Reorganization energy of the medium

The problem of the physical meaning of the quantity Hx and of the reorganization energy of the medium Es has been analyzed in Ref. 11. Following Ref. 11, we write the expression for the transition probability per unit time in the form3... 

Multivalent Mn ions induce dielectric saturation effects in the polar region of the reaction center of PS II, which reduces the reorganization energy of the medium during charge transfer. 

Marcus theory [69] predicts that the rate of non-adiabatic electron transfer with weak exergonicity shows a bell-shaped behavior with respect to the free energy difference (-AG) between electron donor and acceptor giving a maximum rate when AG equals the reorganization energy of the medium. Extensive studies have been published especially on intramolecular electron transfer in this regard, and we shall not review this work here. Instead, this section will review intermolecular electron transfer between a photoexcited redox molecule and the ground state one incorporated in a polymer. 

Thus, in this case F(0 ) represents the change in the free energy of the medium due to the application of the electric field 0 AEt (r). The absolute value of F(0 ) is equal to the energy of the reorganization of the medium when the inertial polarization is changed by the value AP (r) = 0 AP(r) ... 

In reactions of outer-sphere electron transfer between the ions in polar liquids, the main role is played by the low-frequency polarization vibrations with typical energies much smaller than KgT. In the case of classical nuclear motions the medium reorganization energy is the sum of reorganization energies of the set of normal classical oscillators (hco < Kg T) formed by shifts similar to the one shown in Figure 2 ... 

Here 2 is the Einstein frequency, is the energy of the medium reorganization, I It,n is ihe Bessel function of imaginary argument, and pj- is the final-state density. 

The vertical ionization energy and electron affinity of a spherical particle are related to the corresponding adiabatic values by the reorganization energy of the surrounding medium, Aout " ... 

The subscrips in and out introduced here refer to inner- and outer-sphere by analogy with the two reorganization energies of the Marcus theory [equation (4)J. Actually the theory does not assume that high frequencies are associated exclusively with inner-sphere bond vibrations, though this is probably a good approximation. In Jortner s notation vjn and vout are written cos and [Pg.8]

The Xc, in (115) describes the reorganization energy of the dielectric medium (the solvent and, in the semiconductor electrode case, also the solid). The A,- in (115) arises from the change in equiUbrium values of vibrational coordinates of the reactants, including, in the semicOTiductor case, any of its relevant vibrational coordinates. For example, if the reactant(s) undergoes a change Aqr, in the equilibrium value of some collective coordinate, a normal coordinate of a reactant, and if kf and kf are the force constants of that normal mode for the reactant and for the product, respectively, then classically [184]... 

The quantity Ef is the energy of the reorganization of all the classical degrees of freedom of the local vibrations and of the classical part of the medium polarization, and crc is the tunneling factor for quantum degrees of freedom 1) which do not... 

Another important result that was obtained recently concerns the evaluation of the contribution to the reorganization energy arising from the polarization of the medium, protein and solvent from a microscopic model including the residual charges and induced dipoles of the protein as well as bound water molecules, a value of about 0.2 eV was calculated for different eleetron transfer processes [97], This weak value results from the apolar character of the medium, and is compatible with the kinetic data which indicate that reorganization energies are small in the reaction center (Sect. 3.2.2)... 

It is commonly assumed, therefore, that solvent reorganization will dominate electron transfer kinetics and that the reorganization energy in the same medium will be constant within a series of closely related redox partners. With a value of 2.4 kcal/mole for solvent reorganization (as obtained by Rehm and Weller (7) for fluorescence quenching of a series of arenes by substituted anilines in a polar medium) the curve shown in Fig. 2 is obtained. It is clear that substantial solvent-dependent barrier to electron exchange can be encountered. 

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