Site multipole series

In practice, site multipole series for the electric potential are truncated, usually at quadrupoles or less. If higher terms in the series are not actually calculated, the degree of convergence is uncertain. The PD method, discussed in the next section, avoids this problem by optimizing for the best possible model of the electric potential with a given number of multipole terms. Thus in the PD method convergence is always the best possible for a given set of multipole parameters and potential points. 

Indeed, this idea lies at the heart of the venerable notion of assigning partial charges to the atoms in a molecule [17]. One may think of this practice as a representation of the true charge distribution of the molecule by a series of distributed multipoles (in this case, limited to monopoles) at various sites, namely, atomic centers. Even if limited to monopoles, the act of spreading them out over the entire molecule is equivalent in some sense to simulation of high orders of molecular center-based multipoles. 

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