Handbook of Solvents - George Wypych - ChemTech - Ventech!

13.1 Solvent effects on chemical reactivity 749
Dispersion forces are the result of the dipolar
interactions between the virtually excited dipole moments
of the solute and the solvent, resulting in a
nonzero molecular polarizability. Although the average
of every induced dipole is zero, the average of
the product of two induced dipoles is nonzero (Figure
13.1.6).
Induction forces are caused by the interaction
of the permanent solvent dipole with the solvent dipoles
induced by the solute and solvent field (Figure
13.1.7).
Sometimes it is stated that dispersion is a quantum
mechanical effect and induction is not. Thus,
some clarifying comments are at place here. From
the general viewpoint, all effects including
polarizability are quantum mechanical in their origin because
the polarizability of atoms and molecules is a quantum mechanical
quantity and can be assessed only in the framework
of quantum mechanics. However, once calculated, one can
think of polarizability in classical terms representing a quantum
molecular object as a classical oscillator with the mass
equal to the polarizability, which is not specified in the classical
framework. This is definitely wrong from a fundamental
viewpoint, but, as it usually appears with harmonic models, a
quantum mechanical calculation and such a primitive classical
model give basically the same results about the induction
matter. Now, if we implement this classical model, we would
easily come up with the induction potential. However, the dispersion
interaction will be absent. The point is that to get dispersions, one needs to switch
back to the quantum mechanical description where both inductions and dispersions naturally
appear. Thus the quantum oscillator may be used resulting in both types of potentials. 50
If in the same procedure one switches to the classical limit (which is equivalent to putting
the Plank constant zero) one would get only inductions.
The calculation of the dispersive solvation energy is based on perturbation theories
following the Chandler-Andersen-Weeks 51 or Barker-Henderson 52 formalisms, in which
long-range attractive interactions are treated as perturbations to the properties of a hard
body reference system. Essentially, perturbative theories of fluids are a modern version of
van der Waals theory. 53 Figure 13.1.6
Figure 13.1.7
In the papers reviewed here, the Barker-Henderson approach was
utilized with the following input parameters: Lennard-Jones (LJ) energies for the solvent,
for which reliable values are now available, the HS diameters of solvent and solute, the solvent
polarizability, and the ionization potentials of solute and solvent. A weak point is that
in order to get the solute-solvent LJ parameters from the solute and solvent components,
some combining rule has to be utilized. However, the commonly applied combining rules
appear to be adequate only if solute and solvent molecules are similar in size. For the case of
particles appreciably different both in LJ energy and size, the suggestion has been made to
use an empirical scaling by introducing empirical coefficients so as to obtain agreement be-