Abstract
This paper gives a critical account on the present status of the local hardness. We analyze the behavior of hardness related global, local, and nonlocal properties, paying particular attention to local hardness. Although this reactivity index has become very useful in predicting the regioselectivity of chemical reactions, the lack of a rigorous definition in the literature has shown that different approximations can yield different and sometimes contradictory conclusions. The present paper tries to provide insights into this controversial issue, starting from an approximate model of the hardness kernel and analyzing the features of the different models to evaluate the local and global hardnesses.
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