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Energy and Electron Transfer - II. Chapter-7 MMP+. P. H. December 19, 2002. Marcus Theory. - D G = l s + l v. Log k. normal. Inverted. - D G. Acc. Chem. Res., 1996, 29, 522. Example. k R >> k I. J. Am. Chem. Soc., 1989, 111, 8948. l = 0.39eV.

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Energy and Electron Transfer - II

Chapter-7 MMP+

P. H.

December 19, 2002


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Marcus Theory

-DG = ls + lv

Log k

normal

Inverted

-DG

Acc. Chem. Res., 1996, 29, 522


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Example

kR >> kI

J. Am. Chem. Soc., 1989, 111, 8948


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l = 0.39eV



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CRIP & SSRIP - An example

DG2 = 1.8 kcal/mol

k1 values depend on solvent polarity

Dicloromethane -108 ; Hexane > 1010

Also more solvent reorganization for SSRIP than CRIP



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Electron and Energy Transfer Equilibria

Can’t even happen without

Energy transfer equilibrium


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Thermodynamics of the Equlibria

For rigid systems

For example..

DS - 0.04 gibbs/mol

DS - -1.8 gibbs/mol


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Electron Transfer Equilibria

Cannot observe the equlibrium if…

kbet >> k–et



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Role of Diffusion

Diffusion and collision

D*A becomes DA*

DA* breaks up into D and A*


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Rate Constants:

  • kOBS, is close to calculated kDIFF.

  • kOBS is a function of T/.

  • kOBS is essentially invariant for quenchers of widely varying structure.

  • kOBS reach a limiting value which corresponds to the fastest bimolecular rate constant measured for that solvent.

Obscured the Marcus Inverted Region



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Diffusion - Distance/Time Relationship

Diffusion coefficient (D) of benzene (25°C) - 2 x 10–5 cm2/s; if we assume the encounter to be over when one of the molecules has traveled a distance equivalent to the size of several solvent molecules (e.g. x ~ 10 Å, equivalent to about 2 benzene molecules), then we obtain a rough estimate of the time required by applying above equation of about 2.5 x 10–10 s.



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Transient Effects on Quenching

With Incresing Time


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Static Quenching - Perrin Model

ln ( ° / ) = V NA [ A]

R (in Å) = 6.5 [A]1/3

(with [A] in M units)


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