Diabatic solvent reorganization energy

The diabatic solvent reorganization energy is defined by the nuclear response function Xn and by the diabatic field difference... 

The use of the energy-gap reaction coordinate allows us to calculate solvent reorganization energies in a way analogous to that in the Marcus theory for electron transfer reactions.19 The major difference here is that the diabatic states for electron transfer reactions are well-defined, whereas for chemical reactions, the definition of the effective diabatic states is not straightforward. The Marcus theory predicts that... 

Figure 9 illustrates the computed free energies for the reactant and product diabatic states in solution and in the gas phase, and for the solute-solvent interactions. The latter is often used to estimate the solvent reorganization energy... 

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 ... 

Fig. 4 Diabatic solvent reorganization free energy curves for Fe + and Fe [22], The bold solid lines represent the molecular dynamics result, the thin solid lines the best parabolic fit of the region, near the bottom of each well.

BJ theory replaces the classically derived energy surfaces and transition-state model of the MH treatment (Figs. 1 and 2) with a quantum-mechanical tunneling model. The BJ diabatic energy surfaces are shown in Fig. 990 Only the solvent is treated classically, and the X-axis now only represents solvent reorganization. Both energy... 

The situation is fundamentally different from that for outer sphere electron transfer reactions where, according to Marcus theory, the solvent reorganization determines the reaction. In contrast, the model calculations discussed in this section indicate that the energy of activation for the ion transfer step is not related to the electron exchange with the electrode, since the crossing between the two diabatic energy states of 1 and 1° occurs only at such short distances where the ion has already surpassed the solvent barrier. Contrary to the approach discussed here, Xia and Berkowitz [235] assumed the validity of the outer sphere mechanism from the outset. The analysis of the dependence of the solvent barrier on external electric field and temperature indicates that a in Eq. (17) is indeed not constant but depends on temperature. 

In Marcus electron transfer theory, the barrier also arises as a consequence of the intersection of the two diabatic potential energy curves. The barrier height depends mainly on the (solvent and reactant) reorganization energy. 

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