Handbook of Solvents - George Wypych - ChemTech - Ventech!

452 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
which can be easily extracted from the eq. [8.9]. The computational task becomes more and
more exacting in increasing the number of bodies, as well as the dimensions which rise to 18
with fixed geometries of the components, and there are no reasonable perspectives of having
in the future such a systematic scan as that available for dimers.
The studies have been so far centered on four types of systems that represent four different
(and typical) situations:
1) clusters composed of rare gas atoms or by small almost spherical molecules
(e.g., methane);
2) clusters composed of polar and protic molecules (especially water);
3) clusters composed of a single non-polar molecule (e.g., an alkane) and
a number of water molecules;
4) clusters composed of a single charged species (typically atomic ions) and
a number of water molecules.
Inside the four categories, attention has mostly been paid to clusters with a uniform
chemical composition (e.g., trimers AAA more than A 2B or ABC for cases 1 and 2).
Clearly the types of many-body analyses are not sufficient to cover all cases of chemical
relevance for liquids; for example, the mixed polar solvents (belonging to type 2) and the
water solutions containing a cation in presence of some ligand (type 4) are poorly considered.
In spite of these deficiencies the available data are sufficient to draw some general
trends that in general confirm what physical intuition suggests. We combine here below
conclusions drawn from the formal analysis and from the examination of numerical cases.
ES contributions are strictly additive: there are no three- or many body terms for ES.
The term “many-body correction” to ES introduced in some reviews actually regards two
other effects. The first is the electron correlation effects which come out when the starting
point is the HF description of the monomer. We have already considered this topic that does
not belong, strictly speaking, to the many-body effects related to the cluster expansion [8.9].
The second regards a screening effect that we shall discuss later.
The other contributions are all non-additive. The cluster expansion [8.9] applies to
these terms too:
1
1
TERM( ABCDE�) = ∑∑TERM
AB( RAB) + ∑∑∑TERM
ABC( RABC)
+ �
2
6
A
B
A
B
C
[8.65]
The most important are the IND and DIS terms. CT is active for some special systems
(long range electron transfer) but of scarce importance for normal liquids. EX many-body
contributions rapidly fade away with the number of bodies: the three-body terms have been
studied with some details, 29 but they are not yet used extensively to model interaction potentials
for liquids.
The IND many-body contributions are dominated by the first dipole polarizability α
contributions. The field F produced by the charge distribution of the other molecules and
acting on the units for which α is defined, at a first (and good) approximation, as additive.
The non-linearity derives from the fact that the contribution to the interaction energy is related
to the square of the electric field. So in modeling many body effects for IND the attention
is limited to molecular contributions of the type