Energy of reorganization

Thus, the energy of reorganization A from Marcus theory is replaced by the sum A + D, and the activation energy is significantly enhanced. 

As demonstrated in Section 2.2, the energy of activation of simple electron transfer reactions is determined by the energy of reorganization of the solvent, which is typically about 0.5-1 eV. Thus, these reactions are typically much faster than bondbreaking reactions, and do not require catalysis by a J-band. However, before considering the catalysis of bond breaking in detail, it is instructive to apply the ideas of the preceding section to simple electron transfer, and see what effects the abandomnent of the wide band approximation has. 

Energies of reorganization are typically of the order of 0.5 - 1.5 eV applied overpotentials are often not higher than 0.1 - 0.2 V. For small overpotentials, when A 2> eo, the quadratic term in the energy of activation may be expanded to first order in eo this gives the following expression for the rate constant of the oxidation reaction ... 

To obtain an estimate for the energy of reorganization of the outer sphere, we start from the Born model, in which the solvation of an ion is viewed as resulting from the Coulomb interaction of the ionic charge with the polarization of the solvent. This polarization contains two contributions one is from the electronic polarizability of the solvent molecules the other is caused by the orientation and distortion of the... 

During the reaction the dielectric displacement changes from Dox to Dred (or vice versa), and the equilibrium value from Dox/2aeo to Drec[/2a eo. From Eq. (6.5) the contribution of the volume element AV to the energy of reorganization of the outer sphere is ... 

The total energy of reorganization of the outer sphere is obtained by integrating over the volume of the solution surrounding the reactant ... 

Calculate the intersection point of these two parabolas and the energy of reorganization. Prove Eqs. (6.6) and (6.7) for this system. 

From Eq. (6.31) calculate the energy of reorganization of a single spherical reactant in the bulk of a solution. Derive Eq. (6.32) for a reactant in front of a metal electrode. 

If the electronic properties of the semiconductor - the Fermi level, the positions of the valence and the conduction band, and the flat-band potential - and those of the redox couple - Fermi level and energy of reorganization - are known, the Gerischer diagram can be constructed, and the overlap of the two distribution functions Wox and Wred with the bands can be calculated. 

We identify Aj = mjUtjAj/2 as the contribution of the mode j to the energy of reorganization [see Eq. (6.5)]. The thermal averaging is simplified by the fact that the expression does not depend on the nuclear momenta, which dropped out when the two Hamilton functions were subtracted. Explicitly we have ... 

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... 

J. Weiss, Proc. Roy. Soc. London A222 128 (1954). First electron transfer theory in terms of electrostatic changes, including energy of reorganization, opt and stat, adiabatic and nonadiabatic theory, and much else. 

Here is the charge number of the reactant a, v labels the phonon modes, which have freqnencies cOy, dimensionless coordinates and momenta Py, and gy is the interaction constant of the reactant charge with the mode v. For a classical solvent the mnlti-dimensional representation given in Eq. (9) can be replaced by an eqnivalent one-dimensional model. Then the interaction between the solvent and the reactant can be characterized by a single energy of reorganization defined as ... 

It was found that in the overall energy of reorganization, there is a significant contribution from the inner-shell component, roughly comparable with the outer-shell reorganization. 

German, E.D. and Kuznetsov, A.M. (1981) Outer sphere energy of reorganization in charge-transfer processes. Electrochimica Acta, 26, 1595-1608. 

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