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Concept# Octahedron

Summary

In geometry, an octahedron () is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
A regular octahedron is the dual polyhedron of a cube. It is a rectified tetrahedron. It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations.
An octahedron is the three-dimensional case of the more general concept of a cross polytope.
A regular octahedron is a 3-ball in the Manhattan (ℓ1) metric.
Regular octahedron
Dimensions
If the edge length of a regular octahedron is a, the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is
:r_u = \frac{\sqrt{2}}{2} a \approx 0.707 \cdot a
and the radius of an inscribed sphere (tangent to each of the octahedron's faces) is
:r_i = \frac{\sqrt{6}}{6} a \approx 0.408\cd

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In solids, heterogeneous catalysis is inherently bound to reactions on the surface. Yet, atomically efficient preparation of specific surfaces and the characterization of their properties are impeding its applications towards a clean energy future. Here, we present the synthesis of single layered IrOOH nanosheets and investigations of their structure as well as their electrochemical properties towards oxygen evolution under aqueous acidic conditions. The nanosheets are synthesized by treating bulk IrOOH with a tetrabutylammonium hydroxide solution and subsequent washing. Electron diffraction shows that the triangular arrangement of the edge sharing Ir(O,OH)(6) octahedra found in the layers of bulk IrOOH is retained after exfoliation into single layers. When incorporated as an active component in Ti electrodes, the nanosheets exhibit a Tafel slope of 58(3) mV dec(-1) and an overpotential of eta(-2)(10 mA cm) = 344(7) mV in 0.1 M HClO4, while retaining the trivalent oxidation state of iridium. They outperform bulk rutile-IrO2 and bulk IrOOH as electrocatalytic water oxidation catalysts under the same conditions. The results of this study on the structure-property relationships of low valence IrOOH nanosheets offer new pathways for the development of atom efficient, robust and highly active oxygen evolution catalysts.

2018Results of a theoretical study on the properties of Ir4 clusters in the gas–phase and on oxide surfaces are presented. The work is based on density functional theory (DFT) within the generalized gradient approximation (GGA) and ultrasoft pseudopotentials. Properties of a small particle such as Ir4 cluster are entirely determined by its geometry. The already known result that the most stable form of Ir4 in the gas–phase is the square structure which is significantly more stable than the butterfly and tetrahedron is confirmed. This result is in contradiction with experiments which indicate that the oxide supported Ir4 adopts a tetrahedral configuration. It is shown in this thesis that the chemical environment has a strong influence on the relative stability of Ir4 clusters. On MgO(100) surface, the square isomer remains the most stable Ir4 structure, well separated in energy from the other two. Moreover, the tetrahedron is heavily distorted by the interaction with the surface oxygen. Presence of point defects (neutral and charged O vacancies) affects the energy ordering making tetrahedron and square very close in energy, but the structural distortion of the tetrahedron is even bigger and the predicted data do not correspond to experiments. On TiO2(110) the tetrahedron and square structures become degenerate and the butterfly becomes the least stable isomer. Moreover, structural distortions are very small, in agreement with experimental data. It is shown that the TiO2 surface influences the relative stability of the three isomers through a particularly strong electrostatic field. Interactions of Ir4 with H, C and O atoms as well as with CO molecules have been studied. Adsorption of a single C atom strongly influences the relative stability of the three isomers. Upon C adsorption, the butterfly becomes the most stable gas–phase isomer while on both surfaces the tetrahedron is the most probable structure. Adsorption of a single H or O atom does not produce the same effect. The interaction with CO molecules is also important given the experimental procedure used for producing supported Ir4 clusters. It is shown that on MgO(100), CO dissociation is as probable as the competing process CO desorption justifying the presence of carbon adatoms on Ir4 clusters which brings theoretical predictions in better agreement with experimental data.

Described are the synthesis and characterization of two, potentially tetradentate, N2S2 Schiff-base ligands, containing a disulfide bond, N,N'-bis(3-phenylprop-2-en-l-ylidene)-2,2'-disulfanediyldianiline (L-1) and N,N'-bis(3,3-diphenylprop-2-en-1-ylidene)-2,2'-disulfanediyldianiline (L-2), and their reaction with Zn2+. Surprisingly, both L-1 and L-2 undergo reductive disulfide bond scission upon reaction with Zn2+ in alcoholic media to give, under alcohol oxidation, the respective Zn(NS)2 complexes Zn(L-3)(2) (1) and Zn(L-4)(2) (2), where the L-3 and L-4 are the respective bidentate thiolate-imine anions. The ligands L-1 and L-2 and the complexes I and 2 have been characterized spectroscopically, and the crystal and molecular structures of the two complexes have been determined by single crystal X-ray diffraction. The coordination geometry around Zn(II) centers in both complexes is a distorted tetrahedron. In addition, DFT calculations (B3LYP/LANL2DZ/6-311++G(d,p)) support the structure of I. Cyclic voltammetric studies demonstrate that Zn(II) shifts the reduction potential of the disulfide ligands L-1 and L-2 to less negative values thus making them more susceptible to reductive cleavage of the disulfide bond. The results of semi-empirical PM6 calculations offer key insight into the nature of the transition state for this reaction. (C) 2014 Elsevier Ltd. All rights reserved.