An important classification of ET reactions due to H. Taube, is that of inner-sphere and outer-sphere ET reactions: “The distinction between inner-sphere and outer-sphere activated complex... is fundamentally between reactions in which electron transfer takes place from one primary bond system to another (outer-sphere mechanism), and those in which electron transfer takes place within a single primary bond system (inner-sphere mechanism),” from Ref. [45, p. 28].
Using the former nomenclature, we can say that the Marcus theory generally applies to ET reactions with outer-sphere activated complex mechanism. This kind of mechanism operates, for example, for redox reactions both self-exchange and cross-reactions among the complexes in Table 1 of Ref. [44]. Many reactions to which they apply are reported in Ref. [24].
3.18.Atom versus Electron Transfer
“Isotopic exchange reactions may occur by the alternative mechanisms of atom transfer and of electron transfer.” [1, p. 868]. Let us consider for instance the reaction:
In the case of an electron transfer mechanism, an electron would jump from Cr+2 to CrCl+2 and we would directly have the products. In the case of an atom transfer mechanism, a Cl− would transfer from CrCl+2 to Cr+2. The Cr+2–CrCl+2 isotopic exchange reaction has been shown to possess an atom transfer mechanism [46]. “On the other hand reasonable evidence was obtained for a bridge-activated complex electron transfer mechanism for the reduction of
3.19.Three Groups of ET Reactants
M. classifies the reactants “somewhat loosely” in three groups [4, p. 156].
Class I consists of species for which the interatomic distances in the coordination shells of the oxidized and the reduced form are essentially the same.
Class II consists of species in which the bonds of one form are slightly stretched or compressed compared with the other form.
Class III consists of those in which large stretchings or compressions appear.
Examples of Class I:
Examples of Class II: many hydrated metal cations such as
Examples of Class III:
The theory of Marcus in its first formulation applies in general to the “tightly knit covalently bound ions” reactants [3, p. 426] of Class I. The extension of the theory to the consideration of harmonic vibrations in the reactants allows its application to Class II reactants. The theoretical expressions for ΔF* and ΔS*of Class III reactants would contain additional terms beyond those considered in the present form of the theory [4, p. 158].
3.20.Interpretation of the Equations
The former set of equations suggests experimental studies on the dependence of the rate constants, for both chemical and electrochemical ET, from parameters such as:
(i)Standard free energy change or activation overpotential
(ii)Ionic structure and ligand field
(iii)Frequency factor and activation energy
(iv)Added salts
(v)Solvent medium
(vi)Electrode material and surface contamination
It also suggests experiments on:
—The extent of parallelism between both rate constants for a series of reactants
—Correlation between rate constants and between chemical and electrochemical transfer coefficients [4, p. 157].
There is a close relation between the theoretical equations of the chemical and electrochemical processes. In each case, ΔF* decreases with increasing a, decreasing ne, decreasing R, increasing Dop, decreasing Ds (the latter’s effect is perhaps more important on wr and wp), and increasingly negative ΔF0 or −neηa. The physical interpretation of this behavior is simple and related to the ease with which the energy restriction can be satisfied [1, 2]. “For example, ion–solvent interactions decrease with increasing ionic radius a, so that there would be a smaller energy difference between the two hypothetical charge distributions in the original atomic configuration of the reactants and therefore a smaller reorganization energy would be needed to equalize the two energies” [4, p. 158].
“Similarly, the smaller the charge transferred ne, or the smaller the distance between the reactants (or between the ion and its electrostatic image in the electrode), the less the medium can discriminate energywise” between initial and final charge distributions “and therefore the lesser will be the reorganization needed for energy equalization. A larger optical dielectric constant, Dop, serves to partially neutralize the electrostatic fields of the charges and therefore to reduce their energy difference for a given atomic configuration. The more Ds approaches Dop, the smaller the dipolar contribution to the electrical polarization of the medium and the less the necessary rearrangement of the atoms (at least for zero ΔF0 or zero ηa).” [4, p. 158]
From Eqs. (3.18) and (3.34), we see that the effective driving force of the reaction is not just given by the free energy difference (ΔF0 or −neηa) between reactants and products when the reacting species are far apart but rather when they are in the positions they occupy in the activated complex. By lowering the free energy of the final state of the system relative to that of the initial state, these terms reduce the amount of reorganization of atomic configuration of the initial state necessary to satisfy the energy restriction [1].
We have seen that λ in Eqs. (3.17) and (3.18) has become λ/2 in Eqs. (3.33) and (3.34)