AbstractIn a very recent article (Torrent‐Sucarrat et al., J Comput Chem 2007, 28, 574), we have shown how to evaluate the global hardness for polyatomic molecules using a hardness kernel approximation. We present here an extension of this previous work by improving the model used to evaluate the hardness kernel and the Fukui function. In addition, the concept of the local hardness is analyzed in detail, and for the first time, profiles of local hardness with kinetic and exchange‐correlation contributions for polyatomic molecules are reported. Finally, the concept of condensed atomic hardness is introduced and its usefulness as chemical reactivity descriptor is examined. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008