Electron transfer reactions in coordination metal complexes. Structure-reactivity relationships Sebastitio J. Formosinho Departamento de Qui'mica, Universidade de Coimbra, 3049 Coimbra, Portugal Abstract - The current approach of Marcus theory to interpret electron transfer is questioned. Another approach based on an expansion of configuration of the transition states is presented, and the rates are estimated in terms of the following parameters: reaction energy, force constants, equilibrium bond lengths, transition state bond order and capacity to store energy. The model can interpret several anomalous features of these reactions, namely electron-exchanges where the Marcus theory estimates rates several orders of magnitude slower and faster than experiment, "cross-relations", solvent effects, the inverted region and the asymmetry of the Tafel plots of metal-aquo ions, and can assess the nonadiabatic character of some outer-sphere processes. Electron transfer reactions play an essential role in many physical, chemical and biological processes. The investigation of the mechanisms of these reactions rests essentially on the systematic investigation of structure-reactivity relationships that results from the geometric rearrangements which accompany the change in oxidation states of the coordination compounds. Although many theories have been proposed, it is no surprise that the more simpler ones such as Marcus theory are the most popular.1 In spite of the great success of the theory of Marcus in interpreting several of these structure-reactivity relations namely in terms of the reaction energy (AG), changes in equilibrium bond lengths (lred-lox) and metal-ligand force constants (fox and fred), several problems remain. ANOMALOUS FEATURES OF ELECTRON TRANSFERS Marcus theory and related approaches emphasize the importance of the reaction energy barrier of the solvent reorganization around the coordination compounds upon the gain or loss of an e1ectron.l This outer-shell contribution is considered often to be larger than the inner-shell contribution due to the changes in geometry within the coordination shell (first-shell for a solvated metal ion). The recent findings of Nelson et a1.2 on the electron transfer reactions of several a1 kyl hydrazinesO/' which have the same energy barrier in the vapour phase and in solution therefore comes as a surprise. Although these results reveal the importance of the changes in geometry of the different oxidation states of the alkylhydrazines, they reveal also that the outer-shell reorganization is negligible. For example, the estimation of the solvent reorganizatiqn ascording to the theory of Marcus (eq(1)) where y is the solvent polarity parameter (y=(nr -E- ) with tIr the refractive index, E the dielectric constant), pnd r the distance between the centers of the two solvated reactant species, leads to AGout = 9kJ mol-1 in acetonitrile3, which implies electron transfer rates ca. 2x10-2 times slower in solution, contrary to the experimental findings.2 The outer-shell contribution of eq (1) had been previously criticized by several authors: the self-exchange processes for ferrocenium-ferroceng in a variety of solvents, from methanol to dimethylsulfoxide, vary only by a factor of 2 whereas eq (1) predicts a ca. 20 - fold ~ariation;~ self-exchange rates of hydrazine do not follow eq (1) at all, because there is a modest increase in the rates with decreasing E, an order of magnitude smaller than predicted by the theory of Marc~s.~ In contrast, the metallocene self-exchange reactions6 are ca. lo4 times faster in the vapour phase than in solution, a variation too large (ca. 2 o de s of ma ni ude) to be easily interpreted by eq (1). The theory of Marcus considers C0fa4f '+ and Fe 8.65 ' ' as anomalous ion pairs1, because the measured self-exchange rates are about and lo3 times faster than t$ose calculated. In contrast, according to Marcus theory calculated the rates for Fe(phen)$+/ + are ca. lo5 times faster than e~periment.~ Disagreements of the same magnitude have also been found for the intramolecular electron exchanges of 1,3-di cyanobenzene radical anion .3 Marcus8 predicted that very exothermic electron transfer reactions should show an inverted effect on the reaction rates. A few cases9 reveal this effect clearly, but the majority of reactions do not conform with this theory in the inverted region. In consequence several classical 89 1 0 892 S. J. FORMOSINHO and dynamical models have been proposed to interpret the variety of energy-gap laws observed for these reactions.10 Hupp and Weaver11 have reported the existence of strong anodic/cathodic asymmetries on the Tafel plots for metal-aquo redox couples which cannot be interpreted within the framework of the theory of Marcus. The discrepancy amounts typically to calculated rates ca. 102 times faster in the anodic region. The "cross-reaction relations" used to calculate electron transfer rates is possibly the most widely used and tested equation in electron transfer theory.1 In spite of its sucess there are cases where disagreements of many orders of magnitude exist. l2 In view of these "anomalous" features it seems worth exploring alternative theoretical procedures to interpret these reactions. Since the electrical forces decrease with increasing distance from the metal ion, we will admit that the geometric rearrangements which acompany the loss or gain of an electron are large in the coordination shell, but can be neglected for the outer-shell. The inner-shell reorganization barrier from Marcus theory (eq.(2)) $oes not follow this hypqthesis. For example, if lox'lred and foxffred eq (2) leads to AGin'O even though higher AGout contributions can be calculated and a change in the force constants require a reorganization of the coordination shell. Eq (2) implies a transition state bond length intermediate between those of the oxidized and reduced species, lo.x<1*lox,lr d. This geometric arrangement agrees with the requirements of potential energy surfaces fLEPS surfaces), but does not follow the principle of least nuclear motion implicitly assumed by Marcus theory.3

Electron Transfer Reactions
Outer Sphere Electron Transfer
Electron transfer reactions may occur by either of both of two mechanisms: outer or inner sphere mechanisms. In principle all outer sphere mechanism involves electron transfer from reductant to oxidant with the coordination shells or spheres of each staying intact. That is one reactant becomes involved in the outer or second coordination sphere of the other reactant and an electron flows from the reductant to oxidant. Such a mechanism is established when rapid electron transfer occurs between two substitution-inert complexes.

Inner Sphere Electron Transfer
An inner sphere mechanism is one in which the reactant and oxidant share a ligand in their inner or primary coordination spheres the electron being transferred across a bridging group.