Space partitioning based on the atom-centered multipole expansion

2 Space Partitioning Based on the Atom-Centered Multipole Expansion 

The atom-centered multipole expansion used in the density formalisms described in chapter 3 implicitly assigns each density fragment to the nucleus at which it is centered. Since the shape of the density functions is fitted to the observed density in the least-squares minimalization, the partitioning is more flexible than that based on preconceived spherical atoms. 

Two disadvantages of multipole partitioning should be mentioned. The first is that any density not fitted by the model is discarded in the partitioning process. Examination of the residual density is required to ensure the completeness of the set of modeling functions. The second is that very diffuse functions of the model, if included, violate the requirement of locality discussed above, and may lead to counterintuitive results. 

Nevertheless, multipole partitioning leads to very acceptable molecular electrostatic moments, as fully discussed in chapter 7. 

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