The generalized maximum hardness principle revisited and applied to solids (Part 2)

Quadripartite bond length rule applied to two prototypical aromatic and antiaromatic molecules

CONTEXT

In 2000, a remarkably simple relationship was introduced, which connected the calculated geometries of isomolecular states of three different multiplicities. These encompass a ground single state, the first excited triplet state, as well as related radical anion and radical cation. The rule allows the prediction of the geometry of one of the species if the three remaining ones are known. Here, we verify the applicability of this bond length rule for two small planar cyclic organic molecules, i.e., benzene and cyclobutadiene, which stand as prototypical examples of, respectively, aromatic and antiaromatic systems. We see that the rule works fairly well to benzene, and it works independently for quinoid as well as for anti-quinoid minima, despite the fact that radical anion species poses challenges for correct theoretical description.

METHODS

To obtain chosen electronic state equilibrium geometries, three types of computational approaches were utilized: fast and efficient density functional theory DFT, the coupled cluster method CC2, the complete active space self-consistent field (CASSCF) approach, and the most accurate but also resource-consuming perturbation theory with multireference wavefunction (CASPT2) with a default value and without IPEA-shift. Dunning and co-workers correlation-consistent basis sets (aug-)cc-pVXZ (X = D, T, Q) were employed. Gaussian 16 revision A.03, Turbomole 7.1, and Molcas 8.0 computational software were used.

Defect Trapping and Phase Separation in Chemically Doped Bulk AgF2

We report a computational survey of chemical doping of silver(II) fluoride, which has recently attracted attention as an analogue of La₂CuO₄—a known precursor of high-temperature superconductors. By introducing fluorine defects (vacancies or interstitial adatoms) into the crystal structure, we obtain nonstoichiometric, electron- and hole-doped polymorphs of AgF_2±x. We find that the ground-state solutions show a strong tendency for localization of defects and of the associated electronic states, and the resulting doped phases exhibit insulating or semiconducting properties. Furthermore, the distribution of Ag(I)/Ag(III) sites which appear in the crystal structure points to the propensity of the AgF₂ system for phase separation upon chemical doping, which is in line with observations from previous experimental attempts. Overall, our results indicate that chemical modification may not be a feasible way to achieve doping in bulk silver(II) fluoride, which is considered essential for the emergence of high-T_c superconductivity.

A theoretical study of the 1/32, 1/16, and 1/8 electron- and hole-doped AgF₂ reveals that vacancies and adatoms have a tendency for localization, that is, formation of mixed-, rather than intermediate-valence, fluoride systems, which results in a persistent band gap at the Fermi level.

High-temperature superconductivity as viewed from the maximum hardness principle

The Maximum Hardness Principle - and its reformulation by Chattaraj as the Minimum Polarizability Principle - is an immensely useful concept which works in support of a chemical intuition. As we show here, it may also be used to rationalize the scarcity of high-temperature superconductors, which stems - inter alia - from rarity of high-density of state metals in Nature. It is suggested that the high-temperature oxocuprate superconductors as well as their iron analogues - are energetically metastable at T ➔ 0 K and p ➔ 0 atm conditions, and their tendency for disproportionation is hindered only by the substantial rigidity of the crystal lattice, while the phase separation and/or superstructure formation is frequently observed in these systems. This hypothesis is corroborated by hybrid density functional theory theoretical calculations for Na- (thus: hole) or La- (thus: electron) doped CaCu(II)O2 precursor. Non-equilibrium synthetic methods are suggested to be necessary for fabrication of high-temperature superconductors of any sort. Graphical abstract Doped oxocuprate superconductors are shown to be unstable with respect to phase separation (disproportionation) in accordance with the Maximum Hardness Principle; their metastability is mostly due to rigidity of [CuO2] sheets and preparation using high-temperature conditions.