Electronegativity as Connectivity of Atoms in Molecules

One of the special cases of atoms in molecule, yet important, is that when the total molecular energy can be partitioned into a sum of the atomic contributions  

It basically unfolds the sum over the expected values of kinetic energies, of nuclei-electrons, of electrons-electrons and of nuclei-nuclei interactions. 

In this framework, we can consider a spherical distribution of the atoms clouds charge in molecule, so that the molecular energy can be rewritten accordingly (Genechten et al., 1987)  

From the atoms-in-molecules (AIM) energy expression (3.58), the chemical potential, respectively the effective electronegativity with changed sign, for the atom A in molecule automatically results  

Worth noting the dependency of the electronegativity of the A-atom in molecule by the chemical potential and force of the neutral atom,, 7, along 

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