Electron free energy dependence

We can think of eqn (3.8) as providing the adsorption free energy as a function of the electron chemical potential. To a first approximation, only the electron free energy depends on the electrode potential. Corrections can then be added for the potential variance of the Ga value. To make these values relevant to an experimental system, we need to establish a potential reference that is comparable to the experimental potential reference. A simple thermochemical approach is presented in the following section for establishing a reference potential. We use model numbers consistent with Figure 3.5 in labeling each model presented. 

Sekiguchi S, Kobori Y, Akiyama K and Tero-Kubota S 1998 Marcus free energy dependence of the sign of exchange interactions in radical ion pairs generated by photoinduced electron transfer reactions J. Am. Chem. Soc. 120 1325-6... 

Figure 4 Free energy dependence of electron transfer reaction rate for case A where —X is approximately equal to AGS (or AGp) and case B where —X is closer in energy to AGq.

The reverse transfer affects each quantity in Eq. (3.382) but mainly in the region of resonance (AG,- 0). This is the favorable interval for reverse transfer which manifests itself by the high but narrow peak in the free energy dependence of Q [solid line in Fig. 3.49(a)]. There Q > Kg because it accounts not only for primary, but all subsequent ionization acts as well. These acts follow reverse electron transfer, which occurs much more often within than outside resonant interval. However, for the same reasons the quantum yield of irrevocable electron transfer dashed line in Figure 3.49(c). 

Fig. 9. (A) Free-energy dependence of the second- the formation product (/

The first step of the derivation involves the BO approximation separating the characteristic timescales of the electronic and nuclear motions in the system. In this step, the instantaneous free energy depending on the system nuclear coordinates q is defined by... 

Gunner, M. R., Robertson, D. E., and Dutton, P. L., 1986, Kinetic Studies on the Reaction Center Protein form Rps. Sphaeroides Temperature and Free Energy Dependence of Electron Transfer between various Quinones in the QA site and Oxidized Bacteri-ochlorophyll Dimer J. Phys. Chem. 90 378333795. 

Brooks, H. B., and Davidson, V. L., 1994b, Free energy dependence of the electron transfer reaction between methylamine dehydrogenase and amicyanin. J. Am. Chem. Soc. 116 11201911202. 

Figure 18.8. Free-Energy Dependence of Electron-Transfer Rate. The rate of an electron-transfer reaction at first increases as the driving force for the reaction increases. The rate reaches a maximum and then decreases at very large driving forces.

Figure 5. Free-energy dependence of triplet energy transfer from a biacetyl donor trapped within a hemicarcerand cage to several rigid aromatic acceptors in solution. Note that the curve is much narrower, and that the inverted region is reached at a much lower value of AG° than is typically observed in electron-transfer systems. The oscillations in the calculated line are artifacts of the single high frequency mode approximation (from the work of Deshayes, Piotrowiak, et al. [52]).

Figure 4. Free-energy dependence of return electron transfer for contact ion pairs (A D ) and solvent-separated ion pairs (A SD+) for recombination of dicyanonaphthalene anions with al-kylbenzene cation radicals. Solid lines represent fits to the data with values for V and Aj given. From Gould, I. R. Farid, S. Acc. Chem. Res., 1996, 29, 522, with permission from the American Chemical Society.

The question of the free-energy dependence of heterogeneous electron-transfer reactions at liquid-liquid interfaces was addressed by Bard and coworkers. They ex-... 

A quasi-linear correlation of log/c or AG with the ionization potentials of the electron donors as observed in the FeL3 - + reactions is predicted by Marcus theory for outer-sphere electron transfers. Accordingly, the free-energy dependence of AG can be satisfactorily simulated with the Marcus equation (Eq. 90), taking a (constant) value of A = 41 kcal mol as reorganization energy for all tetraalkyltin compounds (see Figure 19A) [32]. 

There are a number of ways to describe this FC term. An early way of describing the nuclear position and free energy-dependent FC term was proposed in Nobel prize-winning work by Marcus [9, 10]. Marcus approximated the reactant and product, before and after electron transfer, as simple harmonic oscillators with intersecting parabolic potential surfaces. As the driving force of the reaction increases and the product potential surface drops further down in energy, the barrier that must be crossed in going from the bottom of the reactant parabola to the bottom of... 

Figure 1. Electron free energy levels calculated for the approximate pH of the oxic-anoxic interface of the Black Sea (pH 7.75). Dissolved species other than H are assumed to have unit activity. The strongest oxidants are at the top, and the strongest reductants are at the bottom. Such diagrams are a simple way to evaluate the feasibility of redox reactions. For example, ammonia and Mn2+ oxidation by nitrate may be feasible, but the actual free energy available will depend on the in situ concentrations at the site of reaction. All such reactions are, most likely, mediated by bacteria. The vertical separation of the different oxidants from organic matter (CH20) is proportional to the energy available from the different respiration reactions (1).

Progress in the understanding of ES reactions now allows ESs to be so well characterized that quencher exchange rates and potentials are being determined from the free-energy dependence of [ RuL3] + quenching rate constants . Study of ES electron transfer permits a detailed examination of very exothermic reactions and provides a probe of the intimate details of electron transfer. 

Fajardo A. M. and Lewis N. S. (1997), Free-energy dependence of electron-transfer rate constants at Si/liquid interfaces , J. Phys. Chem. B 101, 11136-11151. 

Free-Energy Dependence of Electron Transfer in Cytochrome c Labeled with Ruthenium(II)-Polypyridine Complexes... 

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