Moiroux, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1993,
115, 10224. (b) This observation was then used as a probe in the discussion
of the mechanism of hydride transfer in NADH analogues.14a
(15) In ref 10b, R+ and AH‚ are viewed as the primary products of C-C
fragmentation of the cation radical. However, as discussed later on, there
is a considerable driving force advantage for the other mode of fragmentation
forming R‚ and AH+ (reaction 1).
(9) (a) Hapiot, P.; Moiroux, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1990,
112, 1337. (b) Anne, A.; Hapiot, P.; Moiroux, J.; Neta, P.; Save´ant, J.-M.
J. Phys. Chem.. 1991, 95, 2370. (c) Anne, A.; Hapiot, P.; Moiroux, J.; Neta,
P.; Save´ant, J.-M. J. Am. Chem. Soc. 1992, 114, 4694. (d) Anne, A.; Fraoua,
S.; Hapiot, P.; Moiroux, J.; Save´ant, J.-M. J. Am. Chem. Soc. 1995, 117,
7412.
(10) (a) Fukuzumi, S.; Kondo, Y.; Tanaka, T. J. Chem. Soc., Perkin
Trans. 2 1984, 673. (b) Fukuzumi, S.; Tokuda, Y.; Kitano, T.; Okamoto,
T.; Otera, J. J. Am. Chem. Soc. 1993, 115, 8960.
(11) Sinha, A.; Bruice, T. C. J. Am. Chem. Soc. 1984, 106, 7291.
(12) Sankararaman, S.; Perrier, S.; Kochi, J. K. J. Am. Chem. Soc. 1989,
111, 6448.
0002-7863/96/1518-3938$12.00/0 © 1996 American Chemical Society

Dynamics of C-C Fragmentation in Cation Radicals
J. Am. Chem. Soc., Vol. 118, No. 16, 1996 3939
Chart 1
is observed upon scan reversal which has exactly the same
location as the one-electron irreversible cathodic peak of pure
samples of BQAH+, BQCNH+, and MAH+, respectively.
These cathodic peaks cannot be confused with those of the
corresponding tert-butylated cations, since, as observed with
BNAC(CH3)3+, the latter are shifted by more than 200 mV in
the negative direction as compared to the AH+ cations. With
BQAHC(CH3)3 and BQCNHC(CH3)3 the same behavior was
found with other bases, having pKas ranging from 9.4 to 15.6,
with concentrations ranging from 10 to 40 mM, in unbuffered
or buffered conditions. In the case of BQAHC(CH3)3, the
formation of BQAH+ was confirmed by preparative-scale
electrolysis (1 mM substrate in acetonitrile + 0.1 M NEt4BF4
in the presence of 3,5-dimethylpyridine, pKa ) 14.7) using cyclic
voltammetric and HPLC identification.
With MAHC(CH3)3, the formation of MAH+ was observed
with bases having pKas ranging from 9.4 to 15.4, with con-
centrations ranging from 10 to 300 mM, in unbuffered or buf-
fered conditions. With bases of higher pKa, starting with 2,4,6-
trimethylpyridine (pKa ) 15.6), the cation radical of MAHC-
(CH3)3 still loses the tert-butyl group but also the methyl group
borne by the nitrogen, resulting in quantitative formation of
acridine
Figure 1. Cyclic voltammetry of AHC(CH3)3 and AH+ in acetonitrile
+ 0.1 M NEt4BF4.
A
BQA
BQCN
MA
[AHC(CH3)3] (mM)
[AH+] (mM)
1.4
0.2
1.0
0.22
1.7
0.22
as revealed by preparative-scale electrolysis. The same reaction
was also observed to occur with the same bases upon laser pulse
irradiation in the presence of CCl4 used as an oxidative quencher
for triggering the formation of the cation radical.9b The
mechanism of this double fragmentation reaction is not known
at present and shall be the object of further investigations.16
AHR‚+/AHR couple (Table 1) is much more positive than the
standard potential of the C(CH3)3+/C(CH3)3 couple. The
‚
+
C(CH3)3 cation thus produced then reacts rapidly with the
solvent and/or residual water (with BNAHC(CH3)3‚+, the main
product was indeed found to be tert-butyl alcohol14a). The
reaction mechanism thus consists in the following three suc-
cessive steps.
Mechanism and Kinetics of C-C Fragmentation. Two
modes of C-C fragmentation may be envisaged:
AHR•+ h AH+ + R•
(1)
AHR•+ h AH• + R+
(1′)
k1
\
AHR•+ y
z AH+ + R•
(1)
(2)
In terms of standard free energies, ∆G0(1) - ∆G(01′) ) EA0 H
+
‚
k2
/AH
R• + AHR•+ y
\
z R+ + AHR
- E0R ‚, reaction 1 has a strong advantage over reaction 1′,
+
/R
∆G0(1) - ∆G0(1′) (eV) ) -1.195 (A ) BNA), -0.810 (A )
k3
\
R+ + solvent and/or residual water y
z products (3)
BQA), -0.610 (A ) BQCN), -0.555 (A ) MA) as derived
from the previously determined values of EA0 H
and the
‚9c
+
/AH
oxidation potential of the tert-butyl radical, 0.09 V vs SCE.17
With MAHC(CH3)3‚+, C-C fragmentation is not too fast. The
standard potential of the MAHC(CH3)3‚+/MAHC(CH3)3 couple
could thus be derived from the cyclic voltammograms of
MAHC(CH3)3 at a classical 1 mm-diameter gold disk micro-
electrode where reversibility was reached above 20 V/s (Figure
2). Reversible cyclic voltammograms could also be obtained
with BQAHC(CH3)3 and BQCNHC(CH3)3 but only at a 17 µm-
Once R‚ is formed, it is immediately oxidized by a second
molecule of AHR‚+ since the standard potential of the
(16) We already know that demethylation does not occur after the
cleavage of the tert-butyl group has produced MAH+ since we have found
that pure samples of the latter compound are stable toward demethylation
in the presence of the bases used in the present study.

3940 J. Am. Chem. Soc., Vol. 118, No. 16, 1996
Anne et al.
Table 1. Standard free energies of reactions (1) and (2)
A
BNA
0.850
-0.760
1.184
0.129
BQA
1.000
-0.910
1.316
0.223
BQCN
1.210
MA
0.910
-0.820
1.587
0.496
0
a
E
‚+
AHC(CH3)3 /AHC(CH3)3
0
b
-1.120
1.380
∆G
∆G
∆G
‚+
C(CH3)3‚+AHC(CH3)3 fC(CH3)3++AHC(CH3)3
0
‚b
AH2 fAH++H
‚+
0
‚b
0.297
AHC(CH3)3 fAH++C(CH3)3
‚+
a In V vs SCE. b In eV.
Figure 3. Cyclic voltammetry of MAHC(CH3)3 (2 mM) in acetonitrile
+ 0.1 M NEt4BF4 in the presence of 99.4 mM of 3-methylpyridine
(pKa ) 13.5). Temperature 20 °C. Variation of the peak current with
the scan rate (from 2 to 80 V/s). The solid line is the theoretical variation
for log k1 (s-1) ) 1.9 (see text).
Figure 2. Cyclic voltammetry of MAHC(CH3)3 (2 mM) in acetonitrile
+ 0.1 M NEt4BF4 in the presence of 99.4 mM 3-methylpyridine (pKa
) 13.5). Temperature 20 °C.
acetonitrile19 ).
∆G0AH
)
fAH++H•
•+
2
diameter disk ultramicroelectrode18b where reversibility started
to appear at 100 000 and 20 000 V/s, respectively. With
BNAHC(CH3)3‚+, C-C fragmentation is too fast for reversibility
to be reached in the accessible range of scan rates. The standard
potential was therefore derived from redox catalysis experiments
as described further on. The standard potentials thus obtained
are listed in Table 1. The ensuing values of the standard free
energy of reaction 2 are all very negative justifying the
assumption that the reaction is totally irreversible and has a rate
constant equal to the diffusion limit (k2 ) kdif ) 7.9 109 M-1
s-1 9c).
RT ln 10
pKa, AH2•+ + E0
- E0H /H
+
•
AH+/AH•
F
∆G0
equation
was then computed from the following
AHR‚+fAH++R‚
∆G0AHR
) ∆G0AH
+ ∆G0R,f - ∆G0H,f
+
fAH++H•
•
•
fAH++R•
•+
•+
2
0,f
0,f
AHR
0
0
∆G - ∆G
+ E
- E
AH2•+/AH2 AHR•+/AHR
AH2
where the ∆G0,fs represent the free energies of formation of
the subscript species from the elements. ∆G - ∆G
A second thermodynamic factor is required for extracting
the values of the rate constant k1 from the experimental
data, namely, the standard free energy of reaction 1. They
were obtained as follows. The standard free energy
0,f
AH2
0,f
AHR
was
estimated by the Benson’s incremental method, regarding the
functional carbon as bound to two ethylenic carbons when A
) BNA, one ethylenic and one benzenic carbon when A ) BQA
and BQCN, and two benzenic carbons when A ) MA.20 The
free energies of formation of H‚ and of R‚ were obtained from
∆G0AH
for each A was first derived from the follow-
fAH++H
‚+
‚
2
ing equation, using previously determined values of the pKa
and of the standard potential of the AH+/AH‚ couple.9 For
ref 20. The ensuing values of ∆GA0 HC(CH )
are
fAH++C(CH3)3
‚+
‚
E0H ‚, we used the most recent estimate (-2.012 V vs SCE in
3
3
+
/H
listed in Table 1.
As seen from the cyclic voltammograms of MAHC(CH3)3
in Figure 2, reversibility increases upon raising the scan rate,
and, at the same time, the peak current passes from a value that
corresponds to an electron stoichiometry that is larger than 1
to a value corresponding to 1. These variations of the peak
current (ip) are recast in Figure 3, under the form of a ipV-1/2 vs
log V plot. It is seen that the best fitting with the theoretical
variation is obtained for log k1 (s-1) ) 1.9. The theoretical
ipV-1/2 vs log V plots where computed for a reaction scheme
including the electrode reaction below
(17) (a) Wayner, D. D. M.; McPhee, D. J.; Griller, D. J. Am. Chem.
Soc. 1988, 110, 132. (b) Most probably, the value of 0.09 V vs SCE is not
exactly that of the standard potential of the C(CH3)3+/C(CH3)3‚ redox couple
but rather an overall oxidation potential which is also a reflection of the
kinetics of the electrode electron transfer (standard rate constant, kS; transfer
coefficient, R) and of the follow-up reaction of C(CH3)3+ with the solvent
and/or residual water. The later reaction is presumably very fast, making
the electrode electron transfer the rate-determining step. Thus the steady-
state half-wave potential may be expressed as (δ, thickness of the diffu-
sion layer; D, diffusion coefficient): E1/2 ) E0 - (RT/RF) ln (kSδ/D).18a
Since R ≈ 0.5, δ ≈ 10-2 cm, and D ≈ 10-5 cm2 s-1, E0(V) ≈ 0.09 + 0.12
log[103kS(cm-1)]. Although not accurately known, kS should not be too
different from 10-3 cm s-1, taking into account solvent reorganization
‚
and the shortening of the C-C bonds from C(CH3)3 to C(CH3)3+. In
AHR - e- h AHR•+
such a case, E0 ≈ E1/2. Even if this estimate of kS is not very accurate,
driving force advantage of reaction 1 over reaction 1′ is undoubtedly
very large.
(18) (a) Andrieux, C. P.; Save´ant, J.-M. Electrochemical Reactions. In
InVestigations of Rates and Mechanisms of Reactions; Bernasconi, C. F.,
Ed.; Wiley: New York, 1986; Vol. 6, 4/E, Part 2, pp 305-390. (b)
Andrieux, C. P.; Hapiot, P.; Save´ant, J.-M. Chem. ReV. 1990, 90, 723.
and reactions 1-3 as depicted above. For the electrode reaction,
(19) (a) Parker, V. D. J. Am. Chem. Soc.1992, 114, 7458. (b) Parker, V.
D. J. Am. Chem. Soc. 1993, 115, 1201 (erratum).
(20) Benson, S. N. Thermodynamical Kinetics; Wiley: New York, 1976.

Dynamics of C-C Fragmentation in Cation Radicals
J. Am. Chem. Soc., Vol. 118, No. 16, 1996 3941
Figure 4. Cyclic voltammetry in acetonitrile + 0.1 M NEt4BF4 + 30
mM 3,5-dimethylpyridine (pKa ) 14.7) of acetylferrocene (4 mM) in
the absence (dotted line) and presence (solid line) of BQAHC(CH3)3
(2 mM). Scan rate: 0.05 V/s.
the following values were used: standard potential 0.910 V vs
SCE (Table 1), kS ) 0.1 cm s-1, R ) 0.5. For K1 we took the
value, 4.5 × 10-9 M-1 s-1, corresponding to the value of the
standard free energy given in Table 1. Because it has a very
large driving force (second row in Table 1), reaction 2 was
regarded as irreversible with a rate constant equal to the diffusion
limit, 7.9 × 109 M-1 s-1
.
These experiments and analyses were repeated with the
same base in the presence of an equimolar amount of the con-
jugated acid as well as with other bases, namely, 2chloro- and
3-fluoroprydine (pKa ) 6.3 and 9.4, respectively) in unbuffered
and buffered conditions at several concentrations ranging from
50 to 200 mM. Log k1 was found to be the same within
experimental error (log k1 ) 1.9 ( 0.1), thus confirming the
predominance of C-C fragmentation within this pH range.
Although reversibility could be reached in fast scan cyclic
voltammetry for BQAHC(CH3)3 and BQCNHC(CH3)3, allowing
the determination of the standard potentials, the current-poten-
tial responses did not prove of sufficient quality to safely
derive the value of the C-C fragmentation rate constants. We
therefore used the redox catalysis method instead. The princi-
ple of the method consists in oxidizing the substrate by the
oxidized form, Q, of a redox couple, P/Q, generated at the
electrode instead of direct oxidation by the electrode it-
self.18 In the present case, the catalysis reaction scheme is as
follows.
Figure 5. Cyclic voltammetry in acetonitrile + 0.1 M NEt4BF4 + 30
mM 3,5-dimethylpyridine (pKa ) 14.7) of acetylferrocene (Ec0at
)
0.638 V vs SCE) in the presence of BQAHC(CH3)3. Variation of the
normalized catalytic peak current with the dimensionless rate parameter
of reaction 1 (see text) and determination of k1 at various scan rates.
[acetylferrocene] ) 10 (a) and 4 (b) mM. [BQAHC(CH3)3] ) 5.13 (a)
and 2.04 (b) mM.
peak and a partial loss of reversibility. The value of the ratio
ip/i0 of the peak currents in the presence and absence of the
p
substrate provides kinetic information on the set of reactions
that follows the electrode P-Q reaction.18
Figure 5 illustrates the procedure we used for deriving the
rate constant k1 from the ip/i0 ratios obtained from cyclic
p
P - e- h Q
voltammograms such as those represented in Figure 4. For each
set of catalyst and substrate concentrations, the working curves,
represented by the solid lines in Figure 5, were computed
according to the reaction scheme above using the following
values of the various equilibrium and rate constants. The
standard free energy of reaction 0 is 0.362 eV. Therefore, k-0
can be taken as equal to the diffusion limit (7.9 × 109 M-1
Q + AHR yk0z P + AHR•+
(0)
(1)
k-0
AHR•+ yk1z AH+ + R•
k-1
s-1) and thus k0 ) 4.75 × 103 M-1 s-1. K1 ) 9.9 10-5
M
(from ∆GA0 HC(CH )
‚ in Table 1). Reactions 2 and 2′
kdif
R• + AHR•+ 8 R+ + AHR
(2)
fAH++(CH3)3
‚+
3
3
have very large driving forces (0.910 and 0.548 eV, respec-
tively). Their rate constants have thus been taken as equal to
the diffusion limit. Once the working curves have been
kdif
R• + Q 8 R+ + P
(2′)
calculated the experimental values of ip/i0 at each scan rate can
p
k3
R+ + solvent and/or residual water
98 products (3)
be used to determine the value of the dimensionless rate
parameter for reaction 1, and thus of k1, as shown by the arrows
in Figure 5. Over the whole set of scan rate and concentration
values, it was thus found that log k1 ) 5.62 ( 0.02. The same
experiments and data treatments were repeated with the same
base, at two other concentrations, 10 and 90 mM, and with three
Figure 4 shows a typical catalytic response obtained with
BQAHC(CH3)3 and acetylferrocene (E0 ) 0.638 V vs SCE) as
the catalyst. Starting from the reversible wave of the catalyst,
addition of the substrate triggers an enhancement of the anodic

3942 J. Am. Chem. Soc., Vol. 118, No. 16, 1996
Anne et al.
This is because the decay of the cation radical is relatively slow
and therefore reaction 0 acts as a pre-equilibrium in front of
the successive steps. In the case of BQAHC(CH3)3, there is a
slight but significant difference between the two working curves
in Figures 5a,b. This is due to the fact that, decay of the cation
radical being faster, there is mixed kinetic control by reaction
0 and the successive steps.
Application of the redox catalysis method to BNAHC(CH3)3
requires particular care because decay of the cation radical is
the fastest in the whole series and close to the upper limit of
applicability of the method. Also, unlike the two preceding
cases, the decay of the cation radical is too fast for
EA0 HC(CH )
to be derived from fast scan cyclic volta-
‚+
/AHC(CH3)3
3
3
mmetry. This parameter has thus to be determined within the
redox catalysis method itself. Table 2 summarizes the experi-
mental data obtained with two different catalysts, vinylferrocene
and 4-nitrophenylferrocene. The following set of values was
found to fit with all the experimental data as depicted in Table
2. EB0 NAHC(CH )
) 0.85 V vs SCE, k0 ) 322 M-1
‚+
/BNAHC(CH3)3
3
3
s-1, k-0 ) 7.9 × 109 M-1 s-1, K1 ) 0.01 M, k1 ) 4 × 107 s-1
,
k-1 ) 4 × 109 M-1 s-1, k2 ) k2′ ) 7.94 × 109 M-1 s-1. In the
conditions of experiment numbers 1 and 2, ip/i0 is rather
p
insensitive to the characteristics of reaction 1 because reaction
0 is then the rate-determining step. Their main interest is thus
that they allow the determination of EB0 NAHC(CH )
.
‚+
/BNAHC(CH3)
3
3
k1 and K1 were then derived from experiment number 3. In
this experiment, the catalytic current has a plateau shape (Figure
7) instead of a peak shape due to the presence of a large
concentration of substrate and to the fact that the cation radical
decay is fast. In this case, fitting of the experimental data was
carried out as depicted in Figure 7. Experiment number 4 served
to confirm the validity of the preceding determinations using
another catalyst (same parameter values as precedingly except
k0 ) 1.9 × 104 M-1 s-1).
Figure 6. Cyclic voltammetry in acetonitrile + 0.1 M NEt4BF4 + 30
mM 3-fluoropyridine (pKa ) 9.4) of diacetylferrocene (E0cat ) 0.870 V
vs SCE) in the presence of BQCNHC(CH3)3. Variation of the
normalized catalytic peak current with the dimensionless rate parameter
of reaction 1 (see text) and determination of k1 at various scan rates.
[diacetylferrocene] ) 3.16 (a) and 6.32 (b) mM. [BQCNHC(CH3)3] )
1.71 (a) and 3.42 (b) mM.
The decay rate constants of the various cation radicals are
summarized in Figure 8.
Discussion
We see in Figure 8 that there is a strong acceleration of C-C
fragmentation when going from A ) MA to BQCN, BQA, and
BNA (by ca. 6 orders of magnitude on total) as the thermody-
namics go from very uphill to moderately uphill. It appears
that the data points fall on a 1/(0.0582) V straight line
corresponding to the following equation
additional bases, 3-fluoropyridine (pKa ) 9.4), pyridine (pKa
) 12.3), 2,4,6-trimethylpyridine (pKa ) 15.6), at three concen-
trations, 10, 30, and 90 mM as well as with no base added.
Over the whole series of conditions it was found that log k1 )
5.6 ( 0.15.
With BQCNHC(CH3)3, diacetylferrocene (E0cat ) 0.870 V vs
SCE) was used as a catalyst. The decay of the cation radical is
slower than in the preceding case leading to a smaller catalytic
increase of the anodic peak. Figure 6 illustrates the determi-
log k1 ) log k′diff - (F/RT)∆G0
where k′dif is the diffusion limited rate constant multiplied by 1
M. In other words, the reverse (bimolecular) coupling reaction
is under diffusion control.
Although not always realized, the kinetics of a reaction that
is monomolecular in the forward direction and bimolecular in
the reverse direction, as is the present fragmentation of cation
radicals, may be governed by the diffusion of the two products
out of the solvent cage as depicted below.
nation of k1 from the ip/i0 data along the same procedure. The
p
standard free energy of reaction 0 is now 0.340 eV. Therefore,
k-0 can again be taken as equal to the diffusion limit (7.9 ×
109 M-1 s-1), leading to k0 ) 1.14 × 104 M-1 s-1. Since
∆GA0 HC(CH )
(Table 1), K1 ) 7.9 × 10-6 M.
fAH++C(CH3)3
‚+
‚
3
3
Reactions 2 and 2′ still have very large driving forces (1.120
and 0.780 eV, respectively). Therefore their rate constants can
be considered to be at the diffusion limit. From the data in
Figure 6 it is thus found that log k1 ) 4.50 ( 0.02. The same
experiments and data treatments were repeated with the same
base, at two other concentrations, 10 and 90 mM, and with two
additional bases, pyridine (pKa ) 12.3) and 2,4,6-trimethylpy-
ridine (pKa ) 15.6), at three concentrations, 10, 30, and 90 mM
as well as with no base added. Over the whole series of
conditions it was found that log k1 ) 4.5 ( 0.15. We note that
the two working curves in Figure 6a,b are practically the same.
ka+ct
k′dif
A y z (BC) y z B + C
ka-ct
kdif
Adaptation of the Debye-Schmoluchovski classical approach21
for reactions that are bimolecular in both directions to the present
case leads to the following equations.
k′difka+ct
k′dif + k′a-ct
k+ )
and

Dynamics of C-C Fragmentation in Cation Radicals
J. Am. Chem. Soc., Vol. 118, No. 16, 1996 3943
‚+
Table 2. Redox Catalytic Determination of the Decay Kinetics of BNAHC(CH3)3
expt no.
1a
catalyst
E0cat (V vs SCE)
[cat] (mM)
2
[substrate] (mM)
1.04
scan rate (V/s)
ip/i0 theor
ip/i0 exptl
p
p
vinylferrocene
0.420
0.1
0.2
0.1
0.2
0.1
0.2
0.85
1.65
1.16
1.083
1.39
1.22
3.08
2.41
1.64
1.45
1.15
1.083
1.37
1.23
3.04
2.39
1.64
1.40
2a
vinylferrocene
0.420
0.420
0.523
8
8
2
4.2
33
1
3a,c
4b
vinylferrocene
4-nitrophenylferrocene
a In acetonitrile + 0.1 M NEt4BF4 + 10 mM pyridine (pKa ) 12.3). b In acetonitrile + 0.1 M NEt4BF4 + 23 mM pyridine (pKa ) 12.3). c See
Figure 7.
kdifk′a-ct
k′dif + k′a-ct
k- )
where kdif is the bimolecular diffusion-limited rate constant and
k′dif is the first order rate constant obtained by multiplying kdif
by 1 M. k+ and ka+ct are monomolecular rate constants, while
k- and k-act are bimolecular rate constants. k′act is the first
order rate constant obtained by multiplying ka-ct by 1 M.
Thetwo equations above may equivalently be written as21f
kdifka+ct
kdif + ka-ct
k+ )
and
kdifka-ct
kdif + ka-ct
k- )
When the backward activation controlled reaction is faster than
the diffusion of the two fragments out of the solvent cage, the
overall rate constants becomes
k+(s-1) ) kdif(M-1 s-1)K(M) )
k′dif(s-1) exp[-(F/RT)∆G0] k- ) kdif (K ) (k+/k-))
Figure 7. Cyclic voltammetry in acetonitrile + 0.1 M NEt4BF4 + 10
mM pyridine of vinylferrocene in the presence of BNAHC(CH3)3.
Experiment number 3 (Table 2). Solid line: experimental curves,
dots: simulated curves (see text).
and where the first of these two equations corresponds to the
line on which the data points fall in Figure 8.
Figure 9 shows two examples of mixed activation-diffusion
control where activation has been assumed to follow a quadratic
law as defined by the following equations
(21) (a) von Smoluchowski, M. Phys. Z. 1916, 17, 557. (b) von
Smoluchowski, M. Phys. Z. 1916, 17, 585. (c) von Smoluchowski, M. Z.
Phys. Chem. 1917, 92, 129. (d) Debye, P. Trans. Electrochem. Soc. 1942,
82, 265. (e) Andrieux, C. P.; Save´ant, J.-M. J. Electroanal. Chem. 1986,
205, 43. (f) The Debye-Smoluchowski model of the interference of
2
∆G0
∆Gq+ ) ∆Gq0 1 +
q
(
)
4 ∆G0
with
diffusion control in bimolecular reaction kinetics
k+
A + C y
\
k z B + D
F∆Gq+
-
kT
h
ka+ct
)
exp -
treats the reactants as hard spheres and uses the Fick’s law to describe the
spherical diffusion of one of the reactant toward the other.21a-e It is
equivalent to considering the following kinetic scheme
(
)
RT
(∆Gq+, activation free energy; ∆G0, standard free energy of the
reaction; ∆Gq0, intrinsic barrier free energy). It is seen that
when the intrinsic barrier is small (∆Gq0 ) 0.2 eV) the
cleavage rate constant is controlled by the diffusion of the two
fragments out of the solvent cage over the whole endergonic
region as is the case with our cation radicals. The condition to
be fulfilled for the reverse reaction to be under diffusion control
is that its activation free energy is smaller than 0.18 eV.
Is there precedency to the kinetic behavior just described in
cleavage reactions of ion radicals? In this connection, it is worth
examining the kinetic data previously reported for C-C
+
k′act
k′dif
A + C ykdifz (AC) y z (BD) y z B + D
k′a-ct
k′dif
kdif
which also requires the introduction of pseudo-first order rate constants
(noted k′) to obtain the expression of the overall rate constants
act
k
difk′a+ct
k k
dif +
k+
)
)
)
k′dif + k′+act + k′a-ct kdif + ka+ct + k-act
and
act
k
difk′a-ct
k k
dif -
k-
)
k′dif + k′+act + k′a-ct kdif + ka+ct + k-act

3944 J. Am. Chem. Soc., Vol. 118, No. 16, 1996
Anne et al.
Figure 8. C-C fragmentation of AHC(CH3)3 cation radicals. Variation
of the rate constant with the standard free energy of the reaction. Straight
line: log k1 ) log k′dif - (F/RT)∆G0.
Figure 10. Cleavage rate constants of anion and cation radicals of
substituted bibenzyls. b, 1c-h; ], 2; 0, 3, 1, 4a-c; 9, 4d,e,5.
Solvents: Me2SO, CH3CN, CH2Cl2/MeOH, PrCN/EtBr, CH2Cl2, MeOH,
Et2O (4a-c).
from the lower viscosity of this solvent compared to the others.
In ref 13f, diffusion of the products out of the solvent cage was
not taken into account as a possible rate-limiting factor. The
reaction was assumed to be under activation control and the
variation of the rate constant with the driving force was fitted
with a quadratic relationship with a small intrinsic barrier free
energy. The experimental results contained in ref 13 are
described in more details in two publications that appeared after
submission of the present paper.22 Attempted correlations
between the cleavage activation free energies of the ion radicals
and of the parents should in fact be viewed as correlationsbe-
tween the standard free energies of the two reactions resulting
from the thermodynamic relationship
Figure 9. Example of Bro¨nsted plots combining the effect of diffusion
and of an activation obeying a quadratic law. Solid and dotted lines:
∆Gq0 ) 0.2 and 0.5 eV, respectively, kT/h ) 1013 s-1, kdif ) 1010 M-1
∆G0AR
)
fA-/++R•
•-/+
s-1, k′dif ) 1010 s-1
.
0
0
∆G
+/- E
/AR -/+ E0
A-/+/A•
ARfA•+R•
AR•-/+
fragmentation in a remarkably extended series of bibenzyl cation
and anion radicals bearing an electron-donating and an electron-
withdrawing group respectively:13f
This is also true for correlations with the strain energies and
for solvents effects which should mostly influence the two
standard potentials in the above equation.
Turning back to cation radicals of NADH analogues, it has
been observed that MAHCH3‚+ and MAHPh‚+ (as well as with
their deuterated analogues) undergo deprotonation (or dedeu-
teration) rather than C-C fragmentation over the whole range
of pH, unlike the tert-butyl derivatives.9d This behavior is
related to the very poor driving force of C-C fragmentation
for these two cation radicals. Estimation of ∆GA0 HR
‚+
‚
fAH++R
As seen in Figure 10, the data points corresponding to
endergonic reactions fall nicely on the straight-line representing
kinetic control by the diffusion of the two fragments out of the
solvent cage. The three points (solid triangles) which cor-
respond to ether as the solvent falls above the line as expected
along the same procedure as for the tert-butyl derivative leads
to 0.888 and 1.352 eV, respectively. C-C fragmentation rate
(22) (a) Maslak, P.; Narvaez, J. N.; Vallombroso, T. M. J. Am. Chem.
Soc. 1995, 117, 12373. (b) (a) Maslak, P.; Chapman, W. H.; Vallombroso,
T. M.; Watson, B. A. J. Am. Chem. Soc. 1995, 117, 12380.

Dynamics of C-C Fragmentation in Cation Radicals
J. Am. Chem. Soc., Vol. 118, No. 16, 1996 3945
constants are thus predicted to be 4.4 × 10-5 and 4.7 × 10-14
ether (80 mL). After washing with water (3 × 80 mL), the organic
solvent was removed under vacuum. The resulting residue was
subjected to column chromatography on Merck basic alumina (70-
230 mesh) eluted with 98-2 chloroform-methanol. The second eluted
yellow band, corresponding to the crude product, was collected and
subsequently purified by preparative HPLC on a Spherisorb ODS2 250
× 10.5 mm column (84-16 chloroform-methanol). Crystallization
from ethanol/water gave a pure sample of 120 mg (13% yield) of pale
s-1, obviously unable to compete with deprotonation.
Conclusions
Cation radicals of tert-butylated NADH analogues, produced
electrochemically or by reaction with homogeneous single
electron acceptors, undergo C-C fragmentation rather than
deprotonation. The reaction primarily yields AH+ and the tert-
butyl radical (and not AH‚ and the tert-butyl cation). The
1
yellow crystals: mp 187 ( 1 °C; H NMR (CDCl3) δ/ppm 7.65 (s,
1H), 7.42-7.02 (m, 8H), 6.88 (d, 1H, J ) 8.1 Hz), 5.95 (bs, 2H), 4.90
and 4.92 (two innermost peaks, AB q, 2H, JAB ) 16.7 Hz), 3.65 (s,
1H), 0.86 (s, 9H); UV-vis, λmax/nm (ꢀmax/M-1 cm-1) in acetonitrile,
314 (11 370). Anal. Calcd for C21H24N2O: C, 78.71; H, 7.55; N, 8.74.
Found: C, 78.81; H, 7.54; N, 8.72.
‚+
potential required to produce the AHC(CH3)3 cation radical
electrochemically is much more positive than the oxidation
potential of the tert-butyl radical. Likewise, the standard
potentials of the homogeneous single electron acceptors required
to readily oxidize AHC(CH3)3 are much more positive than the
oxidation potential of the tert-butyl radical. The tert-butyl
radical initially formed is thus immediately oxidized to the tert-
butyl cation which rapidly reacts with the solvent and/or residual
water. The cation radical cleavage reaction is fast although
endergonic in all four cases. Plotting of the fragmentation rate
constants against the standard reaction free energies reveals that
the reaction is kinetically controlled by the diffusion of the
fragments out of the solvent cage rather than by activation
parameters. This behavior implies that the intrinsic free energy
is small (less than 0.2 eV) showing that internal and solvent
reorganization energies are small. It is remarkable that the re-
examination of the kinetic data previously reported for C-C
fragmentation in an extended series of bibenzyl cation and anion
radicals bearing an electron-donating and an electron-withdraw-
ing group, respectively,13f indicates the same nature of the kinetic
control in the endergonic region. In all these cases, the gathering
of kinetic data does not provide insights on the nature and
magnitude of the activation parameters but rather leads to the
determination of the reaction thermodynamics. It is remarkable
in this connection that the standard reaction free energies thus
obtained agree so well with those derived indirectly by means
of thermochemical cycles (note in this respect that, in Figure
8, the horizontal errors bars correspond to 1 kcal/mol).
For the synthesis of MAHC(CH3)3, we obtained a much better yield
by addition of (CH3)3CMgCl to MAH+ than by photoreduction of
MAH+ in the presence of (CH3)3CCOOH as described in the literature.25
A 2 M solution of (CH3)3CMgCl (9 mL, i.e., 18 mmol) in ether was
added under argon to a stirred suspension of 10 mmol of MAH+ in 10
mL of ether in an ice bath. The reaction mixture was stirred at 25 °C
for ca. 20 min and then quenched with 40 mL of an aqueous 20%
NH4Cl solution. Filtration gave a precipitate which was extracted with
ether. The ether extracts were combined and washed with water, and
ether was evaporated under vacuum. MAHC(CH3)3 was isolated by
flash column chromatography using 15 µm, grade 60 Merck silica gel
(95-5 chloroform-hexane) and crystallization from ethanol/water, mp
112 °C ( 1. Characterization of the product (1H NMR, elemental
analysis) was consistent with that reported in ref 25.
All chemicals were obtained from Aldrich and were of the highest
purity available. They were used as received with the exception of
1,1′-diacetylferrocene which was recrystallized from a 40-60 dichlo-
romethane-hexane mixture.
Instruments and Procedures. They were the same as previously
described for cyclic voltammetry, redox catalysis, laser flash photolysis,
electrolysis and chromatography.9,14a
Controlled potential electrolyses of the various AHRs were carried
out in deareated acetonitrile + 0.1 M n-Bu4BF4 (20 mL) containing an
appropriate (see the Results section) concentration of base (50-200
mM). The working electrode was a platinum foil whose potential was
set 100 mV beyond the cyclic voltammetric anodic peak potential. The
AR+ and AH+ products were identified and quantified by comparison
of their cyclic voltammetric anodic peaks with those of authentic
samples. The conversion of the starting ARH was derived from the
decrease of its cyclic voltammetric anodic peak current. In the case
of MAHC(CH3)3, HPLC was also used to follow the course of
electrolysis. Aliquots (20 µL) of the electrolyzed solution were injected
into a reverse-phase Hypersil C18 ODS2 column. The mobile phases
were (A) 80-20 methanol-water + 10 mM Na2HPO4 and (B)
methanol. The gradient consisted of a 5 min isocratic step with 100%
A, followed by a 7 min isocratic step with 100% B, and a 5 min linear
Experimental Section
Chemicals. MAHCH2Ph,9d BNAHC(CH3)3,23 and BQCNHC-
(CH3)323 were prepared according to previously described procedures.
The new compound 1-benzyl-4-tert-butyl-3-carbamoyl-1,4-dihy-
droquinoline (BQAHC(CH3)3) was synthesized by addition of the
Grignard reagent, (CH3)3CMgCl, to the benzylquinolinium salt
BQAH+,Br-. The latter compound was prepared as described earlier.24
A 2 M solution of (CH3)3CMgCl (2.9 mL, i.e., 5.8 mmol) in diethyl
ether was added dropwise to a stirred suspension of BQAH+,Br- (1 g,
2.9 mmol) in 5 mL of dry tetrahydrofuran containing cuprous iodide
(25 mg, 0.12 mmol) plus methyl sulfide (0.6 mL, 9 mmol) and
maintained at 0 °C under argon. After 1 h, the mixture was stirred at
25 °C for another hour. Quenching of the mixture with 5% aqueous
sodium hydrogenocarbonate (30 mL) precipitated salts and left a
solution which was separated by decantation and extracted with diethyl
step to initial conditions. The flow rate was 1.0 mL min-1
. The
chromatrographic peaks were identified by UV at 290 and/or 342 nm
by comparison with authentic samples. Quantitation of acridine (tr )
5.4 min), MAH+ (tr ) 6.4 min) and unreacted MAHC(CH3)3 (tr ) 14.9
min) was derived from integrated peak vs concentration calibration
curves. HPLC was also used to analyze solutions of MAHC(CH3)3
(0.16 mM) + CCl4 (0.1%) after irradiation of 1 mL solution with a 95
mJ laser pulse at 308 nm.
(23) Anne, A. Heterocycles 1992, 34, 2331.
(24) (a) Shinkai, S.; Hamada, H.; Kusano, Y.; Manabe, O. J. Chem. Soc.
Perkin Trans. 2 1979, 699. (b) Anne, A.; Moiroux, J. J. Org. Chem. 1990,
55, 4608.
JA9542294
(25) Fukuzumi, S.; Kitano, T.; Tanaka, T. Chem. Lett. 1989, 1231.