Electron transfer cross relationship

Fig. 10. Expected relationship, according to Eq. (28), between the rate constant of the electron transfer steps and the reduction potential of the oxidant for a cross reaction of the type of reaction (24). The reorganizational parameter is given by Eq. (29)...

Thus the Marcus theory gives rise to a free energy relationship of a type similar to those commonly used in physical organic chemistry. It can be transformed into other relationships (see below) which can easily be subjected to experimental tests. Foremost among these are the remarkably simple relationships that were developed (Marcus, 1963) for what have been denoted cross reactions. All non-bonded electron-transfer processes between two different species can actually be formulated as cross reactions of two self-exchange reactions. Thus the cross reaction of (59) and (60) is (61), and, neglecting a small electrostatic effect, the relationship between kn, k22 and kl2... 

By using cyclic voltammetry, Schiffrin and coworkers [26, 186, 187, 189] studied electron transfer across the water-1,2-dichloroethane interface between the redox couple FefCNls /Fe(CN)6 in water, and lutetium(III) [186] and tin(IV) [26, 187] diphthalocyanines and bis(pyridine)-me50-tetraphenylporphyrinato-iron(II) or ru-thenium(III) [189] in the organic solvent. An essential advantage of these systems is that none of the reactants or products can cross the interface and interfere with the electron transfer reaction, which could be clearly demonstrated. Owing to a much higher concentration of the aqueous redox couple, the pseudo-first order electron transfer reactions could be analyzed with the help of the Nicholson-Shain theory. However, though they have all appeared to be quasireversible, kinetic analysis was restricted to an evaluation of the apparent standard rate constant o. which was found to be of the order of 10 cm s [186, 189]. Marcus [199] has derived a relationship between the pseudo-first-order rate constant for the reaction (8) and the rate... 

The operative interest of such a cross-relationship is extreme, since when associated with Eqs. (78) through (80) it allows an a priori estimation of the rate constant of any outer sphere electron transfer reaction provided the corresponding standard reduction potentials and isotopic rate constants are known. Yet a caveat in this approach is the necessity that /c = 1 for all reactions, that is, that there is always sufficient overlap between the orbitals [62]. 

The He(l) photoelectron spectrum shows the first ionization potential at 9.4 eV assigned to the Ge-C (t2) orbital a broad envelope of ionizations follows between 11.5 and 13.5 eV as represented by a figure comparing Ge(C2H5)4 with Ge(C2H5)nH4 n compounds [26]. A linear relationship has been found between the total ionization cross-section and the metal polarizability for M(C2H5)4 compounds where M = Si, Ge, Sn, and Pb [20]. For various MR4 compounds (M = Ge, Sn, and Pb) a relationship also exists between the first ionization potential and the rate of homogeneous electron transfer to an oxidant [27]. 

Potential energy diagram for a cross-electron transfer reaction, showing the relationships between A6°, and AG. ... 

Electrochemical measurements of the Cu(II/I) potentials with the nS4 ligands (n = 12-16) indicate that the Cu(II) and Cu(I) species each exist in two different conformational states [170]. Conformational rearrangement may either precede or succeed electron transfer. Rorabacher and coworkers interpreted their results in light of a square mechanistic scheme that neatly reconciles the sweep rate dependence of the cyclic voltammograms with the requisite change in coordination geometry at Cu. Kinetic studies on the electron transfer [149, 170, 176-177] support this scheme application of the Marcus cross relationship to reduction of Cu(II) and oxidation of Cu(I) yields widely discrepant values, presumably because of the different conformational states involved. 

The kinetics of several electron transfer reactions of the molybdenum cuboidal system [Mo4S4(edta)2]" ( = 2, 3, 4) with cross-reactants such as [Co(edta)]-, [Fe(edta)]-, [Co(dipic)2] , [Fe(H20)e], and [Pta ] -, have been investigated. The electron self-exchange rate constants determined for the [Mo4S4(edta)2] and [Mo4S4(edta)2] couples, by an application of the Marcus relationship, are 1.5 x 10 and 7.7 x 10 M s , respectively. The rate constants for the outer-sphere oxidation of two dimeric complexes, [MoW 0)2(p-edta-AT,lV )]2- and [W2(0)2(p-0)(p-S)(p-edta-Ar,iV )] -, by [IrCl ] in addic aqueous solution have been measured. While the oxidation of the former complex shows a simple second-order rate law, the kinetics of the oxidation of the latter complex exhibited a rate retardation in the presence of the [IrCl6] complex. 

---