Comparison of methods for deriving atomic charges from the electrostatic potential and moments

Four methods for deriving partial atomic charges from the quantum chemical electrostatic potential (CHELP, CHELPG, Merz-Kollman, and RESP) have been compared and critically evaluated. It is shown the charges strongly depend on how and where the potential points are selected. Two alternative methods are suggested to avoid the arbitrariness in the point-selection schemes and van der Waals exclusion radii: CHELP-BOW, which also estimates the charges from the electrostatic potential, but with potential points that are Boltzmann-weighted after their occurrence in actual simulations using the energy function of the program in which the charges will be used, and CHELMO, which estimates the charges directly from the electrostatic multipole moments. Different criteria for the quality of the charges are discussed. The CHELMO method gives the best multipole moments for small and medium-sized polar systems, whereas the CHELP-BOW charges reproduce best the total interaction energy in actual simulations. Among the standard methods, the Merz-Kollman charges give the best moments and potentials, but they show an appreciable dependence on the orientation of the molecule. We have also examined the recent warning that charges derived by a least-squares fit to the electrostatic potential normally are not statistically valid. It is shown that no rank-deficiency problems are encountered for molecules with up to 84 atoms if the least-squares fit is performed using pseudoinverses calculated by singular value decomposition and if constraints are treated by elimination.