The role of homolytic bond dissociation energy in the deprotonation of cation radicals. Examples in the NADH analogues series

Article abstract of DOI:10.1021/ja973725k

The deprotonation of the cation radical of 9-cyanomethylacridane by a series of normal bases is investigated and its pK(a) and homolytic bond dissociation energy determined experimentally. The latter parameter has the largest value in the NADH analogue series, thanks to the strong destabilization of the corresponding cation by the cyano group. It thus allows a significant extension of the attempted correlation between the intrinsic barriers and homolytic bond dissociation energies (D). Aside from members of the series where bulky substituents cause a decelerating steric effect, the correlation is close to a proportionality to D/4. The same correlation applies for all the other cation radicals where the rate constants of deprotonation by normal bases are available. The respective contributions of the homolytic and ionic states in the dissociation of the two types of acid, cation radicals and the conjugate acid of the normal base, are such that a simple model can be developed which regards the deprotonation reaction as a concerted H atom/one-electron transfer. It explains why, for each cation radical, the deprotonation by normal bases gives rise to a single Bronsted plot and why the intrinsic barriers are proportional to D/4. In the NADH analogue series, the deviations from proportionality observed with bulky substituents, and to a lesser extent, upon changing the extent of charge delocalization over the cation radical molecule are accounted for by product and reactant work terms, respectively.

Full text of DOI:10.1021/ja973725k

J. Am. Chem. Soc. 1998, 120, 2951-2958
2951
The Role of Homolytic Bond Dissociation Energy in the
Deprotonation of Cation Radicals. Examples in the NADH
Analogues Series
Agn e` s Anne, Sylvie Fraoua, Val e´ rie Grass, Jacques Moiroux,* and Jean-Michel Sav e´ ant*
Contribution from the Laboratoire d’Electrochimie Mol e´ culaire de l’UniVersit e´ Denis Diderot,
Unit e´ Associ e´ e au CNRS No 438, 2 place Jussieu, 75251 Paris Cedex 05, France
ReceiVed October 27, 1997
Abstract: The deprotonation of the cation radical of 9-cyanomethylacridane by a series of normal bases is
investigated and its pKa and homolytic bond dissociation energy determined experimentally. The latter parameter
has the largest value in the NADH analogue series, thanks to the strong destabilization of the corresponding
cation by the cyano group. It thus allows a significant extension of the attempted correlation between the
intrinsic barriers and homolytic bond dissociation energies (D). Aside from members of the series where
bulky substituents cause a decelerating steric effect, the correlation is close to a proportionality to D/4. The
same correlation applies for all the other cation radicals where the rate constants of deprotonation by normal
bases are available. The respective contributions of the homolytic and ionic states in the dissociation of the
two types of acid, cation radicals and the conjugate acid of the normal base, are such that a simple model can
be developed which regards the deprotonation reaction as a concerted H atom/one-electron transfer. It explains
why, for each cation radical, the deprotonation by normal bases gives rise to a single Br o¨ nsted plot and why
the intrinsic barriers are proportional to D/4. In the NADH analogue series, the deviations from proportionality
observed with bulky substituents, and to a lesser extent, upon changing the extent of charge delocalization
over the cation radical molecule are accounted for by product and reactant work terms, respectively.
Deprotonation of hydrocarbons requires some form of activa-
tion of the carbon atom for the reaction to be amenable to
thermodynamic and kinetic characterization. There are two
main ways for decreasing the pKa of carbon-hydrogen bonds.
One involves the decrease of the electron density on the carbon
atom by means of an electron withdrawing group directly borne
by the carbon or located in a conjugated position to it on an
unsaturated substituent.1 The other consists of oxidizing the
substrate so as to produce the corresponding cation radical. The
resulting decrease in electron density induces a considerable
Scheme 1
the cation obtained after deprotonation of the cation radical and
further electron abstraction (Scheme 1) is stable. The rates of
deprotonation can thus be unambiguously determined in the
framework of the mechanism depicted in Scheme 1. Combining
the use of direct electrochemistry, redox catalysis, and laser flash
photolysis, they could be determined up to the diffusion limit,
-3
4
,5
decrease in the pKa as compared to the parent molecule. The
kinetics of the deprotonation of several families of cation
6
-14
radicals have been measured.
Among them the NADH
(
7) (a) Bacciochi, E.; Del Giacco, T.; Elisei, F. J. Am. Chem. Soc. 1993,
analogues series offers two advantageous features.14 One is that
1
15, 12290. (b) Bacciochi, E.; Bietti, M.; Putignani, L.; Steenken, S. J.
Am. Chem. Soc. 1996, 118, 5952.
(
1) (a) Bell, R. P.; Goodall, D. M. Proc. R. Soc. London, Ser. A 1966,
(8) (a) Dinnocenzo, J. P.; Banach, T. E. J. Am. Chem. Soc. 1989, 111,
8646. (b) Dinnocenzo, J. P.; Karki, S. B.; Jones, J. P. J. Am. Chem. Soc.
1993, 115, 7111.
2
94, 273. (b) Bordwell, F. G.; Boyle, W. J. J. Am. Chem. Soc. 1972, 94,
907. (c) Albery, W. J.; Campbell-Crawford, A. N.; Curran, J. S. J. Chem.
3
Soc., Perkin Trans. 1972, 2206.
2) (a) Bernasconi, C. F. Tetrahedron 1985, 41, 3219. (b) Bernasconi,
C. F. Acc. Chem. Res. 1987, 20, 301. (c) Bernasconi, C. F. AdV. Phys. Org.
Chem. 1992, 27, 119.
(9) (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.
(10) (a) Reitst o¨ en, B.; Parker, V. D. J. Am. Chem. Soc. 1990, 112, 4698.
(b) Parker, V. D.; Chao, Y.; Reitst o¨ en, B. J. Am. Chem. Soc. 1991, 113,
2336. (c) Parker, V. D.; Tilset, M. J. Am. Chem. Soc. 1991, 113, 8778.
(11) (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.
(12) Sinha, A.; Bruice, T. C. J. Am. Chem. Soc. 1984, 106, 7291.
(13) (a) Tolbert, L. M.; Khanna, R. K. J. Am. Chem. Soc. 1987, 109,
3477. (b) Tolbert, L. M.; Khanna, R. K.; Popp, A. E.; Gelbaum, L.;
Bettomley, L. A. J. Am. Chem. Soc. 1990, 112, 2373.
(
(
3) Terrier, F.; Boubaker, T.; Xiao, L.; Farrell, P. G. J. Org. Chem. 1992,
7, 3924. (b) Moutiers, G.; El Fahid, B.; Goumont, R.; Chatrousse, A. P.;
Terrier, F. J. Org. Chem. 1996, 61, 1978.
4) (a) Nicholas, A.; Arnold, D. R. Can. J. Chem. 1982, 60, 2165. (b)
Nicholas, A.; Boyd, R. J.; Arnold, D. R. Can. J. Chem. 1982, 60, 3011.
5) (a) Bordwell, F. G.; Cheng, J. P. J. Am. Chem. Soc. 1989, 111, 1792.
b) Zhang, X.; Bordwell, F. G. J. Org. Chem. 1992, 57, 4163. (c) Zhang,
X.; Bordwell, F. G.; Bares, J. E.; Cheng, J. P. J. Org. Chem. 1993, 58,
5
(
(
(
3
051.
(14) (a) Hapiot, P. ; Moiroux, J.; Sav e´ ant, J.-M. J. Am. Chem. Soc. 1990,
112, 1337. (b) Anne, A.; Hapiot, P.; Moiroux, J.; Neta, P.; Sav e´ ant, J.-M.
J. Phys. Chem. 1991, 95, 2370. (c) Anne, A.; Hapiot, P.; Moiroux, J.; Neta,
P.; Sav e´ ant, J.-M. J. Am. Chem. Soc. 1992, 114, 4694. (d) Anne, A.; Fraoua,
S.; Hapiot, P.; Moiroux, J.; Sav e´ ant, J.-M. J. Am. Chem. Soc. 1995, 117,
7412.
(6) (a) Schlesener, C. J.; Amatore, C.; Kochi, J. K. J. Am. Chem. Soc.
1
984, 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. (d) Sankararaman, S.; Perrier, S.; Kochi,
J. K. J. Am. Chem. Soc. 1989, 111, 6448.
S0002-7863(97)03725-6 CCC: $15.00 © 1998 American Chemical Society
Published on Web 03/13/1998

2952 J. Am. Chem. Soc., Vol. 120, No. 12, 1998
Anne et al.
Scheme 2
Table 1. Thermodynamic Dataa
thus allowing the construction of extended Br o¨ nsted plots, which
is rarely the case for other cation radicals. Another advantage
of this series of cation radicals is that key thermodynamic
parameters, such as their pKa’s and homolytic bond dissociation
energies, can be derived from experimentally measurable
quantities through appropriate thermodynamic cycles.
b
compound
MAHCN
MAH
2
0
0
0
0
.985 ( 0.005
.010 ( 0.002
.370 ( 0.028 ((0.008)
0.860 ( 0.004
-0.465 ( 0.010
E
E
E
•+
AH/AH
0
A /A
0
AH/A ,pH)0
•
+
c
c
c
0.220 ( 0.024 ((0.004)
+
c
c
pKa AH
•+
-4.4 ( 1.1 ((0.4)
0.8 ( 1.1 (( 0.3)
1.800 ( 0.070 ((0.030)
3.125 ( 0.070 ((0.030)
d
c
c
Knowing the pKa’s, extrapolating the Br o¨ nsted plots to ∆pKa
D (eV)
2.115 ( 0.066 ((0.026)
•
e
3.09 ( 0.066 ((0.026)c
•
)
0 has allowed the determination of the intrinsic barrier free
D
AH/A +H
0
energies, i.e., the activation free energy for ∆G ) (RT/F)∆pKa
a
In acetonitrile. All potentials are referred to the aqueous saturated
q
∆
KCl saturated calomel electrode. From ref 14c. c The main part of
the uncertainty ((0.020 V on EMAHZ/MAZ+,pH)0, ( 0.7 on pKa MAHZ
b
)
0, ∆G
0
, of a series of NADH analogues cation radicals.
G )0
q
0
•
+
,
It was observed that a correlation exists between ∆G
0
+
and
∆
G )0
0
•+
•
the homolytic bond dissociation energy, D, (AH T A + H )
suggesting that proton abstraction from these cation radicals may
be viewed as a concerted H-atom/electron transfer rather than
a stricto sensu proton transfer.14
( 0.041 eV on D originates from the uncertainty on ENQH /NQ,pH)0 (see
text and refs 14a,c). The numbers between parentheses represent the
2
d
uncertainty for one NADH analogue relative to the others. Bond
dissociation energy of the cation radical. e Bond dissociation energy
of the parent substrate.
In order to further test the validity of that correlation we have
attempted to enlarge the range of variation of the cation radical
bond dissociation energy by introducing electron-withdrawing
or electron-donating substituents on the carbon bearing the
dissociating hydrogen. The cyano derivative appears to be a
good candidate to obtain a maximal value of D, since the cyano
group is expected to strongly destabilize the cation resulting
from the homolytic cleavage of the carbon-hydrogen bond. This
is indeed what we have found with the cation radical of the
the intrinsic barrier free energy correlates with the bond
dissociation energy. For the reasons given above, the NADH
analogues series will serve as the main experimental example
for a quantitative discussion. The results obtained with other
cations radical cations will also be discussed insofar sufficient
kinetic and thermodynamic data are available.
Concerning point (iii), it is found, in the NADH analogues
q
∆
series, that ∆G
0
varies approximately as D/4. However
G )0
9-cyano derivative of N-methylacridane, MAHCN. The deter-
small deviations from this relationship appear as a function of
the nature of the rings in the AH series depicted in Scheme 2.
More important deviations are observed in the MAHR (R )
Ph, Me, Bz) series (Scheme 2) pointing to the existence of some
sort of steric effect. These two effects will be discussed in the
framework of the proposed model.
mination of the deprotonation rate constant by a series of bases
and of the pertinent thermodynamic parameters is described in
the next section. We have also investigated the 9-methoxy
derivative. However, its deprotonation cannot be observed in
the accessible range of pH’s. Rather, it cleaves off the methoxy
group as well as the methyl group borne by the nitrogen. These
reactions will be described elsewhere.
Results
+
-
MAHCN was prepared by the reaction of MAH with CN
ions as depicted in the Experimental Section. The thermody-
namic and kinetic parameters were determined as follows.
Thermodynamic Characteristics. The data obtained for
MAHCN, following the procedures depicted below are sum-
marized and compared with the values obtained for MAH2 in
Table 1.
The determination of the pKa AH•+’s requires the determination
The second part of the paper is devoted to modeling the
dynamics of cation radical deprotonation based on the main
experimental characteristics of the reaction, namely, (i) the fact
that a single Br o¨ nsted plot is obtained when a cation radical is
opposed to a series of “normal” nitrogen or oxygen bases, (ii)
the fact that the intrinsic barrier is relatively large, large enough
for the deprotonation reaction to be under activation control in
most of the accessible pH range, and (iii) the observation that
0
0
of two one-electron standard potentials, E
and of a two-electron standard potential, E
•+ and E
•
+
,
A /A
AH/AH
0
+
, corre-
AH/A ,pH)0
sponding to the hydride transfer reaction
+
-
+
-
AH h A + 2e + H (H )
taken at pH ) 0:

Deprotonation of Cation Radicals
J. Am. Chem. Soc., Vol. 120, No. 12, 1998 2953
0
0
0
We thus found kf ) 1.0 ( 0.2 M-1 h-1 and kb ) 0.6 ( 0.1
pKaAH•+ ) (2E
+
- E
•+ + E
•
+
)/0.058 (1)
A /A
AH/A ,pH)0
AH/AH
-
1
-1
0
M
V
h . It follows that E
+
) 0.370 ( 0.028
MAHCN/MACN ,pH)0
1
8
0
a value of 0.750 ( 0.020 V.15a The
(
all measurements were carried out at 20 °C).
Determination of the One-Electron Redox Potentials. In
the absence of base, the reversible one-electron oxidation of
MAHCN can be observed by means of cyclic voltammetry
at ultramicroelectrodes at high potential scan rates V (V >
3 000 V/s for Z ) CN instead of V > 1000 V/s for Z ) H).
•+ is then obtained as the half-sum of anodic and
cathodic peak potentials.
using for E
NQH /NQ,pH)0
2
main uncertainty in this determination comes from the electro-
chemical determination of E
0
(0.02 over 0.028).
NQH /NQ,pH)0
2
The same is true for all the other NADH analogues, meaning
that, relative one to the other, the standard potentials are known
with a better precision than the absolute value of each of them.
1
E
0
AH/AH
Determination of the pK . Application of eq 1 then leads
a
to pKa MAHCN•+ ) -4.4 ( 1.1. The main uncertainty again arises
+
MACN gives rise to a reversible one-electron cyclic
0
0
from the E
+
through E
. This rep-
MAHCN/MACN ,pH)0
NQH /NQ,pH)0
2
voltammetric wave even at the lowest scan rate (0.1 V/s),
resents 0.7 unit over 1.1. As for the hydride transfer potential,
the pKa’s are known, relative one to the other, with a better
precision than the absolute value of each of them.
whereas with MAH+ a scan rate of at least 15 000 V/s is
•
required to overcome the dimerization of the MAH radical,
indicating that the dimerization of MACN is slow.
corresponding standard potential is again obtained as the half-
sum of anodic and cathodic peak potentials.
Determination of the Redox Potential for Hydride Trans-
•
15
The
Homolytic Bond Dissociation Energy of the Cation Radi-
cal (D). The homolytic bond dissociation free energy may be
obtained from the following thermochemical cycle
fer. A convenient method for obtaining the standard potential
0
0
0
0
of hydride transfer for an unknown couple, E
+
, is to
∆G •+
+
•
) E
•
+
+ 0.058 pKa,AH•+ - E
H /H
+
•
A1H/A1
AH /A +H
A /A
measure the rate constant of the following hydride transfer
reaction
0
) -2.012 V vs SCE.19 Thus,
) 1.77 ( 0.07 eV and the bond dis-
In acetonitrile, E
•
+
H /H
0
k12
∆G
sociation energy D ) ∆G
MAHCN /MACN +H•
•+
+
+
+
0
A1H + A2 y
\
z A1 + A2H
•
+
•
+ 0.348 ) 2.115 (
k21
MAHCN /MACN +H
+
0
.066 eV, assuming that the entropies of MACN and MAH-
CN are practically the same and taking the entropy of
formation of H as 27.4 eu.
0
•+
involving another NADH analogue couple for which E AH/A+
1
6
•
4a
is known. Then
The last entry of Table 1 gives the values of the bond
dissociation energy in the parent substrate, AH,
0
0
E
+
E
+
- 0.029 log K )
A1H/A1
)
A2H/A2
12
0
E
+
- 0.029 log(k /k )
A2H/A2
12 21
0
0
D
•
•
) E
•+ + D - E
A /A
+
•
AH/A +H
AH/AH
In practice, the time required for reaching the equilibrium is
much too long to avoid the interference of side reactions. The
only possibility is to derive K12 from the rate constants k12 and
k21. The equilibrium constant should not be too different from
unity in order for both rate constants to be measurable. The
very fact that MACN is destabilized by the presence of the
electron withdrawing cyano-group implies not only that D is
large but also that MAHCN is a poor hydride donor. Among
the NADH analogues whose E
The weakening of the bond dissociation energy from the
•
+
substrate, AH to the cation radical, AH results from the
+
•
aromatic character of A as opposed to A . The strengthening
effect of the cyano substituent on the cation radical bond
dissociation energy is the reflection of a stronger destabilization
+
+
of the cation A as compared to the cation radical itself. The
0
fact that the cation radical energy is also affected by CN
’s are known in acetoni-
AH/A
+
0
substitution is revealed by the positive shift of E
•+ and the
trile, the strongest hydride acceptor is N-benzyl-3-cyanoquino-
linium, for which E
AH/AH
0
16b
negative shift of the pKa AH•+ (Table 1). This is confirmed by
the substantial change that CN substitution induces in the UV-
vis spectrum of the cation radical (Figure 1) as obtained from
laser pulse experiments (see Experimental Section).
+
) 0.257 ( 0.026 V.
None-
AH/A ,pH)0
theless, it is not a powerful enough hydride acceptor to abstract
-
H from MAHCN at an appreciable rate in acetonitrile. We,
therefore, had to use a more powerful hydride acceptor at low
pH, namely 1,4-naphthoquinone (NQ),1 to obtain measurable
rate constants. The overall reaction is
4a
Kinetics of Cation Radical Deprotonation. The cyclic
voltammograms of MAHCN at low scan rate obtained in the
presence and in the absence of an excess of a base B, are shown
in Figure 2. In the presence of a base, or in buffered medium
kf
+
+
MAHCN + NQ + H y
\
z MACN + NQH
2
kb
+
BH /B, the anodic peak appearing in the first scan corresponds
to a two-electron irreversible process. The reversible wave
appearing in the second and third scans has the same charac-
teristics as that of an authentic sample of MACN . It is
Thus
+
0
E
+
)
MAHCN/MACN ,pH)0
0
E
- 0.029[pH + log(k /k )]
(17) (a) A spectrophotometric study of the CF3CO2H/pyridine equilibrium
NQH /NQ,pH)0
f
b
2
in acetonitrile gives pKa CF CO H ) 12.9 ( 0.1, using a value of 12.3 for the
3
2
pKa of the pyridinium.1 The pKa’s of the pyridiniums in acetonitrile are
from ref 17b. (b) Cauquis, G.; Deronzier, A.; Serve, D.; Vieil, E. J.
Electroanal. Chem. 1975, 60, 205.
7b
-
17
In the CF3CO2H/CF3COO buffer (pH 12.9 ), both the forward
and reverse reactions, starting with MAHCN + NQ and
MACN + NQH2, respectively, proceed at appreciable rates.
+
(18) It has been previously observed that there is a good parallelism
0
between the values of E
MAHCN/MACN+,pH)0
in acetonitrile and in 4/1
15) It has already been reported that MACN exists in solution.15b (b)
•
2-propanol/water, the values in acetonitrile being 0.290-0.340 V higher
than in the aquoalcoholic mixture.1 MAHCN fits in the same correlation
since the difference between the two solvents is 0.360 V.
(
6a,b
Happ, J. W.; Janzen, E. G.; Rudy, B. R. J. Org. Chem. 1970, 35, 3382.
16) (a) Ostovic, D.; Lee, I.-S. H.; Roberts, R. M. G.; Kreevoy, M. M.
J. Org. Chem. 1985, 50, 4206. (b) Anne, A.; Moiroux, J. J. Org. Chem.
990, 55, 4608.
(
(19) (a) Parker, V. D. J. Am. Chem. Soc. 1992, 114, 7458. (b) Parker,
V. D. J. Am. Chem. Soc. 1993, 115, 1201 (erratum).
1

2954 J. Am. Chem. Soc., Vol. 120, No. 12, 1998
Anne et al.
Table 2. Redox Catalysis Experiments for Determining the
a
Deprotonation Rate Constants of the Cation Radical of MAHCN
scan rate
(V/s)
MAHCN mediator
base
b,c
base
conc.b
conc.b
conc.
3
-fluoropyridine 0.1, 0.2, 0.4
0.9
1.8
1.8
3.6
1.8
3.6
1.8
2
180-1600
120-1200
pyridine 0.5, 1, 2
0
.9
3
3
-methylpyridine 0.2, 0.4, 1, 2
1.8
2.5-72
0
1
.9
,5-lutidine
0.1, 0.2, 0.4
0.5, 1, 2
20-100
6-100
collidine
0.6
1.8
a
The mediator was benzoylferrocene in all cases. b In mM. c Five
•
+
Figure 1. UV-vis absorption spectra of MAHCN (full line) and
to six concentrations in the indicated range.
•
+
MAH
2
(dashed line).
Figure 3. Variation of the deprotonation rate constant of MAHCN•+
Figure 2. Cyclic voltammetry of MAHCN (1.01 mM) in acetonitrile
0.1 M nBu BF at 20 ˚C. Scan rate: 0.2 V/s platinum disk electrode
1 mm diameter). Dashed line: no base added. Continuous line: in
the presence of 50 mM 2,4,6-trimethylpyridine. Potential scans: 0.5
w 1.15 V w -0.2 V w 0.5. Similar results were obtained at a glassy
carbon disk electrode.
with the driving force of the reaction (Lu: lutidine, Coll: collidine).
+
(
4
4
q
The upper and lower lines correspond to ∆G ) 0.69 and 0.66 eV,
0
respectively.
0
.645 V, is close enough to the oxidation potential of the
substrate for obtaining a significant catalytic increase of the peak
height but not too close so that overlapping between the catalytic
wave and the direct oxidation wave of the substrate is avoided.
The driving force of reaction [2] is so large (0.645 V) that its
Scheme 3
10
-1
rate constant is certainly close to the diffusion limit (10
M
-
1
•+
s ). Since MAHCN is a strong acid, reaction [2] is much
faster than the reverse reaction [1]. Forward reaction [1] may
be regarded as irreversible. The ratio of the P oxidation peaks
0
p
in the presence and in the absence of the substrate, ip/i , is
therefore a function of the kinetics of reactions [0] and [1]. The
standard free energy of reverse of reaction [0] is (RT/F)ln(k+e/
k-e) ) -0.330 eV. For the reaction between MAH2 and the
same mediator, benzoylferricenium, the standard free energy is
observed only when the first scan encompasses the irreversible
oxidation wave. We may thus conclude that the two-electron
+
oxidation of MAHCN in the presence of a base yields MACN
1
4
as with the other NADH analogues previously investigated.
The oxidation mechanism is thus as represented in Scheme 1,
9
.5
-1 -1 14c
-
0.200 eV. k-e was then found to be 10
reaction between MAH2 and ferricenium whose standard free
M
s .
The
1
4
the second electron transfer step taking place, as shown before,
1
4c
9.7
-1 -1
energy is -0.450 V is diffusion-controlled.
thus seems a reasonable estimate of k-e in the present case.
The value of k+e, 10
10
M
s
in solution (disproportionation) rather than at the electrode
surface (ECE). Due to its huge driving force (0.975 eV, from
the data in Table 1) the disproportionation reaction is under
diffusion control, and the overall process is kinetically governed
by the deprotonation step.
When no base is added, proton abstraction involves the
substrate. Since the protonated substrate is not oxidized in the
scanned potential range, the height of the whole voltammogram
is divided by two as previously observed with the other NADH
analogues.14
4
.0
-1 -1
M
s , ensues. Knowing k+e and k-e,
the value of the rate constant k was derived, for each base, from
0
the variations of ip/i with the concentrations of MAHCN, of P
p
21
and B in Table 2 using already established working curves.
The data thus obtained are reported in Figure 3 under the form
of a plot of log k vs the driving force of the deprotonation
0
reaction expressed as -∆G ) 0.058 (pKa AH•+ - pKa BH+). It
clearly appears that in the explored driving force range, the
deprotonation reaction is under activation control with a
symmetry factor of ca. 0.3, similarly to what has been previously
observed for the deprotonation of cation radicals of other NADH
The deprotonation rate constant is too large to be conveniently
measured by means of direct cyclic voltammetry. We thus
resorted to homogeneous redox catalysis to measure this
parameter. The principle of the method20 is summarized in
14
analogues. The data points in Figure 3 may be fitted with a
q
quadratic activation driving force equation (∆G is the activation
Scheme 3 (P/Q is the mediator reversible couple). As mediator,
q
free energy and ∆G is the standard activation free energy
0
P/Q
0
we selected benzoylferrocene. Its standard potential, E
)
(21) (a) Andrieux, C. P.; Blocman, C.; Dumas-Bouchiat, J. M.; M’Halla,
(
20) Andrieux, C. P.; Sav e´ ant, J.-M. Electrochemical Reactions. In
F. ; Sav e´ ant, J.-M. J. Am. Chem. Soc. 1980, 102, 3806. (b) Andrieux, C.
P.; Sav e´ ant, J.-M. J. Electroanal. Chem. 1986, 205, 43. (c) Andrieux, C.
P.; Anne, A.; Moiroux, J.; Sav e´ ant, J.-M. J. Electroanal. 1991, 307, 17.
InVestigations of Rates and Mechanisms of Reactions; Bernasconi, C. F.,
Ed.; Wiley: New York, 1986; Vol. 6, 4/E, Part 2, pp 305-390.

Deprotonation of Cation Radicals
J. Am. Chem. Soc., Vol. 120, No. 12, 1998 2955
Figure 4. Correlation between the intrinsic barrier free energy and
the homolytic bond dissociation energy. The dashed straight line
q
represents ∆G ) D/4.
0
(intrinsic barrier):
q
k(M- s ) ) 3 × 10 exp
1
-1
11
-F∆G
,
(
RT
)
0
2
q
q
0
∆G
∆
G ) ∆G 1 +
q
(
)
4
∆G
0
q
0
The best fit is obtained for ∆G ) 0.675 ( 0.015 eV.
Discussion
Figure 4 summarizes the correlation between the intrinsic
q
0
barrier free energy, ∆G , and the homolytic bond dissociation
Figure 5. (a) Homolytic (full line) and ionic (dashed line) dissociation
of the pyridinium ion. (b) Homolytic hypothetical reaction pathways
(dashed line) and actual ionic reaction pathway (full line). Distances
are in Å.
energy, D,14 including the result for the cyano-derivative
obtained as depicted in the preceding section. The error bars
in Figure 4 have been estimated taking into account the
fact that the same systematic error, due to the uncertainty on
2
Gcov ) D{1 - exp[-â(x - x )]}
0
q
0
0
E
, interferes both in ∆G and D. Putting aside, for
NQH /NQ,pH)0
2
the moment, the methylacridane derivatives bearing an alkyl
or aryl group in the R position for which some sort of steric
effect interferes (Vide infra), it is seen that the R-cyanomethyl-
where x the N-H distance, x0 ) 1.033 Å is the equilibrium
-1
-3
-1
distance, D ) 4.90 eV, â (Å ) ) 1.357 10 υ (cm ), and (D
-1/2
23
(eV))
) 2.02. The ionic profile
acridane derivative, which has the largest bond dissociation
q
energy, has also, as expected, the highest value of ∆G . The
1
x
1
0
2
Gionic ) ∆G + D{exp[-â(x - x )]} - C
-
correlation thus observed is close to proportionality between
I
0
(
)
x + a
q
0
∆
G and D/4. We note, however, that the distance between
the D/4 correlation and the data points increases as one passes
from the BNA, to the BQN, BQCN, and MA ring. We propose
the following model to explain these observations as well as
the very fact that single Br o¨ nsted plots are obtained when anyone
of the NADH analogue cation radicals is opposed to a series of
normal nitrogen or oxygen bases.
(∆GI is the heterolytic bond dissociation free energy) was
grossly estimated assuming that, due to the polarizability of the
pyridine molecule, there is a unit positive charge on the
hydrogen and on the para-carbon and a unit negative charge on
the nitrogen (a ) 2.72 Å) with a repulsive term equal to the
Morse repulsive term. C ) 14.4 eV × Å. It thus appears that
+
We consider successively three types of reactions: the self-
exchange reaction between a normal acid and its conjugate base
the dissociation of an isolated PyH molecule in the gas phase
should preferably undergo a homolytic rather than an ionic
dissociation.
(
for example pyridine); the self-exchange reaction between a
•
+
NADH analogue cation radical, AH , and its conjugate base,
Viz., the radical A ; and the reaction of a NADH analogue cation
radical, AH , with a normal base such as pyridine (Scheme
However, in spite of a possibly modest contribution of the
ionic state, as compared to the covalent state in the ground state
•
•
+
+
of PyH , its dissociation triggered by the approach of a pyridine
4
). In all cases, the reaction starts with the formation of a
molecule is far from following a homolytic pathway such as
the one represented by the dashed line in Figure 5b.24 The
approach of the pyridine molecule immediately enhances the
contribution of the ionic state so as to result in the classical
double well profile with a very small activation barrier, if any.
Recent ab initio calculations on water and ammonia, taking into
account electron correlation at the MP2 level, indeed show that
precursor complex and ends with the dissociation of a successor
complex (Scheme 4). In the gas phase, the homolytic and ionic
dissociation profiles of PyH are of the type shown in Figure
+
+
+
5a. Dissociation of PyH into Py and H requires a much larger
+
•+
energy, 9.22 eV, than the homolytic dissociation (PyH TPy
+
•
22
H ), 4.90 eV. The covalent profile is a Morse curve
-
1 23b
23c
(
22) (a) Combining the data from refs 22b and 4a. (b) Aue, D. H.;
(23) (a) υ ) 3300 cm
.
x0 ) 1.033 Å. (b) Socrates, G. Infrared
Bowers, M. T. Stabilities of positiVe ions from equilibrium gas-phase
basicity measurements in Gas Phase Ion Chemistry; Bowers, M. T., Ed.;
Academic Press: New York, 1969; Vol. 2, Chapter 9, p 1.
Characteristic Group Frequencies; Wiley: New York, 1994; p 132. (c)
Handbook of Chemistry and Physics, 72nd ed.; CRC Press: 1991-92; pp
9-11.

2956 J. Am. Chem. Soc., Vol. 120, No. 12, 1998
Anne et al.
Figure 7. Reaction pathway in the reaction AH•+ + B f A + BH .
•
+
Distances are in Å.
to provide a rough idea of the huge energy difference favoring
the ionic pathway over the homolytic pathway.
•
+
•
What happens with the AH + A self-exchange reaction is
illustrated in Figure 6 with the example of methylacridane cation
radical. In the gas phase, the homolytic dissociation is much
27
easier than the ionic dissociation (1.8 eV vs 8.55 eV ). The
+
•
approach of H to A is not likely to result in a strong
stabilization, leading to the notion that the contribution of the
ionic state to the ground state at equilibrium distance should
+
be small, much smaller than in the case of PyH (Figure 6a).
•
Figure 6. (a) Homolytic (full line) and ionic (dashed line) dissociation
Likewise, in the self-exchange reaction, the presence of A in
•
+
•+
of AH . (b) Homolytic hypothetical reaction pathways in the AH +
•+
the vicinity of AH within the encounter complex (Scheme 4)
•
A self-exchange reaction. Distances are in Å.
is not expected to induce a significant stabilization of the ionic
•
+ •
state, A H A. It thus appears that the homolytic pathway
there is practically no barrier in the gas phase and a very small
barrier the liquid phase.26 The results of these calculations are
reproduced in Figure 5b, neglecting the small changes that may
occur when passing from water or ammonia to pyridine, in order
24
represented in Figure 6b should be energetically preferred.
Figure 7 represents what should be the preferred pathway
•+
for the reaction of AH with a normal base such as pyridine.
Within the precursor complex (Scheme 4), the presence of the
base does not induce any particular change in the homolytic
(24) (a) The homolytic reaction profile is obtained by intersection of
the two following surfaces and determination of the saddle point on the
•+
+ •
state describing the cation radical AH (A H) when the C-H
2
4b
intersection
•
elongates. In contrast, the ionic state of the cation radical (A
H) is strongly stabilized by the presence of the base as the
2
2
2
+
Greactants ) D{1 - exp[-â(x - x )]} + D{exp[-â(y - y )]}
0
0
C-H distance increases. Taking into account the absence of
2
Gproducts ) D{exp[-â(x - x )]} + D{1 - exp[-â(y - y )]}
+
0
0
significant barrier in the PyH + Py reaction, we may thus infer
(
x and y are the first and second N-H or C-H distances, respectively, and
that the potential energy curve of the products in the successor
complex simply contains a repulsive term resulting from the
decrease of the distance between the H and C atoms and the
concomitant bending of the C-R bond. The main effect of
the base is thus to poise the height of the repulsive curve at a
value corresponding to the standard free energy change between
x0 and y0 are their equilibrium values). It follows that the reaction pathway
is defined by the following equations
exp[-â(x - x )] + exp[-â(y - y )] ) 1
0
0
2
2
x e x e x + (1/â) ln 2 G ) 2D{exp[-â(x - x )]}
0
0
0
(
y0 + (1/â) ln 2 e y e ∞)
0
the precursor and successor complexes, ∆G ′. The repulsive
curve in the successor complex may be approximated by the
repulsive part of the Morse curve of the reactant system by
analogy with the dissociative electron transfer theory.25 The
reaction path (Figure 7 where the characteristic parameters are
y e y e y + (1/â) ln 2 G ) 2D{exp[-â(y - y )]}
0
0
0
(
x + (1/â) ln 2 e x e ∞)
0
2
4d
The activation barrier is thus equal to D/2. (b) Similarly to a model
recently developed for SN2 substitution based itself on an earlier model
of dissociative electron transfer. (c) Marcus, R. A. J. Phys. Chem. A 1997,
01, 4072. (d) In reality, owing to avoided crossing at the saddle point the
2
4c
•+
0
those of MAH2 and ∆G ′ ) -0.2 eV) and the free energy of
activation may therefore be derived from the following equa-
tions.
25
1
reaction path goes through a rounded maximum, somewhat lower than the
sharp discontinuous maximum shown in Figures 5b and 6b.
(
25) (a) Sav e´ ant, J.-M. J. Am. Chem. Soc. 1987, 109, 6788. (b) Sav e´ ant,
J.-M. Acc. Chem. Res. 1993, 26, 455. (c) Sav e´ ant, J.-M. J. Am. Chem. Soc.
992, 114, 10595. (d) Sav e´ ant, J.-M. Dissociative Electron Transfer in
0
2
G
) D{1 - exp[-â(x - x )]}
reactants, precursor
0
1
AdVances in Electron Transfer Chemistry; Mariano, P. S., Ed.; JAI Press:
0
0
2
G
) ∆G ′ + D{exp[-â(x - x )]}
New York, 1994; Vol. 4, pp 53-116.
products, successor
0
(26) (a) Tu n˜ o´ n, I. ; Tortonda, F. R.; Pascual-Ahuir, J. L.; Silla, E. J.
Mol. Struct. (Theochem) 1996, 371, 117. (b) Tortonda, F. R.; Pascual-Ahuir,
J. L.; Silla, E.; Tu n˜ o´ n, I. J. Phys. Chem. 1995, 99, 12525. (c) Tortonda, F.
R.; Pascual-Ahuir, J. L.; Silla, E.; Tu n˜ o´ n, I. J. Phys. Chem. 1993, 97, 11087.
It follows25 that the free energy for ∆G ′) 0 is one-fourth of
0
the bond dissociation energy.

Deprotonation of Cation Radicals
J. Am. Chem. Soc., Vol. 120, No. 12, 1998 2957
Scheme 4
q
∆
between the successor complex and the separated products, on
the other. The following equations ensue:
∆
G
0
) D/4
G ′ ) 0
2
5
In addition to bond breaking, solvent reorganization is expected
to contribute to the barrier.
0
2
q
q
∆G ′
∆
G ) w + ∆G
0
1 +
R
∆G ′)0
q
(
)
4
∆G
0
q
∆
∆G ′)0
∆
G
0
) (D/4) + (λ /4)
G ′)0 0
2
w - w
q
q
P
R
∆G
0
) w + ∆G
0
1 +
≈
This factor is however likely to be small (of the order of 0.1
∆G )0
R
∆G ′)0
q
(
)
4
∆G
0
2
8
∆G ′)0
eV in view of the dimensions of the species involved ) since
w + w
λ0
the charge in the precursor and successor complexes are spread
R
w + wP
D
4
R
P
q
∆
q
∆
∆G
0
+
≈
+
+
G ′)0
over a rather large volume. ∆G
is related to the intrinsic
G0′)0
2
2
4
q
q
barrier, ∆G ) ∆G
, that we have derived from the rate
data as follows. The total standard free energy of the reaction,
from separated reactants to separated products, ∆G , is related
0
∆G0′)0
The model thus provides an explanation of two important
features of the experimental results, namely, (i) a given cation
radical gives rise to a single Br o¨ nsted plot when opposed to a
series of normal bases and (ii) the correlation between the
0
to the standard free energy change from the precursor to the
0
successor complexes, ∆G ′, according to
-
1
(
27) See footnote d in Table 5 of ref 14c. â ) 2.8 Å was obtained
0
0
∆
G ′) ∆G + w + w
25d 1/2
âAH•+ ) (DAH/DAH•+
) , taking for ν, the frequency found for
-1
R
P
from
acridane, 2900 cm
28) (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.
.
(
where wR and wP are the reactant and product work terms, i.e.,
the standard free energy difference between the precursor
complex and the separated reactants, on the one hand, and
9

2958 J. Am. Chem. Soc., Vol. 120, No. 12, 1998
Anne et al.
Table 3. Thermodynamics and Kinetics of the Deprotonation of
in 50 mL of a DMSO/water mixture (90/10). KCN (0.15 g) was then
added, and the reaction was allowed to proceed in the dark, at room
temperature under a nitrogen atmosphere, for 5 h. Addition of 50 mL
of water brought about the precipitation of MAHCN which was filtered,
•
+
a
(p-An)
2
2
NCH H
by Quinuclidines
q b
q c
pKa BH+
pKa AH•+
-
∆G0
(eV)
log k
∆G
∆G
0
-
1
-1)
(M
s
(eV)
(eV)
washed with CHCl
yield: 60%.
3
, and crystallized from methanol/water. Final
9
8
6
5
.5
.7
.55
.4
-0.54
-0.50
-0.37
-0.31
4.8
4.35
2
0.35
0.38
0.46
0.50
0.59
0.60
0.63
0.65
Instrumentation and Procedures. The instrumentation and pro-
14
cedures were the same as previously described except for the
2.2
determination of the standard redox potential of hydride transfer of
av 0.62
the MAHCN/MACN couple. In 50 mM CF
+
4
COOH + 25 mM Me -
3
+
a
In acetonitrile at 15 °C. ∆G ) 0.05718 (11 - log k). c From
b
q
NOH buffered acetonitrile, MACN exhibits a maximum of absorption
-
1
-1
q
0
q 2
at 384 nm with a molar absorbance of 20 000 M cm . MAHCN as
well as NQ and NQH do not absorb appreciably at this wavelength.
Therefore starting either with MAHCN (2 mM) + NQ (20 mM) or
q
∆
G ) ∆G (1 +∆G /4∆G ) .
0
0
2
intrinsic barrier and the bond dissociation energy is close to a
proportionality of D/4.
The most significant deviation from this proportionality occurs
+
+
2
MACN (1 mM) + NQH (10 mM), the MA CN concentration can
be monitored through the measurement of the absorbance at 384 nm.
Pseudo-first-order kinetics were observed for the production or the
+
in the methylacridane series when one of the hydrogens is
consumption of MACN over periods of 24 h or more.
q
replaced by an aryl or an alkyl group (Figure 4). ∆G then
0
Conclusions
increases in the order H < Ph < Me < Bz, while the bond
dissociation energy remains about the same. From the repre-
sentation of the precursor and successor complexes given in
Scheme 4, we see that the steric hindrance resulting from the
The 9-cyano substituted methylacridane gives rise to a cation
radical that has the highest value of the homolytic bond
dissociation energy in the NADH analogue family owing to the
strong destabilization of the cation by the cyano group.
Deprotonation by normal bases gives rise to an activation
controlled single Br o¨ nsted plot as for the other cation radicals
of the same family. Over the whole series, the intrinsic barrier
correlates with the homolytic bond dissociation energy. In the
absence of significant steric hindrance, the correlation is close
to proportionality of the intrinsic barrier to one-fourth of the
dissociation homolytic bond dissociation energy. The same
result is found for other cation radicals for which previous
studies have shown that their deprotonation by normal bases
gives rise also to single Br o¨ nsted plots (polymethylbenzenes,
p-dianisylmethylamine).
The respective contributions of the homolytic and ionic states
in the dissociation of the two types of acids, cation radical and
the conjugate acid of the normal base, are such that a simple
model can be developed which regards the deprotonation
reaction as a concerted H atom/one-electron transfer. The model
predicts, in agreement with experiment, (i) that, for each radical
cation, the deprotonation kinetics follows an activation con-
trolled single Br o¨ nsted plot and (ii) that the major part of the
intrinsic barrier is related to the homolytic dissociation of the
C-H bond of the cation radical entailing a contribution equal
to one-fourth of the bond dissociation energy.
presence of the aryl or an alkyl groups tends to increase wP,
q
while wR is not affected. An increase of ∆G ensues. It is
0
minimal with MAHPh since the rotation of the phenyl group
around the C-C bond is hindered by its conjugation with the
•
MA ring in the MAHPh radical. It then increases, as expected
from Me to Bz.
We also note that, in the AH series, the deviation from the
proportionality to D/4 increases with the number of rings in
the A moiety. This observation can be explained by a variation
of the reactant work term, wR. With one ring, as with BNAH2,
the interaction between the base and the cation radical is
relatively strong. It decreases when passing to BQAH2 (and
BQCNH2) and to MAH2, owing to the increase delocalization
of the positive charge over a larger and larger molecular
framework.
There are a few other cation radicals for which Br o¨ nsted
plots with opposing normal bases are available. One series
involves the cation radicals of polymethylbenzenes (hexamethyl,
6
b
pentamethyl, 1,2,4,5- and 1,2,3,4-tetramethyl).
As noted
14c
earlier, the intrinsic barriers are very close to D/4 (the intrinsic
barrier is practically the same for all four cation radicals and
equal to 0.6 eV, the bond dissociation energy is also the same,
and D/4 ) 0.59 eV). Another interesting example is the
deprotonation of (p-An)2NCH2H (An: anisyl) by a series of
diversely substituted quinuclidines.8 The results are sum-
marized in Table 3. Here again the intrinsic barrier, 0.62 eV,
is remarkably close to D/4 (0.51 eV).
Deviations from this behavior due to the presence of bulky
substituents on the functional carbon can be explained by the
introduction of a product work term in the model expressing
the difference in free energy between the successor complex
and the separated products. Minor deviations from the D/4
proportionality depending on the extent of charge delocalization
over the cation radical molecule may be accounted for by a
reactant work term expressing the difference in free energy
between the precursor complex and the separated reactants.
•
+
a
Experimental Section
Chemicals. All chemicals, including 9-cyano-10-methylacridinium
+
-
methyl sulfate MACN , CH SO , were from Aldrich Chemical Co.
3 3
Commercial products were of the highest purity available and were
used as received. 9-Cyano-10-methylacridan (MAHCN) was prepared
JA973725K
1
5b
by adaptation of a previously described procedure.
10-Methylacri-
(29) Roberts, R. M. G.; Ostovic, D.; Kreevoy, M. M. Faraday Discuss.
+
-
dinium iodide MAH , I (1.3 g), prepared as in ref 29, was dissolved
Chem. Soc. 1982, 74, 257.