Electronegativity Additive Equalization Principle

Aiming to analytically expressing an atoms-in-molecule expression of electronegativity and chemical hardness, the starting point is to consider the expansion of the atomic eneigy of an atom, around its A-electronic isolated ( 0 ) status, up to the second order, when attempts to a molecular coordination throughout the chaige transfer (AA  

Following above convention, the relation between electronegativity of an atom in coordination and its isolated electronegativity and chemical hardness looks like  

the electronegativity of the total system (molecule) is representable, according with the Sanderson equalization principle of regional electronegativities, consecutively as  

This result, however, seems to prohibit the equality between global and regional electronegativities  

Beyond of the perplexity given by such inequalities, this paradox is simple solved observing that  

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As already mentioned, through DFT, it has been possible to explain the electronegativity equalization principle [1,7,10-13] and the hard and soft acids and bases principle [12,15-22] and, additionally, it has also been possible to introduce new ones like the maximum hardness principle [52,53] and the local hard and soft acids and bases principle [20,54—56]. 

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