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Simple algebraic equations show that the bulk compressibility in spinel-type compounds can be expressed by means of cation oxide polyhedral compressibilities and a term that accounts for the pressure effect on the internal oxygen position in the unit cell. The equations explain ͑i͒ the difference of compressibilities at octahedral and tetrahedral sites, ͑ii͒ why the macroscopic bulk modulus can be estimated as the average of these polyhedral bulk moduli, and ͑iii͒ the uniform behavior found in oxide spinels under hydrostatic pressure. Quantum-mechanical ab initio perturbed ion results on MgAl 2 O 4 , ZnAl 2 O 4 , ZnGa 2 O 4 , and MgGa 2 O 4 direct spinels and on MgGa 2 O 4 inverse spinel are reported to illustrate the interpretative capabilities of the proposed equations.

In this study, structural and electronic properties of CoAl2O4 spinel are investigated for the first time by means of quantum chemical computational tools. Coupling supercell periodic calculations under the density functional theory formalism with a nonempirical quasi-harmonic Debye model, we examine the influence of temperature on the relative stability of several cation distributions of Co2+ and Al3+ over tetrahedral and octahedral interstices of the oxygen sublattice. Our simulations are able to reproduce the experimentally observed trend: (i) the normal spinel is calculated to be the stable structure at static and low-temperature conditions, and (ii) as the temperature increases, the preference of structures with Al3+ at tetrahedral sites (and Co2+ at octahedral sites) is found to progress following an asymptotic conduct. The effects of the cation distributions on geometrical variations of electronic and magnetic properties of CoAl2O4 can be interpreted as dominated by the local behavior of Co2+ at octahedral sites.

The structure, geometry, and vibrational frequencies of several isomers of small group III-V (MX) n clusters (n ) 1, 2, 3; M ) Al, Ga, In; X ) P, As) have been investigated using density functional theory. The results reveal the same behavior as in the nitride clusters for monomers and dimers. The Al trimers exhibit a D 3h structure like the nitride, but the gallium and indium trimers exhibit a three-dimensional structure of C s symmetry. The existence of strong X-X bonds dominates both the structure and the vibrations of the Ga and In trimers.

Calculations based on density functional theory (DFT) were performed on various structural isomers of methyl silsesquioxanes, [MeSiO 3/2 ] n where n ) 4, 6, 8, 10, 12, 14, and 16, to study their structural and electronic properties. The calculated results find the stability of methyl silsesquioxanes, except [MeSiO 3/2 ] 4 , against fragmentation and hydrolysis, and of one isomer of [MeSiO 3/2 ] 14 against hydrolysis. The deformation density plots show that chemical bonding in methyl silsesquioxanes is mainly determined by the building block unit, (MeSiO 3/2 ) as also seen in hydridosilsesquioxanes (HSQ). However, unlike HSQ, the large cages of methyl silsesquioxanes do not develop a localized electronic state in the HOMO-LUMO gap.

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The insertion of diphenylcetylene into a ruthenium-nitrogen bond is a key step in the preparation of the binuclear derivative 2. This is the first example of insertion of a little electrophilic alkyne into a metalnitrogen bond.