Population Analysis of AIM

Related with the chemieal bonding description, there is for first interest also a method for determining the atomic partition function in molecule here the Mulliken picture of the population analysis, a., will be presented yet modified, in the way of assuming the overlapping of charge unequally distributed between the atoms involved in the bond. Considering the linear combination of atomic orbitals (LCAO) expansion of the molecular function, the density assoeiated to the atomic orbitals F. is written (Rychlewski Parr, 1986 Li Parr, 1986)  

Also in this case the optimization condition can be imposed, i.e. 

Noting, for simplicity, that a. = a for all the indices i and j, one obtains (Rychlewski Parr, 1986 Li Parr, 1986)  

Note that when A and B are atoms of the same species, form the 

From all of the analyzed properties of the atoms in molecule, while taking into accoimt the Definition of AIM2, another fundamental principle of the AIM approach can be formulated  

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