Reorganization energy Marcus approximation

Marcus theory. Consider that the reorganization energy for the ET reaction, AAb, can be approximated as the mean of the reorganization energies for the EE reactions Aab = (Aaa + ABb)/2. Show that substitution of this expression into Eq. (10-63) gives the usual form of the Marcus cross relation. 

The flat interface model employed by Marcus does not seem to be in agreement with the rough picture obtained from molecular dynamics simulations [19,21,64-66]. Benjamin examined the main assumptions of work terms [Eq. (19)] and the reorganization energy [Eq. (18)] by MD simulations of the water-DCE junction [8,19]. It was found that the electric field induced by both liquids underestimates the effect of water molecules and overestimates the effect of DCE molecules in the case of the continuum approach. However, the total field as a function of the charge of the reactants is consistent in both analyses. In conclusion, the continuum model remains as a good approximation despite the crude description of the liquid-liquid boundary. 

Marcus theory predicts that the nuclear factor in the electron transfer rate expression will be maximal when - AG° = X. Under these conditions, the electron transfer process will be temperature independent. The first two electron transfer steps in the RC approximately exhibit this behavior. The rate of the D 4>a step actually increases slightly (by a factor of 2-4) as the temperature decreases from 300 to 8 K (180). Consequently, X may be estimated to be in the range 0.3 to 0.5 V (—7-10 kcal/mol) from the A ° values for these two steps (Table IV). These values are approximately 4 times smaller than those observed for ruthenated proteins discussed previously. Sequestration of the redox groups in a membrane-bound protein complex, away from aqueous solution, may serve to decrease the value of X by minimizing the reorganization energy of a highly polar solvent. 

The subscrips in and out introduced here refer to inner- and outer-sphere by analogy with the two reorganization energies of the Marcus theory [equation (4)J. Actually the theory does not assume that high frequencies are associated exclusively with inner-sphere bond vibrations, though this is probably a good approximation. In Jortner s notation vjn and vout are written cos and [Pg.8]

The approximate calculation of the solvent reorganization energy for the charge transfer between spherical reactants was carried out by Marcus [2]. Under the assumption that the distance between the centres of reactants R is much larger than their radii a and b and that the reactants can be described by non-polarizable spheres with the charges strictly and uniformly distributed over their surfaces, the expression for Eg obtained in Ref. [2] has the form... 

There is growing support for the approximations that, in bimolecular electron transfer at least, A can be divided into independent contributions A (A" ), A (B) from the two reactants (c./. an earlier derivation of the Marcus cross relation on this basis), and moreover that A(A ) = A(A) (c/. Ref. 16). Using these assumptions, Frese has calculated reorganization energies for a large number of self-exchange and cross-reactions. In many cases values of A for individual redox couples are consistent from one reaction to another. Of interest are the different values of A for... 

---