Bimolecular electron transfer in the Marcus inverted region

Article abstract of DOI:10.1021/ja960575p

The rates for the photoinduced bimolecular reactions of a homologous series of Ru(II) diimines with cytochrome (cyt) c in its oxidized and reduced forms have been measured. The electronic coupling and reorganization energy of the system have been adjusted such that the inverted region may be accessed at reasonable driving forces. The electron transfer (ET) rate constants for *Ru(II) diimine/Fe(II)cyt c reaction increase monotonically and approach the diffusion limit of 8.8 x 10⁸ M^-1 s^-1 at ΔG° = -0.7 V. At a higher driving force, which may be accessed with the powerfully oxidizing *Ru(diCF₃-bpy)₃²⁺, the rate for ET is observed to drop off. Similarly, the high driving forces achieved with *Ru(II) diimine/Fe(III)cyt c (-ΔG ≤ 1.12 V) are manifested in a decrease of the ET rate constant with increasing exergonicity. The observed ET rates for both systems are well described by a bimolecular model for ET occurring over an equilibrium distribution of reactant separation distances, each having a different formation probability and weighted by the first-order ET rate constant. The unique observation of bimolecular ET in the inverted region is not due to a peculiar reaction pathway engendered by the Ru(II) diimines, which react as do other small-molecule cations at the solvent-exposed edge of the heme. The inherent ET properties of cyt c engender a Marcus curve that is displaced below the diffusion limit and shifted to smaller driving forces.

Full text of DOI:10.1021/ja960575p

6060
J. Am. Chem. Soc. 1996, 118, 6060-6067
Bimolecular Electron Transfer in the Marcus Inverted Region
Claudia Turro´, Jeffrey M. Zaleski, Yanna M. Karabatsos, and Daniel G. Nocera*
Contribution from the Department of Chemistry and the LASER Laboratory,
Michigan State UniVersity, East Lansing, Michigan 48824
ReceiVed February 22, 1996X
Abstract: The rates for the photoinduced bimolecular reactions of a homologous series of RuII diimines with
cytochrome (cyt) c in its oxidized and reduced forms have been measured. The electronic coupling and reorganization
energy of the system have been adjusted such that the inverted region may be accessed at reasonable driving forces.
The electron transfer (ET) rate constants for *RuII diimine/FeIIcyt c reaction increase monotonically and approach
the diffusion limit of 8.8 × 108 M-1 s-1 at ∆G° ) -0.7 V. At a higher driving force, which may be accessed with
the powerfully oxidizing *Ru(diCF3-bpy)32+, the rate for ET is observed to drop off. Similarly, the high driving
forces achieved with *RuII diimine/FeIIIcyt c (-∆G g 1.12 V) are manifested in a decrease of the ET rate constant
with increasing exergonicity. The observed ET rates for both systems are well described by a bimolecular model
for ET occurring over an equilibrium distribution of reactant separation distances, each having a different formation
probability and weighted by the first-order ET rate constant. The unique observation of bimolecular ET in the
inverted region is not due to a peculiar reaction pathway engendered by the RuII diimines, which react as do other
small-molecule cations at the solvent-exposed edge of the heme. The inherent ET properties of cyt c engender a
Marcus curve that is displaced below the diffusion limit and shifted to smaller driving forces.
Introduction
electrostatic complexation.16-19 In all these cases, the distance
between the donor and acceptor is constant, thus circumventing
diffusion, making the ET reaction a unimolecular process.
Indeed the inverted region eluded discovery prior to the early
1980s because most studies focused on bimolecular reactions.
Inverted region kinetics for bimolecular ET reactions are rare
because diffusion of the reactants will conceal Marcus’s classical
formalism, which relates the ET rate constant, ket, with the free
energy of reaction, ∆G°,
One of the most celebrated predictions of Marcus theory is
that the rate of an electron transfer (ET) reaction may decrease
as the free energy of the reaction increases.1 Though long
controversial, this prediction of “inverted region” ET kinetics
is now well-established from experiments on systems with
donor/acceptor distances fixed by protein frameworks,2-4
covalent networks of rigid spacers,5-14 frozen media,15 and
X Abstract published in AdVance ACS Abstracts, June 1, 1996.
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-(λ+∆G°)2
ket ) ket(0) exp
(1)
[
]
4λkBT
where λ is the energy required to structurally reorganize the
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S0002-7863(96)00575-6 CCC: $12.00 © 1996 American Chemical Society

Biomolecular ET in the Marcus InVerted Region
J. Am. Chem. Soc., Vol. 118, No. 25, 1996 6061
of small-molecule and protein ET reactivity during the last
decade,35-40 it should be possible to tailor important controlling
factors of ET, including reorganization energies, electronic
coupling, and driving force, such that the parabolic dependence
predicted by eq 1 is observed for bimolecular ET. Within the
context of Figure 1, this involves lowering the curve (i.e.,
decreasing the activationless ET rate) and shifting it to smaller
driving forces (i.e., lowering the reorganization energy for ET).
In addition, the role that more subtle factors play in circumvent-
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energy excited states in ET41-43 and the distance dependence
of the outer sphere reorganization energy,32,44-46 may be
diminished by the judicious choice of donor/acceptor systems.
The extensive work on cytochrome (cyt) c during the past
decade47-54 suggests that its reactions with small-molecule
substrates are a suitable system to study the kinetics of
bimolecular reactions in the inverted region. The reorganization
energies for ET reactions of covalent and electrostatic donor/
acceptor complexes of cyt c are modest55,56 and primarily
associated with solvent reorganization. Consistent with these
findings are observations of the onset of inverted region kinetics
Figure 1. Parabolic dependence of the ET rate constant on the free
energy driving force. The diffusion limit, signified by the horizontal
solid line, truncates the parabola predicted by eq 1.
are present for a bimolecular ET reaction, the inverted region
is not easily distinguished because the observed reaction rate
constant has the form of a consecutive reaction mechanism
consisting of diffusional (kd) and activated (kact) rate constants
for electron transfer,20-24
kobs ) kactkd/(kact + kd)
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diffusion limit. Consequently, the observed rate constants of
most bimolecular reactions display an increase with increasing
free energy followed by a leveling at the diffusional limit.25-30
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not been sufficiently energetic to permit the ET rates to lie
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recently been achieved by Gray and co-workers in their studies
of the back reaction between the products resulting from the
quenching of an electronically excited binuclear iridium complex
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remain an isolated curiosity. With advances in the knowledge
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6062 J. Am. Chem. Soc., Vol. 118, No. 25, 1996
Turro´ et al.
Table 1. Pertinent Photophysical and Energetics Data for the Reaction of RuII Diimine Complexes with Cytochrome c in Its Oxidized (FeIII)
and Reduced (FeII) States, and Observed Bimolecular ET Rate Constants
FeIIcyt c + *RuII
FeIIIcyt c + *RuII
RuII diimine complex
τ0/µs
E°(+/*)/V
E°(*/-)/V
-∆G°/V
kobs/M-1 s-1
-∆G°/V
kobs/M-1 s-1
2+
Ru(diOMe-phen)3
1.14
1.76
1.18
0.81
-1.20a
-1.02b
-0.87b
-0.11c
0.94a
0.65b
0.77b
1.57c
0.69
0.40
0.52
1.32
5.68 × 108
2.84 × 108
4.36 × 108
3.11 × 108
1.45
1.30
1.12
0.36
2.08 × 108
2.10 × 108
2.65 × 108
8.35 × 107
2+
Ru(diMe-phen)3
2+
Ru(phen)3
2+
Ru(diCF3-bpy)3
a Redox potentials vs NHE ((0.1 V) and excited state energies ((0.05 V) in CH3CN (this work), in H2O (ref 58), and in CH3CN (ref 66).
b
c
The ligands, 1,10-phenanthroline (phen), 4,7-dimethyl-1,10-phenan-
throline (diMe-phen), 4,7-dihydroxy-1,10-phenanthroline (diOH-phen),
and 4,7-di(p-phenylsulfonate)-1,10-phenanthroline (BPS), were pur-
at driving forces of ∼1 eV for the fixed-distance ET reactions
of cyt c covalently linked with RuII diimine complexes,57 and
electrostatically complexed with metalloporphyrins18 and other
chased from Aldrich. The ligand 4,7-dimethoxy-1,10-phenanthroline
redox proteins.2 Similar reorganization energies may be
(diOMe-phen) was synthesized by treating 4,7-dichloro-1,10-phenan-
expected for the bimolecular reactions of cyt c with small
molecules. The strategy developed here is to choose a
homologous series of Ru(II) diimine ET partners that possess
throline (prepared from diOH-phen)63 with NaOMe in benzene.64 The
1
ligand was characterized by H NMR (δ, ppm, A, int area) (aromatic,
8.90, 5.66; 8.22, 6.11; 7.25, 5.80; OCH3, 4.15, 19.6) and melting point
low reorganization energies and driving forces greater than -1
V. This same strategy has been used for the observation of the
inverted region for the fixed-distance, intramolecular ET reac-
tions of Ru-modified proteins, where the replacement of
hydrophilic ammine ligands of a Ru(NH3)5 center attached to
cyt c at His-33 with the more hydrophobic and larger bipyridine
ligands (to form a Ru(bpy)2(imidazole)-His-33-cyt c) reduces
the reorganization energy sufficiently to permit the observation
of the inverted region at reasonable driving forces.57
We now report a systematic study of the driving-force
dependence for the photoinduced bimolecular reaction of cyt c
in its reduced and oxidized states with electronically excited
Ru(II) diimine (*RuII) complexes. Systematic variation of the
substituents of the parent ligand or utilization of mixed-ligand
complexes allows for a wide variation of the excited state
oxidation and reduction potentials,58 which in turn control the
driving force of the *RuII/cyt c ET reaction. Utilizing the known
ET properties of cyt c and the Ru(II) diimine complexes, we
observe inverted region behavior for the forward bimolecular
ET reaction of FeII and FeIII cyt c.
(200 °C).
The Ru(II) diimine complexes were prepared by reported tech-
niques.58,65 Typically RuCl3 was refluxed in ethanol/water (80/20) with
6 equiv of ligand, L, to form the red-orange RuL32+ complexes. After
evaporation of the solvent, the product was readily precipitated from
acetone with ether. The Ru(II) complexes were characterized by
comparison with their known electronic absorption and emission spectra,
emissive lifetimes, and redox potentials.58 The 4,4′-bis(trifluoromethyl)-
2,2′-bipyridine complex, Ru(diCF3-bpy)32+, was prepared and character-
ized by Professor M. Furue66 and was generously provided to us from
his labs.
Methods and Instrumentation. Rate constants for the quenching
of the RuII diimine excited states by cyt c were obtained by lifetime
and transient absorption measurements using laser instrumentation that
has previously been described.67,68 Stock solutions (25 or 50 mL)
containing 6 × 10-5 M of RuII complex were prepared in µ ) 0.1 M,
pH ) 7.4 phosphate buffer. The protein was dissolved in 200 µL of
stock solution and placed in a 1 mm path length cuvette equipped with
a stopcock. The protein concentration was varied by addition of known
volumes of stock solution to the initial 200 µL protein solution.
Solutions were deoxygenated by bubbling with nitrogen. The concen-
tration of cyt c was determined prior to each lifetime measurement
from the absorbance at either 530 or 550 nm, depending on the protein’s
oxidation state, and was corrected for the absorbance of the RuII
complex at each wavelength (typically 0.05-0.07). In this manner,
the concentration of the RuII complex remained constant over the course
of an experiment.
Experimental Section
Materials. Horse heart cyt c type VI was purchased from Sigma
and was purified by standard methods.59 The oxidized protein,
dissolved in µ ) 10 mM, pH ) 7.4 phosphate buffer, was loaded onto
a CM52 (Whatman) cation exchange column and was subsequently
eluted with the same buffer at a higher ionic strength (µ ) 0.1 M).
Ferricytochrome c was reduced by addition of freshly prepared sodium
ascorbate, or was fully oxidized with potassium ferricyanide.60 The
protein was then eluted from a Sephadex G-50 column with µ ) 0.1
M, pH ) 5 ammonium bicarbonate buffer, to allow separation of the
reducing or oxidizing agents. After the eluent was frozen with a dry
ice/acetone bath, the water and buffer were removed under vacuum
(10-3 Torr). All manipulations of FeIIcyt c were performed under
nitrogen, and the oxidation state was carefully monitored utilizing the
characteristic absorption features of the protein. The reduced protein
possesses a sharp absorption band at 550 nm (ꢀ ) 27.7 mM-1 cm-1),61
whereas a broad feature at 530 nm (ꢀ ) 10.1 mM-1 cm-1) is observed
for the protein in its oxidized state.62
Results and Discussion
Table 1 lists the lifetime and excited state redox potentials
of a homologous series of RuII diimine complexes. The
electron-withdrawing or -donating abilities of the substituents
on the aromatic imine skeleton permit a wide range of driving
forces to be achieved for the bimolecular reaction of the RuII
diimines with cyt c. The long-lived excited states of all the
RuII complexes are quenched by FeII and FeIIIcyt c with the
rate constants shown in Table 1, as determined by the Stern-
Volmer lifetime quenching method. Exemplary Stern-Volmer
plots for the quenching of the MLCT excited state of Ru(diMe-
phen)32+ by both redox states of the protein are shown in Figure
(57) Chang, I.-J.; Gray, H. B.; Winkler, J. R. J. Am. Chem. Soc. 1991,
113, 7056.
(58) Juris, A.; Balzani, V.; Barigelletti, F.; Campagna, S.; Belser, P.;
Von Zelewsky, A. Coord. Chem. ReV. 1988, 84, 85.
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Enzymol. 1978, 53, 128.
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ReV. 1975, 15, 321.

Biomolecular ET in the Marcus InVerted Region
J. Am. Chem. Soc., Vol. 118, No. 25, 1996 6063
Figure 3. Stern-Volmer plot of the quenching of electronically excited
Ru(BPS)34- (6.0 × 10-5 M) by FeIIIcyt c in µ ) 0.1 M phosphate buffer
(pH ) 7.0).
Figure 2. Stern-Volmer plot of the quenching of electronically excited
Ru(diMe-phen)32+ (6.0 × 10-5 M) by (a) FeIIcyt c and (b) FeIIIcyt c in
µ ) 0.1 M phosphate buffer (pH ) 7.0).
2. As predicted for a bimolecular reaction,69 the Stern-Volmer
plots for all of the quenchers are linear and exhibit an intercept
of unity. The bimolecular kinetics for this system are ensured
by the properties of the RuII diimine series. In contrast to
anionic reactants,2a,48,70,71 the cationic RuII complexes do not
associate at the large patches of positive charge near the heme’s
solvent-exposed edge. Consequently, a mechanism involving
binding of the small-molecule reactant with the protein followed
by a quenching reaction is disfavored for the RuII diimine series.
Accordingly, Stern-Volmer saturation kinetics in which the
quenching rate constant becomes independent of quencher
concentration, as is observed for negatively charged reac-
tants,18,72 are absent in our system. Indeed, such nonlinear
behavior is uncovered for the RuII diimines when anionic ligands
impart an overall negative charge on the complex. Figure 3
shows the Stern-Volmer plot for the quenching reaction of
Ru(BPS)34- and FeIIIcyt c. The saturation kinetics induced by
association of the anionic RuII complex to the protein is clearly
apparent with a leveling of the quenching rate constant at FeIII-
Figure 4. Transient difference spectrum of an aqueous solution
buffered by phosphate (µ ) 0.1 M, pH ) 7.0) containing FeIIIcyt c
(8.1 × 10-4 M) and Ru(diMe-phen)32+ (1.4 × 10-4 M). The difference
spectrum was recorded 7 µs after a 450 nm excitation pulse.
quenching by simple one-electron transfer. At the concentration
of FeIIIcyt c (8.1 × 10-4 M) utilized in the transient absorption
experiment shown in Figure 4, the emission lifetime decreases
by 23%. If ET is the sole source of excited state quenching in
these systems, then the concentration of redox products is
expected to be 1.6 × 10-6 M. From the measured ∆OD )
0.008 (for a 0.2 cm path length) in Figure 4, and molar extinction
coefficients for FeIIcyt c and FeIIIcyt c at 550 nm of 27 700
M-1 cm-1 and 3300 M-1 cm-1, respectively, we obtain a FeII-
cyt c concentration of 1.6 × 10-6 M with an error of (20%.
Thus, comparison of the lifetime quenching of *Ru(diMe-
phen)32+ by FeIIIcyt c to the formation of the reduced product,
FeIIcyt c, as determined by transient spectroscopy reveals that
quenching proceeds exclusively by ET.
4-
cyt c:Ru(BPS)3 concentrations greater than 1:1.
The transient absorption spectra for the quenching reaction
between the *RuII diimines and cyt c are consistent with ET
products.73,74 The transient difference spectrum accompanying
the Stern-Volmer experiment summarized by Figure 4 shows
the characteristic absorbance of FeIIcyt c at 550 nm. The
appearance of the FeIIcyt c transient shown in Figure 4 occurs
over the same time scale for the Stern-Volmer quenching of
the RuII diimine excited state. These results are consistent with
Figure 5 plots the observed ET rates vs driving force for all
the reactions. The trend in the rate constants may be understood
in terms of eq 2, where the overall observed rate for bimolecular
reaction comprises contributions of both diffusion and activated
ET. The diffusion rate component is given by75
(70) (a) Drake, P. L.; Hartshorn, R. T.; McGinnis, J.; Sykes, A. G. Inorg.
Chem. 1989, 28, 1361. (b) Armstrong, G. D.; Chamber, J. A.; Sykes, A. G.
J. Chem. Soc., Dalton Trans. 1986, 755.
(71) (a) Butler, J.; Chapman, S. K.; Davies, D. M.; Sykes, A. G.; Speck,
S. H.; Osheroff, N.; Margoliash, E. J. Biol. Chem. 1983, 258, 6400. (b)
Augustin, M. A.; Chapman, S. K.; Davies, D. M.; Sykes, A. G.; Speck, S.
H., Margoliash, E. J. Biol. Chem. 1983, 258, 6405.
(72) Brunschwig, B. S.; DeLaive, P. J.; English, A. M.; Goldberg, M.;
Gray, H. B.; Mayo, S. L.; Sutin, N. Inorg. Chem. 1985, 24, 3743.
(73) (a) Nocera, D. G.; Winkler, J. R.; Yocom, K. M.; Bordignon, E.;
Gray, H. B. J. Am. Chem. Soc. 1984, 106, 5145. (b) Winkler, J. R.; Nocera,
D. G.; Yocom, K. M.; Bordignon, E.; Gray, H. B. J. Am. Chem. Soc. 1982,
104, 5798.
∞
4πND
1000
-1
B
kdiff
)
dr e[-U(r)/k T] -2
r
(3)
∫
[
]
r
where the intermolecular potential between reactants, U(r), is
evaluated to a center-to-center separation between reactants, r,
(74) Cho, K. C.; Che, C. M.; Cheng, F. C.; Choy, C. L. J. Am. Chem.
Soc. 1984, 106, 6843.
(75) Smoluchowski, M. V. Z. Phys. Chem. 1917, 92, 129.

6064 J. Am. Chem. Soc., Vol. 118, No. 25, 1996
Turro´ et al.
which the ET rate is mediated by the equilibrium constant for
the formation of a reactive complex at distance r (i.e., kact
)
Kp(r)ket(r)).82 For most bimolecular reactions it is assumed that
ET at distances larger than contact is negligible, and therefore
the evaluation of kact reduces to a fixed-distance problem at r
) σ (σ is the sum of the reactants’ radii, the contact distance).
However, we were concerned that the work associated with
bringing the positively charged reactants together for the systems
reported here would be significant, and consequently ET at
distances larger than r ) σ might contribute to the overall
observed rate. The activation-controlled rate constant for a
bimolecular reaction occurring over a range of distances is
obtained by integrating over the equilibrium distribution of
reactant separation distances, each having a different formation
probability given by ge(r) (from r ) ∞ to r) and weighted by
the first-order ET rate constant ket(r),23,44,83
∞dr g (r) k (r) r2
(6)
4πN
1000
kact
)
∫
e
et
r
For ionic reactants in dilute solution, the equilibrium distribution
function, ge(r), is described by an electrostatic potential
ge(r) ) exp[-U(r)/kBT]
(7)
Figure 5. Semilog plots of kobs vs the free energy driving force for
the bimolecular ET between *RuII diimine complexes (Table 1) and
(a) FeIIcyt c and (b) FeIIIcyt c. The calculated fits of eqs 3-10
(integrated over r ) ∞ to 23 Å, â ) 1.2 Å, V(0) ) 200 cm-1) are
illustrated for kobs (solid curve), kdiff (dotted line), and kact (dashed curve).
with U(r) defined by eq 4. For ket(r), we have chosen to use
the semiclassical expression popularized by Closs and Miller,5,15
ket(r) )
-(λs+∆G+whν)2
4λskBT
1/2
N is Avogadro’s number, and D is the sum of the diffusion
coefficients of the reactants given by the Stokes-Einstein
relationship.76 When both ET partners are charged, as is the
case here, the intermolecular potential is dominated by the
electrostatic forces between reactants. For two spheres, which
is a good geometric description of the cyt c and RuII diimine
reactants, U(r) can be described within a Debye-Hu¨ckel
formalism as81
∞
2π
1
e-SSw
2
|V|
exp
(8)
∑
{
}
[
]
h λskBT
w!
w)0
where the total reorganization energy is composed of solvational
λs and vibrational λv contributions with S ) λv/hν, ν is the high-
energy vibrational frequency associated with the acceptor, V is
the electronic coupling, and w is the density of product
vibrational levels.84 This expression for ket(r) is central to our
studies because it accounts for nuclear tunneling in the inverted
region to excited vibrational states of the acceptor, which is
significant for highly exergonic ET reactions.85 The total driving
force, ∆G, includes electrostatic corrections to ∆G° (Table 1)
for the work required to bring products and reactants together
(∆G ) ∆G° - wp - wr) as described by eq 4.
z1z2e2
U(r) )
(4)
x
Dsr(1 + âDHr µ)
where z1 and z2 are the charges on each reactant, e is the charge
on the electron, Ds is the static dielectric constant of the solvent,
and µ is the ionic strength; âDH is given by
The solvation reorganization energy, λs, has contributions
from the solvent (λsol) and the protein (λp) milieu. The former
can be estimated from the classical dielectric continuum
model1,86
1/2
8πNe2
âDH
)
(5)
[
]
1000DskBT
1
1
1
1
1
λsol ) (∆e)2
+
-
-
(9)
In regard to the activated rate in eq 2, the bimolecular ET
reaction depends implicitly on the reactants, assuming an
internuclear configuration appropriate for the ET event to take
place. Sutin has treated this case with a precursor model in
[
][
]
2rA 2rB r Dop Ds
where Dop and Ds are the optical and static dielectric constants
of the solvent (Dop(H2O) ) 1.77, Ds(H2O) ) 78.5), respectively,
and rA and rB are the reactants’ radii. Because the protein radius
is large compared to the RuII diimine complexes, λsol shows a
much smaller distance dependence than that observed for small-
molecule reactants.29,45 The contribution from the peptide
(76) The diffusion coefficient for reactant A is given by DA ) kBT/6πrAη
where kB is Boltzmann’s constant, T is the temperature, rA is the reactant’s
radius, and η is the viscosity of the water () 0.89 g cm-1 s-1). From this
expression we calculate diffusion coefficients of 1.49 × 10-6 and 3.76 ×
10-6 cm2 s-1 for cyt c and the RuII diimines, respectively. The latter value
was calculated assuming an average radius of 6.5 Å for the complex. These
values compare well to the reported diffusion coeffcients of 1.1 × 10-6
and 2.0 × 10-6 cm2 s-1 for cyt c77,78 and 6.0 × 10-6 and 3.72 × 10-6 cm2
s-1 for RuII and FeIII diimines, respectively.79,80
(77) Albery, W. J.; Eddowes, M. J.; Hill, H. A. O.; Hillman, A. R. J.
Am. Chem. Soc. 1981, 103, 3904.
(78) Santucci, R.; Reinhard, H.; Brunou, M. J. Am. Chem. Soc. 1988,
110, 8536.
(82) (a) Brown, G. M.; Sutin, N. J. Am. Chem. Soc. 1979, 101, 883. (b)
Sutin, N. Acc. Chem. Res. 1982, 15, 275.
(83) Newton, M. D.; Sutin, N. Annu. ReV. Phys. Chem. 1984, 35, 437.
(84) Kuki, A. In Long-Range Electron Transfer in Biology; Structure
and Bonding; Clarke, M. J., Goodenough, J. B., Jørgenson, C. K., Neilands,
J. B., Reinen, D., Weiss, R., Eds.; Springer-Verlag: Berlin, 1991; Vol. 75,
p 58.
(79) Buttry, D. A.; Anson, F. C. J. Electroanal. Chem. 1981, 130, 333.
(80) Zimonyi, M.; Ruff, I. Electrochim. Acta 1973, 18, 515.
(81) Debye, P. Trans. Electrochem. Soc. 1942, 82, 265.
(85) Liang, N.; Miller, J. R.; Closs, G. L. J. Am. Chem. Soc. 1990, 112,
5353.
(86) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265.

Biomolecular ET in the Marcus InVerted Region
J. Am. Chem. Soc., Vol. 118, No. 25, 1996 6065
matrix for FeII and FeIIIcyt c has been calculated to be 0.2 eV,87
which may be directly added to the solvent reorganization at a
given r to give the total outer sphere reorganization energy, λs.88
The distance dependence of V is exponential and given by86
panels a and b of Figure 5). Inspection of Figure 5a,b reveals
that kdiff contributes significantly to the observed rate, and
therefore kobs parallels the rate of diffusion near its maximum;
the contribution of kact leading to a sharp parabolic dependence
of kobs is diminished significantly by the diffusion limit. From
eq 8, the calculated curve exhibits a maximum when λs ) ∆G
+ wr - wp + whν. Accounting for the work terms and whν,
we find from Figure 5a,b that the reorganization energies for
the *RuII/FeIIcyt c and *RuII/FeIIIcyt c reactions are 0.87 and
0.88 eV, respectively. These values accord well with the
reorganization energies of other ET reactions involving cyt
c.18,45a,55,97,98
V ) V(0) exp[-â/2(d-d0)]
(10)
where d is the edge-to-edge distance between the RuII diimine
and the heme of the protein and acceptor and V(0) is the value
of V at d ) d0, which has been defined to be 3 Å to account for
the electron clouds about the outermost atoms of each
reactant.47a,86 For cyt c, â is 1.2 Å-1 and V(0) is 200
cm-1 47a,51,89
It is well established that the ET reactions of
.
The calculated ET curves and the observed ET rate constants
for the reaction of *RuII with FeII and FeIIIcyt c are in good
agreement. For the former reaction, the rate constants for the
Ru(diOMe-phen)32+, Ru(diMe-phen)32+, and Ru(phen)32+ sys-
tems lie in the normal region (Figure 5a). Conversely, the high
oxidation potential of *Ru(diCF3-bpy)32+ places its ET reaction
in the inverted region. As predicted, the experimentally
measured rate constant for this system is reduced and it is
accurately predicted by the formalism established by eqs 2-10
in the inverted regime. The overall trend is reversed for the
ET reactivity of *RuII complexes and FeIIIcyt c. The reaction
cationic metal complexes featuring hydrophobic ligation spheres
proceed at the exposed heme edge of the protein.90,91 Singly
modified peptide and NMR studies show that positively charged
reactants access the recessed heme edge near Lys-27,70,71,92
thereby permitting us to relate the edge-to-edge ET distance, d,
in eq 10, to the protein and RuII diimine center-to-center
distance, r. The distance from the outermost meso position of
the heme to the center of the protein, determined from the crystal
structure of cyt c, corresponds to 9.1 Å.93 This distance leads
directly to the relation r ) d - 9.1 Å - rB, where rB is the RuII
diimine radius of 6.5 Å.
2+
of FeIIIcyt c with *Ru(diCF3-bpy)3 is in the normal region
2+
whereas the corresponding reactions of *Ru(diOMe-phen)3
,
With eqs 3-10 parametrically defined in r, the ET distance
for the reaction of the RuII diimines with cyt c may be directly
calculated by solving eqs 3 and 6. The semilog plots of the
calculated rate constants, determined by evaluating eqs 3-10
for r ) ∞ to r ) 23 Å, vs ∆G° are shown by the solid lines in
Figure 5 along with the experimentally determined rate constants
of the *RuII/FeIIcyt c and *RuII/FeIIIcyt c systems. The activated
(eq 6, dashed line) and diffusion (eq 3, dotted line) rate constants
composing kobs, as described by eq 2, are also shown for
convenience. The ET distance of 23 Å corresponds to a ligand
edge-to-heme edge ET distance of 7.4 Å. This edge-to-edge
distance has been observed for the bimolecular reactions of other
small-molecule ET partners with cyt c;94 accordingly, calcula-
tions using distances of closest approach other than 7.4 Å yield
curves that are not consistent with the observed data. In our
calculations, eq 6 was evaluated by choosing the quantum-
mechanical vibrational frequency to be the 1372 cm-1 breathing
vibration of the heme95,96 and a vibrational reorganization energy
for cyt c of 0.2 eV.55 It is important to emphasize that the
parameters employed in our calculation of the ET rate constants
for both systems, *RuII/FeIIcyt c and *RuII/FeIIIcyt c, were
identical, with the exception of the charges on the reactants and
products, which manifests itself in different values of kdiff for
the two systems (indicated by the different diffusion limits in
*Ru(diMe-phen)32+, and *Ru(phen)32+ lie in the inverted region.
As shown in Figure 5b, with the exclusion of the Ru(diOMe-
phen)32+ system, the data and the calculated curve are consonant.
An ET rate that is faster than predicted for the Ru(diOMe-
phen)32+/cyt c system suggests that this highly energetic ET
reaction is mediated by the formation of the FeIIcyt c (3MLCT)
excited state (∆E ) 1.05 eV).99 This behavior has been
observed for *RuII-FeIIIcyt c f *RuIII-FeIIcyt c and RuI-
FeIIIcyt c f RuII-FeIIcyt c when the driving forces of these
intramolecular reactions exceed -1.25 V. As shown by Figure
5b, the rate/energy leveling occurs at a similar potential for the
bimolecular reaction of FeIIIcyt c with *RuII.
Several important features in Figure 5 pertain to the ET
reactivity of cyt c with *RuII complexes. The observed rate
constants for the bimolecular reaction of *RuII with FeII and
FeIIIcyt c, in the inverted and normal regions, are completely
described by a formalism that accounts for ET occurring over
an equilibrium distribution of distances. The treatment is
detailed enough to not only reveal the inverted region but also
unveil subtle mechanistic features within it such as the
importance of protein excited states in mediating highly
energetic ET. The deviation of the observed rate constants from
predicted inverted behavior occurs at the same energy in both
unimolecular and bimolecular reactions of FeIIIcyt c. That this
mechanism does not depend on the molecularity of the reaction
(87) Churg, A. K.; Weiss, R. M.; Warshel, A.; Takano, T. J. Phys. Chem.
1983, 87, 1683.
(88) Betrand, P. In Long-Range Electron Transfer in Biology; Structure
and Bonding; Clarke, M. J., Goodenough, J. B., Jørgenson, C. K., Neilands,
J. B., Reinen, D., Weiss, R., Eds.; Springer-Verlag: Berlin, 1991; Vol. 75,
p 26.
(89) Gray, H. B.; Winkler, J. R. Pure Appl. Chem. 1992, 64, 1257.
(90) Wherland, S.; Gray, H. B. In Biological Aspects of Inorganic
Chemistry; Addison, A. W., Cullen, W. R., Dolphin, D., James, B. R., Eds.;
Wiley-Interscience: New York, 1977; p 289.
(91) Louie, G. V.; Brayer, G. D. J. Mol. Biol. 1990, 214, 527.
(92) (a) Butler, J.; Davies, D. M.; Sykes, A. G.; Koppenol, W. H.;
Osheroff, N.; Margoliash, E. J. Am. Chem. Soc. 1981, 103, 469. (b) Butler,
J.; Koppenol, W. H.; Margoliash, E. J. Biol. Chem. 1982, 257, 10747.
(93) Brookhaven Protein Data Bank; Brookhaven National Laboratories,
Upton, NY.
3
is understandable since it involves the same MLCT excited
state of protein for both uni- and bimolecular reactions and it
is a satisfying consequence of our analysis. Another important
feature of Figure 5 is that the appropriate behavior is observed
for the Ru(diCF3-bpy)32+ system, which contrasts that of most
*RuII reagents. For the *RuII/FeIIcyt c reaction, Ru(diCF3-
bpy)32+ is inverted whereas the other *RuII complexes with their
more typical excited state potentials lie in the normal region.
For the *RuII/FeIIIcyt c system, the opposite behavior is
observed. Because inverted and normal region kinetics are
(94) Mauk, A. G.; Scott, R. A.; Gray, H. B. J. Am. Chem. Soc. 1980,
102, 4360.
(95) Stallard, B. R.; Callis, P. R.; Champion, P. M.; Albrecht, A. C. J.
Chem. Phys. 1984, 80, 70.
(97) Dixon, D. W.; Hong, X.; Woehler, S. E.; Mauk, A. G.; Sishta, B.
P. J. Am. Chem. Soc. 1990, 112, 1082.
(98) McLendon, G.; Pardue, K.; Bak, P. J. Am. Chem. Soc. 1987, 109,
7540.
(96) Simpson, M. C.; Millett, F.; Fan, B.; Ondrias, M. R. J. Am. Chem.
Soc. 1995, 117, 3296.
(99) Mines, G. A.; Bjerrum, M. J.; Hill, M. G.; Casimiro, D. R.; Chang,
I.-J.; Winkler, J. R.; Gray, H. B. J. Am. Chem. Soc. 1996, 118, 1961.

6066 J. Am. Chem. Soc., Vol. 118, No. 25, 1996
Turro´ et al.
Figure 6. The observed ET rate constants plotted vs -∆G for the
3
reaction of ZnII cyt c with a series of viologen quenchers; these data
were taken from ref 102. The rate constants kobs (solid curve), kact
(dashed curve), and kdiff (dotted line) are calculated by evaluating eqs
3-10 with the same parameters used to generate the respective curves
displayed in Figure 5, with the only modification being the average
radius of the quencher (6.5 Å for the RuII diimine complexes and 3.5
Å for the viologen quenchers).
Figure 7. Semilog plot of the calculated kobs (solid curve) for the
2+
reaction of *Ru(diMeO-phen)3 and FeIIcyt c (∆G ) -0.69 V).
Equations 3-10 were evaluated from r ) ∞ to the distance specified
on the x-axis. The opposing contributions of kact (dashed curve) and
k
diff (dotted line) to kobs result in a maximum ET rate constant that occurs
observed for *RuII/FeIIcyt c and for *RuII/FeIIIcyt c, bimolecular
ET in the inverted region is not a peculiarity of the nature of
the redox process or the *RuII complexes.
at a distance between the donor and acceptor larger than contact.
energies stems from the smaller radii of the viologen reactants,
which consequently engenders a larger solvent reorganization
energy. On this basis, we expect that the bimolecular rate
constant for the reaction of *ZnIIcyt c with viologens will
diminish for acceptors possessing reduction potentials more
positive than +0.3 V vs SCE (-∆G° ) 1.2 V). Analysis of
the bimolecular ET kinetics for the reaction of cyt c with flavins
leads to similar conclusions101 and also accounts for the inability
to observe inverted-region ET effects in these systems.
Our analysis may be generalized to bimolecular ET reactions
of cyt c with other small molecules including inorganic
complexes,100 flavins,101 organic acceptors,102 and porphyrins.103
In all these cases, the driving-force dependence of the observed
ET rate constant approaches the activationless, diffusion-
controlled region, but the decrease in ET rate at high driving
force is not clearly observed. For example, McLendon (GM)
3
et al. have investigated the ET quenching of the ππ* excited
state of *ZnII-substituted cyt c with a homologous series of
viologen dications of varying reduction potentials.102 The ET
rates show a monotonic increase up to driving forces of ∼0.7
eV. Figure 6 shows the driving-force dependence of the rate
constants (solid curve) calculated from eqs 3-10, along with
GM’s experimental data. The calculation was performed with
exactly the same parameters utilized above for the RuII diimine
complexes, except that the appropriate driving force for the
reaction was used and the average radius of the organic acceptors
was 3.5 Å as compared to the 6.5 Å radius of the RuII
complexes. The observed rate data for the viologen system are
fitted extremely well by the calculated curve. Because the same
value for the electronic coupling was used for Figures 5 and 6,
this result suggests that the organic viologen and inorganic RuII
diimine acceptors react at the same location on the protein
surface and at approximately the same edge-to-edge ET
distances. This congruence in the ET pathways is not surprising
in view of the similarity of the electrostatic charges, aromaticity,
and hydrophobicity of the two classes of acceptors. Inspection
of Figures 5 and 6 reveals that the driving forces needed to
attain the inverted region for the ZnIIcyt c/viologen reaction is
∼0.2 eV greater than that for the *RuII diimines with cyt c.
This shift of the parabolic free energy curve to greater free
The analysis presented here underscores the necessity to
consider bimolecular ET occurring over a range of distances.
Although the bimolecular reaction is conducted in a solvent with
a high dielectric constant and at a relatively high ionic strength,
the large positive charge of cyt c gives rise to an appreciable
intermolecular potential (eq 4) that can inhibit the ET reaction
at distances of close approach. This is illustrated for the reaction
2+
of *Ru(diMeO-phen)3 with FeIIcyt c. Figure 7 graphically
depicts the calculated rate constants kact, kdiff, and kobs for this
bimolecular reaction by integrating eqs 3 and 6 to a distance of
r. For the like-charged reactants, there is an increase in kdiff
with increasing r that is opposed by a decrease in kact owing to
poorer electronic coupling (eq 10) of the ET event. From eq
2, these opposing effects lead to a rate maximum at distances
greater than contact. This disparate behavior in kdiff and kact
and their relative contributions to the fastest observed rates of
bimolecular ET emphasize the importance of choosing a
homologous series of ET partners. Moreover, because the
approach of oppositely charged reactants is governed by a
favorable electrostatic potential and would result in an increasing
rate of reaction to a distance of reactant contact, this analysis
suggests that care must be taken when comparing bimolecular
ET reactions of cyt c with reactants of dissimilar charge.103
In conclusion, the ET rate constants for the photoinduced
bimolecular reaction between *RuII diimine complexes and cyt
c decrease at high driving forces. Our ability to observe the
inverted region arises from displacing the Marcus curve verti-
cally below the diffusion limit and shifting it horizontally to
lower driving forces. The intramolecular reorganization energies
for both reactants are minimal, and the modest reorganization
energies associated with solvent lead to a shift of the maximum
of the Marcus curve to lower driving forces. This displacement
(100) English, A. M.; Lum, V. R.; Delaive, P. J.; Gray, H. B. J. Am.
Chem. Soc. 1982, 104, 870.
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Biomolecular ET in the Marcus InVerted Region
J. Am. Chem. Soc., Vol. 118, No. 25, 1996 6067
is coupled with a shift of the Marcus curve to intrinsically slower
ET rates resulting from the weak electronic coupling for ET
pathways at distances greater than close contact (see Figure 7).
In the case here, the inverted-region effect is modest because
the intervening excited state of the protein prevents driving
forces greater than -1.3 V from being attained. Notwithstand-
ing the approach described here to unveil the inverted region
for bimolecular ET reactions is not unique to cyt c and such
effects may be observed in other systems in which the electronic
coupling and reorganization energy are correctly adjusted so
that the Marcus curve emerges from the diffusion limit.
Acknowledgment. We thank Professor M. Furue for gener-
2+
ously providing us with the chloride salt of Ru(diCF3-bpy)3
.
DGN gratefully acknowledges J. Garcia for thoughtful insights
and perspectives. This work was supported by a grant from
the National Institutes of Health (GM 47274).
JA960575P