In a redox process, the oxidizing and reducing centers
can react with or without a change in their coordination spheres.
In some reactions, the electron transfer can only be accomplished
by the transfer of a ligand from reducing agent to the oxidizing
There are two stoichiometric mechanisms: the inner
sphere mechanism involves a ligand transfer, and a transient
shared ligand, while the outer sphere mechanism
includes the simple electron transfers, without the presence of
a shared ligand.
The reduction of the non-labile Co complex by the
aqueous Cr complex produces a reduced Co complex and an oxidized
CrCl complex. The chloride ligand has been transferred between
the metal centers, as proven by the fact that addition of 36Cl-
to the solution results in no incorporation of 36Cl-
into the Cr complex.
The reaction is faster than reactions which
remove Cl- from CoIII or introduce Cl-
to Cr3+(aq), and hence the Cl-
ion must have moved directly from the coordination sphere
of one complex to the other during the reaction.
|The intermediate has a bridging Cl ligand.
The Cl- ion is a good bridging ligand
as it has more than one pair of electrons, and so can form bonds
to each of the metal centers simultaneously. Other good bridging
ligands include SCN-, N2, N3-,
The Outer Sphere Mechanism
When both the species in the redox reaction have non-labile coordination
spheres, no ligand substitution can take place on the very short
time scale of the redox reaction. The electron transfer must proceed
by a mechanism involving transfer between the two complex ions
in outer-sphere contact.
If the redox reaction is faster than the ligand substitution,
then the reaction has an outer-sphere mechanism.
When the reaction involves ligand transfer from an initially
non-labile reactant to a non-labile product, there is no difficulty
in assigning the inner-sphere mechanism.
When the products and reactants are labile, it is difficult to
make an unambiguous assignment of either an inner- or an outer-sphere
The Marcus Equation
When an electron transfer occurs in a redox equation,
it does so after the atoms have adopted the geometries such that
the electron transfer becomes facile, when the electron has the
same energy in each of the two nuclear geometries.
According to the Franck-Condon
principle, the motion of the electrons is much faster than
the motion of the atoms, such that the nuclei can be considered
as stationary during the electronic rearrangement. Therefore,
the rate of electron transfer, and the activation energy for the
process, is determined by the ability of the involved nuclei to
adopt arrangements which are equal in energy.
This can be investigated by considering the self
exchange reaction of hydrated iron.
This is a redox process where an electron is transferred
from the unlabeled iron atom (Fe) to the labeled iron atom (Fe*).
The Fe-O bond lengths are longer for Fe2+ than Fe3+
due to the decreased electrostatic interaction, and so for the
transfer to occur the two complexes must adopt configurations
in which the Fe-O bond lengths are the same. This costs energy,
and this is known as the inner-sphere rearrangement energy,
When the complexes rearrange, there is a resultant
reorganization of the solvation shell around the complex. This
also costs energy, known as the outer-sphere
reorganization energy, ΔG*OS.
We must also consider the change in electrostatic
interaction energy, ΔG*ES,
between the two complexes at the point of electron transfer,
and hence the total activation energy, ΔG*,
can be defined
The rearrangement of the Fe-O systems to give
the same geometry in the two complexes can be examined in terms
of their potential energy surfaces. If the Fe-O stretching vibrations
are assumed to be harmonic, then the potential energy curves
are as shown. The activated complex is at the position of intersection
of the two curves.
|Potential energy diagram for the self transfer in Iron
|The initial reaction coordinates
on the left are those for FeII and Fe*III,
and the product reaction coordinates on the right are
those for FeIII and Fe*II. The activated
complex, where electron transfer occurs, is in the middle.
However, the non-crossing
rule says that molecular energy curves of two states
of the same symmetry do not cross, but instead split into an
upper and a lower curve. This means that the reactants in their
ground states slowly distort to reach the activated complex
point, and then slowly distort, following their minimum energy
pathways, into the reactants in their ground states after the
This mechanism can be extended to cases where
the transfer occurs between non-identical species, when the
energies of the reactants and products are not the same. When
the energy of the products is higher than that of the reactants,
ie. the reaction is endothermic, the activation energy increases
as the energy of the curve crossing point is higher than in
the symmetrical case. Similarly, if the energy of the products
is lower than that of the reactants, ie. the reaction
is exothermic, the activation energy decreases as the energy
of the curve crossing point is lower.
The rate of transfer therefore depends on two
factors: the shape of the potential energy curves and the Gibbs
The shape of the potential
energy curves: If they rise steeply, their crossing
points will be high and so there will be a large activation
energy. This is the case where there are stiff bonds, ie. a
large increase in energy with increasing bond length. If the
curves are shallow, then the activation energy is low.
The standard reaction free
energy: The more negative the reaction free energy,
then the lower the activation energy.
The rate constant, k,
for an outer-sphere reaction can be expressed, in the Marcus
equation, in terms of the exchange rate constants for
each of the redox couples, ki,
and the equilibrium constant for the overall reaction, K.
These reflect, respectively, the shape of the potential energy
surface and the standard reaction free energy.
|The Marcus Equation:
f is a complex parameter which depends
on the rate constants and the complex encounter rate (which
depends on their diffusion), but can be taken as one for approximate
calculations. The overall reaction rate, k, is therefore expressed
in term of a weighted average of the two self-exchange rates,
and so the Marcus equation is also known as the Marcus