Magic numbers for metallic clusters and the principle of maximum hardness.

It is shown that for relatively more stable metallic clusters (those with magic number of atoms) the chemical hardness (I-A) too is relatively larger. Thus the occurrence of magic numbers for metal clusters whose stability is determined by their electronic shell structure can be understood as a manifestation of the principle of maximum hardness. This may also represent a possible way of delineating clusters with stability dominated by their electronic shell structure from those for which the magic numbers occur as a result of their geometric structure.