Electron Transfer: Inner Sphere versus Outer Sphere

The two mechanisms

The experiment that proved inner sphere exists

The decisive evidence is ligand transfer. Take an inert cobalt(III) complex carrying a chloride ligand and react it with a labile chromium(II) species. After reaction, the chloride is found bonded to chromium, not cobalt.

The reasoning is what makes it conclusive. Chromium(II) is substitution-labile, so it can accept a bridging ligand; chromium(III), formed after electron transfer, is substitution-inert, so whatever it holds at that moment stays. Finding chloride on chromium therefore proves the chloride was bonded to chromium at the instant of transfer — which is only possible if it bridged the two metals.

What makes a good bridging ligand

It needs at least two donor atoms, or a lone pair available after coordinating. Halides work because a coordinated halide retains lone pairs. Ligands such as thiocyanate, azide and carboxylates bridge well because they can span two metals.

Ligands with an extended π system can carry the electron over longer distances, and some bridged systems show transfer across surprisingly large separations for this reason.

What controls the rate of outer sphere transfer

Three factors, and Marcus theory combines them.

• The driving force — the difference in reduction potentials. A larger driving force generally means a faster reaction.
• Reorganisation energy — the energy needed to distort both complexes to the geometry they will have after transfer, before the electron moves. This is a consequence of the Franck–Condon principle: nuclei cannot move during the electronic transition, so the rearrangement must happen first.
• Electronic coupling — how well the two orbitals overlap at the encounter distance.

Reorganisation energy explains a pattern that otherwise looks arbitrary. Complexes whose bond lengths change little on changing oxidation state transfer electrons very fast; those with large geometry changes are slow, even with a strong driving force. Comparing two such systems is a standard question.

The Marcus inverted region

Marcus theory makes an unexpected prediction: beyond a certain driving force, increasing it further makes the reaction slower. This inverted region arises because the reaction barrier depends on the square of the difference between driving force and reorganisation energy, so overshooting is as costly as undershooting.

The prediction was doubted for years before being confirmed experimentally, which is why it appears in exams as an example of a theory predicting counter-intuitive behaviour successfully.

How to identify the mechanism in a question

1. Are both complexes substitution-inert? Then transfer must be outer sphere, since no bridge can form.
2. Is there a potential bridging ligand and at least one labile centre? Inner sphere is possible.
3. Does the question mention ligand transfer in the products? That is decisive evidence for inner sphere.
4. Is the rate faster than the substitution rate of either complex? Then it cannot be inner sphere, because substitution is the bottleneck.

Point four is the most elegant of these, and it is often the intended answer when a question supplies substitution rate data alongside the electron transfer rate.

Frequently asked questions

Can a self-exchange reaction be studied if nothing appears to change?

Yes, using isotopic labelling or magnetic resonance line broadening. Self-exchange rates are important because Marcus theory uses them to predict cross-reaction rates.

Why must reorganisation happen before transfer?

Because electrons move far faster than nuclei. By the Franck–Condon principle the nuclear positions are effectively frozen during the transfer, so the system must already be in a geometry suitable for both oxidation states.

Is inner sphere always faster?

No. It is limited by the substitution step forming the bridge, so an outer sphere reaction with low reorganisation energy can be much faster.

How does this connect to biological systems?

Long-range outer sphere transfer through protein structures underlies respiration and photosynthesis. The protein controls the rate by fixing the distance and the reorganisation energy, which is a common context for applied questions.