Population Analysis Based on the Electrostatic Potential

One area where the concept of atomic charges is deeply rooted is force field methods 

One way of eliminating the problem with conformationally dependent charges is to add additional constraints, for example forcing the three hydrogens in a methyl group to have identical charges or averaging over different conformations. The more 

Another problem of atomic charges determined by fitting is related to the absolute accuracy. Although inclusion of charges on all atoms does not significantly improve the results over those determined from a reduced set of parameters, the absolute deviatioiL- 

One area where the concept of atomic charges is deeply rooted is force field methods (Chapter 2). A significant part of the non-bonded interaction between polar molecules is described in terms of electrostatic interactions between fragments having an internal asymmetry in the electron distribution. The fundamental interaction is between the Electrostatic Potential (ESP) generated by one molecule (or fraction of) and the charged particles of another. The electrostatic potential at position r is given as a sum of contributions from the nuclei and the electronic wave function. 

A common way of deriving partial atomic charges in force fields is to choose a set of parameters that in a least squares sense generates the best fit to the actual electrostatic potential as calculated from an electronic wave function. The electrostatic 

If such distributed multipoles are assigned for each pair of basis functions, the electrostatic potential as seen from outside the charge distribution is reproduced exactly. This, however, would mean that -Mbasis different sites are required. In practice, only the nuclei and possibly the midpoints of all bonds are selected as multipole points, and 

The examples in Section 9.1 illustrate that it would be desirable to base a population analysis on properties of the wave function or electron density itsell and not on the basis set chosen for representing the wave function. The electron density is the square of the wave function integrated over Aeiec - 1 coordinates (it does not matter which coordinates since the electrons are indistinguishable). 

The division into atonaic basins requires a choice to be made as to whether a certain point in space belongs to one nucleus or another, and several different schemes have been proposed. 

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Population Analysis Based on the Electrostatic Potential 220 11.7.2 The Dipole Moment of CO 286... 

Population analysis in semiempirical methods fall into two categories. Methods including overlap in the Fock equations use the Mulliken population analysis. The majority of semiempirical methods uses the ZDO approximation, and the net charges are interpreted on the basis of symmetrically orthog-onalized AOs. It is pointed out that this interpretation is not exactly valid, because of truncation and empirical adjustment. But the corresponding nonsymmetrical orthogonalization is not uniquely defined. Charge models based on semiempirical wave functions play an important role in the calculation of molecular electrostatic potentials for reactivity. 

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