(8) Class I charges are derived by using nonquantum mechanical approaches such as classical models of dipoles (9) or by using a model to extract the charges directly from experimental data, (10) e.g., from the experimental dipole moment of a diatomic molecule. We recall here that various schemes for assigning charges in a molecule fall into four distinct categories.
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We note that a model that gives accurate molecular dipole moments for small molecules should give accurate bond dipoles and hence accurate resultant molecular dipole moments for large molecules. Therefore, we will use the molecular dipole moment as the key quantity that the mapped charges should reproduce. Since one may easily normalize the atomic charges to reproduce the total charge on the molecule, the leading error in the molecular charge distribution for molecules lacking inversion symmetry is the molecular dipole moment. Our goal here is to develop a general scheme to map a molecule’s Hirshfeld charges onto a new set of charges that provide a reasonable representation of the electrostatic potential for molecular modeling without the atomic dipoles. If one uses only the charges from Hirshfeld analysis, the molecular dipole moment is reproduced less accurately and is usually underestimated. (7) However, for many purposes in molecular modeling, one wants to use a simplified representation of the molecular charge distribution that involves only atomic charges, i.e., the distributed monopole approximation without higher multipole moments. The molecular dipole moment (as well as all higher multipole moments) can be reproduced exactly using quantities derived from Hirshfeld population analysis (1-6) for the molecular dipole moment, this requires using the atomic charges and atomic dipoles. 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. The CM5 model does not suffer from ill conditioning for buried atoms in larger molecules, as electrostatic fitting schemes sometimes do.
![accurate 5 accurate 5](https://softwareaccuratejkt.com/wp-content/uploads/2019/03/acc-5-300x199.png)
CM5 partial atomic charges are less conformationally dependent than those derived from electrostatic potentials. 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. In addition, the CM5 charge model is essentially independent of a basis set. 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. 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.
![accurate 5 accurate 5](https://i.ytimg.com/vi/syDKigh-CxA/maxresdefault.jpg)
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.
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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. 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. We propose a novel approach to deriving partial atomic charges from population analysis.