The Delta f(r) descriptor characterizes the variations of the absolute hardness when the external potential changes. In this work, the Delta f(r) descriptor is regarded through three different theoretical points of view: its relations with the Fukui functions; its links with the covalent interaction energy; and finally its compliance with the Principle of Maximum Hardness. It appears from the three studies that the sign of the descriptor is able to characterize the electrophilic/nucleophilic behavior of a molecular site. (c) 2006 Elsevier B.V. All rights reserved.