Marcus theory inner-sphere reorganization

There is a small complication in that the frequency to is different for the reduced and oxidized states so that one has to take an average frequency. Marcus has suggested taking u>av = 2woxu>red/(wox + a>reci)-When several inner-sphere modes are reorganized, one simply sums over the various contributions. The matter becomes complicated if the complex is severely distorted during the reaction, and the two states have different normal coordinates. While the theory can be suitably modified to account for this case, the mathematics are cumbersome. 

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

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]

Mixed-valence Compounds.—Intervalence charge-transfer energies have been measured for the three ions [(bipy)2ClRuXRuCl(bipy)2] + [X=pyrazine, 4,4 -bipy-ridyl, or /ra 5 -l,2-bis-(4-pyridyl)ethylene]. The energies Eop increase with increasing metal-metal distance R as predicted by the Marcus-Hush theory [equations (44) and (45)]. Here Ai, Ao= inner- and outer-sphere reorganization energies, / a=... 

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