Redox properties free energy

Whilst this Chapter is primarily concerned with the methods of determining the free energies of tautomeric or ionisation equilibria via computer simulation of free energy differences, many of the issues raised relate also to the determination of other molecular properties upon which behaviour of the molecule within the body may depend, such as the redox potential or the partition coefficient.6 In the next section, we shall give a brief explanation of the methods used to calculate these free energy differences -namely the use of a thermodynamic cycle in conjunction with ab initio and free energy perturbation (FEP) methods. This enables an explicit representation of the solvent environment to be used. In depth descriptions of the various simulation protocols, or the accuracy limiting factors of the simulations and methods of validation, have not been included. These are... 

Hence, the Pi ligand parameter reflects, in an overall way, the combined a- and Tt -electronic properties of the coordination M—L bond. It is noteworthy to mention that it relates to the variation of the free-energy difference of the redox processes (consider the known expression AG = —nFE, in which n is the number of electrons transferred and F is the Faraday constant). It has analogies with the Hammett Up constant [11, 12] defined as og[Kx/Kh), that is, log Kx - log K, in which Kx and ATh are the acidic constants of the p-substituted benzoic acid HOOCCg H4X-4 and of benzoic acid itself, respectively [13] (consider also the known relationship AG = —RT nK). 

Since we have pointed out that an excited molecule D can either be oxidized or reduced, we have to consider also for the unexcited dye molecule D two redox potentials, one, ° (d/d+) for oxidation, the other, ° (d/d-> for reduction. For a better understanding we want to relate the redox potential for both reactions to molecular properties in the gas phase and in the electrolyte. The following scheme gives the cycles from which free energy correlations can be derived for the two reactions ... 

Returning to ionic solvation free energies, such quantifies play important roles in the computation of two common properties of interest, namely values and relative redox... 

We now see that mitochondria contain a variety of molecules—cytochromes, flavins, ubiquinone, and iron-sulfur proteins—all of which can act as electron carriers. To discuss how these carriers cooperate to transport electrons from reduced substrates to 02, it is useful to have a measure of each molecule s tendency to release or accept electrons. The standard redox potential, E°, provides such a measure. Redox potentials are thermodynamic properties that depend on the differences in free energy between the oxidized and reduced forms of a molecule. Like the electric potentials that govern electron flow from one pole of a battery to another, E° values are specified in volts. Because electron-transfer reactions frequently involve protons also, an additional symbol is used to indicate that an E° value applies to a particular pH thus, E° refers to an E° at pH 7. 

It is well known that redox properties of oxides can be modified by the formation of mixed oxides (12). Effect of mixed oxide formation on AG° of M-0 dissociation is illustrated in Figure 1. The free energy changes of the following reactions, AGA° and AGp°, are calculated from thermodynamic data (13, 14). 

In Fig. 7 we have taken a symmetrical reaction where, apart from the isotopic mixing, AG ° = 0. One of the first successes of the Marcus theory was the correlation of rates for such homogeneous reactions with the rates found for the same electron transfer taking place on an electrode (Marcus, 1963). The theory then went on to predict the rates of cross reactions between two different redox couples in terms of the kinetic and thermodynamic properties of the two redox couples. The free energy profile for an unsymmetrical cross reaction such as (17) is shown in Fig. 8. The free energy of activation depends... 

Upon electronic excitation the redox properties of either the electron donor (D) or the acceptor (A) are enhanced. The feasibility of an electron transfer can be estimated from a simple free reaction energy consideration as customary in the frame of the Rehm-Weller approach (Eq. (1)) [11], where Efy2 (P) and 4) represent the oxidation and reduction potential of the donor or the acceptor, respectively. AEexcit stands for the electronic excitation energy, whereas Aiscoui indicates the coulombic interaction energy of the products formed (most commonly radical ions). This simplified approach allows a first approximation on the feasibility of a PET process without considering the more complex kinetics as controlled by the Marcus theory [6c]. For exergonic processes (AG<0) a PET process becomes thermodynamically favorable. 

The importance of Eq. 27 is that it relates Popt, which can be experimentally determined from tbe redox and photophysical properties of the donor and acceptor chromophores, to that is for a preset interchromophore separation, R the redox and photophysical properties of the chromophores must be chosen so that they give a value of Popt which is identical to that calculated from Eq. 28. Conversely, for a given pair of chromophores, there is a unique value of Rc for which the free energy of activation for photoinduced charge separation in the dyad is largely solvent-independent. 

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