Handbook of Solvents - George Wypych - ChemTech - Ventech!

426 Jacopo Tomasi, Benedetta Mennucci, Chiara Cappelli
low on the variational approach, then adding the basic elements of the perturbation theory
approach.
8.4.1 DECOMPOSITION OF THE INTERACTION ENERGY OF A DIMER:
VARIATIONAL APPROACH
Coming back to Figure 8.1, its shape exhibiting a minimum makes it manifest that there are
several types of interactions at work, with different signs and with different distance decays
(at infinity all interactions go to zero). This subject has been amply studied and the main
conclusions (there are details differing in the various schemes of interaction energy decomposition)
are so widely known and intuitive that we feel authorized to introduce them here
before giving a formal definition (that will be considered later). In Table 8.1 we report the
names of these components of the interaction energy.
Table 8.1. The main components of the bimolecular interactions ΔE AB(R)
Component name Acronym Physical Meaning
Electrostatic ES Coulomb interactions between rigid charge distributions
Induction IND Mutual electrostatic deformation of the two charge distributions
Exchange EX Quantum effect due to the Pauli exclusion principle
Dispersion DIS
Interactions among fluctuations in the charge distributions of
the two partners
Charge transfer CT Transfer of electrons between partners
All components of ΔEAB(R) are present in all points of the RAB 6-dimensional space
we have introduced. It is convenient to examine them separately. We shall make references
to a single decomposition scheme 2 that we consider more convenient. Reference to other
schemes will be done when necessary. Another view of methods may be found in Tomasi et
al. 3
The electrostatic term
The ES term may be positive or negative: the shape of the ES(R) function strongly depends
on the electric characteristics of the partners. If both molecules are reduced to dipoles, we
have the two extreme situations (see Figure 8.2) which give rise to repulsive (i.e., positive)
and attractive (i.e., negative) electrostatic contributions to ΔEAB, respectively. With different
orientations of the two dipoles there will be different values of ES that in this simple case
can be obtained with an analytical expression:
( )
ES R, θ μ μ cos θ/
R
=−2 1 2
3
[8.12]
In more complex molecules, the ES(R) function has a complex shape that often determines
the salient features of the whole ΔE AB(R) function. This is the reason why in the studies
of molecular recognition and molecular docking, great attention is paid to a proper
representation of ES(R).
In the various methods for the decomposition of ΔE AB(R) there are no differences in
the definition of ES. This quantity can be easily computed with ab initio methods, and the
following recipe is the speediest and more used way of doing it.