Linear free-energy relationship for electron-transfer processes of pyrrolidinofullerenes with tetrakis(dimethylamino)ethylene in ground and excited states

Article abstract of DOI:10.1039/a901837i

Systematic studies of electron-transfer processes in the ground states and excited triplet states of pyrrolidinofullerenes {C₆₀(C₃H₆N)R [R = H (1), p-C₆H₄NO₂ (2), p-C₆H₄CHO (3), p-C₆H₅ (4), p-C₆H₄Me (5), p- C₆H₄NMe₂ (6)]} with tetrakis(dimethylamino)ethylene (TDAE) have been carried out by steady-state and transient absorption measurements in the visible-NIR region. Analyses of the equilibria of the electron-transfer processes in the ground states indicate that free ion radicals are produced in polar solvents. Photoinduced electron-transfer processes via (T)(C₆₀(C₃H₆N)R)* were observed by applying a perturbation to the equilibria of the electron-transfer reactions in the ground states by laser flash photolysis. Based on the relationship of the thermodynamic data and kinetic data, the electron-transfer rate constants in the ground states (k(et)/(G)) can be evaluated. The k(et)/(G) values are affected by the substituents to a smaller extent compared with the equilibrium constants (K) in polar solvents; α = 0.6 in Δ log k(et)/(G) = α Δ log K. This α value indicates that the activation energies of forward electron transfer in the ground states vary moderately with the thermodynamic stabilities of (C₆₀(C₃H₆N)R)^.-. Electron-transfer rate constants via (T)(C₆₀(C₃H₆N)R)* which are close to the diffusion-controlled limit, do not show a large substituent effect (α = 0), because of their highly exothermic processes. Such a linear free-energy relationship can be extended to other systems such as (T)(C₆₀(C₃H₆N)R)*/N,N-dimethylaniline, from which valuable information for electron-transfer processes can be obtained.

Full text of DOI:10.1039/a901837i

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Linear free-energy relationship for electron-transfer processes of
pyrrolidinofullerenes with tetrakis(dimethylamino)ethylene in ground
and excited states
Chuping Luo,*a Mamoru Fujitsuka,a Chun-Hui Huangb and Osamu Ito*a
a Institute for Chemical Reaction Science, T ohoku University, Katahira, Aoba-ku, Sendai
980-8577, Japan
b State Key L aboratory of Rare Earth Materials Chemistry and Applications, Peking University,
Beijing 100871, China
Received 9th March 1999, Accepted 27th April 1999
Systematic studies of electron-transfer processes in the ground states and excited triplet states of
pyrrolidinofullerenes MC (C H N)R [R \ H (1), p-C H NO (2), p-C H CHO (3), p-C H (4), p-C H OMe
60
3
6
6
4
2
6
4
6
5
6 4
(5), p-C H NMe (6)]N with tetrakis(dimethylamino)ethylene (TDAE) have been carried out by steady-state
6
4
2
and transient absorption measurements in the visibleÈNIR region. Analyses of the equilibria of the
electron-transfer processes in the ground states indicate that free ion radicals are produced in polar solvents.
Photoinduced electron-transfer processes via T(C (C H N)R)* were observed by applying a perturbation to
the equilibria of the electron-transfer reactions in the ground states by laser Ñash photolysis. Based on the
relationship of the thermodynamic data and kinetic data, the electron-transfer rate constants in the ground
states (kG) can be evaluated. The kG values are a†ected by the substituents to a smaller extent compared with
the equilibrium constants (K) in polar solvents; a \ 0.6 in * log kG \ a * log K. This a value indicates that the
activation energies of forward electron transfer in the ground states vary moderately with the thermodynamic
60
3 6
et
et
et
stabilities of (C (C H N)R)~~. Electron-transfer rate constants via T(C (C H N)R)*, which are close to the
60
3
6
60 3 6
di†usion-controlled limit, do not show a large substituent e†ect (a@ \ 0), because of their highly exothermic
processes. Such a linear free-energy relationship can be extended to other systems such as
T(C (C H N)R)*/N,N-dimethylaniline, from which valuable information for electron-transfer processes can be
60
3 6
obtained.
expected that the free ion radicals are formed in highly polar
solvents. Photoinduced electron-transfer processes can also be
observed by laser Ñash photolysis, which causes a pertur-
bation of the equilibria in the ground state. Considering these
thermodynamic and kinetic data, the electron-transfer rate
constants in the ground state can be evaluated. We obtained
both equilibrium and kinetic data; thus, the linear free-energy
relationship (LFER) can be used to explain the substituent
e†ect on the electron-transfer processes. Based on the coeffi-
cients of the LFER, the substituent e†ects observed on the
forward and backward electron-transfer processes can be
explained by the potential energy curves.
Introduction
The high electron-accepting ability of fullerenes has played a
signiÐcant role in fullerene chemistry, which relates to the
studies of functionalization,1 photocurrent generation,2 super-
conductivity,3 ferromagnetism4 and various topics in bio-
logical applications.5 The electrochemical studies pointed out
that the functionalized fullerenes still keep electron-acceptor
ability.6 Thus, some C dyads connected with donors such as
dimethylaniline,7 ferrocene,8 porphyrin9 and carotenoid10
60
have been studied on purpose to establish the efficient photo-
induced charge-separation systems and to mimic photo-
synthetic reaction centers. It is also reported that
intermolecular electron-transfer processes are decelerated by
the functionalized groups11 and a†ected by the site and degree
of functionalization,12 which can be rationalized in terms of
perturbation on the n-system of fullerenes.
Experimental
Materials
It is well known that tetrakis(dimethylamino)ethylene
Pyrrolidinofullerenes were synthesized as reported in our pre-
(TDAE) with a high oxidation potential (E \ [0.75 V vs.
ox
vious paper.2c C ([99.9%) was purchased from Texas Ful-
SCE in acetonitrile)13 forms an ion radical salt with C
,
60
60
lerenes Corp. Tetrakis(dimethylamino)ethylene (TDAE) was of
which shows ferromagnetism at low temperature.4a In
commercially available best grade. Solvents were of spectro-
scopic or HPLC grade.
C
/TDAE solutions, reversible electron transfer takes place
60
in both ground state and excited triplet state as reported in
our previous paper.14
In the present work, the electron-transfer processes of pyr-
rolidinofullerenes (Scheme 1) with TDAE were systematically
studied. By steady-state visibleÈNIR absorption spectra, the
equilibrium constants of electron transfer between TDAE and
C
(C H N)R in the ground state were measurable; it is
Scheme 1
60
3 6
Phys. Chem. Chem. Phys., 1999, 1, 2923È2928
2923

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after electron transfer takes place:
Measurements
kG
et
C
R@ ] TDAE A8B (C R@)~~ ] TDAE`~
(1)
All measurements were carried out in the dark by using a
quartz cell (1 cm) under an Ar atmosphere at room tem-
perature. Steady-state absorption spectra in the visibleÈNIR
region were measured on a JASCO/V-570 spectrometer. EPR
spectra were measured on a Varian E-4. Transient absorption
spectra in the NIR region were measured by means of laser
Ñash photolysis; 532 nm light from a Nd:YAG laser was used
as the exciting source and a Ge avalanche photodiode module
was used for detecting the monitoring light from a pulsed Xe
lamp as described in our previous report.15
60
60
kG
bet
In eqn. (1), the equilibrium constants can be deÐned as
K \ kG/kG , where suffix 2 implies that the backward elec-
2
et bet
tron reactions are bimolecular processes. Then, eqn. (2) can be
derived with the assumption that the concentrations of the ion
radicals are negligible as compared with the initial concentra-
tion of TDAE ([TDAE] ):
0
[TDAE]
Abs
[C R@] [TDAE]
1
0
60
0
0
e [
\
(2)
(Abs)2
K e
2
Results and discussion
Electron transfer in the ground state
where [C R@] refers to the initial concentration of
60
0
C
(C H N)R; Abs and e are the absorbance and molar
60
absorption coefficients of (C (C H N)R)~~ at their maximal
60
peak wavelength, respectively. From eqn. (2), the values of K
3 6
3
6
On addition of TDAE to a benzonitrile/toluene (BN/Tol, v/v
1 : 1) solution of C (C H N)R at room temperature, new
broad absorption bands appear in the NIR region with
2
and e in BN/Tol were evaluated as summarized in Table 1. In
60
3 6
comparison with the K value of C , the K values of
2 60 2
(C H N)R are smaller by factors of 1/50 to 1/240, indicat-
ing that the electron-accepting ability of the C
C
j
B 1000 nm (Fig. 1), which are attributed to the absorp-
60
3 6
max
moiety
tion bands of the anion radicals of pyrrolidinofullerenes
60
decreases after functionalization. The K values of 2 and 3
with electron-withdrawing groups are ca. 4 times larger than
those of other derivatives, suggesting that the electron-
withdrawing groups cause a decrease of the electron density
on the skeleton of the fullerene moiety and result in a recovery
of the electron-accepting ability.
((C (C H N)R)~~) by the similarity to the band of
2
60
3 6
C
~~.11d,16 Therefore, the electron-transfer reactions take
60
place in ground states. Since the shape and the position of the
absorption bands did not change appreciably on addition of
excess TDAE, one-electron transfer takes place predomi-
nantly, indicating that dianions are not produced by two-
electron transfer.17 As the absorption intensities of
(C (C H N)R)~~ increase with the concentration of TDAE
Taking K values into consideration, net absorption spectra
2
of (C (C H N)R)~~/TDAE`~ can be obtained by subtracting
60
3
6
60
3 6
the absorption spectra of C (C H N)R and TDAE (Fig. 2).
(Fig. 1), thermal equilibria exist for these electron-transfer pro-
60
3 6
The e values of (C (C H N)R)~~ at ca. 1000 nm are smaller
cesses as represented in eqn. (1) (R@ \ (C H N)R), in which the
free ion radicals are assumed to be produced in polar solvent
60
3 6
3
6
than that of C ~~ at 1070 nm; j
shifts to shorter wave-
60
max
length with the broadening of each peak, which may result
Fig. 1 Steady-state absorption of
C
((C H N)(C H NO )) (0.15
Fig. 2 Absorption
spectra
of
C
~~/TDAE`~
and
60
3
6
6
4
2
60
mM) with changing concentration of TDAE in argon bubbled
benzonitrile/toluene (v/v 1 : 1) solution at room temperature (optical
length: 1 cm). Insert: Plot according to eqn. (2) (R@ \ (C H N)R).
(C (C H N)R)~~/TDAE`~ in argon bubbled benzonitrile/toluene
60
3 6
(v/v 1 : 1) solution at room temperature obtained by subtracting the
spectra of TDAE and C or C (C H N)R) from the total ones.
3
6
60
60 3 6
Table 1 Absorption maxima (j ) and molar absorption coefficients (e ) of C ~~ and C (C H N)~~ and equilibrium constants (K and K )
max
max
60
60
3
6
2
1
of C and C (C H N)R with TDAEa
60
60 3 6
H
1
C H NO
2
C H CHO
3
Ph
4
C H OMe
5
C H NMe
6
6
4
2
6
4
6
4
6
4
2
C
60
In BN/Tol:
j
/nm
K /10~2
1072
634
23.9
991
3.63
8.41
1002
13.5
7.31
1000
11.2
8.85
995
2.65
8.61
994
2.93
9.53
990
4.53
9.23
max
2
e
/103 mol~1 dm3 cm~1
max
In CB:
/nm
j
1073
40
990
6
0.47
1003
16
0.88
999
13
0.73
1000
7
994
9
0.43
994
10
0.44
max
K /M~1
1
e
/103 mol~1 dm3 cm~1
9.7
0.88
max
a Estimation error: j (^0.1 nm), K (^5%), e (^5%), and K (^7%).
max max
2
1
2924
Phys. Chem. Chem. Phys., 1999, 1, 2923È2928

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cm~1) is the same as that among the neutral molecules as
reported previously.18
In less polar chlorobenzene (CB), the equilibrium data do
not obey eqn. (2), although the absorption spectral shapes and
j
values of (C (C H N)R)~~ are similar to those in
max
60 3 6
BN/Tol. It is assumed that the ion radicals are present as ion
pairs in the less polar solvent [eqn. (3)]:
kG
et
C
R@ ] TDAE A8B [(C R@)~~, TDAE`~]
(3)
60
60
kG
bet
Then, K is deÐned as kG/kG , in which kG is the Ðrst-order
et bet bet
process, but not the second-order process as eqn. (1). The K
1
1
and e values were evaluated by the BenesiÈHildebrand equa-
tion:19
[C R@]
Abs
1
1
1
60
0
\
]
(4)
K e [TDAE]
e
1
0
The e
max
values evaluated by the BenesiÈHildebrand plots in
CB are somewhat smaller than those in BN/Tol (Table 1), sug-
gesting that some extra reactions may occur in addition to a
reversible electron-transfer process. Therefore, one must be
Fig. 3 EPR spectra of C ((C H N)(C H NO )) with TDAE in
careful in using these e
values; in the present study, we did
not employ these values for further study.
60
3
6
6
4
2
max
BN/Tol (top) and in CB (bottom) at room temperature.
The formation of the ion radicals can be detected by EPR
as shown in Fig. 3. In BN/Tol, the EPR spectrum consists of
hyperÐne structures and a narrow signal [Fig. 3(a)]. The
hyperÐne splitting is well simulated by the reported values for
TDAE`~.14 The narrow signal at g \ 2.0002 to
(C (C H N)R)~~ is very close to those of the anion radicals
from the change of n-electron distribution on the spherical
skeleton of C , probably caused by the reduction of molecu-
60
lar symmetry after functionalization. Among these derivatives,
the
withdrawing groups obviously shift to longer wavelength than
those with the electron-donating groups; i.e., j of 2~~ with
j
values for the derivatives with the electron-
max
60
3 6
of other C derivatives.20 Such sharp lines may indicate that
max
NO shifts 10 nm as compared with that of 6~~ with NMe .
60
TDAE`~ and (C (C H N)R)~~ are present as free ion rad-
2
2
among these anion radicals (121
60
3 6
The maximal shift of j
icals in BN/Tol. In CB, only a narrow line signal of
max
(C (C H N)R)~~ was observed [Fig. 3(b)], suggesting that
60
3 6
some reactions occur for TDAE`~; degradation and/or dimer-
ization of TDAE`~ may be considered as reasons for the dis-
appearance of the EPR signals of TDAE`~. This may be
related to difficulties in the analyses of the equilibrium data in
CB.
Electron transfer ¿ia T(C (C H N)R)*
60
3 6
By 532 nm laser irradiation, which predominantly excites
(C (C H N)R), the thermal equilibria of the electron-transfer
60
3 6
processes in the ground state are perturbed. The neutral
(C H N)R in eqn. (1) can be excited to the singlet state,
C
60
3 6
which decays to the triplet states (T(C (C H N)R)*) by inter-
60
3 6
system crossing. Fig. 4 shows the transient absorption spectra
of 2 in the presence of excess TDAE in BN/Tol; the baseline
of absorbance (Abs \ 0) is set at the absorbance of the
Fig. 4 Transient absorption spectra of
C ((C H N)(C H NO ))
(0.16 mM) with TDAE (1.38 mM) in BN/Tol. Insert: Decay at 690 nm
and rise at 1000 nm.
60
3
6
6
4
2
Table 2 Electron-transfer rate constants and back electron-transfer rate constants of C and C (C H N)R with TDAE in the ground and
60
60
3 6
excited triplet statesa
H
1
C H NO
2
C H CHO
3
Ph
4
C H OMe
5
C H NMe
6
6
4
2
6
4
6
4
6
4
2
C
60
In BN/Tol:
kT b/109 mol~1 dm3 s~1
c
c
c
7.2
2.0
7.2
11
1.1
15
9.8
0.99
11
12
2.0
5.3
9.1
2.0
5.9
8.5
2.3
10
–
–
–
et
k2nd/1010 mol~1 dm3 s~1
bet
kG/108 mol~1 dm3 s~1
et
In CB:
kT b/109 mol~1 dm3 s~1
3.3
1.2
48
8.6
0.26
(1.6)
8.3
0.35
(5.6)
6.5
0.29
(3.8)
8.4
0.26
(1.8)
5.8
0.29
(2.6)
7.9
0.28
(2.8)
et
k1st/107 s~1
bet
kG/107 mol~1 dm3 s~1
et
a Estimation error: kT (^5%), k2nd (^7%), k1st(^5%), and kG (^10%). b U values of C (C H N)R in BN/Tol and CB were asssumed to be
et
bet
bet
et
et
60 3 6
unity. c Electron transfer via TC * cannot be observed, because of the large equilibrium constants.
60
Phys. Chem. Chem. Phys., 1999, 1, 2923È2928
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[TDAE] . On considering ' \ 1, the rate constants of elec-
eq
et
tron transfer (kT) via T(C (C H N)R)* were evaluated by the
et
60 3 6
relation kT \ k as summarized in Table 2. In less polar CB,
et
q
the kT values were estimated by assuming ' \ 1, because
et
reliable e
et
values were not obtained. All kT values are
max
et
almost the same and close to the di†usion-controlled limit
(k ). The substituent e†ect on kT is smaller than that on K .
diff
et
2
The small substituent e†ect on kT indicates that electron
et
transfer via T(C (C H N)R)* is highly exothermic for all reac-
tions.
60
3 6
Estimation of k
bet
After reaching the maxima, the absorption intensities of
M(C (C H N)R)~~N in BN/Tol begin to decay gradually as
60
3
6
hl
Fig. 5 Long time-scale proÐle of (C ((C H N)(C H NO )))~~ in
shown in Fig. 5. Each decay curve obeys Ðrst-order kinetics,
60
3
6
6
4
2
BN/Tol. Insert: kobs vs. [TDAE`~].
bet
since large excesses of [TDAE`~]
(\ [TDAE`~]
total
eq
] [TDAE`~] , ca. 0.098 mM) are present with respect to
hl
[(C (C H N)R)~~] (ca. 0.008 mM) as calculated by using
60
3
6
hl
K in Table 1. Then, the back electron-transfer rate constants
(k2nd) for eqn. (6) were evaluated from the slopes of the linear
relation of the plots of the Ðrst-order rate constants vs.
2
bet
thermal equilibrium components at each wavelength. The
absorption band appearing at 690 nm is due to
T(C (C H N)R)*.18 With the decay of T(C (C H N)R)*, the
[TDAE`~] (A [TDAE`~] ) as shown in the insert in Fig. 5:
60
3
6
60 3 6
eq
hl
absorption band at 1000 nm increases, which can be assigned
k2nd
bet
to (C (C H N)R)~~ based on the steady-state absorption
M(C R@)~~N ] MTDAE`~N ÈÈÈÈÈÈÈÈÈ
60
3 6
60
hl
hl
[(C R)~~] , [TDAE`~]
spectrum. The mirror image of the decay time proÐle of
60 eq
eq
T(C (C H N)R)* with the rise time proÐle of
C
R@ ] TDAE (6)
60
3 6
60
(C (C H N)R)~~ suggests that the electron-transfer processes
60
3 6
In the less polar CB, the decays of M(C (C H N)R)~~N
also obey Ðrst-order kinetics; however, the decay rates were
not increased by the concentration of [TDAE`~] , suggest-
ing that the decays are of monomolecular kinetics. Such
behavior would be anticipated, when the contact ion pairs are
predominantly formed and the back electron transfer takes
place within the ion pairs. The k1st values were evaluated as
take place from neutral TDAE to T(C (C H N)R)* after the
60
3
6
hl
60
3 6
laser pulse. The electron-transfer processes can be represented
as eqn. (5), in which M(C R@)~~N and MTDAE`~N are the ion
total
60
hl
hl
radicals produced by laser exposure of (C (C H N)R) in
60
3 6
addition to the ion radicals present at thermal equilibrium,
M(C R@)~~N and MTDAE`~N , before laser exposure:
60
eq
eq
kT
bet
et
listed in Table 2.
T (C R@)* ] MTDAEN È'ÈÈ
Õ
M(C R@)~~N ] MTDAE`~N
60 hl
60
eq
hl
(5)
In CB, the decay of MC ~~N was as fast as the decay of
et
60 hl
TC *; the decay of MC ~~N seems to be inÑuenced by the
60
60 hl
decay of TC *, which is also supported by the fact that the
60
decay rate of MC ~~N increases with the addition of
60 hl
From the ratios of the maximal concentrations of
[TDAE]. These results imply that the ion pair between
M(C (C H N)R)~~N
to those of T(C (C H N)R)*, the
60
3
6
hl
60 3 6
MC ~~N and MTDAE`~N is quite strong in less polar sol-
quantum yields of electron transfer (' ) were evaluated as
60 hl
hl
et
60
vents such as CB. In Table 2, the maximal k1st value is listed.
unity in BN/Tol, indicating that T(C (C H N)R)* are pre-
dominantly consumed by the electron-transfer processes.
bet
3 6
In the cases of the derivatives, such dependence may not
occur, because the ion pairs between M(C (C H N)R)~~N
The decay proÐles of T(C (C H N)R)* obey Ðrst-order
60
3
6
hl
60
3 6
and MTDAE`~N are not as strong as that between MC ~~N
kinetics under the pseudo-Ðrst-order condition, i.e. the equi-
hl
hl
60 hl
and MTDAE`~N , probably due to the steric e†ect of the sub-
librium concentration of TDAE ([TDAE] ) is far in excess of
eq
stituents.
T(C (C H N)R)* produced by a laser exposure. The second-
60
3 6
order electron-transfer rate constants (k ) can be obtained
q
from the slopes by pseudo-Ðrst-order plots with respect to
Evaluation of kG
et
Based on kinetic and equilibrium data evaluated above, the
electron-transfer rate constants in the ground states (kG) in
et
BN/Tol can be calculated by the relation kG \ K k2nd , where
et
2 bet
k2nd \ kG . All the calculated data are listed in Table 2, from
which it is obvious that the introduced substituent consider-
bet
bet
ably inÑuences the kG values. In the case of less polar solvents,
et
kG also can be obtained from K k1st , but K may contain
et
1 bet
1
some ambiguity. Then, the kG values in these solvents are
listed in parentheses.
et
Linear free-energy relationship
The substituent e†ect on kinetic data can be expressed by the
linear free-energy relationship (LFER) on the basis of the sub-
stituent e†ect on the equilibrium constants as eqns. (7) and
(8):21
Fig. 6 Linear free-energy relationship for electron-transfer processes
* log kG \ a * log K
(7)
(8)
et
of C (C H N)R with TDAE in ground (a) and triplet (b) states and
60
3 6
with DMA in triplet state (b) in BN/Tol solution.
* log kG \ [b * log K
bet
2926 Phys. Chem. Chem. Phys., 1999, 1, 2923È2928

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The plots of log kG and log kG vs. logK in BN/Tol are
forward electron-transfer process is slightly exothermic. Both
forward and backward electron-transfer processes need con-
siderable activation energy [Fig. 7(a)] as assumed by the
observed a and b values.
et
bet
2
shown in Fig. 6(a); the signiÐcant substituent e†ect on the
forward electron-transfer processes in the ground state is
apparent with a steeper slope. The slopes yield a and b;
a \ 0.6 and b \ 0.4 [Fig. 6(a)]. The observation a [ b implies
that the forward electron-transfer processes demand consider-
able activation energies, which vary with the di†erence in ther-
modynamic stabilities of the products (ion radicals) and
reactants (neutral molecules). On the other hand, the back-
In less polar solvents such as CB, on the other hand, the
*GG value might be slightly positive because of the small kG
et
et
values (107È108 M~1 s~1). Therefore, the potential curve of
neutral molecules in the ground state crosses near the
minimum of the potential curve of the ion radicals, suggesting
that the activation energies of the back electron-transfer pro-
cesses are quite small [Fig. 7(b)], which is consistent with
b \ 0. From the potential curves in Fig. 7(b), a \ 1 is satisÐed.
A tendency of kT [ kG can also be explained by this potential
ward electron-transfer processes are less dependent on the K
values.
2
In less polar solvents such as CB, a and b are 1.0 and 0,
respectively, although the K values may contain some ambi-
1
et
energy diagram.
et
guity. These slopes indicate that the forward electron-transfer
processes become more dependent on the K values, which
implies that the forward electron-transfer processes become
endothermic with a decrease in the solvent polarity.
For the electron-transfer processes via T(C (C H N)R)*
60
3 6
with DMA in BN/Tol, the potential curve of neutral mol-
ecules in the ground state crosses the minimum of the poten-
tial curve of the ion radicals [Fig. 7(c)]. Then, back
electron-transfer processes are very fast, while the forward
electron-transfer processes strongly depend on the substit-
uents.
In the case of kT [Fig. 6(b)] in BN/Tol, the kT values are
et
et
not remarkably changed with the K values (slope \ 0). This
2
indicates that the electron-transfer reactions via the triplet
state are quite exothermic; thus, the kT values are all close to
et
the di†usion-controlled limit.
The * log K values for TDAE can be applied to other
Conclusion
2
donor systems in the same solvent systems. For example, the
kT values for the electron-transfer reactions between
Substituent e†ects on the electron-transfer processes between
pyrrolidinofullerenes and TDAE were studied in both ground
state and excited triplet state. Complete sets of equilibrium
constants and rate constants for forward and backward
electron-transfer processes in the ground state were obtained
in solvents with di†erent polarities, in addition to the rate
constants of forward electron transfer in the excited triplet
state. Thus, the linear free-energy relationship was invoked to
explain the electron-transfer processes, from which the origin
of the observed substituent e†ects on the electron-transfer
rates can be clariÐed, including a change of the solvent
polarity. From these considerations, the potential energy dia-
grams for the electron-transfer processes in both ground and
triplet states can be unequivocally illustrated.
et
T(C (C H N)R)* and N,N-dimethylaniline (DMA) in BN/
60
3 6
Tol11d are plotted against the K values for TDAE [Fig. 6(b)].
2
The slopes of a@ \ 1 (* log kG \ a@ * log K ) and b \ 0 [eqn.
et
2
(8)] suggest that the activation energies for the forward
electron-transfer processes are higher, while those of the back-
ward processes are quite low. These facts suggest that the sub-
stituent e†ect on forward electron-transfer processes via
T(C (C H N)R)* becomes larger on decreasing the electron-
60
3 6
donating ability of donors.
The relationship can be explained by the energy diagram
(Fig. 7), in which the free-energy changes (*G ) of the
et
electron-transfer processes were calculated by the RehmÈ
Weller relation.11d,23 Based on this relation, the *GT value via
et
T(C (C H N)R)* is ca. [40 kcal mol~1 in BN/Tol, which
60
3 6
conÐrms the high exothermicity of electron transfer via
T(C (C H N)R)*. Thus, in the potential curves shown in Fig.
7(a), the line of the free ion radicals crosses at the minimum
Acknowledgements
60
3 6
The authors would like to thank Dr. A. Watanabe (Tohoku
University) for his assistance in spectroscopic measurements
and Dr. L. Gan and Mr. Y. Huang (Peking University) for
sample preparations. The present work was partly supported
valley of T(C (C H N)R)*, yielding a negligible activation
60
3 6
energy for kT . In the ground state, slightly positive *GG (ca.
et
et
[6 kcal mol~1) was obtained in BN/Tol, indicating that the
Fig. 7 Energy diagram of electron-transfer processes of C R@(R@ \ (C H N)R) with TDAE in BN/Tol (a) and CB (b) and with DMA in BN/Tol
60
3
6
(c).
Phys. Chem. Chem. Phys., 1999, 1, 2923È2928
2927

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S. Nagase, J. Am. Chem. Soc., 1994, 116, 1359; (d) N. Martin,
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