Partial atomic charges and screened charge models of the electrostatic potential

We propose a new screened charge method for calculating partial atomic charges in molecules by electrostatic potential (ESP) fitting. The model, called full density screening (FDS), is used to approximate the screening effect of full charge densities of atoms in molecules. The results are compared to the conventional ESP fitting method based on point charges and to our previously proposed outer density screening (ODS) method, in which the parameters are reoptimized for the present purpose. In ODS, the charge density of an atom is represented by the sum of a point charge and a smeared negative charge distributed in a Slater-type orbital (STO). In FDS, the charge density of an atom is taken to be the sum of the charge density of the neutral atom and a partial atomic charge (of either sign) distributed in an STO. The ζ values of the STOs used in these two models are optimized in the present study to best reproduce the electrostatic potentials. The quality of the fit to the electrostatics is improved in the screened charge methods, especially for the regions that are within one van der Waals radius of the centers of atoms. It is also found that the charges derived by fitting electrostatic potentials with screened charges are less sensitive to the positions of the fitting points than are those derived with conventional electrostatic fitting. Moreover, we found that the electrostatic-potential-fitted (ESP) charges from the screened charge methods are similar to those from the point-charge method except for molecules containing the methyl group, where we have explored the use of restraints on nonpolar H atoms. We recommend the FDS model if the only goal is ESP fitting to obtain partial atomic charges or a fit to the ESP field. However, the ODS model is more accurate for electronic embedding in combined quantum mechanical and molecular mechanical (QM/MM) modeling and is more accurate than point-charge models for ESP fitting, and it is recommended for applications involving QM/MM methods. Since the screened charges describe the electrostatic potentials more accurately than point charges, since they asymptotically act as point charges at long distances, and since the electrostatic potential in terms of the screened charges is still a sum of functions centered at the atoms, the screened-charge representation of the electrostatic potential can be used in the same way as the conventional point-charge representation to model the electrostatic interactions, but it is more realistic. For the H atom and p block elements, the error in the fit to the electrostatic potential is reduced by about a factor of 3, and the sensitivity of the derived partial atomic charges to the choice of fitting points is reduced by about a factor of 2. For s and d block elements, there are also improvements in the inner regions but not necessarily in the outer regions.