Thermodynamic Properties for Applications in Chemical Industry via Classical Force Fields - Multiscale Molecular Methods in Applied Chemistry - page 216

advanced ab initio methods, e.g., the coupled cluster method together with correla-
tion consistent basis sets, can also be used for such calculations [ 83 ].
Electrostatic multipole moments of molecules, i.e., dipoles, quadrupoles, or
octupoles, can also be obtained from QM wave functions. Methods like distributed
multipole analysis (DMA) [ 84 ] or AIM [ 85 ] assign multipole moments to each
atom or to specified sites of a molecule. The DMA method estimates multipole
moments from QM wave functions and the highest obtained multipole moment
depends on the basis set used. There are no limitations in this method on number or
position of the multipoles; anisotropic effects due to lone pairs or

p electrons can

also be considered.
A simpler approach, typically employed for small symmetric molecules, is to
estimate ideal point multipoles by integration over the orbitals resulting from the
calculated electron density distribution. The accuracy of the calculated moments is
highly dependent on the basis set, electron correlation, and molecular geometry
[ 19 ]. The MP2 level of theory with the 6-31G * polarizable basis set is broadly
applied in such calculations. In order to save computational effort, MP2 is often
executed as a single point calculation for a geometry determined on the basis of a
lower level of theory.
In condensed phases, the mutual polarization of solute and solvent molecules
should be considered. This can be done by placing a single molecule into a cavity
that is surrounded by a dielectric continuum and assigning the dielectric constant of
the liquid to it [ 86 ]. Thus, the molecule in the cavity induces polarization in the
surrounding dielectric continuum, which in turn interacts with the electron density
of the molecule. There are numerous techniques of varying complexity; a review
can be found e.g. in [ 87 ]. One of the pioneering techniques is the self consistent
reaction field (SCRF) [ 88 , 89 ] approach. Some variations of this method treat the
continuum solvent as a conductor, such as in the conductor-like screening model
(COSMO) [ 90 ] or the polarizable continuum model (PCM) [ 87 ]. Another rather
simple approach to account for condensed phase polarization is the multipole
scaling procedure [ 80 , 91 ].

3.1.3 Intramolecular Interactions

The geometric parameters of force fields, i.e., reference bond lengths and bond
angles, are commonly assigned according to equilibrium molecular geometries
determined by QM, combined with an energy minimization algorithm. The agree-
ment between ab initio and experimental equilibrium geometries increases with
the size of the basis set and the level of theory. However, the HF level of theory
with a relative small basis set, such as 6-31G, is sufficient to obtain good results
[ 60 , 86 , 92 ]. Fortuitously, the STO-3G basis set often performs well with respect to
molecular geometry, despite its deficiencies. In general, the bond lengths predicted
by the STO-3G basis set are too long, while those obtained with the 6-31G basis set
are too short [ 19 ]. As an alternative QM approach, DFT, using gradient corrected
and hybrid methods, can be applied, since it is known to achieve excellent results