Electron self-exchange, oxidation, and reduction reactions of bis(2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline)copper(II/I) and bis(6,6′-dimethyl-2,2′-bipyridine)copper(II/I) couples in acetonitrile: Gated et for the reduction, oxidation, and self-exchan

Article abstract of DOI:10.1139/v99-171

The electron self-exchange rate constant for the Cu(dmbp)₂^2+/+ couple (dmbp = 6,6′-dimethyl-2,2′-bipyridine) was measured in acetonitrile by the NMR method (k_ex = 5.5 × 10³ kg mol^-1 s^-1, ΔH

Full text of DOI:10.1139/v99-171

1498
Electron self-exchange, oxidation, and reduction
reactions of bis(2,9-dimethyl-4,7-diphenyl-
1,10-phenanthroline)copper(II/I) and bis(6,6′-
dimethyl-2,2′-bipyridine)copper(II/I) couples in
acetonitrile: gated ET for the reduction,
oxidation, and self-exchange processes
Nobuyoshi Koshino, Yoshio Kuchiyama, Shigenobu Funahashi,
and Hideo D. Takagi
2+/+
Abstract: The electron self-exchange rate constant for the Cu(dmbp)2
couple (dmbp = 6,6′-dimethyl-2,2′-
bipyridine) was measured in acetonitrile by the NMR method (kex = 5.5 × 103 kg mol–1 s–1, ∆H* = 35.0 ± 0.3 kJ
2+
mol–1 and ∆S* = –56 ± 1 J mol–1 K–1). Reduction reactions of Cu(bcp)2 (bcp = 2,9-dimethyl-4,7-diphenyl-1,10-
2+
2+
phenanthroline) and Cu(dmbp)2 with Co(bipy)3 (bipy = 2,2′-bipyridine) and ferrocene (Fe(Cp)2 =
bis(cyclopentadienyl)iron(II)), and oxidation reactions of Cu(bcp)2 and Cu(dmbp)2 by Ni(tacn)2 (tacn = 1,4,7-
+
+
3+
3+
triazacyclononane) and Mn(bipyO2)3 (bipyO2 = N,N′-dioxo-2,2′-bipyridine) were also studied in acetonitrile. The
2+/+
2+/+
electron self-exchange rate constants, kex, estimated for the Cu(bcp)2
and Cu(dmbp)2
couples from the
+
+
3+
3+
oxidation reactions of Cu(bcp)2 and Cu(dmbp)2 by Ni(tacn)2 and Mn(bipyO2)3 were consistent with the directly
2+
2+
measured values by NMR, while kex estimated from the reduction reactions of Cu(bcp)2 and Cu(dmbp)2 by
Co(bipy)3 ([Cu(bcp)22+]0, [Cu(dmbp)22+]0 >> [Co(bipy)32+]0) were 103 times smaller than those directly measured
2+
2+
2+
by the NMR method. The pseudo-first-order rate constant for the reduction reaction of Cu(bcp)2 and Cu(dmbp)2
by Fe(Cp)2 was not linear against the concentration of excess amounts of Fe(Cp)2. Analyses of the reactions
2+
2+
revealed that the reductions of Cu(bcp)2 and Cu(dmbp)2 involve slow paths related to the deformation of
Cu(II)N4 center from tetragonal to tetrahedral coordination. The energetic preference for the deformation of Cu(II)
species rather than that of Cu(I) was discussed on the basis of the ligand field activation energy (LFAE).
Key words: electron transfer, copper(II) and copper(I) complexes, gated behavior. 1507
Résumé : Opérant dans l’acétonitrile et faisant appel à la RMN, on a mesuré la constante de vitesse d’auto-échange
2+/+
électronique du couple Cu(dmbp)2
(dmbp = 6,6′-diméthyl-2,2′-bipyridine) (kex = 5,5 × 103 kg mol–1 s–1, ∆H* =
35,0 ± 0,3 kJ mol–1 et. ∆S* = –56 ± 1 J mol–1 K–1). Opérant dans l’acétonitrile, on a aussi étudié les réactions de
réduction du Cu(bcp)2 (bcp = 2,9-diméthyl-4,7-diphényl-1,10-phénanthroline) et du Cu(dmbp)2 par le Co(bipy)3
2+
2+
2+
(bipy = 2,2′-bipyridine) et le ferrocène (Fe(Cp)2 = bis(cyclopentadiényl)fer(II)) et les réactions d’oxydation du
+
+
3+
3+
Cu(bpc)2 et du Cu(dmbp)2 par le Ni(tacn)2 (tacn = 1,4,7-triazacyclononane) et le Mn(bipyO2)3 (bipyO2 = N,N′-
dioxo-2,2′-bipyridine). Les constantes de vitesse d’auto-échange électronique, kex, évaluées pour les couples
2+/+
2+/+
+
+
3+
Cu(bcp)2
et Cu(dmbp)2
à partir des réactions d’oxydation du Cu(bcp)2 et du Cu(dmbp)2 par Ni(tacn)2 et
Mn(bipyO2)33+, sont en accord avec les valeurs mesurées directement par RMN; par ailleurs, les valeurs de kex
évaluées à partir des réactions de réduction du Cu(bcp)2 et du Cu(dmbp)2 par le Co(bipy)3 ([Cu(bipy)22+]0,
2+
2+
2+
[Cu(dmbp)22+]0 >> [Co(bipy)32+]0) sont 103 fois plus faibles que celles mesurées directement par la méthode de
2+
2+
RMN. La constante de vitesse de pseudo-ordre un pour la réaction de réduction du Cu(bcp)2 et du Cu(dmbp)2
par le Fe(Cp)2 n’est pas linéaire par rapports à la concentration de quantités excédentaires de Fe(Cp)2. L’analyse des
2+
2+
réactions révèle que les réductions du Cu(bcp)2 et du Cu(dmbp)2 impliquent des voies lentes reliées à la
déformation du centre Cu(II)N4 d’une coordination tétragonale à tétraédrique. On fait appel à l’énergie d’activation
du champ de ligand pour discuter de la préférence énergétique pour la déformation de l’espèce Cu(II) par rapport à
celle de l’espèce Cu(I).
Received March 23, 1999.
N. Koshino,1 Y. Kuchiyama, S. Funahashi, and H.D. Takagi.1 Inorganic and Analytical Chemistry Division, Department of
Chemistry and Physics, Graduate School of Sciences, Nagoya University, Furocho, Chikusa, Nagoya 464-8602, Japan.
1Authors to whom correspondence may be addressed. Telephone and fax: +81-52-789-5473. e-mail: NK:
nkoshino@chem4.chem.nagoya-u.ac.jp; HDT: htakagi@chem4.chem.nagoya-u.ac.jp
Can. J. Chem. 77: 1498–1507 (1999)
© 1999 NRC Canada

Koshino et al.
1499
Mots clés : transfert d’électron, complexes du cuivre(II) et cuivre(I), comportement intermittent.
[Traduit par la Rédaction]
tron transfer case, and no significant change in coordination
number or coordination geometry had been expected in the
electron transfer processes.
Introduction
Koshino et al.
For ordinary outer-sphere electron transfer reactions, con-
certed inner- and outer-sphere reorganizations are assumed (1,
2). Therefore, the electron transfer reaction is slow for the re-
actions involving a large coordination geometry change dur-
ing the course of the electron transfer process. Recent
theoretical investigations by Hoffman and Ratner (3) and
Brunschwig and Sutin (4) indicate that the “gated
intramolecular process” with high-energy intermediates never
competes with the direct outer-sphere process in the normal
region. This indication, however, does not exclude the “gated
electron transfer” phenomena postulated by Rorabacher et al.
(5–9) in which large stereochemical changes take place prior
to the ordinary outer-sphere electron transfer processes. Al-
though such gated reactions cannot be treated as a simple
outer-sphere process (i.e., the Ratner type cross relation has
the possibility of failing to predict proper electron self-
exchange rate constants for such reactions), the outer-sphere
electron transfer reactions between the deformed species and
the outer-sphere redox reagents may follow the norm of the
Ratner type cross relation (10). Therefore, the classical
“entatic state view,” saying that the rate of the electron trans-
fer is slow for the redox couple with large coordination geom-
etry changes, seems still valid irrespective of the condition
whether the reaction is gated or not (11, 12).
In the case of the gated ET reactions, a slow equilibrium
corresponding to the deformation of one of the reactants pre-
cedes the outer-sphere ET process. For copper(II/I) couples,
a tetragonal four or five coordination (D2d symmetry) is ex-
pected for Cu(II), while tetrahedral geometry is expected for
copper(I). When cyclic polythiaethers were used as ligands,
Rorabacher et al. (5–9) showed that the oxidation reaction of
Cu(I) is gated, which implies that the deformation of Cu(I)
from tetrahedral to tetragonal conformation takes place prior
to the ET process. In such a case, the principle of the micro-
scopic reversibility requires that the deformation of Cu(II) is
energetically less favored compared to that of Cu(I).
In this article, we examined electron transfer reactions of
two Cu(II/I)(N2)2 couples and found that the electron trans-
2+/+
2+/+
fer reactions for Cu(bcp)2
and Cu(dmbp)2
are gated.
When the normal coordination geometry (slightly twisted
structure from the ordinary tetragonal 4 or 5 coordination
preferred by the Cu(II) species) is in equilibrium with the
deformed tetrahedral state, the electron transfer processes in-
volving the deformed tetrahedral Cu(II) may be much faster
than those involving the ground state Cu(II). The energetic
origin of the gated ET is discussed on the basis of the ligand
field activation energies (LFAE) corresponding to the Cu(II)
deformation. A possibility of the mixing of the gated and di-
rect ET was also examined for the electron self-exchange
Results of the early works on the reactions of
Cu(bpy)22+/+, Cu(phen)22+/+, and its derivative Cu(dmp)2
2+/+
2+/+
2+/+
processes of Cu(bcp)2
and Cu(dmbp)2
couples.2
(13–15) indicated the gated ET, as the self-exchange rate
constants for these redox couples estimated by the Marcus
cross relation from the forward and backward reactions were
inconsistent with each other. In 1983, Lee and Anson (16)
pointed out that steric interconversion may have an impor-
tant role in the electron transfer processes of the
Experimental section
Chemicals
Acetonitrile was obtained from Wako Pure Chemicals Inc.
and purified by distillation from phosphorus pentoxide. The
content of the residual water in thus purified acetonitrile was
examined by a Mitsubishi Kasei CA01 Karl–Fisher appara-
tus by which the amount of residual water was determined to
be less than 5 mmol kg–1. Ferrocene (Wako) was purified by
sublimation at ambient pressure. All other chemicals from
Wako, Aldrich, and Fluka were used without further purifi-
cation. Bis(2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline)-
copper(II) and -(I) perchlorate were synthesized by the re-
ported method (32, 33). Anal. calcd. for CuC52H40N4Cl2O8:
C 63.5, N 5.70, H 4.10; found: C 63.8, N 5.62, H 4.18. Anal.
calcd. for CuC52H40N4ClO4: C 70.7, N 6.34, H 4.56; found:
C 71.0, N 6.42, H 4.52. Bis(6,6′-dimethyl-2,2′-bipyridine)-
copper(II) and -(I) perchlorate were synthesized by the re-
ported method (32, 33). Anal. calcd. for CuC24H24N4Cl2O8:
C 45.7, N 8.88; found: C 44.7, N 8.72. Anal. calcd. for
CuC24H24N4ClO4: C 54.2, N 10.5, H 4.55; found: C 54.4, N
9.98, H 4.60.
2+/+
2+/+
Cu(bpy)2
and Cu(phen)2
couples. The studies of elec-
tron transfer reactions for Cu(dmp)22+/+ with various reaction
partners in aqueous solution were also reported (17–22).
However, ambiguities in the coordination structures of these
ions as well as the low solubility of these ions in water made
it difficult to analyze the reactions more precisely. The stud-
ies of the reduction of water-soluble Cu(dpsmp)22– (dpsmp =
2,9-dimethyl-4,7-bis((sulfonyloxy)phenyl)-1,10-phenanthroline)
by Sykes and co-workers (23, 24) and Lappin and co-
workers (25) indicated the involvement of such steric inter-
conversion. There are some cases where electron exchange
is extremely slow even for the near tetrahedral Cu(II/I) cou-
ples (26–28). Most recently, Stanbury and co-workers (29)
reported
Cu(bib)2
a
very slow electron exchange reaction of
(bib = 2,2′-bis(2-imidazoly)biphenyl). The esti-
2+/+
2+/+
mated self-exchange rate constant of Cu(bib)2
is merely
0.16 kg mol–1 s–1. Takagi and Swaddle (30, 31) have been
studying Cu(II/I) electron self-exchange reactions by NMR
where the coordination geometry of Cu(I) and Cu(II) are
constrained to be similar, in which the kinetic behavior was
expected to follow the context of the moderately fast elec-
[Co(bipy)3](ClO4)2, [Ni(tacn)2](ClO4)3, and [Mn(bipyO2)3](ClO4)2
were synthesized by the literature method (34–36). Anal.
calcd. for CoC30H24N6Cl2O8: C 49.6, H 3.33, N 11.6; found:
2 Tables of rate constants (Tables SI to SV) have been deposited as supplementary material and may be purchased from: The Depository of
Unpublished Data, Document Delivery, CISTI, National Research Council Canada, Ottawa, Canada, K1A 0S2.
© 1999 NRC Canada

1500
Can. J. Chem. Vol. 77, 1999
2+/+
2+/+
Table 1. Electron self-exchange rate constants and activation parameters for the reactions of Cu(bcp)2
and Cu(dmbp)2
at 298 K
in acetonitrile.a
b
kCuL2 /kg mol–1 s–1
+/ +
k12/kg mol–1 s–1
Reaction
2
∆H*/kJ mol–1
∆S*/J mol–1 K–1
2+
+
Cu(bcp)2 + Cu(bcp)2
—
1.4 × 103
2.0 × 103
1.2
5.5 × 103
6.7 × 102
1.9 × 103
1.4
38.1 ± 2.4
21.9 ± 0.2
33 ± 2
35.0 ± 0.3
24.9 ± 0.5
32 ± 1
–57 ± 8
–61.9 ± 0.8
–158 ± 0.6
–56 ± 1
–66 ± 2
–75 ± 4
+
3+
Cu(bcp)2 + Ni(tacn)2
5.20 × 105
5.71 × 102
—
2+
2+
Cu(bcp)2 + Co(bipy)3
2+
+
Cu(dmbp)2 + Cu(dmbp)2
Cu(dmbp)2 + Ni(tacn)2
Cu(dmbp)2 + Mn(bipyO2)3
Cu(dmbp)2 + Co(bipy)3
+
3+
9.3 × 104
2.14 × 103
1.92 × 103
+
3+
2+
2+
21.0 ± 0.4
–112 ± 1
aIonic strength of the solutions was adjusted to 0.1 mol kg–1 by (n-Bu4N)ClO4 or (Et4N)BF4.
2+/+
bCalculated by the redox potential (V vs. Fc+/0), self-exchange rate constant (kg mol–1 s–1), and ionic radii (pm): 0.275, 1.40 × 103c, 760 for Cu(bcp)2
;
0.346, 5.5 × 103, 650 for Cu(dmbp)22+/+; 0.555, 6.0 × 103d, 380 for Ni(tacn)23+/2+; 0.435, 80e, 400 for Mn(bipyO2)33+/2+; –0.081, 0.645f, 700 for
3+/2+
Co(bipy)3
.
cReference 33.
dReference 56.
eReference 57.
fReference 58.
2+
which indicates that either Cu(bcp)2+, Cu(dmbp)2+, or Cu2+
Fig. 1. Dependence of kobs on the concentration of Cu(dmbp)2
2+/+
2+
produced by the decomposition of Cu(bcp)22+ or Cu(dmbp)2
for the electron self-exchange reaction of Cu(dmbp)2
.
[Cu(dmbp)2 ] = 7.90 × 10–2 mol kg–1, I = 0.1 mol kg–1 (TBAP).
The symbols represent the data obtained at 319.1 (᭜), 313.1
(᭺), 308.5 (᭹), 302.9 (ٗ), and 297.8 (᭿) K.
+
2+
in solution does not oxidize ferrocene and Co(bipy)3 used
in this study. The absorbance changes at 470 and 454 nm,
+
corresponding to the absorption maxima of Cu(bcp)2 and
+
Cu(dmbp)2 , respectively, were monitored for the kinetic
measurements.
Electrochemical measurements were carried out by a BAS
100BW electrochemical analyzer with a 1.5 mm φ platinum
disk or glassy carbon disk as the working electrode, and a
0.5 mm φ platinum wire as the counter electrode. A sil-
ver/silver nitrate electrode with 0.1 mol kg–1 tetrabutyl-
ammonium perchlorate (TBAP) in acetonitrile was used as a
3+
reference electrode. A solution of Mn(bipyO2)3 was pre-
pared electrochemically in acetonitrile, containing 0.10
mol kg–1 TBAP at carbon electrode (Hokuto Denko HX-
201). The NMR measurements were carried out by a Bruker
AMX-400WB spectrometer.
Results
C 50.0, H 3.23, N 11.6. Anal. calcd. for NiC12H30N6Cl3O12: C
23.42, H 4.91, N 13.66; found: C 23.42, H 4.96, N 13.55.
Anal. calcd. for MnC30H24N6O14Cl2: C 44.0, H 2.96, N 10.3;
found: C 43.2, H 2.87, N 9.87. (Caution: Perchlorate salts of
metal complexes with organic ligands are potentially explosive.)
2+/+
Electron self-exchange rate constant for Cu(dmbp)2
kex
2+
+
+
[1]
Cu(dmbp)2 + *Cu(dmbp)2 → Cu(dmbp)2
2+
+ *Cu(dmbp)2
General
The electron self-exchange rate constant, kex, of the
All manipulations were carried out in an atmosphere of
dry nitrogen to avoid any possible contamination by water
and oxygen from the environment. Unisoku stopped-flow
apparatus was used for the kinetic measurements at various
temperatures controlled by a Hetofrig circulation bath. The
reservoirs for the reactant solutions were kept under nitrogen
atmosphere during the experiments. At least 10 kinetic traces
were collected for each run, and the results were analyzed
by an NEC personal computer fitted with an interface for the
stopped-flow apparatus. Unisoku software was used for the
data analyses. Under the conditions of [Cu(II)] << [L]
(L = dmbp or bcp), no electroactive species other than
Cu(dmbp)22+/+ couple was measured by monitoring the broadening
+
of the methyl proton signal on diamagnetic Cu(dmbp)2 by
2+
the addition of Cu(dmbp)2
.
2+
[2]
kobs = π(νobs – ν0) = kex[Cu(dmbp)2
]
where νobs is the line width of the methyl proton signal at the
half signal height in the presence of Cu(dmbp)22+, while ν0 is
the line width at the half signal height in the absence of
Cu(dmbp)22+. The dependence of kobs on the concentration
of added Cu(dmbp)22+ at constant ionic strength (0.10 mol kg–1
by TBAP) is shown in Fig. 1 at various temperatures. The
estimated electron self-exchange rate constant at 298 K and
the activation parameters are listed in Table 1.
2+
2+
Cu(bcp)2 or Cu(dmbp)2 was observed within the redox
window of acetonitrile (–2 ~ +2 V) by cyclic voltammetry,
© 1999 NRC Canada

Koshino et al.
1501
Fig. 3. Dependence of kobs on the concentration of Fe(Cp)2 for
3+
Fig. 2. Dependence of kobs on the concentration of Ni(tacn)2
+
+
for the oxidation reaction of Cu(bcp)2 . [Cu(bcp)2 ] = 1.50 ×
10–5 mol kg–1, I = 0.1 mol kg–1 (TBAP). The symbols represent
the data obtained at 303.0 (᭜), 298.0 (᭺), 293.2 (᭹), 288.4 (ٗ),
and 283.2 (᭿) K.
the reduction reaction of Cu(bcp)22+. [Cu(bcp)22+] = 8.47 × 10–6
mol kg–1, [bcp]free = 1.01 × 10–4 mol kg–1, I = 0.1 mol kg–1
(TBAP). The symbols represent the data obtained at 308.2 (᭛),
303.2 (᭜), 298.2 (᭺), 293.2 (᭹), and 288.2 (ٗ) K.
temperatures. The second-order rate constants at 298 K and
the corresponding activation parameters for these reactions
are listed in Table 1. The application of the Marcus cross re-
lation to these reactions yielded 1.2 and 1.4 kg mol–1 s–1, re-
spectively, as the electron self-exchange rate constant, which
are some 103 times smaller than those directly estimated by
the NMR method.
+
+
Oxidation reactions of Cu(bcp)2 and Cu(dmbp)2 by
3+
3+
Ni(tacn)2 and Mn(bipyO)3
+
3+
The reaction of Cu(bcp)2 with Ni(tacn)2 in acetonitrile
was first order for up to three half-lives and was described
by eq. [3] under the pseudo-first-order conditions of
+
[Cu(bcp)2 ]0 << [Ni(tacn)23+]0.
k12
+
3+
2+
[3]
Cu(bcp)2 + Ni(tacn)2 → Cu(bcp)2
2+
2+
Reduction reaction of Cu(bcp)2 and Cu(dmbp)2 by
Fe(Cp)2
2+
+ Ni(tacn)2
The kinetic traces were excellently first-order for Cu(II)
up to three half lives.
3+
[4]
kobs = k12[Ni(tacn)2
]
0
The dependence of kobs on the concentration of
d[Cu(II)]
Ni(tacn)23+ at various temperatures is shown in Fig. 2 for the
−
= kobs[Cu(II)]
[5]
+
dt
[Fe(Cp)2 ]0 >> [Cu(II)]0
reaction of Cu(bcp)2 . The second-order rate constants thus
estimated at 298 K, I = 0.1 mol kg–1 are listed in Table 1 for
+
+
the reactions of Cu(bcp)2 and Cu(dmbp)2 , together with
the activation parameters of the reactions. The estimated
However, the dependence of the pseudo-first-order rate
constants on the concentration of Fe(Cp)2 was not linear as
shown in Fig. 3. The curvature in Fig. 3 may be explained
2+/+
electron self-exchange rate constants for the Cu(bcp)2
2+/+
and Cu(dmbp)2
couples by the Marcus cross relation
were 2.0 × 103 and 6.7 × 102 kg mol–1 s–1, respectively, both
of which were in fair agreement with the values (1.4 × 103
and 5.5 × 103 kg mol–1 s–1, respectively) obtained from the
NMR measurements (33) in view of the uncertainties inher-
ent in the Marcus cross relation (37).
by the following two-step mechanism involving
a
conformational change of Cu(II) prior to the fast electron
transfer reaction (Path B in Scheme 1 proposed by
Rorabacher et al. (5–9)).
kOQ
+
3+
The oxidation reaction of Cu(dmbp)2 by Mn(bipyO)3
Cu(II) º Cu(II)*
+
was also carried out under the conditions of [Cu(dmbp)2 ]0
kQO
[6]
>> [Mn(bipyO)33+]0. The second-order rate constants as well
kB2
as the activation parameters are also listed in Table 1. The
Cu(II)* + ARed ¸ Cu(I) + AOx
2+/+
electron self-exchange rate constants for Cu(dmbp)2
was
estimated as 1.9 × 103 kg mol–1 s–1 by the Marcus cross rela-
tion.
2+
where Cu(II), Cu(II)*, ARed, and AOx represent Cu(bcp)2
2+
2+
or Cu(dmbp)2 in the ground state, deformed Cu(bcp)2 or
Cu(dmbp)22+, Fe(Cp)2 and Fe(Cp)2 , respectively. When the
+
2+
2+
Reduction reactions of Cu(bcp)2 and Cu(dmbp)2 by
Co(bipy)3
conformational change (kOQ) is slower than the electron
transfer process (kB2), the pseudo-first-order rate constant is
expressed by eq. [7] by using the terms in Scheme 1.
2+
The reactions were observed under the conditions of
[Cu(bcp)22+]0, [Cu(dmbp)22+]0 >> [Co(bipy)32+]0. The kinetic
traces were first order for up to three half lives. The depend-
ence of the pseudo-first-order rate constant on the concentra-
kB2kOQ
[7]
Rate =
[ARed ][CuIIL]
2+
2+
kB2[ARed ] + kQO
tion of Cu(bcp)2 or Cu(dmbp)2 was linear at various
© 1999 NRC Canada

1502
Can. J. Chem. Vol. 77, 1999
Scheme 1.
2+
2+
Table 2. Estimated rate constants for the reactions of Cu(bcp)2 and Cu(dmbp)2 at 298 K.a
Reaction
∆H*b
∆S*c
2+
Cu(bcp)2 + Fe(Cp)2
40 s–1
32.0 ± 0.3
–107 ± 1
kOQ
6.5 × 106 s–1
6.2 × 10–6
kQO
kOQ/kQO = KOQ
6.6 × 1010 kg mol–1 s–1
d
kB2
2+
Cu(dmbp)2 + Fe(Cp)2
50 s–1
30.5 ± 1.3
–110 ± 4
kOQ
1.7 × 107 s–1
3.0 × 10–6
9.1 × 1010 kg mol–1 s–1
kQO
kOQ/kQO = KOQ
d
kB2
aIonic strength of the solutions was adjusted to 0.1 mol kg–1 by (n-Bu4N)ClO4.
bkJ mol–1.
cJ mol–1 K–l.
2+*/+
2+*/+
dUsing the estimated values of the electron self-exchange rate constant for Cu(bcp)2
(3.8 × 1010 kg mol–1 s–1) or Cu(dmbp)2
(1.3 × 1010 kg mol–1 s–1) and the self-exchange rate constant for Fe(Cp)2 (9 × 106 dm3 mol–1 s–1). Ionic radii for Fe(Cp)2 = 600 pm.
+/0
+/0
Fig. 4. Plots of kobs vs. [Fe(Cp)2]–1 for the reduction reaction
–1
kOQkB2
[8]
kobs
=
[ARed ] ([ARed ] >>[CuIIL])
2+
of Cu(bcp)2 by Fe(Cp)2. The symbols are the same in Fig. 3.
kB2[ARed ] + kQO
Therefore, the plots of the reciprocal value of kobs against
–1
[ARed
]
should be linear with an intercept when [ARed]0
>> [CuIIL]0. Such plots are shown in Fig. 4.
kQO
kobs kOQkB2[ARed
1
1
[9]
=
+
]
kOQ
The values of the rate constant, kOQ, and the correspond-
ing activation parameters are also listed in Table 2. It is clear
that the estimation of kQO and KOQ is possible once the kB2
value is known.
Discussion
from both the oxidation and reduction reactions by using the
Marcus cross relation, which were then compared with the
values measured directly by the NMR method. The esti-
mated self-exchange rate constants from the cross reactions
were 2.0 × 103 and (0.67–1.9) × 103 kg mol–1 s–1 from the
oxidation reactions of Cu(bcp)2 and Cu(dmbp)2 , respec-
tively, while the estimated self-exchange rate constants from
the reduction cross reactions were merely 1.2 and 1.4 kg
mol–1 s–1. As the electron self-exchange rate constants mea-
General
Rorabacher et al. (5–9) explained the “gated” electron
transfer for copper – cyclic thioether ions using the mecha-
nism described by Scheme 1. The reactions proceeded
mostly through Path A for the copper–thioether complexes
by comparing the electron self-exchange rate constants esti-
mated from both the reduction and oxidation cross reactions.
In this study, the electron self-exchange rate constants for
+
+
2+/+
2+/+
the Cu(bcp)2
and Cu(dmbp)2
couples were estimated
© 1999 NRC Canada

Koshino et al.
1503
Table 3. Absorption band maxima for Cu(bcp)2(ClO4)2 and
Cu(dmbp)2(ClO4)2 observed by the diffuse reflectance
spectrophotometry.a
Oxidation reaction:
d[CuIL]
[11]
−
dt
k2BkQO
k2A[AOx] + kPR kB2[ARed ] + kQO
k2AkRP
=
+
[CuIL(R)][AOx
]
CuIIL(O) and CuIL(R) represent the Cu(II) and Cu(I) spe-
2+
cies in the ground state: i.e., CuIIL(O) = Cu(bcp)2 or
2+
+
Cu(dmbp)2 in the D2d symmetry, and CuIL(R) = Cu(bcp)2
+
or Cu(dmbp)2 in the Td symmetry. As the reduction reac-
tions of Cu(bcp)2 and Cu(dmbp)2 take place through
Path B, the rate law is expressed by eq. [7]. When kB2[ARed
2+
2+
]
<< kQO, eq. [7] is reduced to eq. [12], and the dependence of
the pseudo-first-order rate constant on the concentration of
CuIIL becomes linear as seen for the reduction reactions of
2+
2+
2+
Cu(bcp)2 or Cu(dmbp)2 by Co(bipy)3
.
b
b
Assignment
Cu(bcp)2(ClO4)2
Cu(dmbp)2(ClO4)2
kOQkB2
[12] kobs
=
[CuIIL]
([ARed ]0 << [CuIIL]0)
Charge transfer
23697
14064
9891 (broad)
8658 (shoulder)
5984
27027
13698
9900 (broad)
8620 (shoulder)
6042
kQO
2
2B2 → A1
2B2 → Γ6(2E)
On the other hand, when [ARed] >> [CuIIL], the depend-
ence of kobs on [ARed]0 deviates from a straight line as seen
in Fig. 3. The slopes of the plots in Fig. 4 are given by
kQO/kB2kOQ (= 1/KOQkB2).
2
2B2 → B1
2B2 → Γ7(2E)
aThe 10Dq value for the imaginary tetrahedral field was estimated as
6.4 × 103 cm–1 for Cu(bcp)2 and 6.2 × 103 cm–1 for Cu(dmbp)2 from
2+
2+
As the theoretical investigation for intramolecular ET re-
actions by Brunschwig and Sutin (4) suggests that no reac-
tion path with high-λ intermediate compete with the direct
electron transfer in the normal region, the kinetic results ob-
tained in this study strongly indicate the intermolecular
gated electron transfer after a conformational change.
With a d9 configuration, Cu(II) ion prefers tetragonal
structure in general. In the case of Cu(bcp)22+, it has been re-
ported that the ground state structure is already largely dis-
torted from the normal tetragonal structure, and the dihedral
angle between the two phenanthroline planes is close to 60°
(33), while the dihedral angle for Cu(dmbp)22+ is merely 35°
from the ESR measurements (33).3 However, the similar val-
ues of the electron self-exchange rate constants for the
2
2
2
2
the difference between the average value of the B2 → B1 and B2 → A1
transition and the average value of the energy levels of B2, Γ7(2E), and
2
Γ6(2E) (see text).
bBand maximum/cm–l.
sured by the NMR method are 1.4 × 103 and 5.5 × 103 kg
2+/+
2+/+
mol–1 s–1 for the Cu(bcp)2
and Cu(dmbp)2
couples, re-
2+/+
spectively, the reactions involving the Cu(bcp)2
and
couples may also be gated, and the preferred
2+/+
Cu(dmbp)2
pathway for the redox reactions of these couples seems Path
B in Scheme 1, rather than Path A observed for the reactions
of copper – macrocyclic thioether complexes.
According to Scheme 1, Rorabacher and co-workers (5, 6)
derived rate laws for oxidation and reduction reactions cor-
responding to Path A and Path B as follows, by assuming
steady state for the concentrations of the intermediates,
CuIIL(Q) and CuIL(P).
2+/+
2+/+
Cu(bcp)2
and Cu(dmbp)2
couples indicate that either
2+
the coordination geometry or the ligand field in Cu(bcp)2
2+
and Cu(dmbp)2 is similar to each other. The similarity of
the absorption spectra of these ions (Table 3) also indicates
that the ligand fields by the bcp and dmbp ligands are simi-
lar to each other. From the crystal structures, these Cu(II)
species may be the five coordination in solution (39, 40).
However, the water exchange rate constant of five coordi-
′′
nated Cu(II)-2,2′,2 -triaminotriethylamine complex is 2 ×
Reduction reaction:
105 s–1 (41), which is much larger than the conformational
change process, kOQ. Therefore, such a fast solvent exchange
for the fifth coordinated solvent molecule on Cu(II) may not
affect the very slow conformational change from CuIIL(O)
to CuIIL(Q).
d[CuIIL]
[10]
−
dt
The crystal structures of the Cu(I) species have been re-
ported: the dihedral angles between the two ligands for
Cu(bcp)2 and Cu(dmbp)2 are 87.5° and 80.9°, respectively
(32, 42). By considering the flexibility along the C—C bond
kB2kOQ
kA2kPR
=
+
[CuIIL(O)][ARed
]
k2A[AOx] + kPR
k
B2[ARed ] + kQO
+
+
2+
3 ESR parameters, g// and A//, were estimated for Cu(dmbp)2 as 2.22 and 127 G, respectively, in glassy methanol at 77 K in this study. Ac-
cording to the relation of the dihedral angle and g// postulated by Yokoi and Addison (38), an apparent dihedral angle was estimated as 35°.
However, the flexible bipyridine ligands such as dmbp may not follow the norm postulated by Yokoi and Addison.
© 1999 NRC Canada

1504
Can. J. Chem. Vol. 77, 1999
of the dmbp ligand, the coordination structures of Cu(I) spe-
cies examined in this study may be considered to be close to
Td in solution, as the strong preference of the tetrahedral
structure by Cu(I) is well established (43).
It is possible to estimate the energy difference (LFAE) be-
tween the tetragonal CuIIL(O) ground state and the hypothet-
ical tetrahedral CuIIL(Q) state, by calculating the 10Dq
value corresponding to the hypothetical tetrahedral confor-
mation of CuIIL(Q) (4∆o/9) from the diffuse reflectance
spectra of Cu(bcp)2(ClO4)2 and Cu(dmbp)2(ClO4)2 species
(44). The absorption band maxima were observed as shown
in Table 3. As the distortion from the ordinary tetragonal
structure lifts the degeneracy of all d orbitals (45, 46), four
Cu(II) species seems preferred compared with the
2+/+
deformation of Cu(I) for the cases of Cu(N2)2
couples.
The preference of Path A in the case of Cu – macrocyclic
thioether complexes (5–9) may be attributed to the less sta-
ble structures of CuIL(R) species in solution: water or sol-
vent coordination to the fourth position of Cu(I) is suggested
for the [12]aneS4, [13]aneS4, [14]aneS4 complexes, while
corresponding Cu(II) complexes hold relatively planar coor-
dination geometry suitable for the stabilization of CuIIL(O).
Estimation of KOQ and kB2
The value of the kB2 process depends on the nature of the
reaction partner, as this process includes the effect of the in-
ner-sphere free energy change and the redox potential of the
reductant. However, kB2 may be very fast: the deformation
of Cu(bcp)22+ to Cu(bcp)22+* raises the redox potential of the
2
2
2
major absorptions corresponding to B2 → Γ7(2E), B2 →
2B1, B2 → 2Γ6(2E), B2 → 2A1 should appear in the visible
and near IR regions (the notation for the D2d symmetry is
used). The observed band maxima were assigned to these
transitions. Following the method of Gouge et al. (45), the
2
2
+
Cu(bcp)22+*/Cu(bcp)2 couple as much as the structural de-
2+
2+*
formation of Cu(bcp)2 to Cu(bcp)2
before the electron
2+*
transfer process, and the electron transfer (kB2) with minimal
internal rearrangement for Cu(II) species must be very fast.
The rise of the redox potential, which is equivalent to the
LFAE, is estimated by using the Nernst equation.
10Dq values for the hypothetically tetrahedral Cu(bcp)2
2+*
and Cu(dmbp)2 (= CuIIL(Q)) were estimated as shown in
Table 3. It is assumed that the original energy level for the
spherically symmetrical CuN4 geometry lies close to the dif-
ference in the weighted mean energy levels of T and E
terms.4 By using the 10Dq values of hypothetical CuIIL(Q),
the ligand field stabilization energies (LFSE) for the imagi-
nary tetrahedral geometry and the ground state geometry of
RT
[13]
E°Cu2 +* / + = E°Cu2 +/ +
−
ln KOQ
F
where E°Cu2 +* / + , E°Cu2 +/ + , and F are the standard redox po-
2+
d9 Cu(bcp)2 were calculated as –2560 and –7720 cm–1 rel-
tentials of the Cu(bcp)22+*/+ and Cu(bcp)22+/+ couples and the
Faraday constant, respectively. In this study, we obtained
0.275 V as E°Cu2 +/ + with reference to ferricinium/ferrocene
couple. As the value of KOQ (= kOQ/kQO) is expected to be
small (no significant spectral change corresponding to the
existence of such intermediate was observed throughout the
study), E°Cu2 +* / + may be large.
2+
ative to the energy of the spherically symmetric CuN4
(–2500 and –7650 cm–1 were calculated for Cu(dmbp)22+).
2+
The largely distorted tetragonal structures of Cu(bcp)2 and
Cu(dmbp)22+ in the ground state are, therefore, still ca. 62 kJ
mol–1 more stabilized compared with perfectly tetrahedral
geometry for both of the bcp and dmbp complexes, and this
value may be taken as the upper limit of the free energy dif-
To the outer-sphere electron transfer reaction correspond-
ing to the kB2 process, the Marcus cross relation is applica-
ble. Coulombic work terms may be ignored for the reactions
2+
2+
ference between Cu(bcp)2 or Cu(dmbp)2 (= CuIIL(O)) in
2+*
the ground state and hypothetical Cu(bcp)2
or
2+*
Cu(dmbp)2 (= CuIIL(Q)) in the tetrahedral configuration.
It should be noted that the LFAE calculation above does not
include the entropic contribution to the free energy.
2+*
of Cu(bcp)2 with ferrocene (29, 37).
[14] kB2
[15] ln f
=
= kCu2 +* / + kFe+/ 0 KCu2 +* / Fe fW
As it is clear that the reduction reactions of CuIIL(O)
2+
2+
(= Cu(bcp)2 and Cu(dmbp)2 complexes) take place through
Path B in Scheme 1, microscopic reversibility requires that
the oxidation reaction of CuIL(R) should also take place
through Path B. Therefore, CuIL(P) is necessarily less stable
than CuIIL(Q). Cu(I) with d10 electronic configuration is well
known to be stabilized as its tetrahedral form. The less sta-
bility of CuIL(P) (distorted tetragonal form) may, therefore,
be attributed to the nature of Cu(I) with a strong thermody-
namic preference to form the tetrahedral geometry. Such ten-
dency is explained by the possible hybridization of the 3d,
4s, and 4p orbitals and by the covalent character of the
bonding. The tetrahedral Cu(I)(N2)2 is some 100 kJ mol–1
more stable than the hydrated Cu(I) ions, from the stability
constant of Cu(I) species.5 Therefore, the deformation of
[ln KCu2 +* + (w Cu2 +* / Fe−wCu+
) /RT ]2
/ Fe+
/Fe
4[ln (kCu2 +* / + kFe+/ 0 / Z2) + (wCu2 +* / + + wFe+/ 0 ) / RT ]
−(wCu2 +* + wCu+/ Fe+ −wCu2 +* / + −wFe+/ 0
)
/ Fe
[16] W = exp
2RT
37.9zizj
[17] wij
=
(kJ mol−1)
a(1 + 0.481a µ)
where a, z, and µ are the interatomic distances (Å) between
the reacting species, charge on complex ions, and the ionic
4 The octahedral 10Dq value for Cu(en)32+ was reported as 1.64 × 104 cm–1 by Orgel (47). The 4/9 of this value, 7.2 × 103 cm–1, may be taken
as the 10Dq for the tetrahedral coordination. Therefore, the values of 6.4 × 103 and 6.2 × 103 cm–1 obtained here seem reasonable as hypo-
thetical 10Dq for the bcp and dmbp complexes.
+
5 The stability constant for Cu(dmp)2 (dmp = 2,9-dimethyl-1,10-phenanthroline) is reported as 1019.1 in water (48). With a naive assumption
that the chemical potential of the distorted tetragonal form of Cu(I) is close to that for solvated Cu(I), the free energy difference between the
+
+
solvated Cuaq and Cu(dmp)2 in water is estimated as 109 kJ mol–1 at 298 K. This value may be regarded as the upper limit for the energy
difference between CuIL(R) and CuIL(P).
© 1999 NRC Canada

Koshino et al.
1505
Scheme 2.
2+
strength of the solution, respectively. By using the slope of
the plot in Fig. 4, eq. [14] is rearranged to eq. [18].
results were obtained for the reaction of Cu(dmbp)2 with
ferrocene. The kinetic parameters estimated for the reactions
2+
2+
of Cu(bcp)2 and Cu(dmbp)2 are summarized in Table 2.
The large negative activation entropies for the kOQ process
may be explained by the similar effect observed for several
racemization reactions through the “twist” mechanism (50).
The estimated pre-equilibrium constant for Path A (KRP) by
Villeneuve et al. (51) is in the order of 1 × 10–3 to 1 × 10–6
for Cu+ – macrocyclic polythiaether complex. The value for
[18] kB2 = 4.6 ×104 kCu2 +* / + kFe+/ 0 Sf
where S denotes the slope obtained from the plot in Fig. 4,
and 4.6 × 104 represents the equilibrium constant for the
2+
overall reaction of Cu(bcp)2 with ferrocene (∆E° = 0.275
V).
The value of kCu2 +* / + may be estimated as the limiting
electron transfer rate constant by using Marcus theory (1),
assuming this process is essentially controlled by the outer-
sphere reorganization free energy and the electrostatic terms:
2+
KOQ estimated in this study for CuN4 (≈ 10–6) is close to
the lowest limit of the estimated value for Cu+ – macro-
cyclic polythiaether complexes, which indicates that the de-
formation in the Cu(I)-S species is the more preferable to
that in the Cu(II)-S species (intermediate P is the more sta-
ble compared with Q).
12 kJ mol–1 for ∆G*os and 0.5 kJ mol–1 for ∆Gc*oul + ∆G*DH
,
respectively, by setting the ionic radii of both Cu(bcp)22+/+ to
760 pm in acetonitrile at 298 K (33). Using the value of
∆Go*s, kCu2 +* / + can be calculated as 3.8 × 1010 kg mol–1 s–1.
This result was obtained under the assumption that the reac-
tions (each self-exchange reaction and the cross reaction) are
adiabatic with the transmission coefficient, κ, is unity. As
the driving force of the cross reaction is very large, the f fac-
tor in the Marcus cross relation becomes significantly
smaller than 1. As a result, the calculated self-exchange rate
constant for the Cu2+*/+ couple becomes very large. There-
fore, the value of 3.8 × 1010 kg mol–1 s–1 estimated here in-
dicates that the electron self-exchange rate constant for the
Cu2+*/+ couple is taken to be close to the diffusion limit in
acetonitrile. A similar explanation is possible for the value
of kB2 estimated below. With 3.8 × 1010 kg mol–1 s–1 thus es-
timated for kCu2 +* / + , a value of 6.6 × 1010 kg mol–1 s–1 was
obtained for kB2 by using the reported value of kFe+/ 0 , the
Apparent electron self-exchange rate constant directly
measured by NMR for the gated reactions
It is possible that Path B is also the more preferred for the
2+/+
electron self-exchange reactions of the Cu(bcp)2
Cu(dmbp)2
and
2+/+
couples. As the free energy profile for the
electron self-exchange reaction is symmetric along the reac-
tion coordinate (Scheme 2), the rate law of the electron self-
exchange reaction is described by eq. [19], assuming steady
state for CuIIL(Q).
kOQ
CuIIL(O) º CuIIL(Q)
kQO
kET
CuIIL(Q) + *CuIL(R) ¸ CuIL(R) + *CuIIL(Q)
electron self-exchange rate constant for the ferricinium/fer-
rocene couple (49). Therefore, KOQ = 6.2 × 10–6, and kQO
=
kETkOQ/kQO
2+
6.5 × 106 s–1. The free energy difference between Cu(bcp)2
[19] Rate =
[Cu(I)]T[Cu(II)]T
2+*
1 + kOQ/kQO
and Cu(bcp)2
is ca. 31 kJ mol–1, which is rather small
compared with the estimated value, 62 kJ mol–1 from the
LFAE calculation. These results indicate that the structure of
CuIIL(Q) is either not perfectly tetrahedral as assumed for
the above LFAE calculation, or the contribution of the en-
tropy or the steric repulsion between four methyl groups on
the ligands to the free energy is close to 31 kJ mol–1. Similar
−1
[20]
τ
= kex[Cu(II)]T
kETkOQ/kQO
ex
[21] kex
=
1 + kOQ/kQO
© 1999 NRC Canada

1506
Can. J. Chem. Vol. 77, 1999
where [Cu(I)]T and [Cu(II)]T denote the total concentrations
of Cu(I) and Cu(II) species, respectively. When kOQ is small
compared with kQO
CuIL(P) may be underestimated; or (ii) the relation of
eq. [23] is not applicable to the cross reactions with very
large reorganization parameters (1, 2), probably through the
anharmonic nature of the potential surface; or (iii) the direct
ET is nonadiabatic. In either case, the self-exchange, oxida-
[22] kex = kETkOQ/kQO
2+/+
tion, and reduction cross reactions involving Cu(bcp)2
The values of kQO and kOQ are 6.5 × 106 s–1 and 40 s–1 for
and Cu(dmbp)22+/+ are all gated, as the gated process is ener-
getically preferred. It is known that anharmonicity of the po-
tential surface increases the value of transition probability
(52), and quantum mechanical correction also increases the
ET rate (53). Moreover, it is not probable that the reorgani-
zation energy required for the structural change from
CuIL(R) to CuIL(P) is as large as 350 kJ mol–1. Therefore, it
may be concluded that the very slow direct (concerted) elec-
tron exchange between CuIIL(O) and CuIL(R) is attributed to
the nonadiabaticity of the reaction: a poor electronic cou-
pling between CuIL(R) and CuIIL(O) may originate from the
ion pairing, the extensive solvation of these species in
acetonitrile, and (or) the delocalization of the metal d elec-
trons on the central Cu(II)/(I) ions because of the weak or-
bital interactions between Cu(II)/(I) and ligands in the
deformed geometry (49, 54, 55). Nonadiabaticity of the di-
rect ET process was also suggested for a certain directional
(or intramolecular gated) reaction by Brunschwig and Sutin
[4].
2+
the deformation of Cu(bcp)2 while kET (ET rate constant
for the CuIIL(Q)/CuIL(R) couple without structural change,
kCu2 +* / + ) is 3.8 × 1010 kg mol–1 s–1 as estimated above. There-
2+/+
fore, kex for the Cu(bcp)2
couple is calculated as 2.4 ×
105 kg mol–1 s–1, which may be compared with the directly
measured value by NMR (1.4 × 103 kg mol–1 s–1). For the
electron self-exchange of Cu(dmbp)22+/+, a value of 3.9 ×
104 kg mol–1 s–1 was calculated from eq. [22], while kex esti-
mated by the NMR method was 5.5 × 103 kg mol–1 s–1. Such
differences may be attributed to the error introduced by the
rough nature of the estimation of kCu2 +* / + . The activation free
energy for the gated exchange reaction is, therefore, close to
50 ± 10 kJ mol–1.
Direct (concerted) ET and Gated ET
The activation free energies obtained for the cross reac-
tions examined in this study may be compared with those
expected for the direct (concerted) electron transfer pro-
cesses. The reorganization parameter for the cross reaction,
λcrpross, is generally described by eq. [23] (1, 2, 4).
Conclusions
Cu
rp
Fe
λ
+ λ
rp
cross
[23]
λ
=
2+/+
rp
Reduction and oxidation reactions of the Cu(bcp)2
and
2
2+/+
Cu(dmbp)2
couples were examined in acetonitrile. It was
2+
Cu
Fe
found that the reduction reactions of Cu(bcp)2
and
where λ and λ represent the reorganization parameters
rp
rp
2+
Cu(dmbp)2 were regulated by the slow conformational
change, and the reactions proceeded through Path B in
Scheme 1. The conformational change in Cu(II) species was
attributed to the large LFAE from tetragonal CuIIL(O) to the
pseudo-tetrahedral CuIIL(Q).
of the imaginary direct self-exchange reactions for
Cu(dmbp)22+/+ and Fe(Cp)2+/0. The experimental results indi-
2+
cate that the reduction reaction of Cu(dmbp)2 by ferrocene
is gated. As the free energy difference for the reaction of
Cu(dmbp)22+ with ferrocene, ∆G°, is 32 kJ mol–1, the follow-
ing relation should be satisfied to achieve the observed
gated ET
The apparent self-electron exchange rate constants for the
2+/+
2+/+
Cu(bcp)2
and Cu(dmbp)2
couples were examined on
the basis of the gated mechanism through Path B, and the
calculated electron self-exchange rate constants using kOQ
and kQO estimated from the results of the cross reactions
were in fair agreement with the directly measured kex by the
NMR method. Theoretical calculations of the activation free
energies for the direct exchange reaction indicate that all the
reactions, including the self-exchange reactions, examined in
this study are gated through Path B in Scheme 1.
Nonadiabaticity was suggested for the explanation of the
very large free energy barrier of the direct exchange between
CuIIL(O) and CuIL(R).
− ∆G°)2
cross
(λ
rp
[24]
>> ∆G*gated
cross
4λ
rp
where ∆G*gated is the activation free energy observed for the
cross reaction of Cu(dmbp)22+ and ferrocene, ca. 50 kJ mol–1
(k12 = KOQkB2). Therefore, λ >> 388 kJ mol–1 by solving
Cu
rp
inequality [24] as λFrpe/4 is 33 kJ mol–1 (kFe+/ 0 = 9 × 106 dm3
mol–1 s–1). A similar result was obtained for the reactions of
Cu(bcp)22+/+. The expected activation free energy, ∆G*, for
2+/+
the direct exchange reaction of the Cu(L)2
couple (L =
bcp or dmbp) should then be larger than 100 kJ mol–1. The
reorganization parameter for an electron self-exchange reac-
tion is defined as the sum of the free energy of the products
at the equilibrium nuclear configuration of the product’s
state (1, 4). The estimated very large reorganization parame-
Acknowledgments
This research was supported by the Grant-in-Aid for Sci-
entific Research (grant no. 10440193) from the Ministry of
Education, Science, Sports and Culture of Japan. N. Koshino
held a scholarship from Sasagawa Foundation for Young
Scientists.
ter, >>400 kJ mol–1, for the direct self-exchange reaction of
2+/+
Cu(L)2
indicates that the inner-sphere and outer-sphere
contribution to the reorganization parameter is significantly
larger than the sum of the estimated values: 31 kJ mol–1 for
the deformation of CuIIL(O) to CuIIL(Q) and 100 kJ mol–1
for the deformation of CuIL(R) to CuIL(P). Therefore, either
(i) the free energy change for the deformation of CuIL(R) to
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