Numerical stabilities in fitting atomic charges to electric field and electrostatic potential

It is known that electrostatic potential (ESP) derived atomic charges for molecular systems suffer from rank deficiency in least-square fitting. In this paper, we studied numerical properties of atomic charges by fitting to ESP and electric field (EF) for a series of molecular systems, ranging from small molecules to peptides. Our study shows that although atomic charges of certain atoms in a molecule may differ a lot resulting from different fitting schemes, the effect on some observed physical properties of the molecules, such as solvation free energy and radial distributions of the solvent, are negligible. For all the molecules studied in this paper, it is shown that by incorporating EF terms in the least-square fitting, the rank of the least-squares matrix is increased, and the full rank is achieved when only EF terms are included. The current study demonstrates that by using EF, instead of the widely used ESP, in least-square fitting of atomic charges, one can obtain numerically more stable and better defined atomic charges in molecules. Such derived atomic charges may have more desirable properties and better numerical stabilities in studying detailed molecular processes such as in molecular dynamics simulation of macromolecules.