Thermodynamic Properties for Applications in Chemical Industry via Classical Force Fields - Multiscale Molecular Methods in Applied Chemistry - page 215

required. Thus, a large number of molecular separations and mutual orientations
must be considered, which is computationally very demanding. Once the appropri-
ate points of the energy landscape are obtained, they can be fitted to an analytical
function [ 69 ]. Note that the liquid behavior is not well reproduced by ab initio
calculations, since only small clusters can be handled [ 70 ]. A review of QM
methods used for the calculation of interaction energies and potential energy
sampling is given in [ 69 ].

3.1.2 Electrostatic Interactions

Electrostatic properties of molecules can be determined from the electron density
distribution obtained by QM. Different methods have been proposed for this end.
E.g., atomic charges can be estimated using different partitioning methods like
Mulliken and L odwin population analysis [ 71 , 72 ], the charge model 2 (CM2)

formalism [ 73 ], natural population analysis (NPA) [ 74 ], or the theory of atoms in
molecules (AIM) [ 75 ]. A comparison of these methods for the calculation of atomic
charges can be found, e.g., in [ 76 ]. Atomic charges calculated by population
methods are often considered to be inappropriate for force field parameterization
[ 19 ]. The most common approach is to derive the atomic charges from the electro-
static potential (ESP), applying either semi-empirical density functional theory
(DFT), Hartree-Fock (HF), or post HF methods [ 77 ]. The ESP is a QM observable
which can be determined from wave functions. In this method, atomic charges are
fitted to the calculated ESP for a series of points in a three-dimensional spatial grid
surrounding the molecule. The fitting procedure is performed with the constraint
that the sum of the charges equals the net charge of the molecule. The positions
where the potential is evaluated are often chosen just outside the atomic Van der
Waals radii, because the accuracy of electrostatics is most important there. Differ-
ent methods consider different sampling points where the ESP is calculated, i.e., the
distance from the Van der Waals surface [ 19 ]. The CHELP [ 78 ] method considers
spherical shells extended to 3 ˚ from the Van der Waals surface, whereas the
CHELPG [ 79 ] method contemplates a cubic grid of points extended to 2.8 ˚ .
A restrained electrostatic potential (RESP) [ 80 ] fit is often used to include restric-
tions to the obtained charges, e.g., to restrain charges in buried atoms. RESP can
be employed to fit partial charges to the ESP of a single or multiple conformers [ 77 ].
There are various difficulties with the ESP fitting approach, like conformation,
basis set dependency, and the presence of buried atoms. The inclusion of mul-
tiple conformations in the fitting procedure can be employed to overcome
these problems [ 81 ]. A comparison of some commonly applied schemes can be
found in [ 82 ].
The second order Møller-Plesset (MP2) perturbation theory is often adequate in
terms of accuracy and efficiency for describing the ESP [ 10 ]. It is generally
considered that the 6-31G * basis set gives reasonable results [ 19 ]. This basis set
results in dipole moments that are 10-20% larger than expected in the gas phase,
which is desirable for deriving charges for liquid phase simulations [ 80 ]. More

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