Syntheses, structural analyses and redox kinetics of four-coordinate [CuL2]2+ and five-coordinate [CuL2(solvent)] 2+ complexes (L = 6,6′-dimethyl-2,2′-bipyridineor2,9- dimethyl-l,10-phenanthroline): Completely gated reduction reaction of [Cu(dmp)2]2+ in nitromethanet

Article abstract of DOI:10.1039/b415057k

[Cu(2,9-dimethyl-1,10-phenanthroline)₂]²⁺ and [Cu(6,6′-bipyridine)₂]^2+/+ complexes with no coordinated solvent molecule were synthesized and crystal structures were analyzed. Electrochemical measurement were carried out by using a BAS 100B/W electrochemical analyzer. The coordination geometry around the Cu(I) center was in the D_2d symmetry while a D₂ structure was observed for the four-coordinate Cu(II) complexes. The study revealed that the D₂ structure of the Cu(I) complex retained in nitromethane, although a five-coordinate Thp species, was readily formed upon dissolution of the solid in acetonitrile.

Full text of DOI:10.1039/b415057k

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F U L L P A P E R
Syntheses, structural analyses and redox kinetics of four-coordinate
[CuL2]2+ and five-coordinate [CuL2(solvent)]2+ complexes (L =
6,6ꢀ-dimethyl-2,2ꢀ-bipyridine or 2,9-dimethyl-1,10-phenanthroline):
completely gated reduction reaction of [Cu(dmp)2]2+ in
nitromethane†
Sumitaka Itoh,a Nobuyuki Kishikawa,a Takayoshi Suzukib and Hideo D. Takagi*c
a Department of Chemistry, Graduate School of Science, Nagoya University, Furo-cho, Chikusa,
Nagoya, 464-8602, Japan
b Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka,
560-0043, Japan
c Inorganic Chemistry Division, Research Center for Materials Science, Nagoya University,
Furo-cho, Chikusa, Nagoya, 464-8602, Japan. E-mail: h.d.takagi@nagoya-u.jp
Received 28th September 2004, Accepted 2nd February 2005
First published as an Advance Article on the web 16th February 2005
[Cu(2,9-dimethyl-1,10-phenanthroline)2]2+ and [Cu(6,6ꢀ-dimethyl-2,2ꢀ-bipyridine)2]2+/+ complexes with no
coordinated solvent molecule were synthesized and the crystal structures were analyzed: the coordination geometry
around the Cu(I) center was in the D2d symmetry while a D2 structure was observed for the four-coordinate Cu(II)
complexes. Coordination of a water or an acetonitrile molecule was found in the trigonal plane of the five-coordinate
Cu(II) complex in the Tbp (trigonal bipyramidal) structure. Spectrophotometric analyses revealed that the D2
structure of the Cu(II) complex was retained in nitromethane, although a five-coordinate Tbp species (green in color),
was readily formed upon dissolution of the solid (reddish brown) in acetonitrile. The electron self-exchange reaction
between D2d-Cu(I) and D2-Cu(II), observed by the NMR method, was very rapid with kex = (1.1 0.2) × 105 kg
mol−1 s−1 at 25 ◦C (DH* = 15.6 1.3 kJ mol−1 and DS* = −96 4 J mol−1 K−1), which was more than 10 times
larger than that reported for the self-exchange reaction between D2d-Cu(I) and Tbp-Cu(II) in acetonitrile. The cross
reduction reactions of D2-Cu(II) by ferrocene and decamethylferrocene in nitromethane exhibited a completely gated
behavior, while the oxidation reaction of D2d-Cu(I) by [Ni(1,4,7-triazacyclononane)2]3+ in nitromethane estimated an
identically large self-exchange rate constant to that directly obtained by the NMR method. The electron self-exchange
rate constant estimated from the oxidation cross reaction in 50% v/v acetonitrile–nitromethane mixture was 10 times
smaller than that observed in pure nitromethane. On the basis of the Principle of the Least Motion (PLM) and the
Symmetry Rules, it was concluded that gated behaviors observed for the reduction reactions of the five-coordinate
Cu(II)–polypyridine complexes are related to the high-energy C2v → D2d conformational change around Cu(II), and
that the electron self-exchange reactions of the Cu(II)/(I) couples are always adiabatic through the C2v structures for
both Cu(II) and Cu(I) since the conformational changes between D2d, D2 and C2v structures for Cu(I) as well as the
conformational change between Tbp and C2v structures for Cu(II) are symmetry-allowed. The completely gated
behavior observed for the reduction reactions of D2-Cu(II) species in nitromethane was attributed to the very slow
conformational change from the ground-state D2 to the entatic D2d structure that is symmetry-forbidden for d9 metal
complexes: the very slow back reaction, the forbidden conformational change from entatic D2d to the ground-state D2
structure, ensures that the rate of the reduction reaction is independent of the concentration of the reducing reagent.
processes.1,2 Copper enzymes, especially that exhibit strong blue
Introduction
color, possess N2S2 coordination environment around the Cu(II)
Electron transfer reactions involving Cu(II)/(I) centers have
ion and the electron transfer (ET) reactions at these copper sites
attracted attentions of many researchers since these reactions
are extremely rapid compared with those involving ordinary
are strongly related to the biologically important catalytic
Cu(II) complexes with the tetragonally distorted octahedral
coordination environment.3
It has not been long since the gated phenomenon, in which the
electron self-exchange rate constants estimated from the cross
reactions of oxidation and reduction directions are significantly
different from each other,4–6 was recognized for the first time
(Appendix A). The initial explanation by Lee and Anson, that
the correct self-exchange rate constant for such reactions should
be expressed by the geometric mean of the rate constants
estimated from oxidation and reduction cross reactions,7 was
shown to be invalid by the later investigations.
Among investigations carried out to date, intensive and
systematic studies by Rorabacher and co-workers seem to have
largely improved understandings of the gated phenomena: they
examined ET reactions of Cu(II)/(I)–macrocyclic polythioether
† Electronic supplementary information (ESI) available: Table S1: Redox
potentials. Table S2: Dependence of the line width of the methyl
proton signal on the concentration of [Cu(dmp)2]2+ in nitromethane
at various temperatures. Table S3: Dependence of the rate constant
on the concentration of [Ni(tacn)2]3+ for the electron transfer reac-
tion between [Cu(dmp)2]+ and [Ni(tacn)2]3+. Table S4: Dependence
of the rate constant for the reduction reaction of [Cu(dmp)2]2+ by
ferrocene on the concentration of ferrocene in nitromethane at various
temperatures. Table S5: Temperature dependence of the rate constant
for the conformational change of four-coordinate [Cu(dmp)2]2+ from
the D2 to D2d structure in nitromethane. Table S6: Dependence of
the rate constant on the concentration of [Cu(dmbp)2]2+ for the
electron transfer reaction between [Cu(dmp)2]+ and [Cu(dmbp)2]2+. See
http://www.rsc.org/suppdata/dt/b4/b415057k/
1 0 6 6
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8
T h i s j o u r n a l i s
T h e R o y a l S o c i e t y o f C h e m i s t r y 2 0 0 5
©

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complexes and found that the coordination structural change
takes place essentially at the Cu(I) site while the coordination
geometry around the Cu(II) species is not largely altered.8–12
They related this phenomenon to the biologically important
catalytic processes and postulated a dual-pathway Square
Scheme described in Scheme 1. Rorabacher recently reviewed
ET reactions by Cu(II)/(I) centers,13 in which he seems to have
confirmed that the gated ET reactions exhibited by copper
complexes are successfully explained by this scheme.8–12 In
general, ET reactions of Cu(II)/(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: i.e. the self-
exchange rate constant estimated from the non-gated direction is
almost identical to that measured directly by the NMR method.
Rorabacher and co-workers attributed the origin/reason of the
gated phenomena essentially to the sluggish conformational
change of the coordinated multidentate macrocyclic ligands:8–12
the ground-state geometries of Cu(I) and Cu(II) species should
come close to each other at the transition state for the electron
transfer reaction, according to the Marcus theory for the outer-
sphere ET reactions.14–16
reported gated phenomena, it certainly needs further evidence
and explanations to justify the theory (Appendix C).
In this study, we report two different crystal structures for
the [Cu(dmp)2]2+ complex: one of which with coordinated water
or acetonitrile is light green in color while the four-coordinate
complex with no coordinated solvent molecule exhibited reddish
color in the solid and in nitromethane. It was found that the
cross reaction between Cu(I) and Cu(II) complexes each bearing
different didentate ligands is rapid and certainly not gated in
acetonitrile although the ground-state structures of these Cu(I)
and Cu(II) complexes are significantly different (it has been
already reported that the reduction cross reactions of these two
copper complexes with other metals are gated in acetonitrile).17,18
The very different redox behaviors exhibited by four- and five-
coordinate Cu(II) complexes were explained on the basis of the
Symmetry Rules and the Principle of the Least Motion.24–26
Experimental
Materials
Nitromethane, obtained from Wako Pure Chemicals Inc., was
dried over molecular sieves 4A, followed by distillation under
reduced pressure. Acetonitrile was obtained from Wako, and pu-
rified by distillation from phosphorus pentoxide. The content of
the residual water in thus purified nitromethane and acetonitrile
was examined by a Mitsubishi Chemical CA07 Karl-Fisher ap-
paratus, by which the amount of residual water was determined
to be less than 1 mmol kg−1. Tetra-n-butylammonium perchlo-
rate (TBAP) was twice recrystallized from the mixture of ethyl
acetate–pentane solution, and dried under reduced pressure.
Ferrocene (Wako) was purified by sublimation. All other chem-
icals used especially for the synthesis of metal complexes were
purchased from Wako, Aldrich, and TCI, and were used with-
out further purification. Bis(2,9-dimethyl-1,10-phenanthroline)-
and bis(6,6ꢀ-dimethyl-2,2ꢀ-bipyridine)-copper(II) and -(I) per-
chlorate were synthesized by reported methods.20 Anal. Calc.
for [Cu(dmp)2](ClO4)2 = CuC28H24N4Cl2O8: C, 49.5; N, 8.25;
H, 3.56. Found: C, 50.5; N, 8.16; H, 3.65. Anal. Calc.
for [Cu(dmp)2]ClO4 = CuC28H24N4ClO4: C, 58.0; N, 9.67;
H, 4.17. Found: C; 58.6, N, 9.87; H, 4.10. Anal. Calc.
for [Cu(dmbp)2(H2O)](ClO4)2 = CuC24H26N4Cl2O9: C, 44.4;
H, 4.04; N, 8.63. Found: C, 44.8; H, 4.03; N, 8.72.
Anal. Calc. for [Cu(dmbp)2]ClO4 = CuC24H24N4ClO4: C,
54.2; H, 10.5; N, 4.55. Found: C, 54.4; H, 9.98; N, 4.60.
Scheme 1 Square Scheme postulated by Rorabacher et al.
We examined redox reactions of various Cu(II)/(I)–
polypyridine complexes and found that there are cases where
Rorabacher’s Square Scheme may not apply:17–19 (1) the electron
self-exchange rate constants estimated from both reduction
and oxidation directions were very small in the case of the
[Cu(dmbp)2]2+/+ couple (dmbp = 6,6ꢀ-dimethyl-2,2ꢀ-bipyridine)
when the counter reagent was [Ru(hfac)3]0/− (hfac = hexafluo-
roacetylacetonate, see Appendix B), while the directly measured
electron self-exchange rate constant for the [Cu(dmbp)2]2+/+
couple exhibited an ordinarily large value, and (2) most of the
polypyridine ligands used in our studies are didentate and no
sluggish conformational change in the coordinated ligands is ex-
pected for the alterations of the coordination geometries around
Cu(II) and Cu(I) centers. In addition, the results of the original
study concerning the volume analyses of the electron self-
exchange reaction for the [Cu(dmp)2]2+/+ couple (2,9-dimethyl-
1,10-phenanthroline) strongly indicate that the electron self-
exchange reactions between the five-coordinate Cu(II) and four-
coordinate Cu(I) complexes are adiabatic.20 Therefore, we started
to consider that the Square Scheme (Scheme 1), although it
appears to successfully explain some of the observed gated
phenomena, does not describe the exact nature of the gated
behavior. We recently postulated a possible origin of the gated
phenomena on the basis of the physico-chemical consideration
of the electron transfer reactions,19,21 although we have to admit
that a few of our previous spectrochemical analyses on the
basis of the method by Yokoi and Addison22 are invalid:23
since cross reactions, especially with other metal complexes,
of Cu species without low-energy CT bands are slow, uneven
structural changes in the gated electron transfer reactions that
involve large structural changes before the ET process are
important to achieve sufficient electronic coupling between the
reactants so as to provide a low-energy CT-perturbed reaction
pathway. Although this mechanism seems to explain most of the
27
[Ni(tacn)2](ClO4)3 was synthesized by the literature method.
Anal. Calc. 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.)
X-Ray crystal structures
Single crystals of [Cu(dmp)2](ClO4)2·2CH3NO2 and [Cu(-
dmbp)2](ClO4)2 were obtained from recrystallization
with nitromethane–diethyl ether, and a single crystal of
[Cu(dmbp)2]ClO4 was obtained from recrystallization with
acetonitrile–diethyl ether, while [Cu(dmbp)2(H2O)](ClO4)2 was
crystallized from acetonitrile–water solution. Each crystal
suitable for the X-ray diffraction study was mounted with a
cryoloop and flash-cooled by the cold nitrogen stream.
The X-ray intensities were measured on a Rigaku imag-
ing plate area detector Raxis-rapid [−73(2) ◦C, graphite-
˚
monochromated Mo-Ka radiation (k = 0.71073 A), the oscilla-
tion scan mode, 2h < 55◦, 100 × 100 pixel mode]. The structures
were solved by the direct method using SIR92 program,28
and refined on F2 (with all independent reflections) using the
SHELXL97 program.29 All non-hydrogen atoms were refined
anisotropically, and H atoms were introduced theoretically and
treated by riding models. All calculations were carried out using
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8
1 0 6 7

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Table 1 Crystallographic data
Compound
[Cu(dmp)2](ClO4)2·2CH3NO2
[Cu(dmbp)2](ClO4)2
[Cu(dmbp)2(H2O)](ClO4)2
[Cu(dmbp)2]ClO4
Formula
FW
C30H30Cl2CuN6O12
801.04
C24H24Cl2CuN4O8
630.91
C24H26Cl2CuN4O9
648.93
C24H24ClCuN4O4
531.46
T/K
200(2)
200(2)
200(2)
200(2)
Color, shape
Crystal dimensions/mm
Crystal system
Space group, Z
Red brown, prism
0.18 × 0.16 × 0.12
Triclinic
Dark red, columnar
0.32 × 0.20 × 0.18
Triclinic
Green, plate
0.22 × 0.22 × 0.14
Monoclinic
P21/a, 4
14.008(6)
10.951(5)
18.099(5)
90
101.57(3)
90
2720.0(18)
1.585
1332
1.061
5915/361
0.057
0.139
Red, prism
0.28 × 0.18 × 0.12
Monoclinic
P21/a, 4
8.833(5)
21.684(12)
12.384(7)
90
95.68(4)
90
2361(2)
1.495
1096
1.077
5403/308
0.061
0.104
¯
¯
P1, 2
P1, 4
˚
a/A
8.456(4)
13.476(5)
14.730(6)
102.72(3)
91.32(3)
92.46(3)
1635.0(11)
1.627
9.939(8)
14.511(11)
19.074(17)
74.06(8)
86.30(7)
78.02(7)
2587(4)
1.620
˚
b/A
˚
c/A
a/◦
b/◦
c /◦
3
˚
V/A
Dc/Mg m−3
F(000)
822
0.906
7210/460
0.057
0.169
1292
1.108
10610/703
0.040
0.106
l(Mo-Ka)/mm−1
Reflns./param. ratio
R1 [Fo > 2r(Fo2)]
2
wR2 (all reflns.)
GoF
1.000
1.043
1.015
1.001
a teXsan software package.30 Crystallographic data are collected
in Table 1.
CCDC reference numbers 251495–251498.
See http://www.rsc.org/suppdata/dt/b4/b415057k/ for cry-
stallographic data in CIF or other electronic format.
It seems that the factor which governs the N–Cu–N angle is the
bite angles of the didentate dmbp and dmp ligands. The range of
the Cu–N bond distances, 2.021(2)–2.047(2) A, lies within the
range of those previously found for the Cu(I) complexes with
2,2ꢀ-bipyridine ligands. Selected bond lengths and angles are
listed in Table 2. The dmbp ligands are nonplanar and slightly
twisted around the 2,2ꢀ-carbon-carbon bond (2.9(1) for N1 and
N2 and 13.3(1)◦ for N3 and N4). These distortions are also
consistent with those reported for [Cu(dmbp)2]BF4 and [Cu(2,2ꢀ-
bipyridine)2]+ complexes.31–33
˚
Kinetic and electrochemical measurements (Appendix D)
All manipulations were carried out in an atmosphere of dry
argon to avoid any possible contamination by water and oxygen
from the environment. Kinetic measurements were carried out
by a Unisoku RA401 stopped-flow apparatus. The reactions
were monitored by observation of the absorbance change at
456 nm (the absorption maximum of [Cu(dmp)2]+).
Electrochemical measurements were carried out by using a
BAS 100 B/W Electrochemical Analyzer with a standard three-
electrode configuration: a 1.6 mm␾ platinum disk was used as
the working electrode, a platinum wire as the counter electrode,
and a Ag/AgNO3 electrode in 0.1 M solution of TBAP in
acetonitrile was used as the reference electrode. The redox
potentials of complexes are reported with reference to that for
the ferricenium–ferrocene couple in the same solvent (Table S1,
ESI†). The NMR measurements were carried out by a Bruker
AMX-400WB spectrometer.
[Cu(dmp)2](ClO4)2·2CH3NO2 and [Cu(dmbp)2](ClO4)2. The
crystals of these complexes were obtained by recrystal-
lization from nitromethane–diethyl ether mixture, although
[Cu(dmp)2](ClO4)2·2CH3NO2 decomposed immediately by ex-
posing the crystal to the air. The X-ray crystal structures
(Fig. 1(b) and (c) and Table 2) revealed that these complexes
have D2 coordination geometries around the Cu(II) center.
These include the first example of four-coordinate copper(II)
complex bearing 1,10-phenanthroline type ligand.37 The Cu–
2+
˚
O(perchlorate anion) distance (2.485(4) A) in [Cu(dmp)2] is
appreciably shorter than that in the crystal of [Cu(dmbp)2]2+
(2.984(3) for mol1 and 3.014(3) A for mol2), while other bond
˚
distances are identical to each other in these two complexes.
Therefore, there is no significant interaction between the cop-
per(II) center and the perchlorate oxygen, and the relatively short
Cu–O distance is attributed to the crystal packing effect. The
dihedral angles between the planes defined by the copper center
and each◦set of the phenanthroline or◦bipyridine nitrogen atoms
are 60.34 in [Cu(dmp)2]2+, and 61.40 (mol1) and 62.78◦ (mol2)
in [Cu(dmbp)2]2+. These dihedral angles are significantly smaller
than the right angle, and therefore these complexes are clearly in
the D2 symmetry. The D2 structures in these complexes are not
the result of the Jahn–Teller effect for the complexes in the D2d
symmetry, since no low-energy B1 vibration mode is active for d9
Cu(II) in this symmetry. Therefore, the ground-state structures of
these four-coordinate Cu(II) complexes are D2 as a result of the
steric repulsion between the bulky methyl groups on the ligands,
otherwise these complexes are expected to have square-based
structure: the dihedral angle repor◦ted for the four-coordinate
[Cu(bipy)2]2+ complex is only 44.6 .37 Such a conclusion was
verified by the MM calculations (Appendix E).
Results
X-Ray crystal structures
[Cu(dmbp)2]ClO4. The coordination geometry around the
copper center was revealed to have a distorted tetrahedral geom-
etry (Fig. 1(a)). The dihedral angle between the planes defined
by the copper center and each set of the bipyridine nitrogen
atoms is 80.7◦ and is compared with that (80.9◦) reported for
[Cu(dmbp)2]BF4.31 These dihedral angles are slightly smaller
than that expected for the regular D2d geometry and consistent
with those for the other Cu(I)–2,2ꢀ-bipyridine complexes.32,33
Such small distortions have been believed to be caused by
the crystal packing forces, and the structures of these species
in solution are believed to be in the regular D2d geometry:
although the tetrahedral Cu(II) complexes suffer from the first-
order Jahn–Teller distortion to produce species in the D2d
symmetry, there is no reason to rationalize such a distortion
for Cu(I) complexes.34–36 However, the symmetry arguments (see
Discussion) conclude that four-coordinate Cu(I) complexes with
the d10 electronic configuration are fluxional among the C2v, D2d
and D2 structures when they exhibit low-energy MLCT bands.
[Cu(dmbp)2(H2O)](ClO4)2. The crystal structure of [Cu-
(dmbp)2(H2O)](ClO4)2 (Fig. 1(d)) is similar to the one for previ-
ously reported [Cu(dmp)2(H2O)](CF3SO3)2.38 The metal center
has a distorted trigonal bipyramidal, pseudo-D3h, coordination
1 0 6 8
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8

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Fig. 1 ORTEP (50% probability level) of the cationic part of (a) [Cu(dmbp)2]ClO4, (b) [Cu(dmp)2](ClO4)2·2CH3NO2, (c) [Cu(dmbp)2](ClO4)2 and
(d) [Cu(dmbp)2(H2O)](ClO4)2. Hydrogen atoms were omitted for clarity.
structure. The two axial positions are occupied by one of the
nitrogen donor atoms on each bipyridine ligand. The axial Cu–
˚
N distances (1.989(3) and 1.975(3) A) are somewhat shorter
˚
than the bond distances (2.138(3) and 2.057(3) A for Cu–N
˚
and 2.057(3) A for Cu–O) in the equatorial positions, indicating
that the Cu–N bonds at the axial positions are stronger than
those at the equatorial positions: such a distortion is expected
for the transition metal complexes with vacant d-orbital of the
ꢀ
a1 symmetry in the Tbp geometry, while the elongation of the
axial bonds is common for compounds of the typical elements in
the same structute.39 The N1–Cu–N2 and N3–Cu–N4 angles are
somewhat smaller than the right angle. This distortion is caused
by the small bite angle of the didentate dmbp ligand.
Fig. 2 Absorption spectra of [Cu(dmp)2]2+ in various solvents.
Absorption spectra
the solvents (ca. 1 mmol kg−1) within several days and the
[Cu(dmp)2]+ species was recognized by the absorption band
at ca. 456 nm: it was found that the degree of the reduction
of [Cu(dmp)2]2+ in these solvents was proportional to the
amount of the residual water in each organic solvent. The molar
extinction coefficient of the absorption band at ca. 456 nm for
[Cu(dmp)2]ClO4 was ca. 5000 kg mol−1 cm−1 in all solvents:
The UV-Vis absorption spectra of [Cu(dmp)2](ClO4)2 in various
solvents are shown in Fig. 2. The absorption band maxima in
various solvents and those observed in the diffuse reflectance
spectrum of the solid sample are summarized in Table 3. In
nitromethane and namely propylene carbonate, [Cu(dmp)2]2+
was partly reduced to [Cu(dmp)2]+ by the residual water in
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8
1 0 6 9

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◦
◦
˚
Table 2 Selected bond lengths (A), angles ( ) and dihedral angles ( ) between the least-squares’ planes at 200 K
(a) [Cu(dmbp)2]ClO4
(b) [Cu(dmp)2](ClO4)2·2CH3NO2
Cu–N1
Cu–N3
2.047(2)
2.029(2)
Cu–N2
Cu–N4
2.021(2)
2.045(2)
Cu–N1
Cu–N3
Cu · · · O6
1.993(3)
2.054(3)
2.485(4)
Cu–N2
Cu–N4
1.982(3)
1.957(3)
N1–Cu–N2
N1–Cu–N4
N2–Cu–N4
81.13(9)
114.02(9)
128.48(9)
N1–Cu–N3
N2–Cu–N3
N3–Cu–N4
130.42(9)
126.94(9)
81.72(10) N2–Cu–N4
O6 · · · Cu–N1
N1–Cu–N2
N1–Cu–N4
83.62(12)
101.02(11)
152.16(13)
131.0(1)
N1–Cu–N3
N2–Cu–N3
N3–Cu–N4
O6 · · · Cu–N2
O6 · · · Cu–N4
130.00(12)
114.69(11)
83.50(11)
79.2(2)
O6 · · · Cu–N3
98.8(1)
77.2(2)
Plane [Cu1, N1, N2] vs. plane [Cu1, N3, N4]
Plane of pyridine(1)a vs. plane of pyridine(2)b
Plane of pyridine(3)c vs. plane of pyridine(4)d
80.7
2.9(1)
13.3(1)
Plane [Cu1, N1, N2] vs. plane [Cu1, N3, N4]
60.34
Plane of bipyridine(12)e vs. plane of bipyridine(34)f 59.45(4)
(c) [Cu(dmbp)2](ClO4)2
(d) [Cu(dmbp)2(H2O)](ClO4)2
Cu1–N1
Cu1–N2
Cu1–N3
Cu1–N4
2.019(3)
1.955(3)
2.001(3)
1.989(3)
Cu2–N5
Cu2–N6
Cu2–N7
Cu2–N8
2.003(3)
1.981(3)
1.978(3)
1.972(3)
Cu–N1
Cu–N3
Cu–O1
1.989(3)
2.057(3)
2.057(3)
Cu–N2
Cu–N4
2.138(3)
1.975(3)
N1–Cu1–N2
N1–Cu1–N3
N1–Cu1–N4
N2–Cu1–N3
N2–Cu1–N4
N3–Cu1–N4
83.56(11)
133.60(10)
115.41(11)
103.96(12)
146.61(10)
83.10(12)
N5–Cu2–N6
N5–Cu2–N7
N5–Cu2–N8
N6–Cu2–N7
N6–Cu2–N8
N7–Cu2–N8
83.57(12) N1–Cu–N2
132.31(11) N1–Cu–N4
112.44(11) N2–Cu–N4
107.15(11) N1–Cu–O1
146.99(10) N3–Cu–O1
83.79(11)
80.00(15)
169.60(14)
107.42(13)
80.48(12)
N1–Cu–N3
N2–Cu–N3
N3–Cu–N4
N2–Cu–O1
N4–Cu–O1
104.19(13)
104.02(13)
81.41(13)
117.29(13)
89.52(12)
138.52(12)
Plane [Cu1, N1, N2] vs. plane [Cu1, N3, N4]
Plane [Cu2, N5, N6] vs. plane [Cu2, N7, N8]
Plane of bipyridine(12)g vs. plane of bipyridine(34)h
Plane of bipyridine(56)i vs. plane of bipyridine(78)j
61.40
62.78
65.16(3)
68.99(4)
Plane [Cu1, N1, N2] vs. plane [Cu1, N3, N4]
Plane of pyridine(1)a vs. plane of pyridine(2)b
Plane of pyridine(3)c vs. plane of pyridine(4)d
80.3
15.0(2)
10.2(2)
a Defined by N(1) and C(2)–C(6). b Defined by N(2) and C(7)–C(11). c Defined by N(3) and C(14)–C(18). d Defined by N(4) and C(19)–C(23). e Defined
by N(1), N(2), C(2)–C(11), C(13) and C(14). f Defined by N(3), N(4), C(16)–C(25), C(27) and C(28). g Defined by N(1), N(2) and C(2)–C(11). h Defined
by N(3), N(4) and C(14)–C(23). i Defined by N(5), N(6) and C(26)–C(35). j Defined by N(7), N(8) and C(38)–C(47).
deep green color of the previously reported [Cu(bipy)2](PF6)2,37
Table 3 Absorption band maxima of d–d transitions for
[Cu(dmp)2](ClO4)2 in various solvents and in the solid state observed
indicating that the spectral shift depends on the dihedral angle.
by the diffuse reflectance spectrophotometry
On the other hand, the reduction of [Cu(dmp)2]2+ in these
solvents was minimal and did not affect the rate of reduction
Solvent
H2O
Band maximum/cm−1
e/kg mol−1 cm−1
reactions (see footnote for “reduction reaction of [Cu(dmp)2]2+
by ferrocene in nitromethane” in this section, and Appendix D).
13432
9588
133
96
MeCN
13774
9980
96
110
Electron self-exchange rate constant for the four-coordinate
[Cu(dmp)2]2+/+ couple in nitromethane
MeNO2
20235
17521
13822
8846
311
336
165
110
k
ex
[Cu(dmp)2]2+ + [∗Cu(dmp)2]+−→
[Cu(dmp)2]+ + [∗Cu(dmp)2]2+
(1)
Propylene carbonate
Solid state
∼ 19300a
13514
(420)
151
130
The electron self-exchange rate constant, kex, of the [Cu-
(dmp)2]2+/+ couple was measured by monitoring the broadening
of the singlet signal corresponding to the methyl protons on
diamagnetic [Cu(dmp)2]+ with the existence of paramagnetic
[Cu(dmp)2]2+. The rate constant, kobs, was estimated by using
eqn. (2), since no change in the chemical shift of the proton sig-
nals was observed for the samples with different concentrations
of [Cu(dmp)2]2+: the slow exchange limit was assumed.40
9001
22169
18295
13477
9183
—
—
—
—
a Not accurate since the absorption band of Cu(I) which was generated
by the decomposition of Cu(II) complex interfered.
2+
kobs = p(mobs − m0) = kex[Cu(dmp)2
]
(2)
this absorption band has been attributed to the metal-to-ligand
charge transfer, MLCT.
where mobs is the full line width of the methyl proton signal at the
half maximum height (FWHM) in the presence of [Cu(dmp)2]2+,
while m0 is the FWHM of the same signal in the absence of
[Cu(dmp)2]2+. The dependence of kobs on the concentration of
added [Cu(dmp)2]2+ is shown in Fig. 3 (Table S2, ESI†) at various
temperatures. The estimated electron self-exchange rate constant
at 298.2 K and the activation parameters are listed in Table 4.
We failed to record the absorption spectrum of the four-
coordinate [Cu(dmbp)2]2+ species, since this complex was very
sensitive to moisture. The color of the single crystal was reddish
brown, while the powdery sample appeared to be bluish purple.
The colors exhibited by this complex are quite different from the
1 0 7 0
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8

View Article Online
Fig. 4 Dependence of the rate constant for the reduction reaction
of [Cu(dmp)2]2+ by ferrocene on the concentration of ferrocene in
nitromethane at various temperatures. [Cu(dmp)2]2+ = 2.56–4.57 ×
10−5 mol kg−1. I = 0.1 mol kg−1 (TBAP). T = 283.2 K (ꢁ), 288.2 K
(ꢀ), 293.2 K (᭺) and 298.2 K (᭹).
Fig. 3 Dependence of the first-order rate constant estimated from the
broadening of the line width of methyl protons on the concentration of
paramagnetic [Cu(dmp)2]2+ in nitromethane. [Cu(dmp)2+] = 8.5–9.1 ×
10−3 mol kg−1. T = 284.4 K (ꢀ), 291.7 K (ꢁ), 297.8 K (᭜), 307.8 K (᭺)
and 315.7 K (᭹). Ionic strength was not adjusted in these experiments to
avoid possible structural alteration of the Cu(II) species by the ion-pair
formation. Concentrations of [Cu(dmp)2]2+ may have up to 10% errors,
since reduction of the Cu(II) species by residual water gradually took
place during each measurement (it took several days for the completion
of measurements after sealing each sample solution in NMR tubes). At
higher temperatures than 300 K, the reduction reaction was somewhat
faster, and the plots started to scatter.
by a factor of 10, indicating that the oxidation reaction of
[Cu(dmp)2]+ by [Ni(tacn)2]3+ proceeds through different path-
ways when the structure of the product is different.
Reduction reaction of [Cu(dmp)2]2+ by ferrocene in nitromethane
Experiments were carried out under the conditions of
[ferrocene]0 ꢁ [Cu(dmp)2+]0. The kinetic traces were first-order
for up to three half-lives.
Oxidation reaction of [Cu(dmp)2]+ by [Ni(tacn)2]3+ in
nitromethane
The reaction of [Cu(dmp)2]+ with [Ni(tacn)2]3+ in nitromethane
d[Cu(II)]
−
= kobs[Cu(II)]
(5)
(6)
dt
[ferrocene]0 ꢁ [Cu(II)]0
was first order up to five half-lives and was described by eqn. (3)
+
under the pseudo-first-order conditions of [Cu(dmp)2
]
ꢁ
0
[Ni(tacn)23+]0.
As shown in Fig. 4 (Table S4, ESI†), the rate constant, kobs
,
was small and was not dependent on the concentration of
ferrocene within the experimental uncertainty.‡ This is the first
completely gated electron transfer reaction among the redox
reactions involving simple copper–polypyridine complexes
reported to date. The following two-step mechanism that
corresponds to path B in Scheme 1 proposed by Rorabacher
and co-workers may explain the result in Fig. 4.8–10
k
12
[Cu(dmp)2]+ + [Ni(tacn)2]3+−→
[Cu(dmp)2]2+ + [Ni(tacn)2]2+
kobs = k12[Ni(tacn)23+][Cu(dmp)2
(3)
(4)
+
]
Such conditions were chosen because of the instability of
[Ni(tacn)2]3+ in nitromethane: [Ni(tacn)2]3+ was slowly reduced
during the sample preparation period and the concentration of
[Ni(tacn)2]3+ became uncertain when the measurements were
carried out. However, a linear dependence of the observed
rate constant on the concentration of [Ni(tacn)2]3+ was con-
firmed by the preliminary experiments in which the pseudo
first-order conditions were not fulfilled (Table S3, ESI†): the
validity of such treatments have been verified in the previous
publication.41 Therefore, we conclude that the oxidation reaction
of [Cu(dmp)2]+ by [Ni(tacn)2]3+ in nitromethane is described
by eqn. (4). The second-order rate constant, k12, together
with the estimated electron self-exchange rate constant for the
[Cu(dmp)2]2+/+ couple at 298.2 K is listed in Table 4. The
self-exchange rate constant for the [Cu(dmp)2]2+/+ couple in
nitromethane (Table 4) was calculated from the rate constant for
the oxidation cross reaction by [Ni(tacn)2]3+, by assuming that
the self-exchange rate constant for the [Ni(tacn)2]3+/2+ couple is
identical to that observed in acetonitrile (see Appendix F).
This reaction was also examined in the 1 : 1 v/v mixture
of acetonitrile and nitromethane, in order to confirm the
difference in the reactivity of [Cu(dmp)2]2+ in the D2 symmetry
and [Cu(dmp)2(acetonitrile)]2+ in the pseudo-D3h symmetry: the
result is also listed in Table 4. It is clear that the electron self-
exchange rate constant estimated from the oxidation reaction to
produce pseudo-D3h-[Cu(dmp)2(acetonitrile)]2+ is smaller than
that from the oxidation reaction to produce D2d-[Cu(dmp)2]2+
kOQ
ꢀ
Cu(II)
Cu(II)∗
(7)
kOQ
k
B2
Cu(II)∗ + Ared −→ Cu(I) + Aox
(8)
where Cu(II), Cu(II)∗, Ared and Aox represent [Cu(dmp)2]2+
in the ground state, deformed [Cu(dmp)2]2+, ferrocene and
ferricenium, respectively. When kB2[Ared] ꢁ kQO, the observed
first-order rate constant is expressed by eqn. (9).
Rate = kOQ[CuIIL]
(9)
The estimated rate constant, kOQ, corresponding to the con-
formational change in Cu(II) and the activation parameters
are listed in Tables 4 and S5, ESI.† This result, together with
the results described in the previous section indicates that
‡ When water content in nitromethane is more than 10 mmol kg−1
,
[Cu(dmp)2]2+ is reduced within 2–3 h, although when water content
in nitromethane is less than ca. 0.1 mmol kg−1, [Cu(dmp)2]2+ is stable
for several days (identified by electrochemical and spectrophotometric
methods). Therefore, [Cu(dmp)2]2+ is stable enough for the measure-
ments carried out in this study. In addition, no significant dependence of
the rate constants for the reaction between [Cu(dmp)2]2+ and ferrocene
on the concentration of residual water was observed for such sample
solutions. The results shown in the Table was obtained in the solvent with
water content being less than ca. 0.1 mmol kg−1 (see also Appendix D).
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8
1 0 7 1

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Table 4 Rate constants (at 25 ◦C) and activation parameters for the redox reactions involving copper(II)/(I) couples with didentate polypyridine
ligands in aqueous, acetonitrile and nitromethane solutions
Oxidant
Reductant
Solvent logk12 or k21/M−1 s−1 logk11/M−1 s−1 DH*/kJ mol−1 DS*/J mol−1 K−1
Ref.
Bis(2,9-dimethyl-1,10-phenanthroline): CuII/I(dmp)2
2 + /+
2+
2+
2 + /+
2+
CuIIL2
CuIIL2
CuIIL2
CuIIL2
CuIIL2
CuIIL2
CuIIL2
H2Oa
5.3b
24
—
—
28
36
31.5 1.3
33.3 0.5
24
3
−63 10
20h
57i
58
Hydroquinones
Hydroquinone
H2Oc
pH-Dependent
7.40
5.0
—
H2Oc
4.73
—
MeCN
MeCN
MeCN
MeCN
MeCN
MeCN
MeCN
MeNO2
3.70b
1
2
−81
4
6
4
2
2
20h
17
CoII(bpy)2
2.85b
0.20b
−68
−110
−104
−60
—
2+
FeII(Cp)2
Gated
Partly gated
5.43b
[kOQ = 33]d
[kOQ = 34]d
3.70b
17
2+
2+
FeII(PMCp)2
17j
17
NiIII(tacn)2
CuIL2+
1
3+
+
MnIII(bpyO2)3
CuIL2+
4.46b
4.4
4.46b
—
17
—
—
—
3+
CuII(dmbp)2
CuIL2
35.5 1.6
15.6 1.3
30.7 1.2
—
−42
−96
−141
—
5
4
4
2+
e
2 + /+
e,h
CuIIL2
5.0b
2+
e,k
CuIIL2
FeII(Cp)2
MeNO2 Completely gated
[kOQ = 1.17]d
(∼5.3)b,f,l
(4.3)b,f,l
3.48b
NiIII(tacn)2
CuIL2+
MeNO2 (∼6.5)b,f
—
3+
3+
+
e
NiIII(tacn)2
CuIL2
Mixg
(5.9)b,f
—
—
−80
—
e
CuIIL2
Me2CO
29.2 0.6
2
20h
2 + /+
Bis(6,6ꢀ-dimethyl-2,2ꢀ-bipyridyl): CuII/I(dmbp)2
CuIIL2
CuIIL2
CuIIL2
CuIIL2
MeCN
MeCN
MeCN
MeCN
MeCN
MeCN
MeCN
3.74b
35.0 0.3
−56
−47
1
4
1
1
4
2
4
55h
55
55
55
55
55
55
2 + /+
RuII(hfac)3
3.77b
3.28b
Gated
3.38b
4.97b
3.32b
−0.15b
38
1
2+
2+
2+
−
2+
CoII(bpy)2
FeII(Cp)2
0.15b
21.0 0.4
30.5 1.3
−112
−107
−38
[kOQ = 50]d
−0.7b
2.83b
RuIII(hfac)3
CuIL2+
41
24.9 0.5
32
1
+
NiIII(tacn)2
CuIL2+
CuIL2
−66
3+
MnIII(bpyO2)3
3.28b
1
−75
3+
Bis(2,9-dimethyl-4,7-diphenyl-1,10-phenanthrolinedisulfonate): CuII/I(dpsmp)
CuIIL2
CuIIL2
CuIIL2
CuIIL2
CuIIL2
CuIIL2
CuIIL2
CuIIL2
H2O
H2Oa
H2O
H2O
H2O
5.7
—
—
—
—
—
—
—
—
—
59h
58
43
44
44
44
44
44
2 + /+
2+
2+
2+
2+
2+
2+
2+
Hydroquinone
8.15
6.4
—
—
—
—
—
—
—
4−
FeII(CN)6
Gated
Gated
Gated
Gated
Gated
7.2f
[kOQ = 229]d
[kOQ = 137]d
[kOQ = 139]d
[kOQ = 130]d
[kOQ = 136]d
1.0
4−
FeII(CN)6
FeII(EDTA)2−
FeII(CN)5(PPh3)3− H2O
RuII(NH3)5pyz2+
RuII(NH3)5py2+
H2O
H2O
a Chloride ion was used to adjust the ionic strength. b Units: kg mol−1 s−1
.
c Acetate was used to adjust the ionic strength: I = 0.2. d Units: s−1
.
e This
work. f The reaction was too fast to be measured by the stopped-flow method. g 1 : 1 v/v mixture of acetonitrile and nitromethane was used as the
solvent. h Self-exchange rate constant measured directly by the NMR method. i Several parallel reactions. j Combined with a high-energy non-adiabatic
direct reaction: see text. k Only the first-order reaction corresponding to the structural change was observed. l Self-exchange rate constant for the [Ni-
(tacn)2]3+/2+ couple in acetonitrile was used for the calculation of the self-exchange rate constant, k11, of the [Cu(dmp)2]2+/+ couple (see Appendix F).
the redox cross reactions involving the [Cu(dmp)2]2+/+ couple
proceed through a different pathway from that involving the
[Cu(dmp)2(solvent)]2+/[Cu(dmp)2]+ couple. Reduction reaction
of [Cu(dmp)2]2+ with decamethylferrocene in nitromethane was
also carried out as a preliminary experiment, in order to examine
the influence of the counter reagent on kinetic behavior for the
reduction reactions of [Cu(dmp)2]2+ in nitromethane. The reduc-
tion reaction of [Cu(dmp)2]2+ with decamethylferrocene also ex-
hibited completely gated behavior with the rate constant of 0.5
The dependence of the observed rate constant on the con-
centration of [Cu(dmbp)2]2+ at various temperatures is shown
in Fig. 5 (Table S6, ESI†). The second-order rate constant thus
estimated at 298.2 K (I = 0.1 mol kg−1) is listed in Table 4,
together with the activation parameters of the reaction. The
observed rate constant, k12, may be compared with the self-
exchange rate constant for the [Cu(dmp)2]2+/+ couple estimated
from the cross reaction in Table 4: the k12 value is comparable to
that estimated for the self-exchange rate constant observed in the
50% v/v mixture of acetonitrile/nitromethane while the directly
measured self-exchange rate constant for the [Cu(dmp)2]2+/+
couple as well as the self-exchange rate constant estimated
from the oxidation cross reaction in pure nitromethane were
ca. 10 times larger than this k12.
◦
0.3 s−1 at 25 C, which is consistent with the rate constant for
the structural change observed for the reaction of [Cu(dmp)2]2+
with ferrocene, within the experimental uncertainty.
Pseudo-electron self-exchange reaction between [Cu(dmp)2]+ and
[Cu(dmbp)2]2+ in acetonitrile
The reaction of [Cu(dmbp)2]2+ and [Cu(dmp)2]+ in acetoni-
trile was first-order for up to five half-lives and was de-
scribed by eqn. (10) under the pseudo-first-order conditions of
[Cu(dmbp)22+]0 ꢁ [Cu(dmp)2+]0.
Discussion
Background
Since the discrepancy in the k11 values calculated from oxida-
tion and reduction cross reactions was pointed out (detailed
explanations are described in Introduction and Appendix A),
a number of studies42–46 including those by Rorabacher and co-
workers have been carried out to investigate the gated behaviors
exhibited by various Cu(II)/(I) couples.
k
12
[Cu(dmp)2]+ + [Cu(dmbp)2]2+ −→
[Cu(dmp)2]2+ + [Cu(dmbp)2]+
(10)
(11)
2+
kobs = k12[Cu(dmbp)2
]
0
1 0 7 2
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8

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Fig. 5 Dependence of the rate constant for the oxidation reaction of
[Cu(dmp)2]+ by [Cu(dmbp)2]2+ (the pseudo-exchange reaction) on the
concentration of [Cu(dmbp)2]2+ in acetonitrile: [Cu(dmp)2+] = 5.0 ×
10−5 mol kg−1. I = 0.1 mol kg−1 (TBAP). T = 288.2 K (ꢁ), 293.2 K (ꢀ),
298.2 K (᭺) and 303.2 K (᭹).
At present, it seems there are two schools of thoughts for
explanations of the gated reactions: one attributes the gated
phenomena to the sluggish structural change of the coordinated
ligands,8–10 and the other to the non-adiabaticity of the electron
transfer reactions involving the ground-state species with the
CT-perturbed acceleration of the electron transfer process by
means of the conformational change around the Cu center.17–19
The former explanation, although it seems promising at the
first glance, fails to account for the gated reduction reactions of
Cu(II)–polypyridine complexes in which no sluggish structural
change of the coordinated ligand is required upon geometric
changes around the Cu(II) center. On the other hand, the
latter explanation seems to lack direct evidence for the non-
adiabaticity of the reactions involving Cu(II)/(I) complexes in
the ground state although it can account for almost all the gated
reactions reported to date.
Scheme 2 Correlation diagrams for different structures of Cu(II)/
(I)–polypyridine complexes.
Examination of the structural change allowed for Cu(I) and
Cu(II) complexes on the basis of the Symmetry Rules and the
Principle of the Least Motion§
Chemical reactions are considered to proceed through the
vibrational activation of molecules, where the term “vibration”
includes bond stretches and twist motions allowed for each
molecule by the normal coordinate analyses.24,47 An electronic
transition/state mixing is related to the suitable reaction coordi-
nate that is consistent with the corresponding vibrational mode.
Therefore, possible activation states and probable products of
molecular reactions are predictable on the basis of the Symmetry
Rules, which is based on the second-order perturbation theory
developed by Jahn and Teller.34–36 Symmetry Rules require
that the possible reaction coordinate should have the same
symmetry to that of the “direct product” of the electronic
ground state and excited state: the same symmetry as that of the
transition density24 in a sense of the Group Theory. However,
most of molecules possess several reaction manifolds possible
for reactions, and therefore the applicability of the Symmetry
Rules to analyze possible activation modes was considered to
be limited. The Principle of the Least Motion (PLM), that
states “the lowest activation energy for a reaction is the one that
requires the least motion of nuclei and the least disruption of
the original electronic configuration,”25,26 has been successfully
coupled with the Symmetry Rules for the prediction of the
probable directions of reactions.24 The correlation diagram of
electronic orbitals for each structure is shown in Scheme 2.
In this section, we will enforce the latter explanation on the
basis of the experimental evidence and on the basis of the
perturbation theory for the structural reorganization of metal
complexes.
Structures
The newly synthesized four-coordinate [Cu(dmp)2]2+ species
was revealed to be in the D2 symmetry by the X-ray analysis.
Therefore, there are two stable conformers for the [Cu(dmp)2]2+
complex: the green five-coordinate [Cu(dmp)2(solvent)]2+ species
with a trigonal bipyramidal structure and the reddish-brown
four-coordinate [Cu(dmp)2]2+. The latter species is stable in sol-
vents with inferior donor properties such as nitromethane, while
the former complex is stabilized in solvents with large donicity:
the five-coordinate green species is readily formed by dissolving
the four-coordinate complex in acetonitrile (Appendix E).
The absorption spectra of these species in the solid and in
solution (Table 3) can be explained on the basis of the selection
rules: for a four-coordinate D2 complex, four d–d absorption
bands with relatively large molar extinction coefficients are
expected, while only three d–d bands corresponding to the
transitions to the b2 level from the e, b1 and a1 levels are expected
for the D2d species. All but the middle band for the complex
in the D2d symmetry are allowed to a certain degree for either
x-, y- and/or z-polarized light. As for the green complex with
a trigonal bipyramidal, pseudo-D3h, structure in the solid, only
two d–d bands are expected. However, the allowed distortion to
the C2v symmetry will split the eꢀꢀ and eꢀ levels, and therefore up
to four d–d bands are expected to be observed, depending on
the experimental conditions and counter ions17 (Scheme 2).
Cu(I) complexes in the D2d symmetry. Cu(I)–polypyridine
complexes are in the D2d symmetry in the ground state. For the
complexes that exhibit low-energy MLCT bands, possible low-
energy electronic transitions are from the metal b2 or e orbitals
to ligand p* orbitals in either of the a1, b2 or e symmetries. These
electronic transitions/state mixings correspond to vibration of
the A1, B2 and B1 modes: the A1 mode is the totally symmetric
vibration, while the B2 and B1 modes lead to the species in the
C2v and D2 symmetry, respectively. However, these asymmetric
§ When this type of examination is carried out, we may have to consider
the symmetry of the whole molecule. However, it has been generally
accepted to use “simplified” point group that accounts only for the
coordinating atoms around the metal ion for the normal coordinate
analyses.24
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8
1 0 7 3

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Scheme 3 The “allowed” and “forbidden” structural changes between possible conformers of four- and five-coordinate Cu(II) and Cu(I) complexes.
Observed reaction pathways are shown by the thick arrows.
vibration modes are not induced for the Cu(I) complexes without
the low-energy MLCT. Therefore, only Cu(I) complexes in the
D2d symmetry that have low-energy MLCT bands are fluxional
to exhibit structures among C2v, D2d and D2 structures.
conclusion, the dissociation of a coordinated solvent molecule
from [Cu(dmp or dmbp)2(solvent)]2+ in the pseudo-D3h symme-
try readily occurs to produce the [Cu(dmp or dmbp)2]2+ species
in the C2v symmetry, while further deformation of this species to
the one in the D2d symmetry is a high-energy process that should
be rather slow. In Scheme 3, summarized are the “allowed” and
“forbidden” structural changes between the possible conformers
of four- and five-coordinate Cu(II) and Cu(I) complexes.
Cu(II) complexes in the D2d and D2 symmetries. The defor-
mation of the D2d complexes with the d9 electronic configuration
to the D2 symmetry requires the B1 mode of vibration. However,
the direct product for neither the low-energy d–d transitions nor
the d–s, s–d and/or d–p, p–d transitions corresponds to this
mode, and therefore it is concluded that this deformation from
Electron transfer reactions involving [Cu(dmp)2]2+/+ (Scheme 3)
D2d to the D2 structures is forbidden for the Cu(II)–polypyridine
In the case of electron self-exchange reaction of the
[Cu(dmp)2]2+/+ couple in nitromethane, the ground-state struc-
tures in the solid are retained: the Cu(I) complex is in the D2d
symmetry and the Cu(II) complex in the D2 symmetry. The
symmetry argument given above concludes that the change
between the D2d and D2 structures is forbidden for Cu(II), while
it is allowed for Cu(I) species that exhibit low-energy MLCT
bands. Therefore, the direct electron self-exchange reaction
in nitromethane should involve major deformation of only
Cu(I) from the ground-state D2d to the excited D2 structure
(Scheme 3(a)). Since this structural change proceeds smoothly
along the single reaction coordinate (allowed), the reaction is
not gated: the electron self-exchange reaction between the four-
coordinate [Cu(dmp)2]2+/+ complexes takes place in a concerted
manner and rapid as seen in Table 4, although the inner-sphere
structural reorganization may be uneven for the Cu(I) and Cu(II)
species (symmetric bond stretching modes of Cu(II) and Cu(I)
also contribute to the overall activation barrier).
complexes on the basis of the Symmetry Rules.¶ On the other
hand, consideration on the basis of the combined PLM and
Symmetry Rules predicts that the high-energy a1 to b2 electronic
transition/state mixing in the D2d complex is coupled with the
deformation to the C2v structure, and therefore, this structural
inter-conversion is expected to be slow.
Cu(II) complexes in the pseudo-D3h (Tbp) symmetry. The
Eꢀ vibration mode which is related to the low-energy d–d
transition/state mixing allows dissociation of the coordinated
molecule in the equatorial position. This mode of activation is
quite common for transition metal complexes in this symmetry
as has been known for trans-[Ni(CN)2(triphenylphosphine)3].48
A very rapid ligand substitution reaction has been reported
for Cu(II) complexes with the trigonal bipyramid structure.49–52
On the other hand, the structural change between C2v and
D2d structures is a high-energy process as described above. In
The oxidation reaction of [Cu(dmp)2]+ by [Ni(tacn)2]3+ in
nitromethane takes place through the same route: the MLCT
induces the change from the D2d to D2 structure for Cu(I) and this
transition also causes the delocalization of the d electrons over
the ligands’ p* level so as to let the CT-perturbed ET possible19
¶ We examined the direct product of the reverse reaction of the
conformational change from D2d to D2 for the examination of the
reaction modes, since we cannot easily deal with the normal vibration
modes for the D2 point group. We relied on the Principle of Microscopic
Reversibility.
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D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8

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(see later discussion). This activation process is inevitable since
only this route leads to the stable product in nitromethane,
[Cu(dmp)2]2+ in the D2 symmetry (Scheme 3(a)).
of Cu(II) and the d-orbital (HOMO/SOMO) of other metal
complexes, such as [Ni(tacn)2]3+ and [Ru(hfac)3]+/0, is rather
small. The very low HOMO and SOMO energy levels in the
Cu(I) and Cu(II) complexes are evidenced also by the very
large ionization potentials of the copper element: the second
ionization potential of Cu is 20.29 eV while the third ionization
potential is as high as 36.84 eV,56 which are some 2 eV larger
than those for other metals. It seems that the very low d-electron
energy levels in Cu(II)/(I) complexes originate from the very large
effective nuclear charge of central Cu, and cause insufficient
coupling with the d-orbitals of other metal complexes for the
outer-sphere electron transfer reactions.
Symmetry Rules and the PLM indicate that the disso-
ciation of the solvent molecule from the trigonal plane
of [Cu(dmp)2(solvent)]2+ is allowed to form four-coordinate
[Cu(dmp)2]2+ in the C2v symmetry, while the structural change of
this species further to [Cu(dmp)2]2+ in the D2d symmetry requires
high-energy electronic transitions/state mixing. Therefore, the
reaction is gated when the inner-sphere activation of Cu(II)
On the other hand, the reduction reaction of [Cu(dmp)2]2+
in the D2 symmetry by ferrocene should be sluggish, since no
smooth single reaction coordinate (concerted process) that leads
to stable Cu(I) in the D2d structure exists for this reaction,
according to the Symmetry Rules and PLM. Therefore, the
reaction has to proceed through either of the following two
high-energy processes: (1) via the inner-sphere reorganization of
Cu(II) through the very high-energy path without bond rupture
between Cu(II) and N or through the dissociation of one of the
bonds between Cu(II) and N, or (2) via the product excited state,
D2-Cu(I).53,54 The structural rearrangements in (1) take place
prior to the formation of the encounter complex, because these
rearrangements are high-energy activation processes which are
not allowed to occur within the encounter complex, according
to the discussion by Brunschwig and Sutin.53 When the rate
constant for the reverse reaction of structural change, kQO, is very
small compared with the succeeding electron transfer process,
the overall rate constant is independent of the concentration of
the counter reagent as observed in this study. To the contrary,
the observed rate constant should depend on the concentration
of the counter reagent when the reaction proceeds through (2).
Therefore, it is concluded that the reduction reaction of D2-
Cu(II) by ferrocene proceeds through (1) (Scheme 3(b)). The
activation parameters for this reaction, DH* = 30.7 kJ mol−1
and DS* = −141 J mol−1 K−1, may indicate that the inner-sphere
reorganization in (1) takes place without bond dissociation be-
tween Cu(II) and N: a very high-energy twist to form D2d-Cu(II)
may occur, although this process is symmetry-forbidden and is
expected to be non-adiabatic (crossing occurs at the intersection
of the two states with different symmetries).54 The completely
gated phenomenon observed for the reduction of Cu(II) in the
D2 symmetry indicates that the process corresponding to kQO
is either non-adiabatic or requires very high activation energy
(Appendix G). The experimental results tell us that the pathway
(2) requires higher energy than pathway (1), the reason of which
may be given by considering the extremely low energy level of the
d-orbitals in the Cu(II) species (see below): a CT perturbation
in the Cu(II) complexes seems to be essential for the sufficient
overlap between the donor and acceptor orbitals to ensure
rapid ET for the cross reactions with other metal complexes.
It was shown in this study that the Cu(II) complex in the D2
symmetry does not exhibit low-energy LMCT, while Cu(II) in
the D2d symmetry certainly exhibits low-energy LMCT band, as
described in the previous article.19
species occurs along this process, Tbp (pseudo-D3h) → C2v
→
D2d. (Scheme 3(c))
In the electron self-exchange reactions, the C2v complex
produced by the allowed rapid dissociation of a solvent molecule
from the trigonal plane of the Tbp complex may directly react
with [Cu(dmp)2]+ in the same structure, since the structural
change from D2d-Cu(I) to the C2v geometry through the B2
vibration mode is allowed by the MLCT perturbation according
to the Symmetry Rules and PLM. Therefore, the direct self-
exchange reaction between green Cu(II) (Tbp) and red Cu(I)
(D2d), appears concerted through the common activation state
with the C2v structure (Scheme 3(d)) for both Cu(I) and Cu(II)
species, since sufficient electronic coupling is achieved between
the Cu(I) and Cu(II) complexes with like structures. The evidence
for the “concertedness” of the electron self-exchange reaction
has been given by the volume analyses for the self-exchange
reaction of the [Cu(dmp)2]2+/+ couple in acetonitrile.20 However,
this mode of reaction is not favored in the cases of the cross
reduction reactions by metal complexes other than Cu and
cannot compete with the gated pathway through Tbp (pseudo-
D3h) → C2v → D2d, since a sufficient electronic coupling between
the C2v-Cu(II) and the counter reagent cannot be achieved
through this process: the reaction of D2d-Cu(II) with metal
complexes other than Cu are rapid (but gated) since only
D2d-Cu(II) exhibits the LMCT-perturbed enhancement of the
electronic coupling with the counter reagents (Scheme 3(d)).
The experimental results and the symmetry argument indi-
cate that the electron self-exchange reactions between copper
complexes are not gated but concerted. This also explains why
the self-exchange reactions for most of the macrocyclic poly-
thioether complexes reported by Rorabacher and co-workers
are also fast (and probably concerted) while the oxidation cross
reactions of these complexes are gated: the Cu(II) complexes with
polythioether ligands exhibit strong LMCT bands while corre-
sponding Cu(I) complexes are colorless. Relatively low HOMO
and SOMO energy levels in the Cu(I) and Cu(II) complexes
are responsible for the non-adiabaticity of the electron transfer
reactions with other metal complexes: the reduction reaction of
[Cu(dmp)2(solvent)]2+ complex have been reported to be rapid
with compounds of typical elements, such as hydroquinones,
with which the electronic coupling seems sufficient for the
adiabatic ET to occur.57,58
The experimental result for the pseudo electron self-exchange
reaction between [Cu(dmbp)]2+ and [Cu(dmp)2]+ in acetonitrile
(Table 4) indicates that the electron transfer between Cu(II) in
the trigonal bipyramidal (pseudo-D3h) structure and Cu(I) in
the D2d symmetry is fast: the pseudo exchange rate constant
(ca. 104 kg mol−1 s−1) is as large as the self-exchange rate
constant for each redox couple measured directly by the NMR
method. On the other hand, all of the reported cross reduction
reactions of these Cu(II) species by other metal complexes
were gated and the estimated self-exchange rate constants for
these Cu(II)/(I) couples by using the Marcus cross relation are
17,55
much smaller than 104 kg mol−1 s−1.
These observations
strongly indicate that the “reaction mode” is different for the
reactions between Cu(II) and Cu(I) complexes from that between
Cu(II) and other metal centers: the gated electron transfer is
induced only for the cross reactions of Cu(II) species with other
metal complexes (Table 4). Most interestingly, the outer-sphere
reduction reactions of Cu(II) by hydorquinones are very rapid,
and the calculated self-exchange rate constant for the Cu(II)/(I)
couples are as large as 105 dm3 mol−1 s−1 (Table 4): it seems that
the electronic coupling between the d-orbital (SOMO) of Cu(II)
and the HOMO levels of hydroquinones are sufficiently large,
while the electronic coupling between the d-orbital (SOMO)
As a result, we may derive the following conclusions: (1)
it is essential for the occurrence of the gated behavior that
either structural changes expected for the concerted process is
forbidden by the Symmetry Rules or the reaction through the
free energy surface of the concerted process is non-adiabatic,
(2) structural change of the ground-state species occurs so
as to maximize the electronic coupling between the reactants
through the CT-perturbation, (3) structural change in the gated
process can be explained on the basis of the Symmetry Rules
D a l t o n T r a n s . , 2 0 0 5 , 1 0 6 6 – 1 0 7 8
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and PLM, and (4) the high-energy structural changes lead to
the ordinary gated behavior while structural changes through
the symmetry-forbidden processes lead to the completely gated
reaction (since back reaction of this structural change is also
forbidden by the principle of microscopic reversibility). These
conclusions can explain the mysteriously small self-exchange
rate constants estimated for the [Cu(dmbp)2]2+/+ couple from
the oxidation and reduction cross reactions by [Ru(hfac)3]−/0
in acetonitrile18 (note that the electron self-exchange rate
constant measured directly by the NMR method is ca. 104 kg
mol−1 s−1 and rapid, see Appendix B). From the principle of
microscopic reversibility, it is certain that both oxidation and
reduction reactions should proceed through the identical path-
way with the lowest possible activation energy. The four factors
given above indicate that the oxidation/reduction reactions of
[Cu(dmbp)2(acetonitrile)]2+/[Cu(dmbp)2]+ with [Ru(hfac)3]0/−
should either be gated or proceed along the non-adiabatic free-
energy surface. The small self-exchange rate constant estimated
from the oxidation direction indicates that the electronic cou-
pling between Cu(I) and Ru(III) complexes is small and both
oxidation and reduction reactions proceed through the non-
adiabatic process. The fact that the estimated self-exchange rate
constant (0.7 kg mol−1 s−1) for the reactions of [Cu(dmbp)2]2+/+
with [Ru(hfac)3]0/− is comparable to the apparent self-exchange
rate constants for the evidently gated reduction reactions of
[Cu(dmp)2]2+ in acetonitrile (1.6 kg mol−1 s−1)17 indicates that the
apparent free energy barrier for the non-adiabatic reactions of
[Cu(dmbp)2]2+/+ and [Ru(hfac)3]0/− is not significantly different
from that for the gated reduction reactions of [Cu(dmbp)2]2+ in
acetonitrile.
directions should undergo through the identical free-energy
surface. A similar argument was also given by Stanbury et al.
in their recent paper for the reactions with Cu-bite complexes.61
The dependence of the rate constants for the reduction reactions
with [Ru(hfac)3]− on the concentration of [Ru(hfac)3]− was
not saturating but was linear. Although we may tend to say,
“both directions are gated,” it is not true according to the
square scheme. We deduced that both oxidation and reduction
reactions are non-adiabatic. If the reduction reaction is gated,
the following ET process should be rapid. In such a case, the
reverse reaction, the oxidation reaction, should proceed through
the product excited state and rapid according to the theory by
Brunschwig and Sutin.53,54
Appendix C
Recent publication by Garner and co-workers62 seems to verify
our proposal: a four-coordinate Cu(II)/(I) couple with imidazole
ligands did not exhibit gated behavior. It appears that the redox
reactions of Cu(II)/(I) couples with low-energy LM- and MLCT
bands proceed through the ordinary concerted mechanism, since
the LM- and MLCT-perturbed superexchange or sequential ET
is induced for the cross reactions involving such couples.
Appendix D
Under the experimental conditions, observation of the cyclic
voltammogram confirmed that the CV of [Cu(dmp)2]2+ solution
was identical to that for the solution of [Cu(dmp)2]+ with
identical concentration, for more than several hours. The ratio
of the anodic and cathodic currents was always 1 : 1 and no
significant shift of the redox potential was observed within the
experimental uncertainty (decomposition of the Cu(II) complex
was not observed under the experimental conditions).
Appendix A
The use of the term “gated” was referred to, by Hoffman
and Ratner,60 the specific situation in which conformational
change (or similar slow kinetic phenomenon) of one reactant
becomes rate controlling and the reaction becomes truly first-
order. However, the usage of this term became diverted to the re-
actions in which a large conformational change precedes the
electron transfer (ET) process, since the original definition of the
gated ET is taken to be the extreme case where the first-order
rate constant of the back reaction for the conformational change,
When excess dmp was added to the nitromethane solution,
reduction of [Cu(dmp)2]2+ became significant (it took only ca.
1 min. to have all Cu(II) species in the solution reduced to
[Cu(dmp)2]+ when ca. 10 mmol kg−1 of free dmp existed in the
solution). Since addition of free ligand introduces small amount
of water, it seems that the existence of water certainly accelerate
the reduction reaction. However, it should also be noted that the
reduction product was identified as the [Cu(dmp)2]+ complex by
the spectrophotometric and electrochemical analyses, in these
experiments. Although it seems that water molecule acted as
the base, we did not make any effort to identify the reaction
products, since the degree of the reduction was not significant
under the experimental conditions used in this study (typical
value of less than 0.1% for the reduction was estimated from
the electrochemical analyses). Therefore, [Cu(dmp)2]2+ is stable
in nitromethane (and in acetonitrile). A similar result was
reported for another Cu(II) complex in acetone by Swaddle
and co-workers63: although a rapid ligand exchange reaction
was observed by the addition of the didentate free ligand to
the solution of Cu(II) complex, no release of the coordinated
ligand was observed without addition of free ligand. Therefore,
all of the experimental evidence confirms that (1) [Cu(dmp)2]2+
is stable in nitromethane and (2) the structure was certainly
retained in solution as identified by the spectrophotometric and
electrochemical methods.
k
QO, is very small compared with the product of the rate constant
for the ET process, kET, and the concentration of the reagent of
the cross reaction, kQO ꢂ kET[Reducing reagent]. Unfortunately,
there have been very few cases in which a truly first-order
reaction was observed: the reduction reaction of [Cu(dmp)2]2+ by
ferrocene in nitromethane reported in this study is one of such a
rare example. We, therefore, decided to use the term “gated” for
the general cases where the reaction takes place in two steps with
the sluggish conformational change before the ET process, and
the term “Completely gated” was used for the reaction in which
the observed rate constant was actually first-order (independent
of the concentration of the reducing reagent), to refer to the
original definition by Hoffman and Ratner, in this article.
Appendix B
The redox potentials for the [Cu(dmbp)2]2+/+ and [Ru(hfac)3]0/−
couples are similar to each other in acetonitrile, and we
were able to examine both oxidation reaction of [Cu(dmbp)2]+
by [Ru(hfac)3] and reduction reaction of [Cu(dmbp)2]2+ by
[Ru(hfac)3]− in acetonitrile by altering the experimental
conditions.18 Although the oxidation reactions of [Cu(dmbp)2]+
by other metal complexes have never been gated in acetonitrile,
including the self-exchange reaction and the pseudo-exchange
reaction with [Cu(dmp)2]2+, the self-exchange rate constant
estimated from the oxidation reaction of [Cu(dmbp)2]+ by
[Ru(hfac)3]0 was as small as that estimated from the reduction
reaction of [Cu(dmbp)2]2+ by [Ru(hfac)3]−. As for the reactions
of [Cu(dmbp)2]2+/+ with [Ru(hfac)3]0/−, the reactions in both
Appendix E
By the molecular mechanics calculations using a Cache program
(MM3), the formation energies of Cu(II)–dmp complexes were
54.60, 111.55 and 150.14 kcal mol−1 for Tbp (D3h) with water,
D2 and D2d complexes, respectively. These results indicate that
the Tbp complex is stable in solvents that have large donicity,
while D2 conformer is more stable than the D2d conformer in
poor donor solvents such as nitromethane. These results are
consistent with the experimental observations: the structure of
the D2 complex is certainly retained in nitromethane and it
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converts to the Tbp structure in acetonitrile, although the fast
exchange of the coordinated solvent molecule takes place in
acetonitrile, as expected from the Symmetry Rules.
9 N. E. Meager, K. L. Juntunen, M. J. Heeg, C. A. Salhi, L. A.
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10 D. B. Rorabacher, N. E. Meagher, K. L. Juntunen, P. V. Robandt,
G. H. Leggett, C. A. Salhi, B. C. Dunn, R. R. Schroeder and L. A.
Ochrymowycz, Pure Appl. Chem., 1993, 65, 573–578.
11 P. V. Robandt, R. R. Schroeder and D. B. Rorabacher, Inorg. Chem.,
1993, 32, 3957–3963.
12 C. A. Salhi, Q. Yu, M. J. Heeg, N. M. Villeneuve, K. L. Juntunen,
R. R. Schroeder, L. A. Ochrymowycz and D. B. Rorabacher, Inorg.
Chem., 1995, 34, 6053–6064.
13 D. B. Rorabacher, Chem. Rev., 2004, 104, 651–697.
14 R. D. Cannon, in Electron Transfer Reactions, Butterworth, London,
1980.
15 N. Sutin, Prog. Inorg. Chem., 1983, 30, 441–498.
16 R. B. Jordan, in Reaction Mechanisms of Inorganic and Organometal-
lic Systems, Oxford University Press, New York, 2nd edn., 1998.
17 N. Koshino, Y. Kuchiyama, H. Ozaki, S. Funahashi and H. D.
Takagi, Inorg. Chem., 1999, 38, 3352–3360.
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Appendix F
According to the Marcus’ theory,14–16 the self-exchange rate
constant for a redox couple depends essentially on the high- and
low-frequency dielectric constants of the solvent. Since these
parameters are similar to each other for nitromethane and ace-
tonitrile, the self-exchange rate constant for the [Ni(tacn)2]3+/2+
couple in acetonitrile was used for the calculations of the
self-exchange rate constants for the [Cu(dmp)2]2+/+ couple in
nitromethane and 1 : 1 v/v mixture of nitromethane and
acetonitrile.
Appendix G
As for the reactions of four-coordinate Cu(II)/(I) couple, Stan-
bury and co-workers reported a completely gated self-exchange
reaction by the NMR study.61 Authors suggested that the ET is
accelerated by the intervention of the inner-sphere mechanism.
We agree with this idea since we believe that the acceleration of
the ET rate by the inner-sphere mechanism should be treated as
either of the superexchange or sequential transfer in a sense of
quantum mechanics.19 Very different structures of these species
(Td and D4h) seem to be the reason since it requires forbidden
structural inter-conversion (D4h–Td). Therefore, it seems both
directions are regulated by the sluggish geometric changes in
Cu(I) as well as Cu(II). Moreover, the reduction/oxidation
reactions by Ru(III)/(II) couples with Cu(II)/(I)-bite complexes
are similar to those observed for the reactions with Cu(II)/(I)-
dmbp couples in our previous study:18 the reactions have to
be treated on the basis of the microscopic reversibility. The
self-exchange rate constants estimated from both directions are
identical to each other within the experimental uncertainty,
as indicated in their study. On the other hand, results for the
cross reactions have been published later by the same authors:64
although both oxidation and reduction directions seems to be
gated in the cross reactions, the reported rate constants for
the estimated self-exchange reaction was too small to explain
the observed line broadening of the NMR signals for the self-
exchange study of the same couple. If we trust the results
for the cross reactions, it seems both oxidation and reduction
directions are gated. Such sluggish conformational changes
may be attributed to the large energy barrier necessary for the
twist of the macrocyclic ligands. Since an inversion around a
carbon center requires ca. 30–40 kJ mol−1 of activation energy,
the reaction of Cu(II)/(I) couples with macrocyclic ligands
may also be regulated by the distortion within the ligand.
The discussions given in this article do not account for such
distortions, and the authors of the present article admit that
the explanation by Rorabacher and co-workers are valid for
most reactions involving Cu(II)/(I) couples with macrocyclic
polythioether ligands.
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24 R. G. Pearson, in Symmetry Rules for Chemical Reactions, Wiley,
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31 P. J. Burke, D. R. McMillin and W. R. Robinson, Inorg. Chem., 1980,
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