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

Marenich, A. V.; Jerome, S. V.; Cramer, C. J.; Truhlar, D. G.

* J. Chem. Theor. Comput.*
**2012**, *8*, 527
(doi:10.1021/ct200866d).

We propose a novel approach to derive 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 basis set; it can be used with larger basis sets, and thereby this model significantly
improves on our previous charge models CM*x*
(*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.