1.10: Electron Transfer: Inner Sphere

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In some cases, electron transfers occur much more quickly in the presence of certain ligands. For example, compare the rate constants for the following two electron transfer reactions, involving almost exactly the same complexes:

Co(NH₃)₆³⁺ + Cr²⁺ → Co²⁺ + Cr³⁺ + 6 NH₃ k = 10^-4 M^-1 s^-1

Co(NH₃)₅Cl²⁺ + Cr²⁺ → Co²⁺ + CrCl²⁺ + 6 NH₃ k = 6 x 10⁵ M^-1 s^-1

(Note: aqua ligands are omitted for simplicity. Ions, unless noted otherwise, are aqua complexes.)

Notice two things: first, when there is a chloride ligand involved, the reaction is much faster. Second, after the reaction, the chloride ligand has been transferred to the chromium ion. Possibly, those two events are part of the same phenomenon.

Similar rate enhancements have been reported for reactions in which other halide ligands are involved in the coordination sphere of one of the metals.

In the 1960’s, Henry Taube of Stanford University proposed that halides (and other ligands) may promote electron transfer via bridging effects. What he meant was that the chloride ion could use one of its additional lone pairs to bind to the chromium ion. It would then be bound to both metals at the same time, forming a bridge between them. Perhaps the chloride could act as a conduit for electron transfer. The chloride might then remain attached to the chromium, to which it had already formed a bond, leaving the cobalt behind.

Electron transfers that occur via ligands shared by the two metals undergoing oxidation and reduction are termed "inner sphere" electron transfers. Taube was awarded the Nobel Prize in chemistry in 1983; the award was based on his work on the mechanism of electron transfer reactions.

Problem RO10.1.

Take another look at the two electron transfer reactions involving the cobalt and chromium ion, above.

1. What geometry is adopted by these complexes?

2. Are these species high spin or low spin?

3. Draw d orbital splitting diagrams for each complex.

4. Explain why electron transfer is accompanied by loss of the ammonia ligands from the cobalt complex.

5. The chloride is lost from the cobalt comples after electron transfer. Why does it remain on the chromium?

Other ligands can be involved in inner sphere electron transfers. These ligands include carboxylates, oxalate, azide, thiocyanate, and pyrazine ligands. All of these ligands have additional lone pairs with which to bind a second metal ion.

Problem RO10.2.

Draw an example of each of the ligands listed above bridging between a cobalt(III) and chromium(II) aqua complex.

Problem RO10.3

Explain, with structures and d orbital splitting diagrams, how the products are formed in the following reaction, in aqueous solution.

Fe(OH₂)₆²⁺ + (SCN)Co(NH₃)₅²⁺ → (NCS)Fe(OH₂)₅²⁺ + Co(OH₂)₆²⁺ + 5 NH₃

How does the electron travel over the bridge?

Once the bridge is in place, the electron transfer may take place via either of two mechanisms. Suppose the bridging ligand is a chloride. The first step might actually involve an electron transfer from chlorine to the metal; that is, the chloride could donate one electron from one of its idle lone pairs. This electron could subsequently be replaced by an electron transfer from metal to chlorine.

Sometimes, we talk about the place where an electron used to be, describing it as a "hole". In this mechanism, the electron donated from the bridging chloride ligand leaves behind a hole. The hole is then filled with an electron donated from the other metal.

Alternatively, an electron might first be transferred from metal to chlorine, which subsequently passes an electron along to the other metal. In the case of chlorine, this idea may be unsatisfactory, because chlorine already has a full octet. Nevertheless, some of the other bridging ligands may have low-lying unoccupied molecular orbitals that could be populated by this extra electron, temporarily.

Problem RO10.4.

For the iron / cobalt electron transfer in problem RO9.3., show

1. an electron transfer mechanism via a hole migration along the bridge

2. an electron transfer mechanism via an electron migration along the bridge

Problem RO10.5.

One of the many contributions to the barrier for electron transfer between metal ions is internal electronic reorganization.

1. Draw d orbital splitting diagrams for each of the following metal ions in an octahedral environment.

   Ru(II) or Os(II)

   Ru(III) or Os(III)

   Co(II)

   Co(III)

   Flash photolysis is a method in which an electron can be moved instantly “uphill” from one metal to another (e.g. from M₂^II to M₁^III, below); the electron transfer rate can then be measured as the electron “drops” back from M₁^II to M₂^III.

   

2. Explain the relative rates of electron transfer reaction in this system, as measured by flash photolysis in the table below.

   M1^II	M2^III	kobs s^-1
   Os	Ru	> 5 x 10^9
   Os	Co	1.9 x 10^5

3. Does the reaction above probably occur via an inner sphere or by an outer sphere pathway? Why?

Problem RO10.6.

Outer sphere electron transfer rates depend on the free energy change of the reaction (ΔG°) and the distance between oxidant and reductant (d) according to the relation

Rate constant = k = Ae^(-ΔG)e^-d

1. What happens to the rate of the reaction as distance increases between reactants?

   One potential problem in measuring rates of intramolecular electron transfer (i.e. within a molecule) is competition from intermolecular electron transfer (between molecules).

2. What would you do in the flash photolysis experiment above to discourage intermolecular electron transfer?

3. How could you confirm whether you were successful in discouraging intermolecular reaction?

Problem RO10.7.

Stephan Isied and coworkers at Rutgers measured the following electron transfer rates between metal centers separated by a peptide. (Chem Rev 1992, 92, 381-394)

Isied offers a number of possible explanations for the data, all of which involve two competing reaction pathways.

1. The proline repeating unit is crucial in ensuring a steady increase in distance between metal centers with increased repeat units, n. Why?

2. An inner sphere pathway in this case is expected to be somewhat slow because of the lack of conjugation in the polyproline bridge. Explain why.

3. Plot the data below, with logk on the y axis (range from 4-9) and d on the x axis (12-24 Angstroms).

   n	d (Å)	kobs (s^-1 )
   1	12.2	5 x 10^8
   2	14.8	1.6 x 10^7
   3	18.1	2.3 x 10^5
   4	21.3	5.1 x 10^4
   5	24.1	1.8 x 10^4

4. A linear relationship is in agreement with Marcus theory; logk = - c x d. Is your plot linear?

5. Suggest one explanation for the data.