Handbook of Solvents - George Wypych - ChemTech - Ventech!

22 Estanislao Silla, Arturo Arnau and Iñaki Tuñón
the van der Waals surface (WSURF), which is the external surface resulting from a set of
spheres centered on the atoms or group of atoms forming the molecule (Figure 2.1.5a); b)
the Accessible Surface (ASURF), defined by Richards and Lee 45 as the surface generated by
the center of the solvent probe sphere, when it rolls around the van der Waals surface (Figure
2.1.5b); and c) the Solvent Excluding Surface (ESURF) which was defined by
Richards 46 as the molecular surface and defined by him as composed of two parts: the contact
surface and the reentrant surface. The contact surface is the part of the van der Waals
surface of each atom which is accessible to a probe sphere of a given radius. The reentrant
surface is defined as the inward-facing part of the probe sphere when this is simultaneously
in contact with more than one atom (Figure 2.1.5c). We defined 47 ESURF as the surface envelope
of the volume excluded to the solvent, considered as a rigid sphere, when it rolls
around the van der Waals surface. This definition is equivalent to the definition given by
Richards, but more concise and simple.
Each of these types of molecular surfaces is adequate for some applications. So, the
van der Waals surface is widely used in graphic displays. However, for the representation of
the solute cavity in a continuum model the
Accessible and the Excluding molecular
surfaces are the adequate models as far as
they take into account the solvent. The
main relative difference between both molecular
surface models appears when one
considers the separation of two cavities in a
continuum model and more precisely the
cavitation contribution to the potential of
mean force associated to this process (Figure
2.1.6). In fact, we have shown 31 that
Figure 2.1.6. Variation of the area of the Solvent Accessible
Surface and Solvent Excluding Surface of a methane
dimer as a function of the intermolecular distance.
only using the Excluding surface the correct
shape of the potential of mean force is
obtained. The cavitation term cannot be
correctly represented by interactions
among only one center by solvent mole-
cule, such as the construction of the Accessible surface implies. The Excluding surface,
which gives the area of the cavity not accessible to the solvent whole sphere and which
should be close to the true envelope of the volume inaccessible to the solvent charge distribution,
would be a more appropriate model (Figure 2.1.7).
2.1.3.4 Supermolecule models
The study of the dissolution process can also be confronted in a direct manner analyzing the
specific interactions between one or more molecules of solute with a large or larger group of
solvent molecules. Quantum Mechanics is once again the ideal tool for dealing with this
type of system. Paradoxically, whilst on the one hand the experimental study of a system becomes
complicated when we try to make an abstraction of the solvent, the theoretical study
becomes extraordinarily complicated when we include it. In this way, Quantum Mechanics
has been, since its origins, a useful tool and relatively simple to use in the study of isolated
molecules, with the behavior of a perfect gas. For this reason, Quantum Mechanics becomes
so useful in the study of systems which are found in especially rarefied gaseous surroundings,
such as the case of the study of the molecules present in the interstellar medium. 48 Nev-