Born-Onsager solvent-solute model

The energy curves in Figure 22 are closely related to the Marcus-Hush theory for electron transfer. The formalism we employ emphasizes a dipole model for the solute solvent interaction, i.e., an Onsager cavity model. However, a Born charge model based on ion solvation as something in between [135] would be essentially equivalent because we do not attempt to calculate Bop and Bor but rather determine them empirically. 

In the Generalized Born model [2-5], the solvent is described in a extremely simplified way and there is no mutual polarization between solute and solvent. The Onsager model [6] allows for solute-solvent polarization, but the description of the cavity and of the solvent is still very crude. 

The other model for the ionic friction concerns the dielectric response of solvent to the solute perturbation. When an ion is fixed in polar solvent, the solvent is polarized according to the electrostatic field from the ion. If the ion is displaced, the solvent polarization is not in equilibrium with a new position of the ion, and the relaxation of the polarization should take place in the solvent. The energy dissipation associated with this relaxation process may be identified as an extra friction. The extra friction, called the dielectric friction, decreases with increasing ionic radius, thereby, with decreasing electrostatic field from the ion. The dielectric friction model developed by Born [66], Fuoss [67], Boyd [68] and Zwanzig [69, 70] has taken a complete theoretical form due to the work by Hubbard and Onsager [71, 72] who proposed a set of continuum electrohydrodynamic equations in which the electrostatic as well as hydrodynamic strains are incorporated. 

Methods based on multipole expansion The simplest versions of these methods rely on the use of spherical cavities and in the truncation of the multipole expansion at the monopole or dipole level. These methods correspond to the well known models of Born [35] and Bell-Onsager [36,37], whose expressions are given in equations 11 and 12, where q is the charge representing the solute charge distribution, p. is the dipole moment, e is the permittivity and R is the radius of the cavity defining the solute/solvent interface. 

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