Iterative Chemical Hardness of AIM

4 CHEMICAL HARDNESS OF ATOMS IN MOLECULES 3.4.1 ITERATIVE CHEMICAL HARDNESS OF AIM 

The chemical reactivity is a concept with a physical reality which contains the compromise between the tendency of electronegativity to promote the coordination and the inertia of the chemical species manifested by the chemical hardness (Ray et al., 1979 Parr Bartolotti, 1982 Pearson, 1985). 

PRINCIPLE AIM-HDl (of Le Chatelier-Braun) A primary change of the charges number of an atom A in a molecule, say dN, induces a (secondary) redistribution SN of the charges number between the atoms from the rest of the molecule, in order to decrease the primary hardness which produced the change in the atom A charge. The chemical potentials equilibrium and of chemical hardness in molecule will be ultimately accomplished by a readjustment of the net charges between the atoms (molecular fragments) involved in the primary and secondary processes. 

Therefore, by considering the secondary effects of the charges redistribution between the atoms in molecule, there is expected to obtain information about the global chemical strength of the molecule, by the hardness of the atoms or of the fragments of the molecule the forthcoming discussion follows the references (Nalewajski, 1988 Nalewajski  

For the beginning, the case of the diatomic molecule will be considered. In the primary movement of the charges in molecule one considers dN =dN 0,dNg = 0, so that the chemical potentials associated to the atoms as a result of this primary process will become  

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