Effective reorganization energy

Figure 1 Temperature dependence of the reorganization energy and effective charges on...

The flat interface model employed by Marcus does not seem to be in agreement with the rough picture obtained from molecular dynamics simulations [19,21,64-66]. Benjamin examined the main assumptions of work terms [Eq. (19)] and the reorganization energy [Eq. (18)] by MD simulations of the water-DCE junction [8,19]. It was found that the electric field induced by both liquids underestimates the effect of water molecules and overestimates the effect of DCE molecules in the case of the continuum approach. However, the total field as a function of the charge of the reactants is consistent in both analyses. In conclusion, the continuum model remains as a good approximation despite the crude description of the liquid-liquid boundary. 

Such a rate increase at short distances has been observed also by M.E. Michel-Beyerle [12] in time resolved experiments with a photoactivated acri-dinium ion as electron acceptor. This effect can be explained by the influence of the distance on the solvent reorganization energy The solvent reorganization energy is small for charge shifts over short distances, and it increases with the distance until it reaches a plateau. In this plateau area the solvent reorganization energy remains constant and Eq. (1) can be applied ... 

An expression of the type in Eq. (29) has been rederived recently in Ref. 13 for outer-sphere electron transfer reactions with unchanged intramolecular structure of the complexes where essentially the following expression for the effective outer-sphere reorganization energy Ers was used ... 

Here (x)t and (x)f denote the mean values of the relative coordinate x over the states of the proton in the first and second potential wells, respectively. Equation (107) shows that the inertia effects lead to a decrease of the activation factor in the transition probability due to an increase of the reorganization energy. The greater the mass, m of the tunneling particle and the frequency of the vibrations of the atom, w0, the greater is this effect. The above result corresponds to the conclusion drawn in Ref. 66. 

Solvent effects, reaction coordinates, and reorganization energies on nucleophilic substitution reactions in aqueous solution, 38, 161... 

FIGURE 1.22. Solvent reorganization energies derived from the standard rate constants of the electrochemical reduction of aromatic hydrocarbons in DMF (with n-Bu4N+ as the cation of the supporting electrolyte) uncorrected from double-layer effects. Variation with the equivalent hard-sphere radii. Dotted line, Hush s prediction. Adapted from Figure 4 in reference 13, with permission from the American Chemical Society. 

Figure 1. Activation energy of electron-transfer process as a function of electronic energy gap of a reaction. Er = Eg + Ec is the total reorganization energy where Es is the classical solvent reorganization energy and Ec is the reorganization energy of an intramolecular mode, l

Figure 2. Deuterium isotope effect for electron transfer between ammine complexes as a function of the reduced electronic energy gap AE/EC where Er is the total reorganization energy E, = Eg + Ec. Key for parameters — —, hci)H/kBT — 2.0 and Es/Ec = 0 ------------------, Es/Ec = 1 and-------, Es/Ec = 2.

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