Reorganization energy solvents

Here X is tire reorganization energy associated witli the curvature of tire reactant and product free energy wells and tlieir displacement witli respect to one another. Assuming a stmctureless polarizable medium, Marcus computed the solvent or outer-sphere component of tire reorganization energy to be... 

In order to simplify the expression for G, one has to employ a sufficiently simple model for the vibrational modes of the system. In the present case, the solvent contribution to the rate constant is expressed by a single parameter E, the solvent reorganization energy. In addition, frequency changes between the initial and final states are neglected and it is assumed that only a single internal mode with frequency co and with the displacement Ar is contributing to G. Thus the expression for G reduces to [124] ... 

In Eq. (77), x = h(o/2kg T is the reduced internal frequency, q = EJhoi the reduced solvent reorganization energy, p = hElha> the reduced electronic energy gap and / (z) the modified Bessel function of order m. The quantity S is a coupling parameter which defines the contribution of the change in the internal normal mode ... 

In the conversion case, the solvent reorganization energy is very small and thus the one-mode expression [124] for the vibrational overlap factor G is generally adequate such that ... 

Figure 2.4 Adiabatic potential energy E q) for various values of A at equilibrium. The solvent coordinate q has been normalized so that the initial state corresponds to = 0 and the final state to = 1. The reorganization energy was taken as A = 1 eV.

The CDC-MOVB method is the appropriate computational approach for studying properties associated with the adiabatic ground state such as the reaction barrier for a chemical reaction and the solvent reorganization energy. 

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 ... 

Jozefowicz M (2007) Determination of reorganization energy of fluorenone and 4-hydroxy-fluorenone in neat and binary solvent mixtures. Spectrochim Acta A 67 444-449... 

Fig. 13 Energy profiles for C C, Cl in DMF. Curve a potential energy in the gas phase. Curve b potential energy in the solvent (D p = 62 meV). Curve c variation of the solvation free energy. Curve d solvent reorganization energy.

The difference between the energy profiles in the solvent and in the gas phase provides the solvation free energy, Gr.wx- (profile c in Fig. 13). The solvent reorganization energy, Ao, may then be obtained from equation (60) as a function of the R—X distance (profile d in Fig. 13). 

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

The forward and backward activation free energies and the corresponding rate constants thus depend on an extrinsic factor, the standard free energy of the reaction, AG° = E — E°, and an intrinsic factor, the standard activation free energy, that reflects the solvent and internal reorganization energy, Aq and A [equation (1.31)]. 

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