Free energy electron-transfer step

This difference is a measure of the free-energy driving force for the development reaction. If the development mechanism is treated as an electrode reaction such that the developing silver center functions as an electrode, then the electron-transfer step is first order in the concentration of D and first order in the surface area of the developing silver center (280) (Fig. 13). Phenomenologically, the rate of formation of metallic silver is given in equation 17,... 

Describing the dissociative electron transfer step, RX e R + X involves determining the saddle point on the intersection of the two following free energy surfaces.22,31... 

Similar to homogeneous electron-transfer processes, one can consider the observed electrochemical rate constant, k, , to be related to the electrochemical free energy of reorganization for the elementary electron-transfer step, AG, by... 

Fig. 4. Schematic representation of the effect of a change in electrode potential, E, on the free energy—reaction coordinate curves for a heterogeneous single electron transfer step (O + n e - R) at two different electrode potentials (1) E = Ee (solid line) and (2) E

Fig. 15. Plot of the logarithm of the quenching constant vs the free energy change for the electron transfer step according to Eqs. (41), (43) and (45)...

Because the electronic distribution and nuclear configuration of the donor and the acceptor in the (Class II) successor complexes are similar to those of the free donor/acceptor product (i.e. radical pair), it is reasonable to suggest that products can originate directly from the successor complex (pathway Pi). Such a reaction, which includes an electron-transfer step, does not necessarily proceed via a pair of free ion radicals, and the effective activation energy can be even lower than that required by pathway P2. When the follow-up reaction involves the coupling of radicals, the reaction directly proceeding from the (ET) successor complex state can be kinetically favorable (since it excludes diffusional processes). 

Equation (7) expresses an important distinction between the activation free energy for the overall electrochemical reaction in the absence of a net driving force, AG 0, and the intrinsic barrier for the electron-transfer step, AG, t. The former is most directly related to the experimental standard rate constant, whereas the latter is of more fundamental significance from a theoretical standpoint (vide infra). It is therefore desirable to provide reasonable estimates of wp and ws so that the experimental kinetics can be related directly to the energetics of the electron-transfer step. 

The measurement of ket for single electron-transfer reactions is of particular fundamental interest since it provides direct information on the energetics of the elementary electron-transfer step (Sect. 3.1). As for solution reactants, standard rate constants, k t, can be defined as those measured at the standard potential, E, for the adsorbed redox couple. The free energy of activation, AG, at E°a is equal to the intrinsic barrier, AG t, since no correction for work terms is required [contrast eqn. (7) for solution reactants] [3]. Similarly, activation parameters for surface-attached reactants are related directly to the enthalpic and entropic barriers for the elementary electron-transfer step [3],... 

A central preoccupation of electron-transfer models is to provide estimates of the activation free energy of a single electron-transfer step, AG, from the structural and thermodynamic properties of the system [31]. Two key features of these models should be noted at the outset. Firstly, as noted above, it is advantageous to separate AG into intrinsic and thermodynamic components according to [cf. eqn. (6)]... 

Although the foregoing electron-transfer theory is preoccupied with describing the electron-transfer step itself, in order to understand the kinetics of overall reactions it is clearly also important to provide satisfactory models for the effective free energy of forming the precursor and successor states from the bulk reactant and product, wv and ws, respectively. As outlined in Sect. 2.2, it is convenient to describe the influence of the precursor and successor state stabilities upon the overall activation barrier using relations such as... 

Fig. 1. Kinetics and standard free energy changes of electron transfer steps in reaction centers isolated from Rb. sphaeroides. In the chromatophore membrane, a c-type cytochrome (Cyt c,) normally reduces before an electron moves from Qa to Qg. The cytochrome oxidation has a time constant of about 20 fis in Rb. sphaeroides. and 0.5 to 2 p in reaction centers of Rp. viridis and Ch. vinosum, which have bound cytochromes. When the reaction center is excited a second time, Ob" is reduced to...

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