Handbook of Solvents - George Wypych - ChemTech - Ventech!

8.4 Two-body interaction energy 431
dure we shall see in action also in the context of the perturbation theory. At the variational
level considered here, the procedure is called Configuration Interaction (CI): each configuration
corresponds to one of the antisymmetrized products of MO we have introduced, including
the HF one, and the coefficients in front of each component of this linear expansion
of the exact (in principle) wave function are determined by applying the variational principle.
There are numerous alternative methods that introduce electron correlation in the molecular
calculations at a more precise level that can be profitably used. We mention here the
MC-SCF approach (the acronym means that this is a variant of HF (or SCF) procedure starting
from the optimization no more of a single antisymmetric orbital product, but of many
different products, or configurations), the Coupled-Cluster theory, etc., all methods based
on a MO description of single-electron functions.
For readers wishing to reach a better appreciation of papers regarding the formulation
of interaction potentials, we add that there is another way of introducing electron correlation
effects in the calculations. It is based on the density functional theory (DFT). 6 There is a variety
of DFT methods (detailed information can be found in the quoted monograph 6 ); a family
of these methods again makes use of MOs: they are called hybrid functional methods and
give, on average, better results than other correlated methods at a lower computational cost.
The introduction of electron correlation in the description of the monomers produces
changes in their charge distribution and in their propensity to be polarized. For this reason
ES, IND, and EX computed with correlated wave functions are somewhat different with respect
to the values obtained with the corresponding HF wave functions. The procedure
sketched with equations [8.13]-[8.21] can be adapted, with some modifications, to correlated
wave function using a MO basis.
The reader must be warned that here, as well as in other points of this chapter, we have
simplified the discussion by omitting many details necessary for a proper handling and a
fuller understanding the problem, but not essential to grasp the basic points.
What is of more practical interest here is that HF descriptions of the dimer cannot give
a DIS term. This may be recovered by introducing CI descriptions of the system. The simpler
CI description, now largely used in routine calculations on molecules and molecular
aggregates, is called MP2. This acronym means that use has been made of a specialized version
of the perturbation theory (called Møller-Plesset) limited to second order to determine
the expansion coefficients.
MP2 wave functions contain elements able to give an appreciation of DIS, even if of
limited accuracy. It is in fact possible to decompose MP2 values of ΔE AB(R) using the strategy
we have outlined for the HF case, adding to each term the appropriate MP2 correction.
Each term of the decomposition is somewhat modified, because of the MP2 corrections: the
remainder of the MP2 contribution can be taken as a first approximation to DIS.
There are other methods to get DIS values starting from HF wave functions, which
may be more precise. Among them we quote the methods based on the response theory and
on the use of dynamic polarizabilities. This powerful method has been developed during the
years, and the outstanding contributions are due to McWeeny (1984) and Claverie (1986),
to which reference is made for more details. 7