The local hardness, ($) over tilde eta(lambda)(r), a local quantity describing reactivity following Pearson’s hard and soft acids and bases (HSAB) principle, is analyzed in detail. These considerations lead to the introduction of two possible working equations for the local hardness and a new quantity, the hardness density, h lambda(r) better fitting the picture of a counterpart of the local softness. On the basis of the study of intra- and intermolecular reactivity sequences for an electrophilic attack on monosubstituted benzenes PhX (X = O-, NH2, OH, F, CN, NO2, CHO, NH3+, and CHCH2) a better insight into the physical meaning of these density functional theory related quantities, and the molecular electrostatic potential, is acquired. These new insights in turn lead to the introduction of a general form of a new global reactivity index combining the local softness and the newly defined hardness density.