Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.5 Three- and many-body interactions 455
not due to classical polarization effects only, but to all the components of the interaction of S
with A-B, namely dispersion, exchange, etc.
The results of the decomposition of the intermolecular interaction energy of cluster M
are not qualitatively different from those found for the same cluster M in vacuo. There are
quantitative changes, often of not negligible entity and that correspond, in general, to a
damping of the effects.
The use of this approach requires us to consider the availability of efficient and accurate
models and procedures to evaluate the effects of S on M, and at the same time, of M on
S. The basic premises of this approach have been laid many years ago, essentially with the
introduction of the concept of solvent reaction field made by Onsager in 1936, 30 but only recently
have they been satisfactory formulated. There are good reasons to expect that their
use on the formulation of “effective” intermolecular potentials will increase in the next few
years.
Actually, the decomposition of the ΔE M(R) interaction energy is preceded by a step not
present for isolated systems.
There is the need of defining and analyzing the interactions of each monomer A, B,
etc. with the solvent alone. The focused model is reduced to a single molecule alone, let us
say A, which may be a solute molecule but also a component of the dominant mole fraction,
the solvent, or a molecular component of the pure liquid.
This subject is treated in detail in other chapters of this book and something more will
be added in the remainder of this chapter. Here, we shall be concise.
There are two main approaches, the first based on discrete (i.e., molecular) descriptions
of S, the second on a continuous description of the assisting portion of the medium, via
appropriate integral equations based on the density distribution of the medium and on appropriate
integral kernels describing the various interactions (classical electrostatic, dispersion,
exchange-repulsion). Both approaches aim at an equilibration of S with M: there is the
need of repeating calculations until the desired convergence is reached. More details on
both approaches will be given in the specific sections; here we shall limit ourselves to
quoting some aspects related to interaction potentials, which constitute the main topic of
this section.
The approach based on discrete descriptions of the solvent makes explicit use of the
molecular interaction potentials which may be those defined without consideration of S; the
calculations are rather demanding of computation time, and this is the main reason explaining
why much effort has been spent to have simple analytical expressions of such potentials.
The second continuous approach is often called Effective Hamiltonian Approach
(EHA) and more recently Implicit Solvation Method (ISM). 31 It is based on the use of continuous
response functions not requiring explicit solvent-solvent and solute-solvent interaction
potentials, and it is by far less computer-demanding than the simulation approach.
As we shall show in the section devoted to these methods, there are several possible
versions; here it is worth quoting the Polarizable Continuum Model (PCM) for calculations
at the ab initio QM level. 32
PCM it is the only method used so far to get effective two body A-B potentials over the
whole range of distances R (three-body corrections have been introduced in Ref. [33]).
Until now, the EHA approach has been mostly used to study solvent effects on a solute
molecule. In such studies, M is composed of just a single solute molecule (M = A) or of a
solute molecule accompanied by a few solvent molecules (M = AS n). These alternative