Universal Method to Calculate the Stability, Electronegativity, and Hardness of Dianions

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

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, Δη = 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 ΔD = 2D - D ⁺  - D ^-. Quantitative expressions for Δη 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, B₂, O₃, and transition metal compounds. New linear relationships are discovered between the MHP hardness increase Δη _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.

Symmetry laws improve electronegativity equalization by orders of magnitude and call for a paradigm shift in conceptual density functional theory

The strict Wigner-Witmer symmetry constraints on chemical bonding are shown to determine the accuracy of electronegativity equalization (ENE) to a high degree. Bonding models employing the electronic chemical potential, μ, as the negative of the ground-state electronegativity, χ(GS), frequently collide with the Wigner-Witmer laws in molecule formation. The violations are presented as the root of the substantially disturbing lack of chemical potential equalization (CPE) in diatomic molecules. For the operational chemical potential, μ(op), the relative deviations from CPE fall between -31% ≤ δμ(op) ≤ +70%. Conceptual density functional theory (cDFT) cannot claim to have operationally (not to mention, rigorously) proven and unified the CPE and ENE principles. The solution to this limitation of cDFT and the symmetry violations is found in substituting μ(op) (i) by Mulliken's valence-state electronegativity, χ(M), for atoms and (ii) its new generalization, the valence-pair-affinity, α(VP), for diatomic molecules. Mulliken's χ(M) is equalized into the α(VP) of the bond, and the accuracy of ENE is orders of magnitude better than that of CPE using μ(op). A paradigm shift replacing the dominance of ground states by emphasizing valence states seems to be in order for conceptual DFT.

Chemical potential of molecules contrasted to averaged atomic electronegativities: alarming differences and their theoretical rationalization

We present the first large-scale empirical examination of the relation of molecular chemical potentials, μ(0)(mol) = -½(I(0) + A(0))(mol), to the geometric mean (GM) of atomic electronegativities, <χ(0)(at)>(GM) = <½(I(0) + A(0))(at)>(GM), and demonstrate that μ(0)(mol) ≠ -<χ(0)(at)>(GM). Out of 210 molecular μ(0)(mol)values considered more than 150 are not even in the range min{μ(0)(at)} < μ(0)(mol) < max{μ(0)(at)} spanned by the μ(0)(at) = -χ(0)(at) of the constituent atoms. Thus the chemical potentials of the large majority of our molecules cannot be obtained by any electronegativity equalization scheme, including the "geometric mean equalization principle", ½(I(0) + A(0))(mol) = <½(I(0) + A(0))(at)>(GM). For this equation the root-mean-square of relative errors amounts to SE = 71%. Our results are at strong variance with Sanderson's electronegativity equalization principle and present a challenge to some popular practice in conceptual density functional theory (DFT). The influences of the "external" potential and charge dependent covalent and ionic binding contributions are discussed and provide the theoretical rationalization for the empirical facts. Support is given to the warnings by Hinze, Bader et al., Allen, and Politzer et al. that equating the chemical potential to the negative of electronegativity may lead to misconceptions.

Ruling out any electrophilicity equalization principle

Two gas-phase electrophilicity indices, ω(1) and ω(2), introduced by Parr, von Szentpály, and Liu are tested with respect to the recently proposed "principle of electrophilicity equalization." Although electronegativity is equalized in many cases, there is no functioning "hardness equalization principle" nor are the electrophilicity indices principally equalized during molecule formation: they cannot be generally expressed as the mean of the corresponding atomic indices. For large metal clusters and [n]fullerenes, both electrophilicity indices increase proportional to n(1/3) and n(1/2), respectively, as the hardness values converge to zero. Two "principles" are shown to be obsolete: the "geometric mean principle for hardness equalization" and the "principle of electrophilicity equalization", with the latter somewhat relying on the former. An appeal is made to exercise careful judgment before proposing and publishing new structural principles.