Charge Model 5: An Extension of Hirshfeld Population Analysis for the Accurate Description of Molecular Interactions in Gaseous and Condensed Phases

We propose a novel approach to deriving partial atomic
charges
from population analysis. The new model, called Charge Model 5 (CM5),
yields class IV partial atomic charges by mapping from those obtained
by Hirshfeld population analysis of density functional electronic
charge distributions. The CM5 model utilizes a single set of parameters
derived by fitting to reference values of the gas-phase dipole moments
of 614 molecular structures. An additional test set (not included
in the CM5 parametrization) contained 107 singly charged ions with
nonzero dipole moments, calculated from the accurate electronic charge
density, with respect to the center of nuclear charges. The CM5 model
is applicable to any charged or uncharged molecule composed of any
element of the periodic table in the gas phase or in solution. The
CM5 model predicts dipole moments for the tested molecules that are
more accurate on average than those from the original Hirshfeld method
or from many other popular schemes including atomic polar tensor and
Löwdin, Mulliken, and natural population analyses. In addition,
the CM5 charge model is essentially independent of a basis set. It
can be used with larger basis sets, and thereby this model significantly
improves on our previous charge models CMx (x = 1–4 or 4M) and other methods that are prone to
basis set sensitivity. CM5 partial atomic charges are less conformationally
dependent than those derived from electrostatic potentials. The CM5
model does not suffer from ill conditioning for buried atoms in larger
molecules, as electrostatic fitting schemes sometimes do. The CM5
model can be used with any level of electronic structure theory (Hartree–Fock,
post-Hartree–Fock, and other wave function correlated methods
or density functional theory) as long as an accurate electronic charge
distribution and a Hirshfeld analysis can be computed for that level
of theory.