Adiabatic outer-sphere electron transfer

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

Fig. 1 Potential energy surfaces in adiabatic outer sphere electron transfer.

The rates of electron transfer reactions can be well predicted provided that the electron transfer is a type of adiabatic outer-sphere reaction and the free energy change of electron transfer and the reorganization energy (A) associated with the electron transfer are known [5-9], In other words, in an adiabatic outer-sphere electron transfer reaction, the rate of electron transfer is automatically determined once the pair of reactants is fixed. Moreover, the rate of reversible electron transfer, which should be exergonic and thereby thermodynamically favorable, is usually very fast, since the endergonic electron transfer, which would be slow, results in no net electron transfer because of facile back electron transfer. Thus, there would seem to be no need of a catalyst to accelerate further the electron transfer reaction, which is already fast enough. 

Adiabatic Outer-Sphere Electron Transfer Through the Metal-Electrolyte Interface. 

In the absence of ion pairing and rate limitation by solvent dynamics, the volume of activation for adiabatic outer-sphere electron transfer in couples of the type j (z+i)+/z ju principle, be calculated as in equation 2 from an adaptation of Marcus-Hush theory. In equation 2, the subscripts refer respectively to volume contributions from internal (primarily M-L bond length) and solvent reorganization that are prerequisites for electron transfer, medium (Debye-Huckel) effects, the Coulombic work of bringing the reactants together, and the formation of the precursor complex. 

The most important theoretical ideas concerning adiabatic outer sphere electron transfer reactions in solution are summarized. The kinetics of the reduction of a series of different tris-1,10,-phenanthroline complexes of Fe(III) by Fe(CN) were measured in order to test the influence of the redox-potential on these reactions. The lectron exchange rate of the complexes Fe(dipy), Ru(dipy) and 0 (dipy) was derived from the study of their reduction by Fe(CN). Using the edox reaction between the anionic complexes of Fe(CN) and the effect of added... 

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. 

In typical outer sphere electron transfer on metal electrodes, A is in the weakly adiabatic region and thus sufficiently large to ensure adiabaticity, but too small to lead to a noticeable reduction of the activation energy. In this case, the rate is determined by solvent reorganization, and is independent of the nature of the metal [Iwasita et al., 1985 Santos et al., 1986]. 

Unlike the simplest outer-sphere electron transfer reactions where the electrons are the only quantum subsystem and only two types of transitions are possible (adiabatic and nonadiabatic ones), the situation for proton transfer reactions is more complicated. Three types of transitions may be considered here5 ... 

Fe3+X6...Fe2+X6, which is the reactant of the outer-sphere electron transfer reaction mentioned above when X = Y. Clearly the ground state involves a symmetric linear combination of a state with the electron on the right (as written) and one with the electron on the left. Thus we could create the localized states by using the SCRF method to calculate the symmetric and antisymmetric stationary states and taking plus and minus linear combinations. This is reasonable but does not take account of the fact that the orbitals for non-transferred electrons should be optimized for the case where the transferred electron is localized (in contrast to which, the SCRF orbitals are all optimized for the delocalized adiabatic structure). The role of solvent-induced charge localization has also been studied for ionic dissociation reactions [109],... 

An important conclusion that can be drawn from the above discussion is that most outer-sphere electron transfer reactions of metal complexes are, at best, marginally adiabatic and that the reaction will rapidly become nonadiabatic with increasing separation of the reactants. In view of these considerations, eq 11 can be integrated to give (50)... 

In contrast to the experimentally based work discussed above, in the most recent comprehensive theoretical discussion [21d], Bixon and Jortner state that the question of whether non-adiabatic or adiabatic algorithms describe electron-transfer reactions was settled in the 1960s, and that the majority of outer-sphere electron-transfer reactions are non-adiabatic. This is certainly true for the reactions that occur in the Marcus inverted region in which these authors are interested, but we think the question of whether reactions in the normal region are best treated by adiabatic theory that includes an electronic transmission coefficient or by non-adiabatic equations remains to be established. 

Hush N. S. (1961), Adiabatic theory of outer sphere electron transfer at electrodes , J. Chem. Soc. Faraday Trans. 57, 557-580. 

In summary, the key predictions of Eqs (5.5)-(5.8) are (1) that AVj is usually the dominant part of and (2) that AV (and hence AV ) will be negative for simple outer-sphere electron transfer reactions in solution, regardless of whether electron transfer is fully adiabatic - with the caveat that predictions of the magnitude of are unlikely to be reliable for solvents of low e. 

For outer-sphere electron transfer, the rate equations (62.IV) and (63.IV) for non-adiabatic and adiabatic reactions may be used by introducing the electrode potential cp through the relation (107.IV) or the overvoltage through equation (114.IV), instead of the reaction heat Q. For inner-sphere redox reactions the expressions (83 IV) and (85.IV) can be used in a similar way for electronically non-adiabatic and adiabatic reactions, respectively. The conditions of validity of the Tafel equation are then given by ( 12.IV) or (116.IV). 

Outer-sphere reactions are also considered. For the hypothetical reaction [Cr i Clsl +ECr Cls] ", it is suggested that the inclusion of a Na+ ion in the transition state is sufficient to transform the reaction from non-adiabatic to adiabatic, and that the overall effects of counterions on such reactions are too great to be regarded as mere electrostatic stabilization of the encounter complex. Less credible is the conclusion that water molecules themselves can act as effective catalysts for outer-sphere electron transfer, a single water molecule between the reacting complexes leading to a resonance energy increase of 6 kcal mol . 

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