Handbook of Solvents - George Wypych - ChemTech - Ventech!

458 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
Potential 1 is extremely simple: the only parameter is the radius of the sphere. In spite
of this simplicity, an impressive number of physical results have been obtained using the HS
potential on the whole range of densities and aggregations. Also, mixtures of liquids have
been successfully treated, introducing in the computational machinery the desired number
of spheres with appropriate radii. The HS model is at the basis of the Scaled Particle Theory
(SPT), 38 which still constitutes a basic element of modern solvation methods (see later for
more details).
Of course, HS cannot give many details. A step toward realism is given by potential 2,
in which the hard potential is replaced by a steep but smoothly repulsive potential. It is
worth reminding readers that the shift from HS to SS in computer simulations required the
availability of a new generation of computers. Simulations had in the past, and still have at
present, to face the problem that an increase in the complexity of the potential leads to a
large increment of the computational demand.
Potentials 3 and 4 have been introduced to study ionic solutions and similar fluids containing
mobile electric charges (as, for example, molten salts). In ionic solutions the appropriate
mixture of charged and uncharged spheres is used. These potentials are the first
examples of potentials in our list, in which the two-body characteristics become explicit.
The interaction between two charged spheres is in fact described in terms of the charge values
of a couple of spheres: Q kQ l/r lk (or Q kQ l/εr lk).
Potentials 5 and 6 are the first examples in our lists of anisotropic potentials. The interaction
here depends on the mutual orientations of the two dipoles. Other versions of the dipole-into-a-sphere
potentials (not reported in Table 8.5) include induced dipoles and
actually belong to a higher level of complexity in the models, because for their use there is
the need of an iterative loop to fix the local value of F. There are also other similar models
simulating liquids in which the location of the dipoles is held fixed at nodes of a regular 3D
grid, the hard sphere potential is discarded, and the optimization only regard orientation and
strength of the local dipoles. This last type of model is used in combination with solutes M
described in another, more detailed way.
Potentials 7-11 add more realism in the description of molecular shape. Among them,
the Gay-Berne 35 potential (10) has gained a large popularity in the description of liquid crystals.
The quite recent potential (11) 36 aims at replacing Gay-Berne potential. It has been
added here to show that even in the field of simple potentials there is space for innovation.
Potentials 12 and 13 are very important for chemical studies on liquids and solutions.
The Lennard-Jones potential (12) includes dispersion and repulsion interactions in the
form:
LJ ⎛ ⎞
LJ: E AB = ⎜ ⎟ −
⎝ R⎠R ⎛
12 6
⎡ σ σ⎞⎤
ε ⎢ ⎜ ⎟ ⎥
⎣⎢
⎝ ⎠ ⎦⎥
[8.70]
The dependence of the potential on the couple of molecules is here explicit, because
the parameters εand σdepend on the couple. In the original version, εis defined as the depth
of the attractive well and σ as the distance at which the steep repulsive wall begins.
More recently, the LJ expression has been adopted as an analytical template to fit numerical
values of the interaction, using independently the two parameters.: