CHARGES FIT TO ELECTROSTATIC POTENTIALS .2. 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 o f the CHELP method for fitting atomic charges to electrostatic potenti als. Results from singular value decompositions (SVDs) of the least-sq uares matrices show that, in general, the least-squares matrix for thi s fitting problem will be rank deficient. Thus, statistically valid ch arges 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. Impr ovement in the rank can best be achieved by selecting points closer to the molecular surface. Basis set has, as expected, no effect on the n umber of charges that can be assigned. Finally, a well-defined, comput ationally efficient algorithm (CHELP-SVD) is presented for determining the rank of the least-squares matrix in potential-derived charge fitt ing schemes, selecting the appropriate subset of atoms to which charge s can be assigned based on that rank estimate, and then refitting the selected set of charges. (C) 1996 by John Wiley & Sons, Inc.