Linear interaction energy with continuum

These points indicate that the continuum theory expression of the free energy of activation, which is based on the Born solvation equation, has no relevance to the process of activation of ions in solution. The activation of ions in solution should involve the interaction energy with the solvent molecules, which depends on the structure of the ions, the solvent, and their orientation, and not on the Born charging energy in solvents of high dielectric constant (e.g., water). Consequently, the continuum theory of activation, which depends on the Born equation,fails to correlate (see Fig. 1) with experimental results. Inverse correlations were also found between the experimental values of the rate constant for an ET reaction in solvents having different dielectric constants with those computed from the continuum theory expression. Continuum theory also fails to explain the well-known Tafel linearity of current density at a metal electrode. ... 

The biexciton states described above have energies outside the free-exciton two-particle continuum and can decay only due to exciton-photon or exciton-phonon interactions. However, if the biexciton energy lies in the continuum, such a biexciton can decay spontaneously into states with two free (unbound) excitons. These quasibound states display themselves as resonant peaks in the two-particle continuum and can be observed in linear and nonlinear optical processes if these resonances are sufficiently narrow, e.g. if they are situated in the region of low density of two-particle states. 

Cavity surfaces Earliest continuum models made use of oversimplified cavities for the insertion of the solute in the dielectric medium such as spheres or ellipsoids. In the last decades, the concept of molecular surface as become more common. Thus, the surface has been used in microscopic models of solution. Linear relationships were also found between molecular surfaces and solvation free energies. Moreover, given that molecular surfaces can help us in the calculation of the interaction of a solute molecule with surroundings of solvent molecules, they are one of the main tools in understanding the solution processes and solvent effects on chemical systems. Another popular application is the generation of graphic displays. ... 

---