Net atomic charges reproducing the electrostatic potential

For a study of nonbonded interactions, it is of practical importance to identify the net atomic charges that best reproduce the potential on the periphery of the 

The methods adjust the atomic net charges q in a least-squares minimization with a discrepancy function equal to the sum of the potential differences over all n sampling points  

The observed and fitted potentials in the region of a peptide link are compared in Fig. 8.6. Except for the inner regions, the agreement is satisfactory. In particular, the pronounced negative areas in the proximity of the oxygen atom are well reproduced. 

Francl et al. (1996) examined the conditioning of the least squares matrix in the fitting procedure, and conclude that the method cannot be used to assign statistically valid charges to all atoms in a given molecule. This problem cannot be alleviated by the selection of more sampling points, and thus may require the introduction of chemical constraints to reduce the number of charges to be determined. 

Rather than fit the potential at the periphery of the molecule, Su (1993) has fitted 0 at the nuclear positions. The potential at the nuclear positions can be directly related to the total energy of a molecule (chapter 9) (Polizer 1981), as well as to the atomic ionization energies (as discussed in section 8.4). 

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