David M. Gange

Charges fit to electrostatic potentials. II. Can atomic charges be unambiguously fit to electrostatic potentials

The present work examines the conditioning of the least‐squares matrix for obtaining potential derived charges and presents a modification of the CHELP method for fitting atomic charges to electrostatic potentials. Results from singular value decompositions (SVDs) of the least‐squares matrices show that, in general, the least‐squares matrix for this fitting problem will be rank deficient. Thus, statistically valid charges cannot be assigned to all the atoms in a given molecule. We find also that, contrary to popular notions, increasing the point density of the fit has little or no influence on the rank of the problem. Improvement in the rank can best be achieved by selecting points closer to the molecular surface. Basis set has, as expected, no effect on the number of charges that can be assigned. Finally, a well‐defined, computationally efficient algorithm (CHELP‐SVD) is presented for determining the rank of the least‐squares matrix in potential‐derived charge fitting schemes, selecting the appropriate subset of atoms to which charges can be assigned based on that rank estimate, and then refitting the selected set of charges.

Beyond CHELP: improved potential derived charges for sugars.

The partitioning of the overall molecular charge distribution into atom centered monopole charges, while quantum mechanically ill-defined, is nevertheless a technique which finds applications in several broad classes of chemical problems. Charges derived from fits to electrostatic potentials have an intuitive appeal since, in principle, these could be derived from either theoretical or experimental data. It has been noted, however, that such potential derived charges can be conformationally dependent in ways that do not appear to reflect the changes in the molecular wavefunction. Both the algorithm used for selecting points at which the molecular electrostatic potential will be fit and the density of points used in the fit have been suggested to influence the resultant charges. Recently [Stouch TR, Williams DE (1992) J Comp Chem 13: 622–32; Stouch TR, Williams DE (1993) J Comp Chem 14: 858–66] it has been noted that numerical difficulties may make it impossible to fit all the atomic charges in a molecule. Singular value decomposition (SVD) of the linear least squares matrices used in fitting atom based monopoles to molecular electrostatic potentials provides a tool for evaluating the integrity of the calculated charges. Based on the SVD analysis for a selected group of molecules we have noted particularly that increasing the molecular size reduces the fraction of charges which can be validly assigned. Users of PD derived charges, especially those who are using those charges for tasks other than reproduction of the MEP, should be aware that there is a high probability that a significant portion of those charges are statistically unreliable. Therefore, charges in many biological molecules, such as sugars, prove to be difficult to obtain by potential derived (PD) methods such as CHELP or CHELPG. Results from the SVD can be used to both assess PD charges and to generate an improved, albeit incomplete, set. Improved PD fits are presented for a series of simple saccharides. Abbreviations: HF, Hartree-Fock; LLS, linear least squares; MEP, molecular electrostatic potential; PD, potential derived; SVD, singular value decomposition