Information Theory, the Shape Function, and the Hirshfeld Atom

Following the work of Nalewajski and Parr, there has been a surge of interest in the use of information theory to describe chemical bonding and chemical reactions. However, the measure of “information” used by Nalewajski and Parr is not any of the usual conventional entropies, chiefly because the electron density is not normalized to one. The consequences of this are discussed, and a solution is constructed using the shape function and an “entropy of mixing” term. The same revision, however, cannot be made when if the Tsallis entropy, instead of the Shannon form, is used. This serves to emphasize that the Hirshfeld atom is a very specific result, associated only with logarithmic measures of information. A less specific derivation due to Nalewajski provides one resolution to this quandary; this derivation is analyzed in detail.