Reorganization Parameters

Fig. 14. Dependence of the quantity (fito/gy l V )k where k is the rate constant for spin conversion on halkgT as calculated from the single-mode approximation Eq. (79) solid lines) and the full expression Eq. (77) for the value q = 0.3 of the solvent reorganization parameter dashed lines). Data are given for p = — 2.0, 0, -I- 2.0 and for the value of the coupling parameter S = 15. According to Ref. [117]...

Comparison between Experimental Reorganization Parameters for some Electrochemical and Homogeneous Exchange Reactions... 

Comparison of the corresponding electrochemical and homogeneous reorganization parameters reveal that 2A( e > AG ... 

Plots of the Ru(His33)Zncyt c, Ru(His39)Zncyt c, and the Ru(His62)Zncyt c data are shown in Fig. 7. Although the reorganization parameter X is nearly the same for the ET reactions in the three proteins ( 1.2 eV), the H g value... 

Rather than employ eqn. (16), values of AG for electrochemical reactions can therefore be obtained more appropriately from the intersection point of the individual free-energy curves for the oxidized and reduced forms [37]. The individual curves can be defined conveniently in terms of "reorganization parameters , Af and Ar, for the forward and reverse reactions [cf. eqn. (16)]... 

This chapter concerns the energetics of charge-transfer (CT) reactions. We will not discuss subjects dealing with nuclear dynamical effects on CT kinetics. " The more specialized topic of employing the liquid-state theories to calculate the solvation component of the reorganization parameters is not considered here. We concentrate instead on the general procedure of the statistical mechanical analysis of the activation barrier to CT, as well as on its connection to optical spectroscopy. Since the very beginning of ET research, steady-state optical spectroscopy has been the major source of reliable information about the activation barrier and preexponential factor for the ET rate. The main focus in this chapter is therefore on the connection between the statistical analysis of the reaction activation barrier to the steady-state optical band shape. 

There is an additional, more fundamental, issue involved in applying the standard diabatic formalism. The solvent reorganization energy and the solvent component of the equilibrium free energy gap are bilinear forms of A ab and (Fav (Eqs. [45] and [47]). A unitary transformation of the diabatic basis (Eq. [27]), which should not affect any physical observables, then changes A b and v, affecting the reorganization parameters. The activation parameters of ET consequently depend on transformations of the basis set ... 

The curves have identical force constants / and their minima are separated by uq. The vertical difference between the free energies of the reactants and products of a self-exchange reaction at the reactants (or products ) minimum (equilibrium configuration) is the reorganization parameter i = /ao /2. Denoting the displacement along the reaction coordinate by x, a dimensionless reaction coordinate X may be defined as x/cq X varies from 0 to 1 as the reaction proceeds and, with X as the... 

The reorganization parameter is usually broken down into inner-shell (vibrational) and outer-shell (solvational) components. 

To illustrate the approach used to calculate the iimer-shell contribution to the reorganization barrier we consider the symmetrical stretching vibrations of the two reactants in the Fe(H20)6 " -Fe(H20)6 + self-exchange reaction (Eq. la). The inner-shell reorganization term is the sum of the reorganization parameters of the individual reactants, i.e. ... 

The relationship between the vertical reorganization parameter and the activation energy and the effect of using different criteria for the inner-shell reorganization have recently been considered in some detail [15]. The reorganization energy and the contributions of the individual reactants turn out to be quite sensitive to the model used. 

If nuclear-tunneling effects are neglected, then the experimental activation parameters are related to the reorganization parameters by ... 

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