The Standard Mulliken Formula

Mulliken s population analysis is rooted in the LCAO (linear combination of atomic orbitals) formulation it is not directly applicable to other types of wavefunctions. With Cr i representing the coefficient of the rth type of atomic orbital (li, 2s, etc.) of atom k in the ith molecular orbital, we describe the latter by 

Atomic Charges, Bond Properties, and Molecular Energies, by Sandor Fliszar Copyright 2009 John Wiley Sons, Inc. 

The problem with this analysis is that the selection of one or another basis set dramatically affects the calculated charges and occasionally leads to unphysical results [44]. Overlap populations (8.2) are largely responsible for this situation. 

Mulliken s formula for Nk implies the half-and-half (50/50) partitioning of all overlap populations among the centers k,l. involved. On one hand, this distribution is perhaps arbitrary, which invites alternative modes of handling overlap populations. On the other hand, Mayer s analysis [172,173] vindicates Mulliken s procedure. So we may suggest a nuance in the interpretation [44] departures from the usual halving of overlap terms could be regarded as ad hoc corrections for an imbalance of the basis sets used for different atoms. But one way or another, the outcome is the same. It is clear that the partitioning problem should not be discussed without explicit reference to the bases that are used in the LCAO expansions. 

A modified partitioning procedure is considered in the next section. 

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