Electron transfer rate constants, function

In summary, to apply the Marcus theory of electron transfer, it is necessary to see if the temperature dependence of the electron transfer rate constant can be described by a function of the Arrhenius form. When this is valid, one can then determine the activation energy AEa only under this condition can we use AEa to determine if the parabolic dependence on AG/ is valid and if the reaction coordinate is defined. 

Fig. 1. The Marcus parabolic free energy surfaces corresponding to the reactant electronic state of the system (DA) and to the product electronic state of the system (D A ) cross (become resonant) at the transition state. The curves which cross are computed with zero electronic tunneling interaction and are known as the diabatic curves, and include the Born-Oppenheimer potential energy of the molecular system plus the environmental polarization free energy as a function of the reaction coordinate. Due to the finite electronic coupling between the reactant and charge separated states, a fraction k l of the molecular systems passing through the transition state region will cross over onto the product surface this electronically controlled fraction k l thus enters directly as a factor into the electron transfer rate constant...

The expression for ket in equation (29) is still not a complete expression for the total electron transfer rate constant. Both the electronic coupling term V and A0 are dependent upon the interreactant separation distance r, and, therefore, so is ktt in equation (29). The dependence of /.0 on r is shown in equation (23) in the dielectric continuum limit. The magnitude of V depends upon the extent of donor-acceptor electronic orbital overlap (equation 17) and the electronic wave-functions fall off exponentially from the centers of the reactants. In order to make comparisons between ktt and experimental values of electron transfer rate constants, it is necessary to include the dependence of ktt on r as discussed in a later section. 

Assuming that FCWDel is distance independent, the electron-transfer rate constants are also expected to decay exponentially as a function of distance 1... 

Thus, from fluorescence lifetime and transient absorption measurements we gathered the electron-transfer rate constants, i.e. both for charge-separation and for charge-recombination. Next, we plotted these rate constants as a function of donor-acceptor distance. From the resulting linear dependence (Fig. 9.26) it is possible to determine the attenuation factors p for the presented donor-acceptor... 

Intramolecular electron transfer rate constants k (s-1) as a function of the free energy difference for the reaction Biphenyl( )-androstane-/4 —> Biphenyl-androstane-v4( ), estimated from the electrochemical reduction potentials in 2-methyltetra-hydrofuran the inverted region for electron transfer rates is prominent. Redrawn from Miller et al. [10]. 

The subscript c and superscript + of j indicate that the current is generated via the conduction band and is an anodic current. k0 is the electron-transfer rate constant. p(E) is the distribution of energy states in the semiconductor. f(E) is the Fermi energy distribution function as given in... 

Improta et studied large molecules with a well-separated electron donor and electron acceptor pair. In this case, the electron-transfer process may lead to a dissociation of the molecule. Improta et al. applied the Marcus theory to obtain an expression for the electron transfer rate constant. Subsequently, the values of the parameters entering this expression were calculated using a density-functional approach for the solute together with the polarizable continuum model for the solvent. They applied their approach for a specific system (for the present purpose, the details are less important) and found the results of Table 24. Here, three different... 

The electronic coupling of the reactant state with the product state, F, is a function of the overlap of the donor and acceptor orbitals. This in turn depends on energetic, spatial, geometric, and symmetry factors. At relatively large donor acceptor separations, it can be assumed that the relevant orbitals decay exponentially with distance. In these cases, the electron transfer rate constant will depend on this separation as per Eq. 2, where Rda is the donor-acceptor separation and y is a constant that expresses the sensitivity of the... 

The cyclodextrin-sandwiched porphyrin 18 of Kuroda [98] effectively recognizes hydrophobic quinones in water, with association constants ranging from A a = 7.4 X 10 M for 1,4-naphthoquinone to Ka > 5 x 10 M for an adamantyl-functionalized benzoquinone. In contrast, the association of p-benzoquinone is negligible. Molecular modeling predicts that the quinone approaches the porphyrin from an out-of-plane direction. Time-resolved fluorescence measurements give an estimate of the intramolecular electron transfer rate constant on the order of 10 s for all quinones studied. 

For the TMDAB, the logarithm of the electron transfer rate constant In ket is clearly a linear function of the Pekar factor yp (fig. 7.22). On the other hand, a plot of In ket against In xp for the same data yields a weak linear correlation with a positive slope (fig. 7.23). This correlation is the opposite to that expected in other words, the rate constant should decrease with increase in xp if the reactions were adiabatic. The estimate of A G((, for this reaction is 6.4kJmol the value of A Gos depends on the nature of the solvent but it is close to in most solvents considered. The reason that the reaction is diabatic is clearly due to the weak... 

Figure 6 Electron transfer rate constants as a function of free-energy change, AG, by radical anions for intermolecular ET in rigid 2-MTHF glass (top) (17), and intramolecular ET in 2-MTHF fluid at room temperature (bottom) (18), in molecules of the form ASB, where B = biphenyl, S = 3,16-androstane, and A is one of eight acceptor molecules shown. In both parts of the figure, the rate vs. AG ° curves are of equation 1 and have identical parameters except for the temperature and solvent reorganization energy.

First-order electron-transfer rate constant k > in acetonitrile as a function of the donor-acceptor distance R for a variety of the free energy change A O. 

In studies of molecular charge transfer systems a transient method is generally used to determine an electron transfer rate constant from the variation of the concentration of a reactant or product as a function of time. By contrast, in characterizing charge transfer processes in electrochemical cells or at metal-molecule- metal junctions the parameter of interest is usually the resistance or conductance (reciprocal of resistance) of the cell or junction. The conductance of the cell or junction is generally determined from the variation of the current through the system as a function of applied voltage. Here we briefly consider the relationship between electron transfer rate constants and conductances. 

Fig. 9. The observed forward electron transfer rate constant k B os a function of pH for native (Rb. sphaeroides R-26 or 2.4.1) and mutant (EQ212) RCs. Native RCs show a decrease in k s above pH 9.5. The kinetics in mutant RCs are approx. pH independent. Modified from ref 13.

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