Journal Article

Hardness maximization or equalization? New insights and quantitative relations between hardness increase and bond dissociation energy

von Szentpály, László

2017

Overview

It has been overlooked that the change of hardness, η , 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, Δ η  =  η mol – < η at >, of the molecular hardness, η mol , and the averaged atomic hardness, < η 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 Δ D =  2 D – D +   − D − . Quantitative expressions for Δ η 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, η VS , instead of the conventional ground state (GS) hardness, η 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 Be 2, B 2 , O 3 , and transition metal compounds. New linear relationships are discovered between the MHP hardness increase Δ η VS and the intrinsic bond dissociation energy D i . For bond formations, MHP and HEP are not compatible, and HEP does not qualify as an ordering rule.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V
• Subject: Approximation / Association reactions / Bonding / Characterization and Evaluation of Materials / Chemical bonds / Chemical reactions / Chemistry / Chemistry and Materials Science / Computer Appl. in Life Sciences / Computer Applications in Chemistry / Energy / Energy of dissociation / Equalization / Festschrift in Honor of Henry Chermette / Free energy / Hardness / Heat of formation / Metal compounds / Molecular Medicine / Original Paper / Principles / Symmetry / Theoretical and Computational Chemistry / Transition metal compounds / Valence / Validity