Further links between the maximum hardness principle and the hard/soft acid/base principle: insights from hard/soft exchange reactions

Ayers, Parr, and Pearson recently showed that insight into the hard/soft acid/base (HSAB) principle could be obtained by analyzing the energy of reactions in hard/soft exchange reactions, i.e., reactions in which a soft acid replaces a hard acid or a soft base replaces a hard base [J. Chem. Phys., 2006, 124, 194107]. We show, in accord with the maximum hardness principle, that the hardness increases for favorable hard/soft exchange reactions and decreases when the HSAB principle indicates that hard/soft exchange reactions are unfavorable. This extends the previous work of the authors, which treated only the "double hard/soft exchange" reaction [P. K. Chattaraj and P. W. Ayers, J. Chem. Phys., 2005, 123, 086101]. We also discuss two different approaches to computing the hardness of molecules from the hardness of the composing fragments, and explain how the results differ. In the present context, it seems that the arithmetic mean of fragment softnesses is the preferable definition.