Handbook of Solvents - George Wypych - ChemTech - Ventech!

432 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
The decomposition of the interaction energy through a variational
approach: a summary
We have so far given a description of the elements in which ΔEAB(R) may be decomposed
using variational approaches. We report here the final expression:
ΔE AB = ES + PL + EX + CT + COUP + DIS
[8.22]
At the HF level, all terms (but one: DIS) can be obtained with almost zero computational
cost with respect to the numerical determination of ΔE AB; in the HF decomposition of
the interaction energy there is a small additional term (called COUP) describing further couplings
between the other components, which is often left as it is obtained (i.e., as the difference
between the original ΔE AB value and the sum of the other four components) or
subjected to further decompositions.
8 The last term, DIS, may be
calculated at this level using
specialistic time-dependent formulations
of the HF procedure.
Going beyond the HF level, the
decomposition can be obtained at
the MP2 level essentially using
the same techniques (DIS may be
appreciated by separating some of
the MP2 contributions that are
strictly additive).
The variational approaches
we have considered are able to describe,
and to decompose, the interaction
energy at the level of
Figure 8.3. Decomposition of the interaction energy ΔE in
H 2O�HOH.
accuracy one wishes, once the
necessary computational resources
are available. In fact, as
we shall see later, there is no need
of reaching extreme precision in the preliminary calculations to model interaction potentials
for liquids, because other approximations must be introduced that will drastically reduce the
accuracy of the description.
We report in Figure 8.3 as an example the decomposition of the interaction energy of
the water dimer, in the same orientation Ω used in Figure 8.1.
At large distances the interaction is dominated by ES; this contribution also gives a
reasonable approximation to ΔE at the equilibrium distance. The IND decays with the distance
more rapidly than ES; this contribution is particularly sensitive to the quality of the
expansion basis set {χ}. Old calculations of IND using restricted basis sets are not reliable.
EX is a short ranged term: its contribution is however essential to fix the position of the minimum
(and to describe portion III of the PES). CT and DIS terms have both a short-range
character.
This schematic analysis is valid for almost all the dimeric interactions where at least
one partner has a dipolar character. The presence of a hydrogen bond (as is the case for the