As in the original RESP procedure, a hyperbolic restraint function on each atomic charge is added to the mean square difference to reduce the over polarization certain atomic groups, which proved beneficial when fitting to both methylated base caps as well as lone-pair / host atom combinations. Here, the atomic charge q is defined as the sum of an atom's nuclei, electrons, and any lone-pair populations associated that that atom. Additionally, a cost function on the density exponents is also added to the Lagrangian to prevent them from becoming to large, essentially making them more point-like. Some carbon-bonded hydrogens and certain nitrogens were assigned an α parameter that was very large compared to it's neighboring atoms, yet a much smaller, more diffusive parameter resulted an an overall RMSD that was nearly identical. To mitigate the effect, we added an additional cost function to L DRESP to ensure that all ζ frz were not to dissimilar from each other. As a result, the scaling factor f (ζ frz i ) was set to zero if ζ frz i was less than d and equal to unity if greater than d. We found that c = 0.003 a.u. and d = 5 bohr -1 remedied this exponential enlargement problem and had only a minimal effect on the overall ESP fit.