An interpretation of gated behavior: Kinetic studies of the oxidation and reduction reactions of bis(2,9-dimethyl-1,10-phenanthroline)copper(I/II) in acetonitrile

Article abstract of DOI:10.1021/ic9810687

Reduction reactions of Cu(dmp)₂ ²⁺(dmp = 2,9-dimethyl-1,10-phenanthroline) by ferrocene (Fe(Cp)₂= bis(cyclopentadienyl)iron(II)), decamethylferrocene (Fe(PMCp)₂= bis(pentamethylcyclopentadienyl)iron(II)), and Co(bpy)₃ ²⁺(bpy = 2,2′-bipyridine) and oxidation reactions of Cu(dmp)₂ ⁺by Ni(tacn)₂ ³⁺(tacn = 1,4,7-triazacyclononane) and Mn(bpyO₂)₃ ³⁺(bpyO₂= N,N′-dioxo-2,2′-bipyridine) were studied in acetonitrile for the purpose of interpreting the gated behavior involving copper(II) and -(I) species. It was shown that the electron self-exchange rate constants estimated for the Cu(dmp)₂ ^2+/+couple from the oxidation reaction of Cu(dmp)₂ ⁺by Ni(tacn)₂ ³⁺(5.9 × 10²kg mol^-1s^-1) and Mn(bpyO₂)₃ ³⁺(2.9 × 10⁴kg mol^-1s^-1) were consistent with the directly measured value by NMR (5 × 10³kg mol^-1s^-1). In contrast, we obtained the electron self-exchange rate constant of Cu(dmp)₂ ^2+/+as 1.6 kg mol^-1s^-1from the reduction of Cu(dmp)₂ ²⁺by Co(bpy)₃ ²⁺. The pseudo-first-order rate constant for the reduction reaction of Cu(dmp)₂ ²⁺by Fe(Cp)₂was not linear against the concentration of excess amounts of Fe(Cp)₂. A detailed analysis of the reaction revealed that the reduction of Cu(dmp)₂ ²⁺involved the slow path related to the deformation of Cu(dmp)₂ ²⁺(path B in Scheme 1). By using Fe(PMCp)₂(the E° value is 500 mV more negative than that of Fe(Cp)₂ ^+/0) as the reductant, the mixing with another pathway involving deformation of Cu(dmp)₂ ⁺(path A in Scheme 1) became more evident. The origin of the Gated Behavior is discussed by means of the energy differences between the normal and deformed Cu(II) and Cu(I) species: the difference in the crystal field activation energies corresponding to the formation of pseudo-tetrahedral Cu(II) from tetragonally distorted Cu(II) and the difference in the stabilization energies of the tetrahedral and tetragonal Cu(I) for the activation of Cu(I) species. The reduction reaction of Cu(dmp)₂ ²⁺by Fe(PMCp)₂confirmed that the mixing of the two pathways takes place by lowering the energy level corresponding to the less favorable conformational change of Cu(I) species.

Full text of DOI:10.1021/ic9810687

3352
Inorg. Chem. 1999, 38, 3352-3360
An Interpretation of Gated Behavior: Kinetic Studies of the Oxidation and Reduction
Reactions of Bis(2,9-dimethyl-1,10-phenanthroline)copper(I/II) in Acetonitrile
Nobuyoshi Koshino, Yoshio Kuchiyama, Hiroshi Ozaki, Shigenobu Funahashi, and
Hideo D. Takagi*
Inorganic and Analytical Chemistry Division, Department of Chemistry and Physics, Graduate School of
Sciences, Nagoya University, Furocho, Chikusa, Nagoya, 464-8602 Japan
ReceiVed September 4, 1998
2+
Reduction reactions of Cu(dmp)2 (dmp ) 2,9-dimethyl-1,10-phenanthroline) by ferrocene (Fe(Cp)2 ) bis-
(cyclopentadienyl)iron(II)), decamethylferrocene (Fe(PMCp)2 ) bis(pentamethylcyclopentadienyl)iron(II)), and
2+
+
3+
Co(bpy)3 (bpy ) 2,2′-bipyridine) and oxidation reactions of Cu(dmp)2 by Ni(tacn)2 (tacn ) 1,4,7-
3+
triazacyclononane) and Mn(bpyO2)3 (bpyO2 ) N,N′-dioxo-2,2′-bipyridine) were studied in acetonitrile for the
purpose of interpreting the gated behavior involving copper(II) and -(I) species. It was shown that the electron
self-exchange rate constants estimated for the Cu(dmp)22+/+ couple from the oxidation reaction of Cu(dmp)2+ by
3+
3+
Ni(tacn)2 (5.9 × 102 kg mol-1 s-1) and Mn(bpyO2)3 (2.9 × 104 kg mol-1 s-1) were consistent with the
directly measured value by NMR (5 × 103 kg mol-1 s-1). In contrast, we obtained the electron self-exchange rate
as 1.6 kg mol-1 s-1 from the reduction of Cu(dmp)2 by Co(bpy)32+. The pseudo-
2+/+
2+
constant of Cu(dmp)2
first-order rate constant for the reduction reaction of Cu(dmp)22+ by Fe(Cp)2 was not linear against the concentration
2+
of excess amounts of Fe(Cp)2. A detailed analysis of the reaction revealed that the reduction of Cu(dmp)2
involved the slow path related to the deformation of Cu(dmp)22+ (path B in Scheme 1). By using Fe(PMCp)2 (the
E° value is 500 mV more negative than that of Fe(Cp)2+/0) as the reductant, the mixing with another pathway
+
involving deformation of Cu(dmp)2 (path A in Scheme 1) became more evident. The origin of the “Gated
Behavior” is discussed by means of the energy differences between the “normal” and deformed Cu(II) and Cu(I)
species: the difference in the crystal field activation energies corresponding to the formation of pseudo-tetrahedral
Cu(II) from tetragonally distorted Cu(II) and the difference in the stabilization energies of the tetrahedral and
tetragonal Cu(I) for the activation of Cu(I) species. The reduction reaction of Cu(dmp)22+ by Fe(PMCp)2 confirmed
that the mixing of the two pathways takes place by lowering the energy level corresponding to the less favorable
conformational change of Cu(I) species.
Introduction
al. precisely explored such “gated behavior” caused by slug-
gishness in the geometric interconversion and discovered that
Concerted inner- and outer-sphere reorganizations are as-
sumed to occur for most of the outer-sphere electron-transfer
reactions.1,2 Therefore, the electron-transfer reaction is slow
when the reaction involves a large change in the coordination
geometry during the electron-transfer process. Vallee and
Williams pointed out for the electron exchange reactions
involving copper(II/I) couples that the rate of the electron
transfer is slow for the redox couple with normally preferred
coordination geometries, i.e., the tetrahedral four coordination
for copper(I) and the tetragonal five- or six-coordination for
copper(II).3
the oxidation of tetrahedral Cu(I) to tetragonal Cu(II) is slow
in most cases when macrocyclic thioether ligands were used.
In such cases, the electron exchange rate constant estimated by
the application of the Marcus cross relation to the oxidation
reaction of Cu(I) was not consistent with the directly measured
electron exchange rate constant by using NMR. However, when
the energy required for the geometric change from the tetrahedral
to the tetragonal structure is not large, such gated behavior
diminishes and the Marcus cross relation is successfully applied
to the estimation of the self-exchange rate constant.9
Early works on the outer-sphere reactions of copper cpm-
The electron-transfer regulated by the slowness of the change
in coordination geometry has been reported for some copper(II/
I) couples with tetrathiamacrocyclic ligands.4-8 Rorabacher et
2+/+
plexes centered on reactions of Cu(bpy)22+/+, Cu(phen)2
,
2+/+ 10-12
and its derivative Cu(dmp)2
.
In 1983, Lee and Anson
pointed out that the steric interconversion may have an important
(1) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441.
(2) Cannon, R. D. Electron-Transfer Reactions; Butterworth: London,
1980.
(3) Vallee, B. L.; Williams, R. J. P. Proc. Natl. Acad. Sci. U.S.A. 1968,
58, 498.
(4) Martin, M. J.; Endicott, J. F.; Ochrymowycz, L. A.; Rorabacher, D.
B. Inorg. Chem. 1987, 26, 3012.
(5) Meagher, N. E.; Juntunen, K. L.; Salhi, C. A.; Ochrymowycz, L. A.;
Rorabacher, D. B. J. Am. Chem. Soc. 1992, 114, 10411.
(6) 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.
(7) Meagher, N. E.; Juntunen, K. L.; Heeg, M. J.; Salhi, C. A.; Dunn, B.
C.; Ochrymowycz, L. A.; Rorabacher, D. B. Inorg. Chem. 1994, 33,
670.
(8) Salhi, C. A.; Yu, Q.; Heeg, M. J.; Villeneuve, N. M.; Juntunen, K.
L.; Schroeder, R. R.; Ochrymowycz, L. A.; Rorabacher, D. B. Inorg.
Chem. 1995, 34, 6053.
(9) Vande Linde, A. M. Q.; Westerby, B. C.; Ochrymowycz, L. A.;
Rorabacher, D. B. Inorg. Chem. 1993, 32, 251.
(10) Yoneda, G. S.; Blackmer, G. L.; Holwerda, R. A. Inorg. Chem. 1977,
16, 3376.
(11) Augustin, M. A.; Yandell, J. K. J. Chem. Soc., Chem. Commun. 1978,
370.
10.1021/ic9810687 CCC: $18.00 © 1999 American Chemical Society
Published on Web 06/22/1999

Interpretation of Gated Behavior
Inorganic Chemistry, Vol. 38, No. 14, 1999 3353
Scheme 1
oxidation and reduction cross reactions involving sterically
constrained complex ions, Cu(dmp)22+/+. The results indicate
2+/+
that the electron-transfer reactions of Cu(dmp)2
proceed
through path B. The energetic origin of the “gated behavior” is
explained on the basis of the ligand field activation energy
corresponding to the deformation of Cu(dmp)22+, and the
energetic inter-mixing of the two independent reaction pathways
corresponding to path A and path B for the Cu(dmp)22+/+ redox
couple was demonstrated in acetonitrile. The expression for the
electron self-exchange rate constant was derived for path B in
Scheme 1, and the estimated electron self-exchange rate constant
2+/+
for the Cu(dmp)2
couple was compared with that reported
previously.27 The free-energy profile of the gated electron-
transfer process involving Cu(dmp)2
2+/+
2+/+
was discussed on the
role in the electron-transfer processes of the Cu(bpy)2
and
basis of the experimental and calculated results.
Cu(phen)22+/+ couples.13 The studies of electron-transfer reac-
tions for Cu(dmp)22+/+ with various reaction partners in aqueous
solution were reported.14-19 The studies of the reduction of the
Experimental Section
2-
water-soluble Cu(dpsmp)2 (dpsmp ) 2,9-dimethyl-4,7-bis-
Chemicals. Acetonitrile was obtained from Wako Pure Chemicals
Inc. and purified by distillation twice from phosphorus pentoxide. The
content of the residual water in thus purified acetonitrile was examined
by a Mitsubishi Kasei CA01 Karl Fischer apparatus, by which the
amount of residual water was determined to be less than 1 mmol/dm3.
Ferrocene (Wako) and decamethylferrocene (Aldrich) were purified by
sublimation. All other chemicals from Wako and Aldrich were used
without further purification. Cu(dmp)2(ClO4)2 and Cu(dmp)2ClO4 were
synthesized by reported methods.27,31 Anal. Calcd for CuC28H24N4-
Cl2O8: 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.
((sulfonyloxy)phenyl)-1,10-phenanthroline) by Sykes et al.
indicated the involvement of such steric interconversion.20-22
However, there are some cases where electron exchange is slow
even for the near-tetrahedral Cu(II/I) couples.23-25 Most recently
Stanbury et al. reported the slow electron-exchange reaction of
2+/+
Cu(bib)2
(bib ) 2,2′-bis(2-imidazoly)biphenyl).26 The es-
2+/+
timated electron self-exchange rate constant of Cu(bid)2
is
0.16 kg mol-1 s-1. Takagi and Swaddle have been studying
Cu(II/I) electron-exchange couples by NMR where the coor-
dination geometries of Cu(I) and Cu(II) are constrained to be
similar, the kinetic behavior is expected to follow the context
of the moderately fast electron-transfer case, and no significant
change in coordination number or coordination geometry was
expected prior to the electron-transfer processes.27,28
34
[Co(bpy)3](ClO4)2,32 [Ni(tacn)2](ClO4)3,33 and [Mn(bpyO2)3](ClO4)2
were synthesized by literature methods. Anal. Calcd for CoC30H24N6-
Cl2O8: 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. Anal. Calcd for MnC30H24N6O14-
Cl2: C, 44.0; H, 2.96; N, 10.3. Found: C, 43.2; H, 2.87; N, 9.87.
(Caution! Perchlorate salts of metal complexes with organic ligands
are potentially explosiVe.)
The gated electron-transfer process has been successfully
interpreted by the square scheme, postulated by Rorabacher et
al., as shown in Scheme 1. The theoretical studies of the gated
electron transfer have been reported.29,30 However, the energetic
origin of conformational change has not yet been well under-
stood to date. In this article, we have observed inconsistency
of the electron exchange rate constants estimated from the
General. All manipulations were carried out in an atmosphere of
dry nitrogen to avoid any possible contamination of water and oxygen
from the environment. A Unisoku stopped-flow apparatus was used
for the kinetic measurements at various temperatures controlled by a
Hetofrig circulation bath. The reservoirs for the reactant solutions were
kept under nitrogen atmosphere during the experiments. At least 10
kinetic traces were collected for each run, and the results were analyzed
by an NEC personal computer fitted with an interface for the stopped-
flow apparatus. Unisoku software was used for the data analysis.
(12) Yandell, J. K. Copper Coordination Chemistry: Biochemical and
Inorganic Perspectives; Adenine Press: Guilderland, NY, 1983; p 157
and references therein.
(13) Lee, C.-W.; Anson, F. C. J. Phys. Chem. 1983, 87, 3360.
(14) Augustin, M. A.; Yandell, J. K. Inorg. Chem. 1979, 18, 577.
(15) Clemmer, J. D.; Hogaboom, G. K.; Holwerda, R. A. Inorg. Chem.
1979, 18, 2567.
(16) Holwerda, R. A. Inorg. Chem. 1982, 21, 2107.
(17) Davies, K. M. Inorg. Chem. 1983, 22, 615.
(18) Davies, K. M.; Byers, B. Inorg. Chem. 1987, 26, 3823.
(19) Lappin, A. G.; Youngblood, M. P.; Margerum, D. W. Inorg. Chem.
1980, 19, 407.
(20) Al-Shatti, N.; Lappin, A. G.; Sykes, A. G. Inorg. Chem. 1981, 20,
1466.
2+
Preliminary experiments revealed that Cu(dmp)2 releases a small
amount of dmp after several hours. However, this decomposition was
suppressed successfully by the addition of excess amounts of dmp in
2+
the solution. Moreover, no electroactive species other than Cu(dmp)2
was observed within the redox window of acetonitrile (-2 V ∼ +2 V)
by cyclic voltammetry, which strongly indicates that neither Cu(dmp)2+
nor Cu2+ produced by the decomposition of Cu(dmp)2 oxidizes
2+
ferrocene or decamethylferrocene used in this study. The absorbance
increase at ca. 456 nm, corresponding to the absorption maximum of
Cu(dmp)2+, was monitored for the kinetic measurements.
(21) Leupin, P.; Al-Shatti, N.; Sykes, A. G. J. Chem. Soc., Dalton Trans.
1982, 927.
(22) Allan, A. E.; Lappin, A. G.; Laranjeira, M. C. M. Inorg. Chem. 1984,
23, 477.
(23) Lappin, A. G.; Peacock, R. D. Inorg. Chim. Acta 1980, 46, L71.
(24) Knapp, S.; Keenan, T. P.; Zhang, X.; Fikar, R.; Potenza, J. A.; Schugar,
H. J. J. Am. Chem. Soc. 1990, 112, 3452.
(25) Flanagan, S.; Dong, J.; Haller, K.; Wang, S.; Scheidt, W. R.; Scott,
R. A.; Webb, T. R.; Stanbury, D. M.; Wilson, L. J. J. Am. Chem. Soc.
1997, 119, 8857.
(26) Xie, B.; Elder, T.; Wilson, L. J.; Stanbury, D. M. Inorg. Chem. 1999,
38, 12.
(27) Doine (Takagi), H.; Yano, Y.; Swaddle, T. W. Inorg. Chem. 1989,
28, 2319.
(30) Brunschwig, B. S.; Sutin, N. J. Am. Chem. Soc. 1989, 111, 7457. The
authors of refs 29 and 30 dealt with the energetics of the gated
intramolecular electron-transfer processes and concluded that the
process with high energy intermediate never compete with the direct
outer-sphere process. However, the reactions investigated in this study
and by Rorabacher et al. involve intermolecular electron-transfer
process after deformation of one of the reactants.
(31) Davies, G.; Loose, D. J. Inorg. Chem. 1976, 15, 694.
(32) Burstall, F. H.; Nyholm, R. S. J. Chem. Soc. 1952, 3570.
(33) McAuley, A.; Norman, P. R.; Olubuyide, O. Inorg. Chem. 1984, 23,
1938.
(28) Metelski, P. D.; Hinman, A. S.; Takagi, H. D.; Swaddle, T. W. Can.
J. Chem. 1995, 73, 61.
(29) Hoffman, B. M.; Ratner, M. A. J. Am. Chem. Soc. 1987, 109, 6237.
(34) Simpson, P. G.; Vinciguerra, A.; Quagliano, J. V. Inorg. Chem. 1963,
2, 283.

3354 Inorganic Chemistry, Vol. 38, No. 14, 1999
Koshino et al.
at 298 K in Acetonitrilea
2+/+
Table 1. Calculated Electron Self-Exchange Rate Constants for Cu(dmp)2
E°/V vs Fc+/0
r/pm
k12
k22
k11
∆H*/kJ mol-1
28 ( 1
∆S*/J mol-1 K-1
-81 ( 4
b
c
d
+
Cu(dmp)22+ + Cu(dmp)2
0.28
650
-
-
5.0 × 103 e
oxidant
Ni(tacn)2
0.555
0.435
380
400
(2.7 ( 0.2) × 105
6.0 × 103 f
5.9 × 102
24 ( 1
-60 ( 2
3+
Mn(bpyO2)3
(2.9 ( 0.1) × 104
80g
2.9 × 104
-
-
3+
reductant
Co(bpy)3
(7.0 ( 0.2) × 102
0.645h
1.6
36 ( 2
-68 ( 6
2+
-0.081
700
a Ionic strength of the solutions was adjusted to 0.1 mol kg-1 by (n-Bu4N)ClO4. b The rate constant for each cross reaction (kg mol-1 s-1). c The
self-exchange rate constant for oxidizing or reducing reagent (kg mol-1 s-1). d The self-exchange rate constant for Cu(dmp)2
(kg mol-1 s-1).
2+/+
e Reference 27. Macartney, D. H. Inorg. Chim. Acta 1987, 127, 9. g Macartney, D. H.; Thompson, D. W. J. Chem. Res., Synop. 1992, 344. h Reference
f
58.
2+
Reduction Reaction of Cu(dmp)2 by Co(bpy)32+. The
2+
reaction was observed under the conditions of [Cu(dmp)2
]
0
. [Co(bpy)32+]0. The monitored absorption increase at 456 nm
2+
for every run confirmed that the decomposition of Co(bpy)3
before mixing was minimal. The kinetic trace was satisfactorily
first-order for up to 3 half-lives. The dependence of the pseudo-
first-order rate constant on the concentration of Cu(dmp)22+ was
linear at various temperatures as shown in Figure 2. The second-
order rate constant at 298 K and the corresponding activation
parameters are listed in Table 1. From the reduction of Cu-
2+
(dmp)2 by Co(bpy)32+, we obtained the self-exchange rate
as 1.6 kg mol-1 s-1. This value is
2+/+
constant of Cu(dmp)2
smaller than those estimated from the NMR measurement and
from the oxidation reactions of Cu(dmp)2+, which strongly
2+
indicates that the reduction of Cu(dmp)2 is “gated.” As it is
3+
Figure 1. Dependence of kobs on the concentration of Ni(tacn)2 for
shown later, this reaction is also gated through path B: kB2-
the oxidation reaction of Cu(dmp)2+. [Cu(dmp)2+] ) 1.50 × 10-5 mol
kg-1, I ) 0.1 mol kg-1 (TBAP). The symbols represent the data obtained
at 303.2 (closed lozenges), 298.2 (open circles), 293.2 (closed circles),
288.2 (open squares), and 283.2 K (closed squares).
[Co(bpy)32+] , kQO in Scheme 1.
Reduction Reaction of Cu(dmp)22+ by Fe(Cp)2. The kinetic
traces were excellently first-order for Cu(dmp)22+ up to 3 half-
lives.
Electrochemical measurements were carried out by a BAS 100BW
electrochemical analyzer with a 1.5 mm φ platinum disk or glassy
carbon as the working electrode, and a 0.5 mm φ platinum wire as the
counter electrode. A silver/silver nitrate electrode with 0.1 mol kg-1
tetrabutylammonium perchlorate (TBAP) in acetonitrile was used as a
+
d[Cu(dmp)2 ]
2+
) kobs[Cu(dmp)2
]
(3)
dt
2+
3+
reference electrode. A solution of Mn(bpyO2)3 was prepared elec-
[Fe(Cp)2]0 . [Cu(dmp)2
]
0
trochemically in CH3CN, containing 0.10 mol kg-1 TBAP at carbon
electrode (Hokuto Denko HX-201).
However, the dependence of kobs on the concentration of Fe-
(Cp)2 was not linear. This tendency may be explained by the
following two-step mechanism including a conformational
change of Cu(II) prior to the fast outer-sphere electron-transfer
reaction (kB2).
Results
Oxidation Reactions of Cu(dmp)2+ by Ni(tacn)23+ and Mn-
+
3+
(bpyO2)33+. The reaction of Cu(dmp)2 with Ni(tacn)2 in
acetonitrile shows pseudo-first-order behavior up to 3 half-lives
under conditions where [Cu(dmp)2+]0 , [Ni(tacn)23+]0.
kOQ
2+
Cu(dmp)22+ y z Cu(dmp)2
*
(4)
(5)
kQO
kOx
Cu(dmp)2+ + oxidant 8 Cu(dmp)22+ + reductant (1)
kB2
Cu(dmp)22+* + ARed 8 Cu(dmp)2+ + AOx
+
rate ) kOx[Cu(dmp)2 ][oxidant]
(2)
where ARed and AOx represent Fe(Cp)2 and Fe(Cp)2+, respec-
tively. When the reduction reaction is gated as suggested from
the results for the reaction with Co(bpy)32+, the conformational
change corresponding to the kOQ process may be slow. In such
a case, the rate law is expressed by eq 6.
Figure 1 shows the dependence of kobs ()kOx[oxidant]) on the
3+
concentration of Ni(tacn)2
at various temperatures. The
second-order rate constant at 298 K, I ) 0.1 mol kg-1 is listed
in Table 1, together with the activation parameters of the
reaction. The reaction of Cu(dmp)2 with Mn(bpyO2)3 was
+
3+
+
observed under the conditions of [Cu(dmp)2
]
. [Mn-
0
kB2kOQ
rate )
[ARed][CuIIL] ) kobs[CuIIL] (6)
(bpyO2)33+]0. The estimated electron self-exchange rate con-
stants for the Cu(dmp)22+/+ couple by the Marcus cross relation
kB2[ARed] + kQO
from the oxidation reactions of Cu(dmp)2+ by Ni(tacn)23+ and
-1
3+
Mn(bpyO2)3 were 5.9 × 102 and 2.9 × 104 kg mol-1 s-1
,
Therefore, the plot of the reciprocal value of kobs against [ARed
]
respectively. These values were in agreement with the reported
value (5.0 × 103 kg mol-1 s-1) obtained from the NMR
measurement considering the accuracy of the Marcus rela-
tion.35,36
(35) Jordan, R. B. Reaction Mechanisms of Inorganic and Organometallic
Systems; Oxford University Press: New York, 1991.
(36) Wilkins, R. G. Kinetics and Mechanism of Reactions of Transition
Metal Complexes, 2nd ed.; VCH: New York, 1991.

Interpretation of Gated Behavior
Inorganic Chemistry, Vol. 38, No. 14, 1999 3355
Table 2. Estimated Rate Constants for the Reactions of Cu(dmp)2 at 298 Ka
2+
reaction
Cu(dmp)22+ + Fe(Cp)2
kOQ
kQO
33 ( 3 s-1
b
7.7 × 107 s-1
c
4.3 × 10-7
c
kOQ/kQO ) KOQ
c
kB2
3.0 × 1011 kg mol-1 s-1
(3.2 ( 0.1) × 1012 kg mol-1 s-1
(2.5 ( 0.1) × 104 kg mol-1 s-1
Cu(dmp)22+ + Fe(PMCp)2
kB2
kA2
d
a Ionic strength of the solutions was adjusted to 0.1 mol kg-1 by (n-Bu4N)ClO4. b The rate constant were estimated from the slope and the
intercept of Figure 3. c Calculated from the estimated value of the electron self-exchange rate constant for Cu(dmp)2
*
(see text). d The rate
2+ /+
constants were obtained by the least-squares analysis of the plot in Figure 4. kOQ and kQO values were fixed for the least-squares calculation.
Figure 2. Dependence of kobs on the concentration of Cu(dmp)22+ for
Figure 4. Dependence of kobs on the concentration of Fe(PMCp)2 for
2+
the reduction reaction of Cu(dmp)2 by Co(bpy)32+. [Co(bpy)32+] )
the reduction reaction of Cu(dmp)22+. [Cu(dmp)22+] ) 5.56 × 10-6
0.1 mol kg-1 (TBAP). Symbols are as in Figure 3.
-
1.50 × 10-5 mol kg-1, I ) 0.1 mol kg-1 (TBAP). The symbols represent
the data obtained at 302.9 (closed lozenges), 298.0 (open circles), 293.2
(closed circles), 288.1 (open squares), and 283.1 K (closed squares).
1.01 × 10-5 mol kg-1, [dmp]free ) (0.53-2.0) × 10-4 mol kg-1, I )
pseudo-first-order behavior up to 3 half-lives under conditions
where [Cu(dmp)22+]0 , [Fe(PMCp)2]0. However, the plot of
kobs against the initial concentration of Fe(PMCp)2 showed
curvatures as shown in Figure 4. Such curvature was reported
previously by Rorabacher et al., for the oxidation reaction of
CuI-thioether complex.5,7,8 The dependence in Figure 4 may be
explained by the “mixing” of both path B and path A caused
+/0
by the 500 mV more negative potential of Fe(PMCp)2 as
discussed later. In such case, kobs is expressed by eq 8, using
the rate constants in Scheme 1.
k
OQkB2
kobs ) kA2
+
[ARed
]
(8)
(
)
kB2[ARed] + kQO
The best-fit values of each rate constant estimated by the least-
squares analysis (a curve fitting program, SIGMA PLOT) are
listed in Table 2.
Figure 3. Plot of kobs vs [Fe(Cp)2]-1 for the reduction reaction of
-1
Cu(dmp)2 by Fe(Cp)2. [Cu(dmp)22+] ) 4.87 × 10-6-1.05 × 10-5
2+
mol kg-1, [dmp]free ) (1.0-1.1) × 10-4 mol kg-1, I ) 0.1 mol kg-1
(TBAP). The symbols represent the data obtained at 308.2 (open
lozenges), 303.2 (closed lozenges), 298.2 (open circles), 293.2 (closed
circles), and 288.2 K (open squares).
Discussion
Application of Square Scheme. Rorabacher et al. tried to
explain the “gated” electron transfer for copper-cyclic thioether
ions using the mechanisms described in Scheme 1.4-8 They
found that the reactions proceed mostly through path A for the
copper-thioether complexes by comparing the electron exchange
rate constants estimated from both the reduction and oxidation
cross reactions.
should be linear with an intercept when [ARed 0
]
. [Cu-
(dmp)22+]0.
kQO
1
1
)
+
(7)
kobs
kOQ
kOQkB2[ARed
]
The plots of 1/kobs vs 1/[Fe(Cp)2]0 at various temperatures are
shown in Figure 3. The values of kOQ, ∆H*, and ∆S* are 33 (
In this study, the electron self-exchange rate constant for the
2+/+
Cu(dmp)2
couple was estimated from both the oxidation
3 s-1, 31 ( 2 kJ mol-1, and -110 ( 10 J mol-1 K-1
,
reactions of Cu(dmp)2+ by Ni(tacn)23+ and Mn(bpyO2)33+ and
the reduction reaction of Cu(dmp)22+ by Co(bpy)32+. By using
the Marcus cross relation, the estimated self-exchange rate
constants were 5.9 × 102 and 2.9 × 104 kg mol-1 s-1 from the
respectively.
2+
Reduction Reaction of Cu(dmp)2 by Fe(PMCp)2. The
2+
reduction reaction of Cu(dmp)2 by Fe(PMCp)2 also shows

3356 Inorganic Chemistry, Vol. 38, No. 14, 1999
Koshino et al.
results of the oxidation reactions, while the result for the
reduction reaction gave merely 1.6 kg mol-1 s-1. As the electron
exchange rate constant directly measured by the NMR method
complex is very fast (2 × 105 s-1).38 Therefore, the solvent
dissociation process may not compete with the kOQ process. The
activation entropy for the kOQ process was estimated as -110
( 10 J mol-1 K-1. Such large negative activation entropies were
also reported for several racemization reactions through the
“twist” mechanism in which similar a structural change to that
for the kOQ process is expected.39 As the theoretical investigation
for intramolecular ET reactions by Brunschwig and Sutin
suggests that no gated process involving conformational change
of intramolecular ET can compete with the direct electron
transfer in the normal region,30 the kinetic results obtained in
this study strongly indicate that the reaction involves a confor-
mational change prior to the outer-sphere electron transfer.
Calculation of the Ligand Field Activation Energy. With
the d9 configuration, Cu(II) ion prefers a tetragonal structure in
general.3 When the intermediate, CuIIL(Q), is the same for
reduction reactions with any reductant, the Marcus type cross
relation may be applicable to the kB2 process.40 The deformation
from ground-state Cu(II) ion to pseudo-tetrahedral Cu(II) ion
lowers the crystal field stabilization energy of the Cu(II) ion
and also raises the redox potential for the cross reaction to occur
more rapidly. This situation is shown in Scheme 2 by assuming
a tetragonal structure for O ()Cu(dmp)22+) in the ground state
and a pseudo-tetrahedral structure for Q ()Cu(dmp)22+*).
In case of Cu(dmp)22+, it has been reported that the ground
state structure is originally strongly distorted from the normal
tetragonal structure and the dihedral angle between the two
is 5 × 103 kg mol-1 s-1 27
,
it is obvious that the reaction
couple is also “gated,” and the
2+/+
involving the Cu(dmp)2
preferred pathway for the redox reaction of this couple is path
B in Scheme 1. The results for the reduction reaction of
Cu(dmp)22+ by Fe(Cp)2 also strongly indicates that the reaction
is “gated” and proceeds through path B in Scheme 1.
According to Scheme 1, Rorabacher et al. derived rate laws
for oxidation and reduction reactions corresponding to path A
and path B as follows, by assuming steady state for the
concentrations of the intermediates, CuIIL(Q) and CuIL(P).4,5
Reduction Reaction
d[CuIIL]
kA2kPR
kB2kOQ
-
)
+
×
(
)
dt
k2A[AOx] + kPR kB2[ARed] + kQO
[CuIIL(O)][ARed] (9)
Oxidation Reaction
d[CuIL]
k2AkRP
k2BkQO
-
)
+
×
(
)
dt
k2A[AOx] + kPR kB2[ARed] + kQO
[CuIL(R)][AOx] (10)
where ARed and AOx denote the reducing reagent and the
oxidizing reagent, respectively. When the reactions proceed
through path B, the rate laws are expressed by the second term
of the right-hand side of eqs 9 and 10. As the reduction of Cu-
2+
N-CuII-N planes are close to 60°.37,41,42 Therefore Cu(dmp)2
exhibits D2d symmetry. In this study, we tried to calculate the
energy difference (ligand field activation energy, LFAE)
between this largely deformed tetragonal ground state and the
pseudo-tetrahedral state, by estimating the 10Dq value corre-
sponding to the tetrahedral conformation of Cu(dmp)22+* (4∆o/
9) from the diffuse reflectance spectrum of Cu(dmp)2(ClO4)2.43
The observed band maxima (in cm-1) for Cu(dmp)2(ClO4)2 are
listed in Table 3. For a Cu(II) species with the perfect D2d
symmetry, three d-d bands corresponding to the transition from
2+
(dmp)2 is “gated” through path B, the rate law is expressed
by eq 6. In the case where the reaction corresponding to kOQ is
slow, the reverse reaction for the conformational change in Cu-
(II) species, kQO, may be very fast. The validity of this
assumption is given later. When the concentration of ARed is
large enough, the two processes, kB2[ARed] and kQO start to
compete. Therefore, the slope of the plot in Figure 3 corresponds
to kQO/kOQkB2 ()1/KOQkB2). On the other hand, when the
concentration of ARed is small compared with [CuIIL], i.e., kB2-
[ARed] , kQO, the rate law is reduced to eq 11 and the
dependence of the pseudo-first-order rate constant on the
concentration of CuIIL is linear as seen for the reaction of Cu-
2
2
2
2B2 to E, B1, and A1 are predicted. Further distortion from
2
D2d to D2 or Cs, and/or the spin-orbit coupling causes E to
split into Γ6 and Γ7.44,45 As the strong distortion from the
ordinary tetragonal structure lifts the degeneracy of all d
orbitals,46,47 four major absorptions corresponding to 2B2 f Γ7-
(2E), 2B2 f 2B1, 2B2 f Γ6(2E), and 2B2 f 2A1 should appear in
the visible and near-IR region. Each observed band maximum
was assigned as shown in Table 3. It is assumed that the energy
level for spherically symmetric CuN4 geometry lies close to
the difference in the weighted mean energy levels of T and E
terms. Therefore, the tetrahedral 10Dq may be close to 6260
2+
2+
(dmp)2 with Co(bpy)3
.
kOQkB2
kQO
kobs
)
[CuIIL]
(11)
(
)
cm-1 for Cu(dmp)22+. The octahedral 10Dq value for Cu(en)3
2+
Similar results to those shown in Figure 3 were reported by
Sykes et al. for the reaction of Cu(dpsmp)2
was reported as 1.64 × 104 cm-1 by Orgel.48 Therefore, the
2- 20,21
.
The rate
2-
constant (kOQ) for the conformational change of Cu(dpsmp)2
was reported as ca. 140 s-1. The difference of kOQ for the
deformation of Cu(dmp)22+ and Cu(dpsmp)22- may be attributed
to the difference in the basicity of dmp and dpsmp2- ligands:
in the studies of Cu(dmp)22+ and Cu(dpsmp)22- in water, a water
molecule is coordinated to Cu(II) ion where the hydrolysis
constants of Cu(dmp)22+ and Cu(dpsmp)22- have been obtained
5.8 and 5.3.22,37 For the reaction of Cu(dmp)22+/+ in acetonitrile,
it is also likely that a solvent molecule is coordinated to Cu-
(38) Rablen, D. P.; Dodgen, H. W.; Hunt, J. P. J. Am. Chem. Soc. 1972,
94, 1771.
(39) Lawrance, G. A.; Stranks, D. R. Inorg. Chem. 1977, 16, 929.
(40) Ratner, M. A.; Levine, R. D. J. Am. Chem. Soc. 1980, 102, 4898.
(41) Kuchiyama, Y.; Kobayashi, N.; Takagi, H. D. Inorg. Chim. Acta 1998,
277, 31.
(42) van Meerssche, M.; Germain, G.; Declercq, J. P. Cryst. Struct.
Commun. 1981, 10, 47.
(43) Figgis, B. N. Introduction to Ligand Fields; John Wiley and Sons
Inc.: New York, 1966.
(44) Lever, A. B. P Inorganic Electronic Spectroscopy, 2nd ed.; Elsevier:
New York, 1984.
(45) Ferguson, J. J. Chem. Phys. 1964, 40, 3406.
(46) Gouge, E. M.; Geldard, J. F.; Sinn, E. Inorg. Chem. 1980, 19, 3356.
(47) Gouge, E. M.; Geldard, J. F. Inorg. Chem. 1978, 17, 270.
(48) Orgel, L. E. An Introduction to Transition-Metal Chemistry; Meth-
uen: London, 1960.
(dmp)2 .
2+ 27 However it has been reported that the rate constant
for the water exchange in the CuII-2,2′,2′′-triaminotriethylamine
(37) Tran, D.; Skelton, B. W.; White, A. H.; Laverman, L. E.; Ford, P. C.
Inorg. Chem. 1998, 37, 2505.

Interpretation of Gated Behavior
Inorganic Chemistry, Vol. 38, No. 14, 1999 3357
2+
Scheme 2. Free Energy Diagrams for the Species in the Reactions of Cu(dmp)2 with Ferrocene and Decamethylferrocene at
298 K
2+
Table 3. Absorption Band Maximum for Cu(dmp)2(ClO4)2
difference between Cu(dmp)2 in the ground state and the
tetrahedral Cu(dmp)22+*: the deformation from sterically
constrained Cu(dmp)22+ to Cu(dmp)22+*. As the relaxation from
the steric interaction between the bulky methyl groups on
different dmp ligands takes place, it is concluded that the free
Observed by the Diffuse Reflectance Spectrophotometrya
band maximum/cm-1
assignment
24390
13260
9765 (broad)
9033 (shoulder)
5981
charge transfer
2B2 f 2A1
energy difference between Cu(dmp)2 and Cu(dmp)22+* is
2+
2B2 f Γ6(2E)
2B2 f 2B1
somewhat smaller than 60 kJ mol-1
.
2B2 f Γ7(2E)
2+
From the fact that the reduction of Cu(dmp)2 takes place
through path B in Scheme 1, microscopic reversibility requires
that the oxidation reaction of Cu(dmp)2 (the reverse process)
a The 10Dq value for the imaginary tetrahedral field was estimated
as 6260 cm-1 from the difference between the average value of the
2B2 f 2B1 and 2B2 f 2A1 transition and the average value of the energy
+
should also take place through path B. Therefore, it is required
2
levels of B2, Γ7(2E), and Γ6(2E) (see text).
that CuIL(P) [) Cu(dmp)2+*] is less stable compared with
CuIIL(Q) [) Cu(dmp)22+*] (cf. Schemes 1 and 2). In Cu(dmp)2
+
with d10 electronic configuration, no change in the LFSE is
expected for the change in the coordination geometry. Therefore,
+
the free-energy difference between Cu(dmp)2 in the ground
state (tetrahedral) and Cu(dmp)2+* (distorted tetragonal) should
be attributed to the nature of Cu(I) with a strong thermodynamic
preference to form the tetrahedral geometry.3 It is known that
the energy gap between the filled 3d orbital and the vacant 4s
orbital is small in Cu(I), and that the combination of 3d-4s
hybrid orbitals with the pz orbital forms a stable linear
conformation of d10 metal complexes.49,50 In the same manner,
many copper(I) species achieve the stable tetrahedral geometry.51
It is a very difficult task to estimate the electronic energy levels
of tetrahedral and tetragonal forms of CuIN4 system. However,
the free energy difference between tetrahedral and tetragonally
distorted CuIN4 geometries in solution may be roughly estimated
by using the stability constant of tetrahedral Cu(dmp)2+ because
the stability constant includes not only the contribution of
geometric change but also the contribution of solvation free-
energy changes accompanying the particular geometric change.
10Dq value for the corresponding tetrahedral CuN4 system is 7
× 103 cm-1. Thus the value of 6.26 × 103 cm-1 estimated for
2+
Cu(dmp)2 seems reasonable.
By using this value, the ligand field stabilization energies
(LFSE) for the imaginary tetrahedral geometry and the ground-
state geometry of d9 Cu(dmp)2 are calculated as -2500 and
2+
-7600 cm-1 relative to the spherically symmetric geometry.
Therefore, the largely distorted tetragonal structure of Cu-
(49) Orgel, L. E. J. Chem. Soc. 1958, 4186.
(dmp)2 in the ground state is still ca. 61 kJ mol-1 more
2+
(50) Fisher, K. J.; Drago, R. S. Inorg. Chem. 1975, 14, 2804.
(51) Gillespie, R. J.; Hargittai, I. The VSEPR Model of Molecular Geometry;
Allyn and Bacon: Boston, MA, 1991.
stabilized compared with perfectly tetrahedral Cu(dmp)22+*, and
this value can be taken as the upper limit of the enthalpy

3358 Inorganic Chemistry, Vol. 38, No. 14, 1999
Koshino et al.
The equilibrium constant for the following reaction is reported
as 1019.1 in water.52
solution.26 The slope of the plot of eq 7 gives 1/KOQkB2.
Therefore, eq 14 is rearranged to eq 18.
+
Cu+ + 2dmp h Cu(dmp)2
(12)
kB2 ) 5.4 × 104kCu2+*/+kFe+/0Sf
(18)
By making a na¨ıve assumption that the chemical potential of
the distorted tetragonal form of Cu(I) is close to that for solvated
Cu(I) (although it is known that Cu(I) in acetonitrile is
tetrahedrally coordinated and stabilized), we estimate the free-
where S denotes the slope obtained from the plot in Figure 3,
and 5.4 × 104 is the equilibrium constant for the reaction of
2+
Cu(dmp)2 and ferrocene.
2+*/+
The value of kCu
may be estimated by Marcus theory,1
+
+
energy difference between the solvated Cuaq and Cu(dmp)2
because this process is essentially controlled by the outer-sphere
reorganization free energy and the electrostatic terms: 14.0 kJ
in water to be 109 kJ mol-1 at 298 K. The transfer free-energy
from water to acetonitrile is less than 10 kJ mol-1 for singly
charged cations such as Cu(I).53,54 Therefore, the free energy
change for the equilibrium expressed by eq 12 in acetonitrile
mol-1 for ∆G*os and -2 kJ mol-1 for ∆G*coul + ∆G*DH
,
respectively by setting the ionic radii of both Cu species at 650
pm in acetonitrile at 298 K.27 With 4.8 × 1010 kg mol-1 s-1
may be close to 100 kJ mol-1
.
11
thus estimated for kCu , a value of 3.0 × 10 kg mol-1 s-1
2+*/+
Estimation of the Conformational Equilibrium Constant
(KOQ). In the square scheme, kA2, k2A, kB2, and k2B represent
the rate constants of electron-transfer reactions. Once these
values are estimated, the conformational equilibrium constant
can be obtained. The value of kB2 depends on the nature of the
reaction partner, as this process includes the effect of the inner-
sphere free energy change and the redox potential of the
reductant. However, we have a good reason to assume that kB2
+/0
was obtained for kB2 by using the reported value of kFe , the
electron self-exchange rate constant for the ferricinium/ferrocene
couple (9 × 106 dm3 mol-1 s-1, ionic radii ) 600 pm).55
Therefore, KOQ ) 4.3 × 10-7, and a value of 7.7 × 107 s-1
was estimated for kQO. The free energy difference between Cu-
(dmp)22+ and Cu(dmp)22+* is, therefore, ca. 36 kJ mol-1, which
is rather small compared with the estimated value, 60 kJ mol-1
,
2+
2+
from the LFAE calculation. In the LFAE calculation, it is
assumed that the bond lengths between Cu(II) and nitrogen
donor atoms do not change while the dihedral angle varies from
ca. 60 to 90°. Therefore, a rather small energy difference
between Cu(dmp)22+ and Cu(dmp)22+* may indicate the exist-
ence of a metastable form of Cu(dmp)22+* with different CuII-N
lengths from those for ground-state Cu(dmp)22+. Such a structure
may be possible as the steric repulsion between methyl groups
is large in the ground-state Cu(dmp)22+: the Cu-N bond length
in Cu(dmp)22+ complex is 206 pm, which is almost identical to
that for the typical CuI-N bond length,41,42 while a value of
199 pm is reported for the Cu(II)-N bond length for pseudo
is very fast: the deformation of Cu(dmp)2 to Cu(dmp)2
*
2+ /+
pushes up the redox potential of the Cu(dmp)2
*
couple
significantly, as the stability of Cu(dmp)22+* is reduced as much
as the potential gap between Cu(dmp)22+ and Cu(dmp)22+* prior
to the outer-sphere electron-transfer process. The rise of the
redox potential, which is equivalent to the LFAE, is estimated
by using the Nernst equation.
RT
F
E°Cu2+*/+ ) E°Cu2+/+
-
ln KOQ
(13)
2+*/+
2+/+
where E°Cu , E°Cu , and F are the standard redox potentials
2+
*
/+ and Cu(dmp)22+/+ couples and the Faraday
tetrahedral Cu(2,9-diphenyl-1,10-phenanthroline)22+ 56
.
The mea-
of the Cu(dmp)2
constant, respectively. In this study, we obtained 0.280 V as
2+
sured second-order rate constant for the reaction of Cu(dmp)2
with Co(bpy)32+, 7.0 × 102 kg mol-1 s-1 at 298K, corresponds
to kB2kOQ/kQO. As KOQ is independent of the nature of the
reducing reagent, kB2 value for the reaction of Cu(dmp)22+ with
2+/+
E°Cu
with reference to the ferricinium/ferrocene couple. As
2+*/+
it is expected that the value of KOQ () kOQ/kQO) is small, E°Cu
may be large. As a result, the kB2 process is accelerated by a
large driving force (∆G° ) -FE°Cu ) to achieve a very rapid
2+*/+
Co(bpy)3 was calculated as 1.6 × 109 kg mol-1 s-1, which
2+
electron transfer. Such a situation may be demonstrated on the
basis of the Marcus cross relation. For the cross reaction of
Cu(dmp)22+* and ferrocene, the coulombic work terms are
relatively small and may be ignored (w11 for the Cu(II)/(I) self-
exchange reaction is merely 1 kJ mol-1 and W is close to
unity).35,36
seems reasonably smaller than kB2 for the reaction of Cu-
2+
(dmp)2 with ferrocene as the electron self-exchange rate
3+/2+
constant for the Co(bpy)3
couple is small.57,58
Interpretation of the Mixing of two Paths. The free energy
2+
difference between the ground-state Cu(dmp)2 and distorted
Cu(dmp)22+* is not affected by changing reducing reagent, as
the change in the reaction partner merely influences the free
energy gap, ∆G°OQ, as shown in Scheme 2A and 2B. When a
more powerful reducing reagent is employed for the reduction
of Cu(dmp)22+, it is clear from Scheme 2 that the mixing of
path B and path A is expected to occur. Such case was observed
kB2
)
k
k
+/0KCu2+*/FefW
(14)
(15)
Cu2+*/+ Fe
x
[ln KCu2+/Fe + (wCu2+*/Fe - wCu /Fe+)/RT]2
4[ln kCu2+*/+kFe+/0/Z2 + (wCu2+*/+ - wFe+/0)/RT]
+
ln f )
2+
for the reaction of Cu(dmp)2 with Fe(PMCp)2 in this study.
-(wCu2+*/Fe + wCu /Fe+ - w
- wFe )
+
+/0
Cu2+*/+
This phenomenon strongly indicates that the interchange in the
activation process may take place for the gated electron-transfer
W ) exp
(16)
(17)
(
)
2RT
9.05zizj
wij )
(kcal mol-1)
(54) Cox, B. G.; Hedwig, G. R.; Parker, A. J.; Watts, D. W. Aust. J. Chem.
1974, 27, 477.
(55) McManis, G. E.; Nielson, R. M.; Gochev, A.; Weaver, M. J. J. Am.
Chem. Soc. 1989, 111, 5533.
(56) Miller, M. T.; Gantzel, P. K.; Karpishin, T. B. Inorg. Chem. 1998,
37, 2285.
x
a(1 + 0.481a µ)
where z is the charge on complex ions, a is the sum of the ionic
radii of each reacting species (Å), µ is the ionic strength of the
(57) Lappin, A. G. Redox Mechanisms in Inorganic Chemistry; Ellis
Horwood: Chichester, U.K., 1994.
(58) Dunn, B. C.; Ochrymowycz, L. A.; Rorabacher, D. B. Inorg. Chem.
1995, 34, 1954.
(52) Sillen, L. G., Martell, A. E., Eds. Stability Constants of Metal-Ion
Complexes; Alden Press: Oxford, 1971.
(53) Cox, B. G.; Parker, A. J. J. Am. Chem. Soc. 1972, 94, 3674.

Interpretation of Gated Behavior
Inorganic Chemistry, Vol. 38, No. 14, 1999 3359
reactions when the potential gap between the reactants and
products are very large. The 500 mV larger potential difference
for the reaction of Cu(dmp)2 with Fe(PMCp)2 lowers the
Scheme 3
2+
difference in the free energy levels between [Q + ARed′] and
[P + AOx′] as shown in Scheme 2B, and the effective mixing
of path A and path B takes place. A computer calculation for
eq 8 gave a best-fit value of (2.5 ( 0.1) × 104 and 3.2 × 1012
kg mol-1 s-1 for kA2 and kB2 by setting kOQ and kQO to 33 and
7.7 × 107 s-1, respectively. The activation free energy corre-
sponding to the kA2 process is 48 kJ mol-1, which implies that
the mixing of paths A and B takes place effectively and that
the energy level of the [P + AOx′] state in Scheme 2B is
somewhat smaller than this value. Therefore, the upper limit of
the original energy gap between [P + AOx′] and [R + AOx′]
states in Scheme 2B is ca. 123 kJ mol-1 (∆G°2 + ∆G*A2), while
the lower limit is 63 kJ mol-1 (the energy level of [Q + ARed
]
× 104 kg mol-1 s-1, which may be compared with the directly
measured value by NMR (5 × 103 kg mol-1 s-1).27 Similar
calculations were reported by Rorabacher et al.59 The above
discussion implies that any outer-sphere electron exchange
process, gated or not, causes extra line broadening which
depends on the concentration of the paramagnetic species, [Cu-
(II)] (eq 20). Recently, Stanbury et al. reported a [Cu(II)]-
independent rate constant for the Cu(bite)2+/+ electron exchange
reaction (bite ) biphenyldiiminodithioether).25 They suggested
that the traditional entatic state view which attributes rapid
electron transfer at the blue copper sites to small structural
differences between the Cu(I) and Cu(II) states60,61 may be
incorrect. However, the results in this study indicate that the
classical entatic state view seems still valid, and the results
observed for the Cu(bite)2+/+ couple seems to be an exception
relative to [R + AOx]: ∆G°1 + ∆GOQ. Thus, the free-energy
difference between Cu(dmp)2+ and Cu(dmp)2+* estimated from
the stability constant for reaction 12 (109 kJ mol-1) seems
acceptable.
A direct electron-exchange rate constant between CuIIL(O)
and CuIL(P) without any structural change, which corresponds
to path A, can be calculated by using kA2 and the self-exchange
rate constant for the Fe(PMCp)2+/0 couple as 5 × 10-11 kg mol-1
s-1 (∆G*)118 kJ mol-1) from the Marcus cross relation.
Therefore, it is shown that the direct electron exchange (path
A) does not compete with the electron exchange reaction through
path B.
Electron Self-Exchange Reaction. The electron exchange
reaction proceeds through the pathway with lower activation
energy. Therefore, the electron self-exchange reaction for the
Cu(dmp)22+/+ couple proceeds also through path B. As the free
energy profile for the electron self-exchange reaction is sym-
metric along the reaction coordinate, it may be described as
shown in Scheme 3. According to Scheme 3, the rate law of
the electron-exchange reaction is described by eq 19, assuming
steady state for Cu(dmp)22+*.
compared with the other reported results including the
2+/+
Cu(dmp)2
couple.
Conclusion
A complete analysis of the electron-transfer reactions involv-
2+/+
ing the Cu(dmp)2
couple in acetonitrile was carried out in
this study. It was shown that the reduction reaction of Cu-
2+
(dmp)2 was “gated” because of the relatively slow confor-
mational change in Cu(dmp)22+. The slow conformational
change in Cu(II) ion was attributed to the large LFAE from
ground-state Cu(dmp)22+ (the dihedral angle between two dmp
planes is close to 60°) to the pseudo-tetrahedral Cu(dmp)22+*.
The mixing of path A (direct electron transfer) and path B
(involving slow conformational change prior to the outer-sphere
ET process) was observed for the reduction reaction of Cu-
kOQ
2+
Cu(dmp)22+ y z Cu(dmp)2
*
kQO
kET
%
+
Cu(dmp)22+* + Cu(dmp)2
kETkOQ/k
rate )
QO [Cu(I)]T[Cu(II)]T
(19)
(20)
(21)
1 + kOQ/kQO
2+
(dmp)2 by Fe(PMCp)2. The preference of path B for the
τ-1ex ) kex[Cu(II)]T
kETkOQ/kQO
2+/+
Cu(dmp)2
couple was explained by the relative instability
of Cu(dmp)2+* compared to Cu(dmp)22+*. The direct electron
exchange rate constant for path A was estimated as 5 × 10-11
kg mol-1 s-1 from the results obtained for the cross reaction of
Cu(dmp)22+ with Fe(PMCp)2. Although we cannot observe the
kex
)
1 + kOQ/kQO
minor intermediate, Cu(dmp)22+*, the existence of such species
where [Cu(I)]T and [Cu(II)]T denote the total concentrations of
Cu(I) and Cu(II) species, respectively. When kOQ is small
2+
was suggested as the kinetic evidence. Whether the Cu(dmp)2
*
species has a distinct tetrahedral structure or not is an open
question. The LFAE calculation may not lead to a certain
potential minimum for the suitable structure of the intermediate,
as discussed above. However, the reported Cu(II)-N distance
in Cu(dmp)22+ is rather long because of the repulsion between
compared with kQO, which is the case observed for the reaction
2+/+
of the Cu(dmp)2
couple, eq 21 is reduced to eq 22.
kex ) kETkOQ/kQO
(22)
The values of kQO and kOQ are 7.7 × 107 s-1 and 33 s-1
,
(59) Robandt, P. V.; Schroeder, R. R.; Rorabacher, D. B. Inorg. Chem.
1993, 32, 3957.
(60) Williams, R. J. P. Eur. J. Biochem. 1995, 234, 363.
(61) Kaim, W.; Schwederski, B. Bioinorganic Chemistry: Inorganic
Elements in the Chemistry of Life; Wiley: Chichester, U.K., 1994.
respectively, while kET (ET rate constant within the precursor
10
2+*/+
complex without structural change, kCu ) is 4.8 × 10 kg
mol-1 s-1 as estimated above. Therefore, kex is calculated as 2

3360 Inorganic Chemistry, Vol. 38, No. 14, 1999
Koshino et al.
four methyl groups.41 Therefore, the existence of a certain high-
energy metastable Cu(dmp)22+* with a shorter Cu-N bond
length may be possible.
The authors express their thanks to the kind and stimulating
suggestions and thoughtful instructions of the reviewers.
Supporting Information Available: Tables of the rate constants
corresponding to the plots in Figures 1-4. This material is available
free of charge via the Internet at http://pubs.acs.org.
Acknowledgment. This research was supported by a Grant-
in-Aid for Scientific Research (Grant No. 10440193) from the
Ministry of Education, Science, Culture and Sports of Japan.
IC9810687