Self-consistent held procedure

Equation 4.7 has the form of a self-consistency problem. The solution to the equation is rffj(fi), but the exact form of the equation is determined by (/ y(/r) itself. It must be solved by an iterative procedure (called the self-consistent held, or SCF approach), in which convergence is taken to occur at the step where both sj and (/ y(/r) do not differ appreciably from the prior step. 

A large variety of continuum models have been proposed and many are available in popular quantum chemical modeling packages. They differ in the sophistication of the procedure used to determine the shape of the cavity. In the simplest case, this is just a sphere, but most models nowadays use more tailored cavities (as in Figure 10.3), generated, for example, from the combination of a set of spheres placed around individual solute atoms. In most cases, the models include a relaxation of the electronic structure in response to the electric held created by the solvent around it, and in most cases this is then treated fully self-consistently. This effect can be quite important in some cases, as a polar solute may become considerably more polar due to interactions with a polar solvent. Different models are also parameterized in different ways. 

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