Electron self-exchange reactions Marcus cross relation

Electron self-exchange reaction between O2 and 02 was then discussed, and developments before and after an experimentally determined rate constant for this reaction was published, were also summarized. Related to this, the problem of size differences between O2 or 02 and their typical metal-complex electron donors or acceptors was recently solved quantitatively by addition of a single experimentally accessible parameter, A, which corrected the outer-sphere reorganization energy used in the Marcus cross relation. When this was done, it was found that rate constants for one electron oxidations of the superoxide radical anion, 02 , by typical outer-sphere oxidants are successfiiUy described by the Marcus model for adiabatic outer-sphere electron transfer. 

It was recently shown (Ratner and Levine, 1980) that the Marcus cross-relation (62) can be derived rigorously for the case that / = 1 by a thermodynamic treatment without postulating any microscopic model of the activation process. The only assumptions made were (1) the activation process for each species is independent of its reaction partner, and (2) the activated states of the participating species (A, [A-], B and [B ]+) are the same for the self-exchange reactions and for the cross reaction. Note that the following assumptions need not be made (3) applicability of the Franck-Condon principle, (4) validity of the transition-state theory, (5) parabolic potential energy curves, (6) solvent as a dielectric continuum and (7) electron transfer is... 

Rate constants for outer-sphere electron transfer reactions that involve net changes in Gibbs free energy can be calculated using the Marcus cross-relation (Equations 1.24—1.26). It is referred to as a cross-relation because it is derived from expressions for two different self-exchange reactions. 

Both involve high-pressure electrochemistry. One is the measurement of the pressure dependence of the rate constant for electron transfer in a given couple at an electrode, but it is not immediately clear how feg] and the corresponding volume of activation relate to feex and AV, respectively, for the self-exchange reaction of the same couple. This is a major theme of this chapter, and is pursued in detail below. The other method involves invocation of the cross relation of Marcus [5], which expresses the rate constant ku for the oxidation of, say, A by B+ in terms of its equilibrium constant and the rate constants kn and fe22 for the respective A+/A and B+/B self-exchange reactions ... 

Test of the Marcus cross-relation for protein-protein reactions [37]. Some electron-transfer reactions between two metallic redox centres in different proteins can be examined to see how closely they follow the Marcus cross-relation (Section 9.2.2.2). This is possible in systems where the self-exchange rates can be determined by nmr or epr, i.e., where the metal ions are such that line-broadening techniques can be applied. (Such a test is not available for most of the donor-acceptor systems discussed above.) Some results are shown in Table 9.6. The observed and calculated values for the six reactions are seen to agree within... 

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... 

The reactions of SO2 with [Cr(NN)3] (NN = bpy, phen, and derivatives) when subjected to visible light (laser pulse) are threefold. " Quenching yields [Cr(NN)3] which undergoes back electron transfer. The predominant reaction is electron transfer between SO2 and [Cr(NN)3] yielding the transient SO2. The rate constants obtained may be utilized in a Marcus cross-correlation relation to calculate a self-exchange rate of between 1 x 10" M s and 18 x 10" s for... 

The title paper was enormously important by itself, but in addition it was the first step (and the cornerstone) in a long series of papers on electron-transfer reactions which were published by Marcus from 1956 to 1965. During those years he extended [3, 4] the theory to include, for instance, intramolecular vibrational effects, numerically calculated rates of self-exchange and cross reactions, electrochemical electron-transfer reactions (i.e. including electrodes), chemiluminescent electron transfers, the relation between nonequilibrium and... 

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