1. Electron Transfer Reactions

2. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging ligand, and the electron is transferred from the reductant to the oxidant through the bridging ligand

3. In an outer sphere mechanism, there is an encounter between the reductant and the oxidant. The electron is transferred from one to the other whilst there is no change in the coordination sphere of either.

5. Common bridging ligands

6. Oxide and hydroxide. But water is a very poor bridging ligand

7. Common bridging ligands Ligands which have more than one donor atom (called ambident nucleophiles) _ Other examples 2-

8. Common bridging ligands Ligands which have more than one donor atom separated by a delocalised  electron system

9. How do we distinguish an inner sphere from an outer sphere mechanism? Henry Taube’s classic experiment [Co III (NH 3 ) 5 Cl] 2+ [Cr II (H 2 O) 6 ] 2+ Inert: d 6 Co(III) Labile: d 4 Cr(II) Cl - is a bridging ligand; neither H 2 O nor NH 3 are Observation: products (in acidic medium) are [Co II (H 2 O) 6 ] 2+ + [Cr III (H 2 O) 5 Cl] 2+ and this allowed him to deduce the mechanism

10. The reaction could have occurred through an inner sphere pathway: [Co III (NH 3 ) 5 Cl] 2+ + [Cr II (H 2 O) 6 ] 2+  [Co III (NH 3 ) 5  Cl  Cr II (H 2 O) 5 ] 4+ electron transfer [Co II (NH 3 ) 5  Cl  Cr III (H 2 O) 5 ] 4+ break apart Co(II) is labile Cr(III) is inert [Co II (NH 3 ) 5 (H 2 O)] 2+ + [Cr III (H 2 O) 5 Cl] 2+ hydrolysis, in acid [Co II (H 2 O) 6 ] 2+ + 5NH 4 +

11. Or it could have gone through an outer sphere pathway: [Co III (NH 3 ) 5 Cl] 2+ + [Cr II (H 2 O) 6 ] 2+ electron transfer Co(II) is labile Cr(III) is inert hydrolysis, in acid [Co II (H 2 O) 6 ] 2+ + 5NH 4 + + Cl  [Co II (NH 3 ) 5 Cl] 2+ + [Cr III (H 2 O) 6 ] 2+

12. [Co II (H 2 O) 6 ] 2+ [Cr III (H 2 O) 6 ] 2+ Observation: products (in acidic medium) are [Co II (H 2 O) 6 ] 2+ + [Cr III (H 2 O) 5 Cl] 2 + So there would have had to be a subsequent anation of [Cr III (H 2 O) 6 ] 2+ by Cl  Rate of [Cr III (H 2 O) 6 ] 2+ by Cl  : k = 2.9  10 -8 M -1 s -1 Rate of electron transfer: k = 6  10 +5 M -1 s -1 Rate of electron transfer is 13 orders to magnitude faster than rate of anation

13. The reaction could not have proceeded through an outer sphere mechanism Taube’s postulate: A reaction will have proceeded through an inner sphere mechanism if one of the products is substitution inert and it retains the bridging ligand i.e., the rate of the electron transfer reaction is much faster than the rate of formation of the product by subsequent anation Corollary: If the rate of electron transfer is much faster than the rate of ligand substitution on either metal ion, the reaction must proceed through an outer sphere mechanism

14. Example V 2+ is inert (d 3 ion, high LFSE – like Cr 3+ ) Ru 3+ is inert (2 nd transition series) Now [Ru III (NH 3 ) 5 Br] 2+ + [V II (H 2 O) 6 ] 2+ e transfer, k = 5.1  10 3 M -1 s -1 [Ru II (NH 3 ) 5 Br] + + [V III (H 2 O) 6 ] 3+ But [V II (H 2 O) 6 ] + Br   [V II (H 2 O) 5 Br] + + H 2 O k = 5.0  10 1 s -1 Hence cannot form the inner sphere complex fast enough – the anation reaction is too slow. The reaction must have been outer sphere.

15. Barriers to electron transfer Donor Acceptor e-e- Ψ D Ψ A Rate of an electronic transition   H DA > 2 where (Atkins, 8 th ed., Chapter 9; 9 th ed., Chapter 8) Hamiltonian operator that describes the coupling of the two wavefunctions Distance

16. If the coupling is relatively weak, edge-to-edge distance between D and A Parameter that measures the sensitivity of the coupling to distance Electron coupling when A and D are in direct contact (r = 0) and it turns out that the rate constant for electron transfer between D and A is (Atkins, 8 th ed., p. 897; not in 9 th ed.)

17. D A Will be a constant if D and A are the same ln k ET r

18. Nature often uses large, conjugated macrocycles to do electron transfer Examples: Porphyrins Chlorophylls

19. Effectively increases radius of D and A, cutting down separation, and hence increasing rate of e - transfer effective distance distance between metals

20. Q-cytochrome c oxidoreductase – Complex III or the bc 1 complex

21. which is often written in simplified form as nuclear frequency factor electronic factor 0 ≤ κ ≤ 1 For fast electron transfer, maximise κ E

22.  minimise the reorganisation energy, λ, of inner and outer sphere

23.  use appropriate electronic configurations When an e - is transferred from the D to the A molecule, it cannot change its spin. In many cases this is not a problem: [Co(phen) 3 ] 3+ + [Co(bipy) 3 ] 2+ → [Co(phen) 3 ] 2+ + [Co(bipy) 3 ] 3+ low spin low spin e g t 2g

24. But in some cases - especially if there is a change of spin state - this is a barrier to electron transfer [Co(NH 3 ) 4 Cl 2 ] 3+ + [Co(OH 2 ) 6 ] 2+ → [Co(NH 3 ) 4 Cl 2 ] 2+ + [Co(OH 2 ) 6 ] 3+ low spin high spin high spin low spin S = 0 S = 3/2 S = 3/2 S = 0 e g t 2g This cannot be a single step

25. [Co(NH 3 ) 4 Cl 2 ] 3+ + [Co(OH 2 ) 6 ] 2+ → {[Co(NH 3 ) 4 Cl 2 ] 3+ }* + [Co(OH 2 ) 6 ] 2+ low spin high spin excited state 1 high spin e g t 2g

26. {[Co(NH 3 ) 4 Cl 2 ] 3+ }* + [Co(OH 2 ) 6 ] 2+ → {[Co(NH 3 ) 4 Cl 2 ] 3+ }* + [Co(OH 2 ) 6 ] 2+ excited state 1 high spin excited state 2 high spin e g t 2g

27. {[Co(NH 3 ) 4 Cl 2 ] 3+ }* + [Co(OH 2 ) 6 ] 2+ → [Co(NH 3 ) 4 Cl 2 ] 2+ + [Co(OH 2 ) 6 ] 3+ excited state 2 high spin high spin excited state 3 e g t 2g [Co(OH 2 ) 6 ] 3+ low spin and finally

28. Faster electron transfer occurs if an electron is removed from and added to a non-bonding orbital (less reorganisational energy λ ) Recall that in complexes with σ only ligands the t 2g orbitals are non-bonding and e g orbitals are antibonding

29. Compare self-exchange rate constants: [Cr(OH 2 ) 6 ] 3+/2+ t 2g 3 /t 2g 3 e g 1 1 × 10 -5 M -1 s -1 [Fe(OH 2 ) 6 ] 3+/2+ t 2g 3 e g 2 /t 2g 4 e g 2 1.1 × 10 -5 M -1 s -1 [Ru(OH 2 ) 6 ] 3+/2+ t 2g 5 /t 2g 6 20 × 10 -5 M -1 s -1 electrons going in and out of the t 2g orbitals makes for fast electron transfer

30. The Inner Sphere Mechanism The rate-determining step could be the formation of the bridged complex (i.e., the precursor complex) the electron transfer step (most commonly rate determining) the break-up of the successor complex

31. We can often rationalise which step will be rate-determining [Ru III (NH 3 ) 5 Cl] 2+ + [Cr II (H 2 O) 6 ] 2+  [Ru III (NH 5 ) 5  Cl  Cr II (H 2 O) 5 ] 4+ + H 2 O K e transfer [Ru II (NH 5 ) 5  Cl  Cr III (H 2 O) 5 ] 4+ + H 2 O k1k1 [Ru II (NH 3 ) 5 (H 2 O)] 2+ + [Cr III (H 2 O) 5 Cl ] 2+ Both Ru(II) and Cr(III) are inert – so we would expect the breakup of the successor complex to be rate-limiting

32. Changes in mechanism are often accompanied by substantial changes in rate The following reactions must be outer sphere reactions (why?) oxidantreductantk [Co III (NH 3 ) 5 (H 2 O)] 3+ [Ru II (NH 3 ) 6 ] 2+ 3.0 M -1 s -1 [Co III (NH 3 ) 5 (OH)] 2+ [Ru II (NH 3 ) 6 ] 2+ 0.04 M -1 s -1 and the hydroxo complex reacts some 100 times slower than the aqua complex oxidantreductantk [Co III (NH 3 ) 5 (H 2 O)] 3+ [Cr II (H 2 O) 6 ] 2+ 0.1 M -1 s -1 [Co III (NH 3 ) 5 (OH)] 2+ [Cr II (H 2 O) 6 ] 2+ 1.5  10 6 M -1 s -1 The hydoxo complex in this case must be reacting through an inner sphere mechanism

33. For the first row of the d block: If electron transfer is rate-determining, then the rate depends markedly on 1. the identity of the metal ion These are the same factors that controlled rate in the outer sphere mechanism (see later) 2.the nature of the bridging ligands The ability of the ligand to act as an electron conductor

34. 2.The ability of the ligand to act as an electron conductor para meta k = 100 M -1 s -1 k = 1.6  10 -3 M -1 s -1

35. If formation of the precursor complex is rate determining, then the rate is usually not very sensitive to the nature of the bridging ligand This is because the ligand substitution reactions of the first row d metals are usually dissociative  hence does not depend strongly on the nature of the entering ligand [L 5 M ox X] + [L 5 M red Y] [L 5 M ox ] + X + [L 5 M red Y] [L 5 M ox  Y  M red L 5 ] [L 5 M red  Y  M ox L 5 ] etc rate limiting Example: V 2+ (aq) is oxidised to V 3+ (aq) by a long series of Co 3+ oxidants with different bridging ligands

36. Inner sphere mechanism always suspected if good bridging ligands are available: Cl - Br - I - N 3 - CN -

37. The Outer Sphere Mechanism Rudolph Marcus

38. Energy changes during electron transfer – the Frank-Condon Principle  Electron transfer is fast compared to nuclear motion  Hence the nuclei are essential frozen in space during the electron transfer step Now consider the following situation: [Fe II (H 2 O) 6 ] 2+ + [*Fe III (H 2 O) 6 ] 3+  [Fe III (H 2 O) 6 ] 3+ + [*Fe II (H 2 O) 6 ] 2+ Fe(II)-O = 2.02-2.07 ÅFe(III)-O = 2.00 Å

39. So suppose Fe(II)  OH 2 + *Fe(III)  OH 2 e Fe(III)  OH 2 + *Fe(II)  OH 2 bond too long for Fe(III) bond too short for Fe(II) spontaneous (exothermic) Fe(III)  OH 2 + *Fe(II)  OH 2 getting energy from nothing – which would be a violation of the First Law

40. e transfer What actually happens: Fe(II)  OH 2 + *Fe(III)  OH 2 shrinks stretchesENDOTHERMIC Fe(III)  OH 2 + *Fe(II)  OH 2 rearrangement EXOTHERMIC Fe(III)  OH 2 + *Fe(II)  OH 2 G‡G‡ Frank- Condon Energy Fe(II)  OH 2 + *Fe(III)  OH 2 bonds now about the same length

41. A given system can (in principle) be represented by a wavefunction,  Represents hypersurface of the reactants,  reac represents changes to all structural parameters (bond lengths, angles, torsions, etc) during the reaction

42. Parabolic function because bond stretching and angle bending terms can be approximated by Hooke’s law behaviour: x0x0 E0E0 For example, [Fe 3+ (H 2 O) 6 ] with a short Fe–O bond, x o

43.  products For example, [Fe 2+ (H 2 O) 6 ] with a long Fe–O bond

44. Electron transfer from the reactants to products can occur when the reactant deforms along the reaction coordinate until it structurally resembles the product (at  )  For example, Fe 3+ ––O must stretch

45. λ is the reorganisation energy, the energy that would be expended to reorganise the reactant form to the product form if no electron transfer took place λ

46. For an exothermic (exergonic) reaction:

50. ‡

52. ‡

53. and rearranging: Show, using similar reasoning, that for an endothermic (endergonic) reaction

54. So in general

55. So when ΔG o << λ

56. Circles Diamonds: ΔG o /kJ mol -1 λ = 200 kJ mol -1 ΔG ‡ /kJ mol -1

57. Circles Diamonds: ΔG o /kJ mol -1 λ = 200 kJ mol -1 ΔG ‡ /kJ mol -1 Simplified eqt only good in this region, i.e., when |ΔG o | << λ

58. G‡  GoG‡  Go But  G o =  nFE o G‡  EoG‡  Eo  G ‡  E o The height of the activation energy barrier to electron transfer becomes smaller and the reaction becomes faster as the redox potential of the couple increases

61. Reaction becomes activationless when ΔG o = -λ

62. As ΔG o becomes very large (ΔG o < -λ), ΔG ‡ increases again. Hence k ET goes through a maximum when ΔG o = -λ /2

63. ΔG o /kJ mol -1 λ = 200 kJ mol -1 ΔG ‡ /kJ mol -1 ΔG ‡ = 0 when G o = -λ (here, -200 kJ mol -1 )...

64. Relative rate GoGo +ve-ve Inverted Marcus region...so RATE goes through a maximum

65. Inverted Marcus region demonstrated experimentally by Harry Gray (Caltech) 1990 for an iridium complex

66. For fast electron transfer, minimise the reorganisation energy, λ, of inner and outer sphere Reorganisation of solvent often major component Hexaaqua ions: λ > 100 kJ mol -1 Redox centres in proteins (buried, shielded from solvent): λ ~ 25 kJ mol -1

67. Reorganisation of solvent often major component Hexaaqua ions: λ > 100 kJ mol -1 Redox centres in proteins (buried, shielded from solvent): λ ~ 25 kJ mol -1 Fe porphyrin cytochrome c

68. Bulky, hydrophobic chelating ligands shield the metal from solvent, lowering λ bipyridyl (bipy) [Ru(OH 2 ) 6 ] 3+/2+ k ET = 20 M -1 s -1 [Ru(bipy) 3 ] 3+/2+ 4 × 10 8 M -1 s -1

69. The speed of an electron transfer reaction depends on the reactivity of the complex This can be measured by the self-exchange rate [Fe II (H 2 O) 6 ] 2+ + [*Fe III (H 2 O) 6 ] 3+  [Fe III (H 2 O) 6 ] 3+ + [*Fe II (H 2 O) 6 ] 2+ E o because  G ‡  E o other factors such as the collision geometry and the collision frequency (the pre-exponential factor in the Arrhenius equation) The Marcus cross-relationship

70. Suppose, as a special case, we have a redox reaction where the electron donor, D, and the acceptor A, reversibly form an encounter complex; where the rate determining step is the electron transfer step; and where break up of the successor complex is fast

71. Assume [D] t ~ [D] 0 [A] t ~ [A] 0

72. If ΔG o « λ then ΔG o2 /4λ is negligibly small

73. For the reaction A + A → A + + A - ΔG o = 0, so and similarly Hence We will assume that λ DA is the arithmetic mean of λ AA and λ DD

74. Since Marcus Cross Relationship

76. Example Predict k obs for [Co III (bipy) 3 ] 3+ + [Co II (terpy) 2 ] 2+  [Co II (bipy) 3 ] 2+ + [Co III (terpy) 2 ] 3+ bipy terpy Data (0 o C) Self-exchange rate constants [Co II/III (bipy) 3 ] 2+/3+ k AA = 9.0 M -1 s -1 [Co II/III (terpy) 2 ] 2+/3+ k DD = 48 M -1 s -1 Redox potentials: bipy complex0.34 V terpy complex0.31 V

78. Experimental value: 62 M -1 s -1

79. Example 2 For [Co III (NH 3 ) 5 Cl] 2+ + [Eu II (H 2 O) 8 ] 2+  [Co II (NH 3 ) 5 Cl] + + [Eu III (H 2 O) 8 ] 3+ [Co II (H 2 O) 6 ] 2+ apply Marcus equation and find k 12 = 2.7 M -1 s -1 The experimental value is 390 M -1 s -1 The Marcus theory was developed for an outer sphere reaction. The experimental value is very different to the theoretical value. This suggests that this reaction did not occur through an outer-sphere mechanism, but rather through an inner sphere mechanism with Cl  as bridging ligand