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A Non-Marcus Model for Electrostatic Fluctuations in Long Range Electron Transfer

A Non-Marcus Model for Electrostatic Fluctuations in Long Range Electron Transfer. Stephen Fletcher. Department of Chemistry Loughborough University Leicestershire LE11 3TU UK. Motivation. To find a simple, elegant derivation of the reorganization energy of electron transfer.

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A Non-Marcus Model for Electrostatic Fluctuations in Long Range Electron Transfer

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  1. A Non-Marcus Model for Electrostatic Fluctuations in Long Range Electron Transfer Stephen Fletcher Department of Chemistry Loughborough University Leicestershire LE11 3TU UK

  2. Motivation To find a simple, elegant derivation of the reorganization energy of electron transfer.

  3. Common Heritage All electron transfer reactions are tunnelling reactions. Tunnelling takes place with conservation of energy. Tunnelling takes place so quickly that atomic nuclei are effectively “motionless” while it happens (Franck-Condon Principle).

  4. Thermodynamic Potential Profiles (Randles, 1952) Different theories give different models for l.

  5. Equation for l (Marcus, 1956) Pekar factor diverges to zero when

  6. Marcus, Nobel Lecture, 1992 “For a bimolecular reaction, work terms, principally electrostatic, are involved in bringing the reactants together and in separating the reaction products, but are omitted… for notational brevity.” • Ions not screened by counter-ions... • …so Marcus theory violates Debye-Hückel theory!

  7. Historical Interlude

  8. Max Born (1882-1970)

  9. Born Energy (1920) Concentrating charges on a neutral sphere requires energy to overcome their mutual repulsion

  10. Born Energy

  11. Effect of Mobile Counter-ions (Peter Debye, 1923) Sommerfeld, Schrödinger, Debye

  12. “Supermolecule” Concept (Without Charge Fluctuations in Shell) The outer radius r is the maximum distance that the ionic charge can exert an effect.

  13. Model of a Supermolecule (With Charge Fluctuations in Shell) The work to inject charge fluctuations into the solvation shell is supplied by the outside world.

  14. Equivalent Circuit of Charge Fluctuations in Shell Two limiting cases… low-screened(electrons only) and high-screened(electrons + nuclei).

  15. Work Needed to Form Charge Fluctuations in Shell Low-screened High-screened (Capacitance values depend on the solution.)

  16. The Reorganization Energy (graphical representation) Low-screened High-screened Marcus theory neglects the work to form fluctuations. It considers only the work to un-screen them.

  17. The Reorganization Energy (mathematical representation)

  18. Conclusions • Marcus theory violates Debye-Hückel theory and gives a divergent formula for l. • The new equivalent circuit model removes these contradictions. [ S. Fletcher, J Solid State Electrochem11, 965–969 (2007) ] • A new theory of electron transfer is now in prospect.

  19. Any Questions?

  20. Postscript: Labelled Axes

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