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Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms...

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Electron Transfer Reactions
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Page 1: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Electron Transfer Reactions

Page 2: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

Page 3: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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.

Page 4: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.
Page 5: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Common bridging ligands

Cl

Page 6: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Common bridging ligands

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

Page 7: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Common bridging ligands

Ligands which have more than one donor atom (called ambident nucleophiles)

S C N_

Other examples

N

O O

_S

S

OO

O

2-

Page 8: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Common bridging ligands

Ligands which have more than one donor atom separated by a delocalised electron system

Page 9: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

How do we distinguish an inner sphere from an outer sphere mechanism?

Henry Taube’s classic experiment

[CoIII(NH3)5Cl]2+

[CrII(H2O)6]2+

Inert: d6 Co(III)

Labile: d4 Cr(II)

Cl- is a bridging ligand; neither H2O nor NH3 are

Observation: products (in acidic medium) are

[CoII(H2O)6]2+ + [CrIII(H2O)5Cl]2+

and this allowed him to deduce the mechanism

Page 10: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

The reaction could have occurred through an inner sphere pathway:

[CoIII(NH3)5Cl]2+ + [CrII(H2O)6]2+ [CoIII(NH3)5ClCrII(H2O)5]4+

electron transfer

[CoII(NH3)5ClCrIII(H2O)5]4+

break apart

Co(II) is labileCr(III) is inert

[CoII(NH3)5(H2O)]2+ + [CrIII(H2O)5Cl]2+

hydrolysis, in acid

[CoII(H2O)6]2+ + 5NH4+

Page 11: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Or it could have gone through an outer sphere pathway:

[CoIII(NH3)5Cl]2+ + [CrII(H2O)6]2+

electron transfer

Co(II) is labileCr(III) is inert

hydrolysis, in acid

[CoII(H2O)6]2+ + 5NH4+ + Cl

[CoII(NH3)5Cl]2+ + [CrIII(H2O)6]2+

Page 12: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

[CoII(H2O)6]2+ [CrIII(H2O)6]2+

Observation: products (in acidic medium) are

[CoII(H2O)6]2+ + [CrIII(H2O)5Cl]2+

So there would have had to be a subsequent anation of [CrIII(H2O)6]2+ by Cl

Rate of [CrIII(H2O)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

Page 13: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Rate of electron transfer is 13 orders to magnitude faster than rate of anation

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

Page 14: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

ExampleV2+ is inert (d3 ion, high LFSE – like Cr3+)Ru3+ is inert (2nd transition series)

Now

[RuIII(NH3)5Br]2+ + [VII(H2O)6]2+

e transfer, k = 5.1 103 M-1 s-1

[RuII(NH3)5Br]+ + [VIII(H2O)6]3+

But[VII(H2O)6] + Br [VII(H2O)5Br]+ + H2O

k = 5.0 101 s-1

Hence cannot form the inner sphere complex fast enough – the anation reaction is too slow. The reaction must have been outer sphere.

Page 15: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Barriers to electron transfer

Donor Acceptor

e-

ΨD ΨA

Rate of an electronic transition HDA>2 where

DADA A DˆH H d

(Atkins, 8th ed., Chapter 9; 9th ed., Chapter 8) Hamiltonian operator that describes the coupling of the two wavefunctions

• Distance

Page 16: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

If the coupling is relatively weak,2 o 2

DA DArH H e

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

2 1/ 2o 3DA /

ET

2

4

r

G RTH e

k eh RT

(Atkins, 8th ed., p. 897; not in 9th ed.)

Page 17: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

2 1/ 2o 3DA /

ET

2

4

r

G RTH e

k eh RT

n

D

A

Will be a constant if D and A are the same

ETln( ) constantk r

ln kET

r

Page 18: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Nature often uses large, conjugated macrocycles to do electron transfer

Examples:

Porphyrins Chlorophylls

Page 19: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Effectively increases radius of D and A, cutting down separation, and hence increasing rate of e- transfer

effective distance

distance between metals

Page 20: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Q-cytochrome c oxidoreductase – Complex III or the bc1 complex

Page 21: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

2 1/ 2o 3DA /

ET

2

4

r

G RTH e

k eh RT

/ET N E

G RTk e

which is often written in simplified form as

nuclear frequency

factor

electronic factor

0 ≤ κ ≤ 1

• For fast electron transfer, maximise κE

Page 22: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

1/ 23

E 4

RT

• For fast electron transfer, maximise κE

minimise the reorganisation energy, λ, of inner and outer sphere

Page 23: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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 low spin low spin

eg

t2g

Page 24: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

But in some cases - especially if there is a change of spin state - this is a barrier to electron transfer

[Co(NH3)4Cl2]3+ + [Co(OH2)6]2+ → [Co(NH3)4Cl2]2+ + [Co(OH2)6]3+

low spin high spin high spin low spinS = 0 S = 3/2 S = 3/2 S = 0

eg

t2g

This cannot be a single step

Page 25: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

[Co(NH3)4Cl2]3+ + [Co(OH2)6]2+ → {[Co(NH3)4Cl2]3+}* + [Co(OH2)6]2+

low spin high spin excited state1 high spin

eg

t2g

Page 26: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

{[Co(NH3)4Cl2]3+}* + [Co(OH2)6]2+→ {[Co(NH3)4Cl2]3+}* + [Co(OH2)6]2+

excited state1 high spin excited state2 high spin

eg

t2g

Page 27: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

{[Co(NH3)4Cl2]3+}* + [Co(OH2)6]2+→ [Co(NH3)4Cl2]2+ + [Co(OH2)6]3+

excited state2 high spin high spin excited state3

eg

t2g

[Co(OH2)6]3+

low spin

and finally

Page 28: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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 t2g orbitals are non-bonding and eg orbitals are antibonding

Page 29: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Compare self-exchange rate constants:

[Cr(OH2)6]3+/2+ t2g3/t2g

3eg1 1 × 10-5 M-1s-1

[Fe(OH2)6]3+/2+ t2g3eg

2/t2g4eg

2 1.1 × 10-5 M-1s-1

[Ru(OH2)6]3+/2+ t2g5/t2g

6 20 × 10-5 M-1s-1

electrons going in and out of the t2g

orbitals makes for fast

electron transfer

Page 30: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

Page 31: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

We can often rationalise which step will be rate-determining

[RuIII(NH3)5Cl]2+ + [CrII(H2O)6]2+ [RuIII(NH5)5ClCrII(H2O)5]4+ + H2OK

e transfer

[RuII(NH5)5ClCrIII(H2O)5]4+ + H2O

k1

[RuII(NH3)5(H2O)]2+ + [CrIII(H2O)5Cl ]2+

Both Ru(II) and Cr(III) are inert – so we would expect the breakup of the successor complex to be rate-limiting

Page 32: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Changes in mechanism are often accompanied by substantial changes in rate

The following reactions must be outer sphere reactions (why?)

oxidant reductant k

[CoIII(NH3)5(H2O)]3+ [RuII(NH3)6]2+ 3.0 M-1 s-1

[CoIII(NH3)5(OH)]2+ [RuII(NH3)6]2+ 0.04 M-1 s-1

and the hydroxo complex reacts some 100 times slower than the aqua complex

oxidant reductant k

[CoIII(NH3)5(H2O)]3+ [CrII(H2O)6]2+ 0.1 M-1 s-1

[CoIII(NH3)5(OH)]2+ [CrII(H2O)6]2+ 1.5 106 M-1 s-1

The hydoxo complex in this case must be reacting through an inner sphere mechanism

Page 33: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

Page 34: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

2. The ability of the ligand to act as an electron conductor

N [RuII(NH3)4(H2O)]

O

O[(H3N)5CoIII]

N [RuII(NH3)4(H2O)]

O

O

[(H3N)5CoIII]

para

meta

k = 100 M-1 s-1

k = 1.6 10-3 M-1 s-1

Page 35: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

[L5MoxX] + [L5MredY]

[L5Mox] + X + [L5MredY]

[L5MoxYMredL5]

[L5MredYMoxL5]

etc

rate limiting

Example: V2+(aq) is oxidised to V3+

(aq) by a long series of Co3+ oxidants with different bridging ligands

Page 36: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Inner sphere mechanism always suspected if good bridging ligands are available:

Cl- Br- I- N3- CN-

N

N N

N

N

NMe2

pyrazine 4,4'-bipyridyl N,N-dimethylaminopyridine

Page 37: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

The Outer Sphere Mechanism

Rudolph Marcus

Page 38: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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:

[FeII(H2O)6]2+ + [*FeIII(H2O)6]3+ [FeIII(H2O)6]3+ + [*FeII(H2O)6]2+

Fe(II)-O = 2.02-2.07 Å Fe(III)-O = 2.00 Å

Page 39: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

So suppose

Fe(II)OH2 + *Fe(III)OH2

e

Fe(III)OH2 + *Fe(II)OH2

bond too long forFe(III)

bond too short forFe(II)

spontaneous (exothermic)

Fe(III)OH2 + *Fe(II)OH2

getting energy from nothing – which would be a violation of the First Law

Page 40: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

e transfer

What actually happens:

Fe(II)OH2 + *Fe(III)OH2

shrinks stretches ENDOTHERMIC

Fe(III)OH2 + *Fe(II)OH2

rearrangement EXOTHERMIC

Fe(III)OH2 + *Fe(II)OH2

G‡

Frank-Condon Energy

Fe(II)OH2 + *Fe(III)OH2

bonds now about the same length

Page 41: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

Page 42: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

20 0( )E k x x E

Parabolic function because bond stretching and angle bending terms can be approximated by Hooke’s law behaviour:

x0

E0

For example, [Fe3+(H2O)6] with a short Fe–O bond, xo

Page 43: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

products

For example, [Fe2+(H2O)6] with a long Fe–O bond

Page 44: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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, Fe3+––O must stretch

Page 45: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

Page 46: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

For an exothermic (exergonic) reaction:

Page 47: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.
Page 48: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.
Page 49: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.
Page 50: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Page 51: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.
Page 52: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Page 53: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

and rearranging:

Show, using similar reasoning, that for an endothermic (endergonic) reaction

Page 54: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

So in general

Page 55: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

2o

2o

o 2

2

2 o o2

14

4

( )

41

( 2 )4

GG

G

G

G G

So when ΔGo << λ 2 o

o

o

1( 2 )

4

( 2 )41

( 2 )4

G G

G G

G G

Page 56: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

0

10

20

30

40

50

60

70

-40 -30 -20 -10 0 10 20 30 40

Circles o1

( 2 )4 G G

Diamonds:

ΔGo /kJ mol-1

λ = 200 kJ mol-1

ΔG

‡ /k

J m

ol-1

Page 57: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

-300

-200

-100

0

100

200

300

400

500

600

700

-600 -400 -200 0 200 400 600

Circles o1

( 2 )4 G G

Diamonds:

ΔGo /kJ mol-1

λ = 200 kJ mol-1

ΔG

‡ /k

J m

ol-1

Simplified eqt only good in this region, i.e., when |ΔGo| << λ

Page 58: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

G‡ Go

But Go = nFEo

G‡ Eo

G‡ Eo

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

o1( 2 )

4G G

Page 59: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.
Page 60: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.
Page 61: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Reaction becomes activationless when ΔGo = -λ

Page 62: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

As ΔGo becomes very large (ΔGo < -λ), ΔG‡ increases again. Hence kET goes through a maximum when ΔGo = -λ

/2

/2

Page 63: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

0

100

200

300

400

500

600

700

-600 -400 -200 0 200 400 600

ΔGo /kJ mol-1

λ = 200 kJ mol-1

ΔG

‡ /k

J m

ol-1

ΔG‡ = 0 when Go = -λ (here, -200 kJ mol-1)...

Page 64: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Rel

ativ

e ra

te

Go+ve -ve

Inverted Marcus region

...so RATE goes through a maximum

Page 65: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

Page 66: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

• 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

Page 67: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

Page 68: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Bulky, hydrophobic chelating ligands shield the metal from solvent,lowering λ

N N

bipyridyl (bipy)

[Ru(OH2)6]3+/2+ kET = 20 M-1s-1

[Ru(bipy)3]3+/2+ 4 × 108 M-1s-1

Page 69: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

The speed of an electron transfer reaction depends on

• the reactivity of the complex

This can be measured by the self-exchange rate

[FeII(H2O)6]2+ + [*FeIII(H2O)6]3+ [FeIII(H2O)6]3+ + [*FeII(H2O)6]2+

• Eo

because G‡ Eo

• other factors such as the collision geometry and the collision frequency (the pre-exponential factor in the Arrhenius equation)

The Marcus cross-relationship

Page 70: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

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

DA

ET + -

+ - + -

D + A DA

DA D A

D A D + A

K

k

fast

Page 71: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

DA

ET + -

+ - + -

D + A DA

DA D A

D A D + A

K

k

fast

ET obs 0 0

d[ ] d[ ] = [DA] = [D] [A]

d d

P Pk k

t t

DA t t 0 0

DA 0 0

[DA] [DA] [D] [A] [D] [A]

[DA] = [D] [A]

K

K

Assume [D]t ~ [D]0

[A]t ~ [A]0

ET DA 0 0

d[ ] = [D] [A]

d

Pk K

t

obs ET DA= k k K

DA /obs DA N E= G RTk K e

Page 72: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

2

2

2 22

2

= 1 + 4

4

1 2

4

4 2 4

o

o

o o

o o

GG

G

G G

G G

If ΔGo « λ then ΔGo2/4λ is negligibly small

=4 2

oGG

Page 73: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

For the reactionA + A → A+ + A-

ΔGo = 0, so

AAAA =

4G

AA DD/ 4 / 4AA AA DD DD

JJ N(JJ) E(JJ)

= =

=

RT RTk Z e k Z e

where Z

DD AADA

+ =

2

and similarly DDDD =

4G

Hence

We will assume that λDA is the arithmetic mean of λAA and λDD

DD AADA = + +

2 8 8

oDAG

G

Page 74: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

DA DD AA/ 2 /8 /8obs DA DA =

oG RT RT RTk K Z e e e

DA /DA DA DAln( ) = - / or =

oG RToK G RT K e

Since

oDA /o

DA DA DA

1/2 1/21/2 DD AA

obs DA DA DA 1/2 1/2DD AA

1/2 1/2 1/2DA DADA DD AA1/2 1/2

DD AA

2 2DA DA

obs DA DD AADD AA

ln( ) = / or =

=

=

=

G RTK G RT K e

k kk K Z K

Z Z

K ZK k k

Z Z

K Zk K k k f where f

Z Z

Marcus Cross Relationship

Page 75: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

obs DA DD AA

2 2DA DA

DD AA

=

1

k K k k f

where

K Zf

Z Z

Page 76: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Example

Predict kobs for

[CoIII(bipy)3]3+ + [CoII(terpy)2]2+ [CoII(bipy)3]2+ + [CoIII(terpy)2]3+

N N

N

N

N

bipy

terpy

Data (0 oC)

Self-exchange rate constants[CoII/III(bipy)3]2+/3+kAA = 9.0 M-1s-1

[CoII/III(terpy)2]2+/3+ kDD = 48 M-1s-1

Redox potentials:bipy complex 0.34 Vterpy complex 0.31 V

Page 77: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

cell 0.34 V - 0.31 V = 0.03 VE

12lnG RT K nFE

DA

-1 -1

-1 -1

exp

1 96485 C mol 0.03 J Cexp

8.315 J K mol × 273 K

3.58

nFEK

RT

Page 78: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

12 AA DD DA

-1 -1

9 48 3.58 1

39 M s

k k k K f

Experimental value: 62 M-1 s-1

Page 79: Electron Transfer Reactions. Electron transfer reactions occur by one of two fundamental mechanisms In an inner sphere mechanism, there is a common bridging.

Example 2

For [CoIII(NH3)5Cl]2+ + [EuII(H2O)8]2+ [CoII(NH3)5Cl]+ + [EuIII(H2O)8]3+

[CoII(H2O)6]2+

apply Marcus equation and find k12 = 2.7 M-1s-1

The experimental value is 390 M-1s-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


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