The gyrobifastigium, not an uncommon shape in chemistry

Effect of particle anisotropy on the thermodynamics and kinetics of ordering transitions in hard faceted particles

Monte Carlo simulations were used to study the influence of particle aspect ratio on the kinetics and phase behavior of hard gyrobifastigia (GBF). First, the formation of a highly anisotropic nucleus shape in the isotropic-to-crystal transition in regular GBF is explained by the differences in interfacial free energies of various crystal planes and the nucleus geometry predicted by the Wulff construction. GBF-related shapes with various aspect ratios were then studied, mapping their equations of state, determining phase coexistence conditions via interfacial pinning, and computing nucleation free-energy barriers via umbrella sampling using suitable order parameters. Our simulations reveal a reduction of the kinetic barrier for isotropic-crystal transition upon an increase in aspect ratio, and that for highly oblate and prolate aspect ratios, an intermediate nematic phase is stabilized. Our results and observations also support two conjectures for the formation of the crystalline state from the isotropic phase: that low phase free energies at the ordering phase transition correlate with low transition barriers and that the emergence of a mesophase provides a steppingstone that expedites crystallization.

Solvents and Ligands Matter: Structurally Variable Palladium and Nickel Clusters Assembled by Tridentate Selenium- and Tellurium-Containing Schiff Bases

Structurally variable organochalcogen clusters containing palladium(II) and nickel(II) ions were assembled starting from the salicylidene-substituted dichalcogenides (Y-C₆H₄-N═CH-C₆H₄-OH)₂ ({HL^Y}₂, where Y = Se or Te), and palladium or nickel acetate. The tetrameric palladium clusters contain reduced chalcogenolato ligands {Y-C₆H₄-N═CH-C₆H₄-O)}^2- ({L'^Y}^2-, where Y = Se or Te), while the initially formed trimeric nickel clusters contain the intact, coordinated dichalcogenides. The palladium clusters have a general formula of [Pd₄(L'^Y)₄] and represent the first examples of palladium complexes where both a gyrobifastigial and a pseudocubane arrangement of the central Pd₄Y₄ unit could be established with the same ligand, only depending on the solvents used for crystallization. Reduced density gradient (RDG) considerations based on density functional theory calculations suggest that the commonly referred to stabilizing chalcogen-palladium or palladium-palladium interactions for the two geometric arrangements are weak van der Waals contacts resulting from the contact of two nonbinding lone pairs. In the case of the pseudocubane arrangement, a repulsive steric effect, which is indicated by RDG analysis, is clearly supported by the cuplike distortions detected in the solid-state structure of the compound. In contrast to the reactions with palladium acetate, where the dichalcogenides were cleaved, during similar reactions with nickel acetate, the dichalcogenides remained intact and trimeric clusters of the composition [Ni-μ²-κ²-(Ni{κ⁵-L^Y}₂)₂-μ²-(OAc)₂] (Y = Se, Te) were formed. Air oxidation and hydrolysis of [Ni-μ²-κ²-(Ni{κ⁵-L^Te}₂)₂-μ²-(OAc)₂] gave a rare example of a hexanuclear nickel cluster of the composition [Ni₂-κ⁵-(Ni₄-κ⁶-μ⁶-{(L'^Te₂O₃)(L'^TeO₂)₂}₂)-μ²-(H₂O)₂], which is composed of a well-defined framework consisting of tellurinic anhydride and tellurinate units, which proves the comparably higher oxidation sensitivity of the trinickel dichalcogenide complexes. Electron spray ionization mass spectrometry spectra of both the palladium and nickel clusters indicate that they show fluctional behavior with varying nuclearity in solution and can adopt multiple charge states especially because of the noninnocence of the chalcogen-based ligands. The complexes were fully characterized by spectroscopic methods, elemental analyses, and X-ray diffraction.