Energy and Electron TransferEnergy and Electron ransfer

Survival Strategy: Photosynthesis

Light Energy Harvested by Plants

6 CO2 + 6 H2O + light energy → C6H12O6 + 6 O2

Importance of Photosynthesis

P id f l tProvides energy for plants

d f l hProvides energy for animals that eat plants

Provides energy for animals that eat animals that ate plants

Provides energy for organisms that break down all of the abovedown all of the above

Provides the energy for most ecosystems on earth

Photosynthesis and Solar EnergyThe Nobel Prize in Chemistry 1961y

M. Calvin1911-1997

Joseph Priestley1733–1804

The Nobel Prize in Chemistry 1992The Nobel Prize in Chemistry 1988 The Nobel Prize in Chemistry 1992y

R. MarcusJ. Deisenhofer R. Huber H. Michel

D* A {D*A}kdiff

D* A {D*A}+

{D*A} {DA*}{D*A} {DA*}k

{DA*} D A*k-diff

+

8RTkDIF 8RT

3000

Possibilities

1D* + A  D + 1A*

1 * 3 *1D* + A  D + 3A*

3D* + A D + 1A*3D  + A  D + 1A

3D* + A  D + 3A*

Energy Requirement

Allowed ForbiddenED > EA ED < EA

Mechanisms

• Radiative Energy TransferT i i l ET• Trivial ET

• Non-Radiative Energy Transfer• Resonance ET

• Exchange ETg

Trivial energy transfer (radiative energy transfer)gy gy

*D A A

• no electronic interaction between D* d A

*D A Band A

• D* emits a quantum of light which is absorbed by Ay

A physical encounter between A and D* is not required, the photon must only be emitted in an appropriate direction and the medium must be transparent in order to allow transmission.m

Non-Radiative Energy Transfer-1

Exchange Energy Transfer

Dexter Energy Transfer

Collisional Energy Transfer gy

Exchange Energy Transfer

kET (exchange) = KJ exp(–2rDA/L)

where K is related to the specific orbital interactions such as thedependence of orbital overlap to the instantaneous orientations of *Ddependence of orbital overlap to the instantaneous orientations of Dand A.

J is the normalized spectral overlap integral, where normalized meansthat both the emission intensity (ID) and extinction coefficient (A) havebeen adjusted to unit area on the wavenumber scale. It is importantthat J, by being normalized does not depend on the actual magnitude ofA.

rDA is the donor-acceptor separation relative to their van der WaalsrDA is the donor acceptor separation relative to their van der Waalsradii, L

Non-Radiative Energy Transfer-2

Dipole-Dipole Energy Transfer

Coulombic Energy Transfer

Resonance Energy Transfer

Förster Energy Transfer

Förster Resonance Energy Transfer (FRET)

A Transmitter-Antenna Receiver-Antenna Mechanism

Förster Resonance Energy Transfer (FRET)

∆E (*D D) ∆E (A *A)∆E (*D D) = ∆E (A *A)

2

kET (Dipole - dipole) E2 DA

RDA3

2

D

2A2

RDA6

DA DA

Differences between Förster (dipole-dipole interaction) and Dexter (electron exchange) energy transfer processes

• The rate of dipole-induced energy transfer decreases as R–6 whereas the rate of exchange-induced transfer decreases as exp–(2r/L). g p ( )Quantitatively, this means that kET(exchange) drops to negligibly small values (relative to the donor lifetime) as the intermolecular (edge-to-edge) distance increases more than on the order of one or two molecular diameters (5-10Å)

• The rate of dipole-induced transfer (Forster ET) depends on the ill t t th f th *D D d A *A di ti t iti b toscillator strength of the *D D and A *A radiative transitions, but

the rate of the exchange-induced transfer is independent of the oscillator strength of the *D D and A *A transitionsoscillator strength of the D D and A A transitions

D* + A D + A*

kET total D* A He D A* 2

Electron exchange

+ D* A Hc D A* 2 c

Electron dipole-dipole interactions

222

kET (Dipole-dipole)E 2 DA

RDA3

DA

RDA6

Distance dependence, when it can be measured accurately, is a basis for distinguishingenergy transfer that occurs by dipole–dipole interactions from electron exchangeinteractions, since the latter generally falls off exponentially g y p ywith the separation RDA

Energy Transfer: A Spectroscopic RulerL. Stryer and R. Hauhland, PNAS, 58, 719 (1967)

Making Use of Förster Resonance Energy Transfer

Spin in Energy Transfer

1D* + A D + 1A*1D* + A  D + 1A*

1D* + A  D + 3A*

3D* + A  D + 1A*

3 * 3 *3D* + A  D + 3A*

Spin Allowed Energy Transfer ProcessesSpin Allowed Energy Transfer Processes

1D* + A  D + 1A* Forster

3D* + A D + 3A* DexterD  + A  D +  A Dexter

A Theory of Sensitized Luminescence in Solids, D. L. Dexter, J. Chem. Phys. 21, 836 (1953)Transfer mechanisms of electronic excitation, Th. Forster, Discussions Faraday Soc. 27, 7, (1959)

Comparison of Electron Transfer and Energy Transfer

Photoinduced electron transfer

PhotoinducedPhotoinducedElectron TransferCharge Separation

∆Get =   (IP)D – (EA)A 

*∆G    =     (IP)D ‐ (EA)A  ‐ E*D 

Electron Addition and Removal is Easier in the Excited State than in the Ground State

Get E1/2ox (D)E1/2

red (A)Eexc (A)ECoulombicet 1/2 ( ) 1/2 ( ) exc ( ) Coulombic

Free energy of activation expressed in terms of the free energy of reaction (G) and free energy of activation (G#) ( energy of reaction (G) and free energy of activation (G ) (

for a hypothetical iso-energetic self-exchange reaction.

D*  +  A

D.+ +  A.—

Get E1/2ox (D)E1/2

red (A)E*(A)ECoulombic

Rehm-Weller Equation

Dependence of the electron transfer rate on the driving force G0 and the free energy of activation G‡

D. Rehm and A. Weller, Isr. J. Chem., 8, 259, 1970

force G0  and the free energy of activation G‡

A WellerA. Weller

Rehm-Weller Plot

The value of ket reaches a plateau value of ~ 2 x 1010 M-1s-1 after an exothermicity of ~ 10 kcal mol-1 and the value of k remains the diffusion

Rehm-Weller Plot

exothermicity of ~ -10 kcal mol 1 and the value of ket remains the diffusion controlled value to the highest negative values of achievable.

R. A. Marcus, J. Chem. Phys., 24, 966, 1956.

R. A. Marcus, Electron transfer Reactions in Chemistry: Theory and Experiment, (Nobel Lecture) Angew. Chem. Int. Ed.,32, 1111, 1993.

R. A. Marcus and N. Sutin, Biochemica et Biophysica Acta, 811, 265, 1985.

R MR. A. MarcusRates are expected: to be slow for weakly exothermic reactions, y to increase to a maximum for moderately exothermic

reactions and then reactions, and then to decrease with increasing exothermicity for highly

exothermic et reactionsexothermic et reactions.

The re-emergence of the activation barrier (∆G‡) at large negative G0 valueslarge negative G values

Experimental conditions to observe the Marcus “inverted region”?

For most donor acceptor (DA) systems the inverted region is For most donor-acceptor (DA) systems the inverted region is obscured by the diffusion limit.

This can be circumvented by:This can be circumvented by: freezing the donor-acceptor distribution (glassy medium) covalently linking the donor and the acceptor covalently linking the donor and the acceptor lowering the donor-acceptor interaction (electronic coupling V)

so that the maximum rate for -G0 = is lower than the so that the maximum rate for G = is lower than the diffusion limit.

G. Closs

G. Closs and J. R. Miller, Science, 240, 440‐447 (1988) 

The Nobel Prize in Chemistry 1992The Nobel Prize in Chemistry 1992

The Nobel Prize in Chemistry 1983 was awarded to Henry Taube "for his work on the 

h f l fmechanisms of electron transfer reactions, especially in metal complexes".

The Nobel Prize in Chemistry 1992 was awarded to Rudolph A. Marcus "for his contributions to the theory of electron

f i i h i l "transfer reactions in chemical systems".

Triplet Sensitization

Electron transfer sensitizer