Marcus rate equation for

DERIVATION OF HIGH-TEMPERATURE LIMIT MARCUS RATE EQUATION FOR HOMOGENEOUS ELECTRON TRANSFER USING DENSITY-OF-STATES APPROACH 

The high-temperature limit semiclassical Marcus expression for the rate of ET in homogeneous solution, eq. 4.47, and the expressions for the rate of ET at an electrode (eqs. 4.63 and 4.64) were derivedby different approaches, which makes it hard to see that there is a link between them. Here we demonstrate this link by deriving eq. 4.47 using the overlapping density-of-states approach used to derive eqs. 4.63 and 4.64. 

This is identical with the high-temperatnre limit semiclassical equation, eq. 4.47, provided that the reorganisation energy A for the reaction can be taken as equal to (Aa + Ad). Thus this method of derivation is appropriate only for the limiting case that there is no interaction between the solvent spheres of D and A. The method presented in Section 4.5 is more general in that it allows for A (A + A ). 

Adams D. M., Brus L., Chidsey C. E. D., Creager S, Creutz C., Kagan C. R., Kamat P. V., LiebermanM., Lindsay S., Marcus R. A., Metzger R. M., Michel-Beyerle M. E., Miller J. R., Newton M. D., Rolison D. R., Sankey O, Schanze K. S., Yardley J. andZhuX. (2003), Charge transfer on the nanoscale current status , J. Phys. Chem. 5107, 6668-6697. 

Bixon M. and Jortner J. (1982), Quantum effects on electron transfer processes , Faraday Discuss. Chem. Soc. 74, 17-29. 

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