The family of SCRF models

An analytical solution for equation (1) exists if the potential 0(r) in equation (1) can be composed as the sum of the contribution of the multipoles of the solute interacting with the dielectric continuum. At an arbitrary point P(r, 0, x) it can be written as 

Rivail s group [24-29] made the most important contribution toward the development of this kind of models. Adopting their notations, one can introduce the interaction energy E between solvent and solute as follows 

The coefficients // are called the reaction field factors and have an analytical expression depending on the shape of the cavity (sphere [30], ellipsoid [27,28,31]). Thus, the modified Hartree-Fock operator has the form 

Here M denotes the electronic part of the quantum mechanical operator associated with the m elements of multipole of rank / The methods based on the definition given by the equation (9) are referred as self-consistent reaction field methods (SCRF). 

The continuum models presented in previous sections are focused only on electrostatic effect which is accompanied by insertion of a solute in a solvent, namely the bulk polarization of the solvent by the field of the solute. However, all these models neglect some other physical effects [36]. Among them probably the most important are the dispersion and the cavitation forces. 

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