calculations are, by and large, the easiest and most popular way of treating solvent
effects.
The key steps in current continuum solvation models are the calculation of the
size and shape of the solvent cavity and of the interaction energy of the solute with
the solvent. Details of these calculations have been presented in, for example,
the books by Cramer [ 16 ] and Jensen [ 17 ], and in very detailed journal reviews
[ 18 , 19 ]. Here I will only outline the basic features and illustrate some applications
of continuum solvation calculations. The simplest cavity for a solute molecule is a
spherical one, the next most complex ellipsoidal. For the great majority of mole-
cules, which are not spherical or ellipsoidal, models based on these are quite
unrealistic, and for quantitative or even much semiquantitative work such models
are obsolete. Realistic continuum models place the solute molecule in a cavity
designed to match its shape, although there are degrees of accuracy for defining this
shape, as well as the size of the cavity. The shape and size of the cavity define the
solvent-accessible surface area (SASA), a quantity needed by the method. The
simplest tailored shape would be that resulting from the exposed surfaces of an
overlapping spheres molecular model (Fig.8.1); the spheres have scaled van der
Waals atomic radii. However, the V-shaped crannies between some nearby over-
lapping spheres are inaccessible to solvent, and a more realistic measure of SASA is
the surface defined by a sphere (of empirical radius for various solvents) rolling
over the molecular surface. A still more sophisticated way of smoothing the over-
lapping-spheres surface is to project onto it a large number of small polygons or
tessellations (to tessellate¼to tile), called tesserae (tessera¼a small fragment used in
making a mosaic), as in one implementation of the conductor-like screening solvation
model of Klamt and coworkers (COSMO; see below) by Barone and Cossi [ 20 ].
Having obtained a cavity corresponding to a realistic SASA, the energy of
interaction of the solute molecule with the solvent it “sees” is calculated. This
interaction energy can be conceptually divided into terms: (1) the energy needed
to make the cavity in the first place; although one might say that the solute was
formally absent when the cavity was being “prepared”, this cavitation energy
...
..
...rolling
sphererolling
sphereFig. 8.1The surface area of a molecule from overlapping spheres and from the surface generated
by a sphere rolling over the molecular surface. Like the solvent, the rolling sphere cannot reach
into V-shaped cavities, so the area of the surface it defines is a more realistic measure of the
solvent-accessible surface than is the overlapping-spheres surface
8.1 Solvation 525