First investigation at elevated pressures to confirm the exact nature of the gated electron-transfer systems: Volume profiles of the gated reduction reaction and nongated reverse oxidation reaction involving a [Cu(dmp) 2(solvent)]2+/[Cu(dmp)2]+ couple (dmp = 2,9-Dimethyl-1,10-phenanthroline)

Article abstract of DOI:10.1021/ic061591i

Redox reactions involving the [Cu(dmp)²]^2+/+ couple (dmp = 2,9-dimethyl-1,10-phenanthroline) in acetonitrile were examined at elevated pressures up to 200 MPa. Activation volumes were determined as -8.8 and -6.3 cm³ mol^-1 for the reduction cross-reaction by [Co(bipy)₃]²⁺ (bipy = 2,2′-bipyridine) and for the oxidation cross-reaction by [Ni(tacn)₂]³⁺ (tacn = 1,4,7-triazacyclononane), respectively. The activation volume for the hypothetical gated mode of the self-exchange reaction estimated from the reduction cross-reaction was -13.9 cm³ mol^-1, indicating extensive electrostrictive rearrangement of solvent molecules around the Cu ^II complex during the change in the coordination geometry before the electron-transfer step. On the other hand, the activation volume for the self-exchange reaction estimated from the oxidation cross-reaction was -2.7 ± 1.5 cm³ mol^-1. Although this value was within the range that can be interpreted by the concept of the ordinary concerted process, from theoretical considerations it was concluded that the reverse (oxidation) cross-reaction of the gated reduction reaction of the [Cu(dmp) ₂(CH₃CN)]²⁺/ [Cu(dmp)₂]⁺ couple proceeds through the product excited state while the direct self-exchange reaction between [Cu(dmp)₂(CH₃CN)]²⁺ and [Cu(dmp)₂]⁺ proceeds through an ordinary concerted process.

Full text of DOI:10.1021/ic061591i

Inorg. Chem. 2007, 46, 1419−1425
First Investigation at Elevated Pressures To Confirm the Exact Nature
of the Gated Electron-Transfer Systems: Volume Profiles of the Gated
Reduction Reaction and Nongated Reverse Oxidation Reaction Involving
+
+
a [Cu(dmp)2(solvent)]2 /[Cu(dmp)2] Couple (dmp
)
2,9-Dimethyl-1,10-phenanthroline)
Sumitaka Itoh, Kyoko Noda, Ryouhei Yamane, Nobuyuki Kishikawa, and Hideo D. Takagi*
Graduate School of Science and Research Center for Materials Science, Nagoya UniVersity,
Furo-cho, Chikusa, Nagoya 464-8602, Japan
Received August 22, 2006
+/+
Redox reactions involving the [Cu(dmp)2]2 couple (dmp
)
2,9-dimethyl-1,10-phenanthroline) in acetonitrile were
1
examined at elevated pressures up to 200 MPa. Activation volumes were determined as
for the reduction cross-reaction by [Co(bipy)3]2 (bipy
−8.8 and −
6.3 cm3 mol-
+
) 2,2′-bipyridine) and for the oxidation cross-reaction by
+
[Ni(tacn)2]3 (tacn
)
1,4,7-triazacyclononane), respectively. The activation volume for the hypothetical gated mode
of the self-exchange reaction estimated from the reduction cross-reaction was
electrostrictive rearrangement of solvent molecules around the CuII complex during the change in the coordination
geometry before the electron-transfer step. On the other hand, the activation volume for the self-exchange reaction
−
13.9 cm3 mol-1, indicating extensive
estimated from the oxidation cross-reaction was
−2.7 ±
1.5 cm3 mol-1. Although this value was within the range
that can be interpreted by the concept of the ordinary concerted process, from theoretical considerations it was
+
concluded that the reverse (oxidation) cross-reaction of the gated reduction reaction of the [Cu(dmp)2(CH3CN)]2
/
[Cu(dmp)2]+ couple proceeds through the product excited state while the direct self-exchange reaction between
+
[Cu(dmp)2(CH3CN)]2 and [Cu(dmp)2]+ proceeds through an ordinary concerted process.
Scheme 1
Introduction
Gated electron-transfer (ET) reactions involving CuII/CuI
centers are related to the biologically important catalytic
processes.1,2 Among investigations carried out to date,
systematic studies by Rorabacher and co-workers have
largely improved the understanding of the gated phenom-
ena: they postulated a dual-pathway square scheme (Scheme
1).3-5 In the square scheme, only one of the reactants [CuIL-
(R) or CuIIL(O), where L stands for the coordinated ligands]
changes its structure before the ET step, and the choice of
path A or path B depends on the energy of the deformed
species, P or Q. In general, ET reactions of copper(II)/copper-
(I) polythioether complexes proceed through path A in
Scheme 1, and the direction in which the estimated self-
exchange rate constant is much smaller than that directly
measured by NMR is gated. Rorabacher and co-workers
attributed the cause of the gated phenomena to the sluggish
conformational change of the coordinated multidentate
macrocyclic polythiaether ligands3-5 because structures of
CuI and CuII species should come close to each other at the
* To whom correspondence should be addressed. E-mail: h.d.takagi@
chem.nagoya-u.ac.jp.
(1) Williams, R. P. J. Eur. J. Biochem. 1995, 234, 363-381.
(2) Kaim, W.; Schwederski, B. Bioinorganic Chemistry: Inorganic
Elements in the Chemistry of Life; Wiley: Chichester, U.K., 1994.
(3) Martin, M. J.; Endicott, J. F.; Ochrymowycz, L. A.; Rorabacher, D.
B. Inorg. Chem. 1987, 26, 3012-3022.
(4) Rorabacher, D. B.; Meagher, N. E.; Juntunen, K. L.; Robandt, P. V.;
Leggett, G. H.; Salhi, C. A.; Dunn, B. C.; Schroeder, R. R.;
Ochrymowycz, L. A. Pure Appl. Chem. 1993, 65, 573-578.
(5) Rorabacher, D. B. Chem. ReV. 2004, 104, 651-697.
10.1021/ic061591i CCC: $37.00
Published on Web 01/19/2007
© 2007 American Chemical Society
Inorganic Chemistry, Vol. 46, No. 4, 2007 1419

Itoh et al.
transition state, according to the Marcus theory for the outer-
sphere ET reactions.6,7
On the other hand, for redox reactions involving CuII/CuI
complexes with polypyridine ligands, the reduction direction
is always gated,8-10 although no sluggish conformational
change of the coordinated ligands is necessary for the
alterations of the coordination geometries around the CuII
and CuI centers in the case of these bidentate ligands. In the
most recent publication,11 we reported that consideration of
the direction for structural changes on the basis of the second-
order perturbation theory (symmetry rules and the principle
of least motion, PLM)12,13 successfully explains the gated
phenomena exhibited, at least, by copper(II)/copper(I) poly-
pyridine complexes. However, the pathway of the reverse
direction of the gated reaction as well as the direct self-
exchange reaction has to be confirmed for the better
understanding of the gated reactions.
In this study, we took advantage of the preciseness of the
volume analyses to clarify the exact nature of the gated
reaction systems: it has been proven that the volume analyses
are effective to precisely determine profiles of outer-sphere
ET reactions.14-16 We also revisited the results reported in
198917 for the activation volume of the direct self-exchange
reaction of the [Cu(dmp)2]2+/+ (dmp ) 2,9-dimethyl-1,10-
phenanthroline) couple in acetonitrile (Appendix A).
Figure 1. Pressure dependence of the electrode potentials for various redox
couples in acetonitrile: (O) [Cu(dmp)22+] ) 1.0 × 10-3 mol kg-1; (0)
[Ni(tacn)22+] ) 1.0 × 10-3 mol kg-1; (]) [Co(bipy)33+] ) 1.0 × 10-3
mol kg-1. The sweep rate is 0.1 V s-1. T ) 298 ( 1 K. I ) 0.1 mol kg-1
(TBAP). E0 denotes the redox potential at 0.1 MPa.
oven. However, it was shown that the complex exists as a five-
coordinate [Cu(dmp)2(solvent)]2+ species in donor solvents.11
18
[Co(bipy)3](ClO4)2 (bipy ) 2,2′-bipyridine) and [Ni(tacn)2]-
(ClO4)3 (tacn ) 1,4,7-triazacyclononane) were synthesized by the
literature methods.19 Anal. Calcd for CoC30H24N6Cl2O8: C, 49.6;
H, 3.33; N, 11.6. Found: 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. Caution! Perchlorate salts of metal
complexes with organic ligands are potentially explosiVe.
General Procedures. All manipulations were carried out in an
atmosphere of dry nitrogen to avoid possible contamination of water
and oxygen from the environment. The reaction volumes were
measured by the pressure dependence of the redox potentials at 25
°C by using a BAS 100B/W electrochemical analyzer. The pressure
vessel for the measurements was reported previously.10 We used a
glass electrochemical cell equipped with a 2.0-mm-diameter Pt disk
and a 1.0-mm-diameter Pt wire as the working and counter
electrodes, respectively. A silver/silver nitrate electrode used as a
reference was made by placing a solution (1.0 × 10-3 mol kg-1 of
AgNO3 with 0.10 mol kg-1 of nBu4NClO4 as the supporting
electrolyte) in a collapsible Teflon tube equipped with a vicor plug.
Kinetic measurements at ambient pressure were carried out by a
Unisoku RA401 stopped-flow apparatus, while the measurements
at elevated pressures were carried out by a Hi-Tech HPSF-50
apparatus. The reactions were monitored by observation of the
absorption change at 456 nm (the absorption band maximum of
[Cu(dmp)2]+). Paraffin oil was used as the pressurizing fluid, after
deaeration by dry nitrogen for 1 h.
Experimental Section
Chemicals. Acetonitrile was obtained from Wako Pure Chemi-
cals Inc. and purified by distillation from phosphorus pentoxide
and from 4A molecular sieves. The content of residual water in
thus purified acetonitrile was examined by a Mitsubishi Chemical
CA-07 Karl Fischer apparatus, by which the amount of residual
water was determined to be less than 1 mmol kg-1. Tetrabutylam-
monium perchlorate (nBuNClO4, TBAP) from Aldrich was twice
recrystallized from the mixture of an ethyl acetate/pentane solution
and dried under reduced pressure. All other chemicals from Wako
and Aldrich were used without further purification. [Cu(dmp)2]-
(ClO4)2 and [Cu(dmp)2]ClO4 were synthesized by the reported
methods.11 Anal. Calcd for CuC28H24N4Cl2O8: C, 49.5; N, 8.25;
H, 3.56. Found: C, 50.5; N, 8.16; H, 3.65. Anal. Calcd for
CuC28H24N4ClO4: C, 58.0; N, 9.67; H, 4.17. Found: C; 58.6, N,
9.87; H, 4.10. We were able to obtain [Cu(dmp)2](ClO4)2 by
removing the loosely coordinated solvent molecule using a vacuum
(6) Cannon, R. D. Electron Transfer Reactions; Butterworth: London,
1980.
Results
(7) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441-498.
(8) Koshino, N.; Kuchiyama, Y.; Ozaki, H.; Funahashi, S.; Takagi, H. D.
Inorg. Chem. 1999, 38, 3352-3360.
The reaction volumes of the redox couples used in this
study were determined from the pressure dependence of the
redox potentials at 298 K.
(9) Itoh, S.; Funahashi, S.; Koshino, N.; Takagi, H. D. Inorg. Chim. Acta
2001, 324, 252-265.
(10) Itoh, S.; Funahashi, S.; Takagi, H. D. Chem. Phys. Lett. 2001, 344,
441-449.
∂∆G°
∂P
∂E°
∂P
∆Vcell° )
) -nF
(1)
(
)
(
)
T
T
(11) Itoh, S.; Kishikawa, N.; Suzuki, T.; Takagi, H. D. Dalton Trans. 2005,
1066-1078.
(12) Pearson, R. G. Symmetry Rules for Chemical Reactions; Wiley: New
York, 1976.
All redox couples examined in this study were either
electrochemically reversible or quasi-reversible. The pressure
dependence of the electrode potentials is shown in Figure 1
for each redox couple (Table S1 in the Supporting Informa-
(13) Rice, F. O.; Teller, E. J. Chem. Phys. 1938, 6, 489-496.
(14) Swaddle, T. W. Inorg. Chem. 1990, 29, 5017-5025.
(15) Grace, M. R.; Takagi, H. D.; Swaddle, T. W. Inorg. Chem. 1994, 33,
1915-1920.
(16) Swaddle, T. W. In Inorganic High Pressure Chemistry, van Eldik,
R., Ed.; Elsevier: Amsterdam, The Netherlands, 1985; Chapter 4.
(17) Doine (Takagi), H.; Yano, Y.; Swaddle, T. W. Inorg. Chem. 1989,
28, 2319-2322.
(18) Davies, G.; Loose, D. J. Inorg. Chem. 1976, 15, 694-700.
(19) McAuley, A.; Norman, P. R.; Olubuyide, O. Inorg. Chem. 1984, 23,
1938-1943.
1420 Inorganic Chemistry, Vol. 46, No. 4, 2007

Volume Profiles InWolWing [Cu(dmp)2(solWent)]2+/[Cu(dmp)2]+
Table 1. Reaction Volumes for Various Redox Couples in Acetonitrilea
Scheme 2
redox couple
∆Vcell°/cm3 mol-1
[Cu(dmp)2]2+/+
[Ni(tacn)2]3+/2+
[Co(bipy)3]3+/2+
19.8 ( 0.7
16.9 ( 0.5
18.4 ( 0.4
a I ) 0.1 mol kg-1 (TBAP).
tion). The overall reaction volumes (∆Vcell°) corresponding
to Scheme 2, calculated from the slopes of the plots in Figure
1, are listed in Table 1. To determine the reaction volume
of a cross-reaction, it is not necessary to isolate ∆VM
1)+°, provided that the identical reference electrode is used
for all measurements of ∆Vcell°.20
was isolated from solvents with relatively large basicity such
as water and acetonitrile, while the complex with a four-
coordinate D2 structure was isolated from solvents with low
basicity such as nitromethane. In the former structure, one
of the coordination sites in the trigonal plane is occupied by
a solvent molecule. Kinetic measurements revealed that the
reduction reaction of the latter species in nitromethane was
the first example of the fully gated reaction: the reduction
reaction was completely regulated by the rate of the slow
(symmetrically forbidden) structural change (kOQ ) 1.17 s-1
at 25 °C).11 On the other hand, it was reported8,9 that the
reductions of the five-coordinate complex in acetonitrile
proceeded through the gated mechanism with a faster
structural change (kOQ ) ca. 30 s-1 at 25 °C) followed by
the rapid ET.8 With these results, we postulated two essential
factors that are necessary for the occurrence of gated
reactions:9,11 (1) the nonadiabatic nature of the direct ET
reactions involving the ground-state species (“O” in Scheme
1) and (2) slow structural changes so as to induce better
electronic coupling with the counter-reagent through the
charge-transfer (CT)-perturbed superexchange-type interac-
tion. According to the theoretical discussion by Brunschwig
and Sutin, the structural change is required to take place prior
to the formation of the encounter complex because a high-
energy (slow) structural activation before the ET process
within the encounter complex cannot compete with the
ordinary concerted reaction,21 which is nonadiabatic and very
slow for the reaction systems that exhibit gated behaviors.
The activation process of a redox-active species is
independent of the counter-reagent when the cross-relation
holds for cross-reactions with various counter-reagents:22 the
activation volume for the hypothetical self-exchange reaction
estimated from a cross-reaction reflects the activation mode
of the reactant in the cross-reaction. As shown in Table 2,
the activation volumes corresponding to the same hypotheti-
cal self-exchange process estimated from the oxidation and
reduction cross-reactions were different from each other for
the [Cu(dmp)2(CH3CN)]2+/[Cu(dmp)2]+ couple. This indi-
cates that the activation process/mode is certainly different
for the Cu species in two directions because the counter-
reactants are typical outer-sphere reagents for which the
activation process is always the same for all redox reactions.
In the gated reduction cross-reactions, two consecutive
structural activation steps are expected for [Cu(dmp)2(CH3-
CN)]2+ so as to maximize the electronic coupling with the
counter-reagent: (1) a change from the pseudo-D3h structure
of the ground-state geometry for CuII to the C2V structure by
n+/(n-
∆Vcell ) ∆VM0 n+/(n-1)+ + ∆V 0
(2)
0
reference
Pressure dependences of the rate constants are shown in
Figures 2 and 3 (Tables S2 and S3 in the Supporting
Information) for the examined oxidation and reduction cross-
reactions. The activation volumes corresponding to the
hypothetical electron self-exchange reaction between [Cu-
(dmp)2(CH3CN)]2+ and [Cu(dmp)2]+ were then calculated
by the following volume cross-relation, which has been
verified by Grace et al.15
∆V/11 + ∆V2/2 + ∆V12°
∆V/12
)
+ C
2
C )
X∆V12° ln K12 - 2(ln K12)2(∆V1/1 + ∆V/22 - ∆V1W1 - ∆V2W2)
X 2
k11k22
Z 2
w11 + w22
X ) 4 ln
+
(3)
(
)
[
]
RT
where ∆V/12 is the activation volume of the cross-reaction,
∆V/ , ∆V/ , k11, and k22 are the activation volumes and
11
22
corresponding rate constants for each electron self-exchange
reaction, ∆V12° is the reaction volume of the cross-reaction,
Z is the collision frequency, which is usually taken to be
1011, and wii and ∆VWii are the Coulombic work terms and
the corresponding volumes, respectively. Because the con-
tribution of the C term in the above equation was less than
1 cm3 mol-1 for both of the examined cross-reactions, this
term was ignored in the calculation: it has been known that
the uncertainty in the estimated activation volumes is
generally (1 cm3 mol-1. In Table 2, listed are the activation
volumes for the self-exchange reaction between [Cu(dmp)2-
(CH3CN)]2+ and [Cu(dmp)2]+ calculated from both directions
of the cross-reactions, together with the measured activation
volumes for each cross-reaction.
Discussion
We reported in the previous study that [Cu(dmp)2]2+
crystallized in two different forms, depending on the solvent
used for the syntheses:11 the complex with a five-coordinate
pseudo-trigonal-bipyramidal structure, [Cu(dmp)2(CH3CN)]2+,
(21) Brunschwig, B. S.; Sutin, N. J. Am. Chem. Soc. 1989, 111, 7454-
7465.
(20) Doine (Takagi), H.; Whitcombe, T. W.; Swaddle, T. W. Can. J. Chem.
1992, 70, 81-88.
(22) Ratner, M. A.; Levine, R. D. J. Am. Chem. Soc. 1980, 102, 4898-
4900.
Inorganic Chemistry, Vol. 46, No. 4, 2007 1421

Itoh et al.
allowed E normal-mode vibration takes place with a time
scale of 10-13 s, which is much shorter than the lifetime of
the encounter complex, ca. 10-10 s-1.
Because the observed overall reduction cross reaction is
gated,8 it is certain that the CuII-solvent bond completely
breaks at the first stage of the reaction. However, this solvent
dissociation process is not the sole reason for the observed
gated behavior: (1) the observed kOQ value (ca. 30 s-1) is
much smaller than the rate constant for this solvent dissocia-
tion, 106 s-1,24,25 and (2) CuII in C2V symmetry does not
exhibit a low-energy CT band, which is necessary for the
rapid ET reactions to occur.10 The succeeding structural
change from [Cu(dmp)2]2+ in C2V symmetry (the solvent CH3-
CN molecule is already removed) to the D2d structure is also
allowed through the normal B2 twist mode. Therefore, the
structural change that regulates the overall ET process
includes both of the pseudo-D3h to C2V and C2V to D2d
interconversions before the formation of the encounter
complex in which a rapid ET takes place. This situation is
expressed by the following mechanism.
Figure 2. Pressure dependence of the rate constant for the cross-reaction
between [Cu(dmp)2]+ and [Ni(tacn)2]3+ in acetonitrile. [Cu(dmp)2+] )
(1.44-1.71) × 10-5 mol kg-1. [Ni(tacn)23+] ) (1.48-1.72) × 10-4 mol
kg-1. T ) 298 ( 1 K. I ) 0.1 mol kg-1 (TBAP).
K
CuII(pseudo-D3h) y
\
z CuII(C2V) + solvent
CuII(C2V) yk1z CuII(D2d)
k-1
kB2
CuII(D2d) + Red ' CuI(D2d) + Ox
(4)
Figure 3. Pressure dependence of the rate constant for the cross-reaction
between [Cu(dmp)2]2+ and [Co(bipy)3]2+ in acetonitrile. [Cu(dmp)22+] )
(1.05 or 5.19) × 10-4 mol kg-1. [Co(bipy)32+] ) (2.57 or 4.93) × 10-5
mol kg-1. T ) 298 ( 1 K. I ) 0.1 mol kg-1 (TBAP).
The observed rate constant kobs is then expressed by the
following equation, by assuming a steady state for CuII in
D2d symmetry.
releasing the loosely coordinated solvent molecule and (2)
a further structural change to achieve the same symmetry as
that of CuI in the ground state, the D2d structure. Therefore,
it is necessary for the five-coordinate CuII species, [Cu(dmp)2-
(CH3CN)]2+, to form a four-coordinate intermediate (C2V),
in the first stage of the structural activation.
The symmetry rules and PLM12,13 indicate that the dis-
sociation of the solvent molecule from the trigonal plane of
the five-coordinate [Cu(dmp)2(CH3CN)]2+ in pseudo-D3h
symmetry is allowed to form a species in C2V symmetry
through the E normal-mode vibration. This kind of disso-
ciation process is quite common for transition-metal com-
plexes with D3h symmetry such as trans-[Ni(CN)2(triphe-
nylphosphine)3].23 Although this solvent dissociation from
CuII in pseudo-Tbp symmetry is as rapid as ca. 106 s-1,24,25
it may not take place within the encounter complex (the
Kk1kB [Red]
2
kobs
)
(5)
k [Red] + k-1
B2
In this case, Kk1 corresponds to kOQ in Scheme 1. The
equilibrium constant K is small because CuII(C2V) is consid-
ered to be an intermediate for the solvent-exchange reac-
tion: when the solvent-exchange (dissociation) rate constant
is ca. 106 s-1,24,25 the K value is estimated as ca. 1 × 10-5
M because the back reaction is expected to be diffusion-
controlled (ca. 1011 kg mol-1 s-1). Therefore, when Kk1 is
ca. 30 s-1,8 k1 is ca. 3 × 106 s-1. As a result, the time scale
of this twisting process, >10-7 s, is longer than the ordinary
lifetime of the encounter complex (ca. 10-10-10-12
s
depending on the charges on the reactants), and this twist
process also takes place prior to the formation of the
encounter complex. However, it should be noted that the
bond stretching by the E mode combined with the partial
twisting through the B2 mode may be acceptably rapid for
the concerted reaction to occur if the electronic coupling
between CuII and the counter-reagent is sufficiently large.
Such a case may be met when the counter-reagent is also a
copper polypyridine complex: the pseudo-self-exchange rate
constant for the reduction reaction of [Cu(dmbp)2(CH3CN)]2+
by [Cu(dmp)2]+ (dmbp ) 6,6′-dimethyl-2,2′-bipyridine, and
the reduction reaction of [Cu(dmbp)2(CH3CN)]2+ has been
known to be gated) was as fast as log k12 ) 4.4.11
lifetime of the encounter complex is in a range of 10-10
-
10-12 s, depending on the charges on the reactants). On the
other hand, structural deformation from pseudo-D3h to C2V
symmetry without dissociation of the coordinated solvent
molecule is also allowed to occur within the encounter
complex because this type of deformation through the
(23) Grimes, C. G.; Pearson, R. G. Inorg. Chem. 1974, 13, 970-977.
(24) Powell, D. H.; Merbach, A. E.; Fabian, I.; Schindler, S.; van Eldik,
R. Inorg. Chem. 1994, 33, 4468-4473.
(25) Nubrand, A.; Thaler, F.; Korner, M.; Zahl, A.; Hubbard, C.; van Eldik,
R. J. Chem. Soc., Dalton Trans. 2002, 957-961.
1422 Inorganic Chemistry, Vol. 46, No. 4, 2007

Volume Profiles InWolWing [Cu(dmp)2(solWent)]2+/[Cu(dmp)2]+
Table 2. Activation Volumes for the Self-Exchange Reaction of [Cu(dmp)2]2+/+ Estimated from the Cross-Reactions of Oxidation and Reduction
Directionsa
cross-reaction
∆V/12
∆V/22
∆V12°
∆V/11
[Cu(dmp)2]+ + [Ni(tacn)2]3+
[Cu(dmp)2]2+ + [Co(bipy)3]2+
-6.3 ( 0.3
-8.8 ( 0.1
-7 ( 1b
-2.9 ( 1.2
1.4 ( 0.9
-2.7 ( 2.8
-13.9 ( 2.5
-5.1 ( 1.4c
a cm3 mol-1 b Estimated value using the SHM equation.14,16 c Braum, P.; van Eldik, R. J. Chem. Soc., Chem. Commun. 1985, 1349-1350.
.
In the current reduction reaction of [Cu(dmp)2(CH3CN)]2+
by [Co(bipy)3]2+, kobs is given by eq 6, by defining new KOQ
as Kk1/k-1, under the experimental conditions [Red] , [CuII].
However, it has been pointed out by Brunschwig and Sutin
that a process through the product excited state is preferred
to the concerted process in the normal region. We, therefore,
safely conclude that the oxidation cross-reactions of [Cu-
(dmp)2]+ proceed through the product excited state (CuII in
D2d symmetry) without much change in the coordination
structure of D2d-CuI: this process corresponds to path B in
Scheme 1 (see also path B′ in Scheme 3-1 and Appendix
B). At this point, it is clear that the volume analyses cannot
distinguish the reaction through path B from the concerted
process because neither mechanism involves a significant
volume change at the rate-determining ET step.
On the other hand, we will encounter a difficulty when
the direct self-exchange reaction between [Cu(dmp)2(CH3-
CN)]2+ and [Cu(dmp)2]+ is considered: the direct self-
exchange reaction cannot proceed through the product excited
state for both CuII and CuI species because the overall
reaction profile of the self-exchange reaction should be
symmetric along the reaction coordinate. This situation is
graphically described in Scheme 3-2 (path A′; see also
Appendix B). As a result, the direct self-exchange reaction
may proceed through path B, as was shown in the previous
article (Scheme 3-1).8 However, the self-exchange rate
constant through path B is expressed by eq 9,8 and hence
the observed activation volume should exhibit the contribu-
kobs ) KOQkB
(6)
2
In this equation, kB stands for the rate constant of ET
2
between [Cu(dmp)2]2+ in D2d symmetry, CuIIL(Q), and the
counter-reagent (Scheme 1). Because the observed rate
constant is defined by eq 6, the calculated activation volume
for the reduction reaction is expressed by eq 8. Because the
∆V12 value (and, hence, K12 and ∆E12) reflects the difference
of the volume (free energy) between the initial and final
states, it does not include any information of the reaction
pathway. Therefore, the following discussion is valid, as the
hypothetical self-exchange reaction between CuII and CuI
both in the ground states is discussed.
∂ ln kobs
∆V/obs ) -RT
(7)
(8)
(
)
∂P
T
∆V/obs ) ∆VOQ + ∆V/B
2
where ∆VOQ and ∆V/ are the volume change from pseudo-
B2
D3h to D2d for CuII and the activation volume for the
succeeding ET between CuII in D2d symmetry and [Co-
tion of ∆VOQ
.
(bipy)3]2+, respectively. Because the kB process is governed
2
essentially by the outer-sphere contributions to the activation
kex ) KOQkET
(9)
process, ∆V/B is expected to be ca. -5 cm3 mol-1 according
2
to the Stranks-Hush-Marcus (SHM) theory:15,17 ∆VOQ
∼
∆V/ex ) ∆VOQ + ∆V/ET
(10)
-9 cm-3 mol-1. This large negative ∆VOQ may be attributed
to the solvation of the released solvent molecule from [Cu-
(dmp)2(CH3CN)]2+ and the solvent reorganization around
[Cu(dmp)2]2+, the latter of which is a result of the increased
CT interaction in D2d-[Cu(dmp)2]2+ compared with that in
C2V-[Cu(dmp)2]2+.
where kET corresponds to the rate constant for the ET process
between [Cu(dmp)2]2+ and [Cu(dmp)2]+, both of which are
in D2d symmetry, and hence the activation volume for this
process is ca. -5 cm-3 mol-1 from the SHM theory.15,17 From
eq 10, the activation volume for the self-exchange reaction
should be ca. -14 cm-3 mol-1, which is much more negative
compared with the directly measured activation volume, -3.4
cm3 mol-1.17 We, therefore, have to conclude that the direct
self-exchange reaction does not proceed through path B (see
also path B′ in Scheme 3-1), from the results obtained in
this study (Appendix B).
When the self-exchange reaction is concerted, both D2d-
CuI and pseudo-D3h-CuII structurally activate within the
encounter complex, without dissociation of the solvent
molecule from CuII (Scheme 3-3). As noted above, the time
scale for the bond stretching between CuII and the solvent
molecule (without the bond rupture) by the E mode (10-13
s), together with the partial twisting through the normal B2
mode (10-11-10-13 s), is sufficiently rapid to occur within
the encounter complex. However, this type of activation leads
On the other hand, the estimated activation volume for
the hypothetical self-exchange reaction, -2.7 ( 1.5 cm3
mol-1, by application of eq 3 to the result of the oxidation
cross-reaction of [Cu(dmp)2]+ by [Ni(tacn)2]3+, is consistent
with the activation volume calculated on the basis of the
SHM equation14,16 within experimental uncertainty. If the
oxidation reaction requires a large structural change of CuI,
from D2d to C2V, a large positive activation volume is
expected: Path A requires a structural change from D2d to
C2V and the polarity change in this activation process is the
reverse process to the activation of CuII. Therefore, we can
conclude that the oxidation cross-reaction of [Cu(dmp)2]+
by [Ni(tacn)2]3+ does not proceed through path A: this
oxidation process proceeds either through the concerted
mechanism or through the product excited state (path B).
Inorganic Chemistry, Vol. 46, No. 4, 2007 1423

Itoh et al.
Scheme 3. Modes of the Electron Self-Exchange Reaction between [Cu(dmp)2(solvent)]2+(pseudo-D3b) and [Cu(dmp)2]+(D2d)]2
Scheme 4. Reactions Involving a [Cu(dmp)2(solvent)]2+/[Cu(dmp)2]+
Couple
Appendix A
The gate behavior in the reduction reactions of [Cu-
(dmp)2]2+ was well established in the previous articles.8-11
The hypothetical self-exchange rare constant (1.6 M-1 s-1),
which was calculated by application of the Marcus cross-
relation to the reduction cross-reaction by [Co(bipy)3]2+,
indicates that the reduction reaction is controlled by the
structural change prior to the ET process because it is too
small compared with the hypothetical self-exchange rate
constant estimated from the oxidation cross-reactions.
the ET reaction only when the electronic coupling between
the two reactants is sufficiently large. We believe that the
electronic coupling between [Cu(dmp)2(CH3CN)]2+ and [Cu-
(dmp)2]+ is sufficiently large because the energy levels of
the d orbitals are much closer to each other compared with
those for the cross-reactions of [Cu(dmp)2(CH3CN)]2+ with
other metals. Such a situation was demonstrated by the
previously reported pseudo-self-exchange reaction between
[Cu(dmbp)2(CH3CN)]2+ and [Cu(dmp)2]+.11
It seems that the smaller self-exchange rate constant for
the [Cu(dmp)2(CH3CN)]2+/[Cu(dmp)2]+ couple, ca. 103 M-1
s-1, than those for blue copper proteins such as plastocyanin
or azurin, ca. 105-106 M-1 s-1, is a result of the extensive
inner-sphere rearrangement within the encounter complex
including (1) the elongation of the CuII-solvent bond to
induce structural activation to the C2V structure and (2) the
deformation of CuI to C2V, probably with the partial interac-
tion of C2V-CuI with the solvent molecule that is to be
released from C2V-CuII. The self-exchange rate constants
estimated from the oxidation cross-reactions are almost
always consistent with or slightly larger than the directly
measured value by using NMR.8,26 The difference in the
activation free energies for the concerted process and for
the reaction through the product excited state (path B) may
have been obscured by the uncertainty inherent in the Marcus
cross-relation (up to 2 orders of the magnitude for the
estimated self-exchange rate constant). The redox reactions
involving the [Cu(dmp)2(CH3CN)]2+/[Cu(dmp)2]+ couple are
summarized in Scheme 4.
Appendix B
For the direct self-exchange reaction, three independent
pathways may be considered in the current situation: (1)
path B′, in which structural change of only CuII takes place
prior to the ET process, (2) path A′, in which the ET process
takes place without structural change in both CuI and CuII,
or (3) the concerted process (a process that involves the
structural change of CuI prior to the ET process may not
have to be considered because this process requires much
higher energy than path B′). When a nonconcerted self-
exchange reaction takes place, the reaction profile should
be symmetric along the reaction coordinate. Because the
reaction profile of path A′ does not fulfill this requirement
(path A′ corresponds to the middle figure in Scheme 3), the
reaction through path A′ is not allowed to occur. On the other
hand, path B′ is allowed as the nonconcerted process,
according to the left-hand figure in Scheme 3.
Path B′ is possible when the electronic coupling between
the CuII and CuI species is not sufficient: this corresponds
to the gated self-exchange process.8 In such a case, it is
known that the self-exchange rate constant is expressed by
kex ) KOQkET. Although KOQ is small (∼10-5), kET may be
large enough (ca. 108 M-1 s-1), and kex may not be
distinguishable from the value expected for the concerted
process (ca. 103 M-1 s-1). On the other hand, the contribution
of KOQ may be clearly observed when the volume analysis
of the reaction is carried out: the volume contribution of
kET is expected to be small (ca. -3 to -5 cm3 mol-1) from
the theory. In this study, it was shown that the volume
(26) Clemmer, J. D.; Hogaboom, G. K.; Holwerda, R. A. Inorg. Chem.
1979, 18, 2567-2572.
1424 Inorganic Chemistry, Vol. 46, No. 4, 2007

Volume Profiles InWolWing [Cu(dmp)2(solWent)]2+/[Cu(dmp)2]+
contribution of KOQ is ca. -9 cm-3 mol-1. Therefore, the
overall activation volume should be ca. -12 to -14 cm3
mol-1 when the direct self-exchange reaction proceeds
through path B′. On the other hand, the reported activation
volume from the measurement of the direct self-exchange
reaction is only -3.4 cm3 mol-1.17 Therefore, it is clear that
the direct self-exchange reaction between [Cu(dmp)2-
(solvent)]2+ and [Cu(dmp)2]+ proceeds through the concerted
process.
Supporting Information Available: The pressure dependence
of the electrode potential for the redox couples in acetonitrile (Table
S1), the pressure dependence of the rate constant for the cross-
reaction between [Cu(dmp)2]+ and [Ni(tacn)2]3+ in acetonitrile
(Table S2), and the pressure dependence of the rate constant for
the cross-reaction between [Cu(dmp)2]2+ and [Co(bipy)3]2+ in
acetonitrile (Table S3). This material is available free of charge
via the Internet at http://pubs.acs.org.
IC061591I
Inorganic Chemistry, Vol. 46, No. 4, 2007 1425