Potential-Derived Multicenter Multipole Models

From the purely mathematical point of view, the main considerations in choosing the type of model representing the electric potential around a molecule are accuracy and convergence. There is no unique way to satisfy these requirements. The location of the expansion centers is arbitrary, and the number of terms in the expansion can vary. From the purely chemical point of view, the main considerations are chemical reasonableness and transferability. Neither of these goals is easy to even define, let alone achieve. Chemical reasonableness implies a consistency with related established concepts in chemistry. Transferability implies the ability to predict behavior of related molecules without detailed calculations. 

Purely mathematical models can be criticized as curve fitting exercises with very little appeal to chemical intuition and very little transferability. But models that seem reasonable chemically can be inaccurate, and maybe they will not be transferable either. To set some stakes on this rugged landscape, let us first examine the atomic multipole model, In this model each atom is a multipolar center which makes a contribution to the electric potential. 

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