Handbook of Solvents - George Wypych - ChemTech - Ventech!

450 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
It may be convenient to introduce a loose classification of the origin of changes in the
internal geometry of molecules in clusters and liquids, and to use it for the dimer case we are
considering here:
1) permanent or semipermanent molecular interactions;
2) internal dynamism of the molecule;
3) molecular collisions.
In the variety of liquid systems there are quite abundant cases in which relatively
strong interactions among partners induce changes in the internal geometry. The formation
of hydrogen-bonded adducts is an example of general occurrence (e.g., in water solutions).
The interactions of a metal cations and their first solvation shells is a second outstanding example
but the variety of cases is very large. It is not easy to give general rules on the distinction
between permanent and semipermanent interactions of this type. In general it depends
on the time scale of the phenomenon being studied, but it is clear that the long residence
time of water molecule (in some cases, on the order of years 28 ) in the first solvation shell
around a cation leads us to consider this effect as permanent.
In such cases, it is convenient to reconsider the definition of the cluster expansion and
to introduce some extra variables in the nuclear coordinate subspace to span for the analysis.
For example, in the case of a dimer M n+ ·H 2O, it is convenient to add three coordinates corresponding
to the internal coordinates of the water molecule (the total number of degrees of
freedom in such case is again 6, because of the spherical symmetry of the metal cation).
There is no need of repeating, for this model, the variational decomposition of the energy
(the PT approaches have more difficulties to treat changes in the internal geometry). The
conclusions do not change qualitatively, but the quantitative results can be sensibly modified.
Another important case of permanent interactions is related to chemical equilibria
with molecular components of the liquid. The outstanding example is the prototropic equilibrium,
especially the case AH + B → A - +HB + . There are water-water potentials, including
the possibility of describing the ionic dissociation of H 2O.
The semipermanent interactions are generally neglected in the modeling of the potentials
for liquids. Things are different when one looks at problems requiring a detailed local
description of the interactions. Molecular docking problems are a typical example. In such
cases, use is made of variational QM calculations, or especially for docking, where one molecule
at least has a large size, use is made of molecular mechanics (MM) algorithms, allowing
local modification of the systems.
The second category corresponds to molecular vibrations; rotations of a molecule as a
whole have been already considered in, or definition of, the ΔE(R) potential. The third category,
molecular collisions, gives rise to exchange of energy among molecules that can be
expressed as changes in the translational and rotational energies of the rigid molecule and
changes in the internal vibrational energy distributions. In conclusion, all the cases of
non-rigidity we have to consider here can be limited to molecular vibrations considered in a
broad sense (couplings among vibrations and rotations are generally neglected in
intermolecular potentials for liquids).
The vibrations are generally treated at the classical level, in terms of local deformation
coordinates. The local deformation functions are of the same type of those used in molecular
mechanics (MM) methods. Nowadays, MM treats geometry changes for molecules of
any dimension and chemical composition.