Orbital vs. Density Electronic Localization in Bonding

Let s assume that, for instance, after the Hartree-Fock SCF computation is undertaken the set of canonical molecular one-electronic orbitals are determined so that the Slater determinantal wave function for 2N 

It has to be transformed into the corresponding localization wave function 

Fortunately, such orbital transformation is allowed by the flexibility carried by the determinantal wave function respecting aimitary transformation that takes the canonical into localized orbitals through the matrix (T) 

In order to complete the localization picture some physical criterion has to be assumed in order that matrix (T) to be determined. Such constraints may refer to the maximization of the distance between the electrons of the spatially non-localized orbitals, i.e., the so called Boys condition (Chakraborty, 2007)  

When employing the last condition one firstly gets  

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