Abstract
It has been overlooked that the change of hardness, $\eta$, upon bonding is intimately connected to thermochemical cycles, which determine whether hardness is increased according to Pearson's ``maximum hardness principle'' (MHP) or equalized, as expected by Datta's ``hardness equalization principle'' (HEP). So far the performances of these likely incompatible ``structural principles'' have not been compared. Computational validations have been inconclusive because the hardness values and even their qualitative trends change drastically and unsystematically at different levels of theory. Here I elucidate the physical basis of both rules, and shed new light on them from an elementary experimental source. The difference, $\Delta$$\eta$ = $\eta$mol -- <$\eta$at>, of the molecular hardness, $\eta$mol, and the averaged atomic hardness, <$\eta$at>, is determined by thermochemical cycles involving the bond dissociation energies D of the molecule, D+ of its cation, and D− of its anion. Whether the hardness is increased, equalized or even reduced is strongly influenced by $\Delta$D = 2D -- D+ − D−. Quantitative expressions for $\Delta$$\eta$ are obtained, and the principles are tested on 90 molecules and the association reactions forming them. The Wigner-Witmer symmetry constraints on bonding require the valence state (VS) hardness, $\eta$VS, instead of the conventional ground state (GS) hardness, $\eta$GS. Many intriguingly ``unpredictable'' failures and systematic shortcomings of said ``principles'' are understood and overcome for the first time, including failures involving exotic and/or challenging molecules, such as Be2, B2, O3, and transition metal compounds. New linear relationships are discovered between the MHP hardness increase $\Delta$$\eta$VS and the intrinsic bond dissociation energy Di. For bond formations, MHP and HEP are not compatible, and HEP does not qualify as an ordering rule.
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