Octahedral Point Group Research Articles

From the “Brazuca” ball to octahedral fullerenes: their construction and classification

A simple cut-and-patch method is presented for the construction and classification for fullerenes belonging to the octahedral point groups, O or $$O_h$$ . In order to satisfy the symmetry requirement of the octahedral group, suitable numbers of four- and eight-member rings, in addition to the hexagons and pentagons, have to be introduced. An index consisting of four integers is introduced to specify an octahedral fullerenes. However, to specify an octahedral fullerene uniquely, we also found certain symmetry rules for these indices. Based on the transformation properties under the symmetry operations that an octahedral fullerene belongs to, we can identify four structural types of octahedral fullerenes.

Theoretical investigation of MnFe2O4

Generalized gradient approximation (GGA) and GGA + U (U is the Hubbard parameter) were applied to scrutinize the electronic structure and magnetic properties of the spinel ferrite MnFe2O4. Compression between GGA and GGA + U calculations were carried out. Oxygen position (z), total unit crystal spin magnetic moment, and lattice parameters were optimized. The optimized structure parameters are in good agreement with the experimental values. The experimental results described by the GGA + U calculations are better than the normal frame work. A new method for calculating U has been introduced. The calculations show that Mn ferrite has cubic structure with ordered spins. The compound should experience insulating behaviors which is experimentally observed. Such insulating behavior and spin ordering increase the ability of using Mn ferrite in high frequency applications. The moments are predominantly due to the ionic model behaviors for this compound. High spin state is favorable for the two cations Mn and Fe. From the anomalous explanation of DOS it is observed that, a ferrimagnetic spin current between Fe-3d and Mn-3d through O-2p is yielded. The flat bands, which are the more atomic-like lead to a high density of states and magnetic instability of local moment character. The effect of decreasing octahedral point group from Oh to D4h, C4v and C3v were carried out. The octahedral deformation has not been found in Mn ferrite. Total picture study for Hubbard parameter U has been carried out where accurate value for U was determined by comparing the energy gap with that obtained experimentally. Correlated behavior was proved for Manganese ferrite.

Electronic structure calculations forZnFe2O4

Local density approximation was applied to scrutinize the electronic structure and magnetic properties of the spinel ferrite ${\mathrm{ZnFe}}_{2}{\mathrm{O}}_{4}$. Various cation distributions were established to obtain the ground state for the system. In magnetic crystals, the position of the atoms is not enough for symmetry determination. A structure prediction by decreasing the octahedral point group symmetry ${\mathrm{O}}_{h}$ of Fe to ${\mathrm{D}}_{4h}$, ${\mathrm{C}}_{4v}$, and ${\mathrm{C}}_{3v}$ was carried out. The effect of the exchange and correlation terms on the band structure of ${\mathrm{ZnFe}}_{2}{\mathrm{O}}_{4}$ was studied by the generalized gradient approximation $+$ the Hubbard correlation parameter $U$. The optimized structure parameters, which are in good agreement with the experimental values, were used as the input parameters for the calculations. In agreement with experimental studies, the semiconducting behavior for the studied compound, taking the effect of spin arrangement on symmetry into account, was obtained.

Comparative architecture of octahedral protein cages. II. Interplay between structural elements

In paper I [Janner (2008). Acta Cryst. A64, 494-502], the enclosing forms of the monomers of four octahedral holoenzymes (bacterio and mitochondrial ferritins, small heat-shock protein and sulfur oxygenase reductase) were derived, with vertices at points of a cubic lattice and indexed accordingly. The correspondence between vertices and neighboring residues allows a sequential ordering of the vertices within the polyline defined by the C(alpha) atoms of the primary structure. The alignment of these sequences shows that the form vertices denoted as turning points delimit the elements of the secondary structure (alpha-helices, beta-strands and loops). This relation is analyzed further in a plot of angular changes in orientations of the polyline segments and planes as a function of the residue numbers and of the form vertices, respectively, leading to an alternative characterization of the ternary structure. Finally, two simple connectivity models of monomers, oriented according to the symmetry axes of the octahedral point group 432, suggest possible patterns in the self-assembly process from clusters of monomers to the quaternary structure of the cubic cage.

Quantum spin configurations inTb2Ti2O7

Low-energy collective angular momentum states of the ${\mathrm{Tb}}^{3+}$ ions in ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ are classified according to the irreducible representations of the octahedral point group. Degeneracy lifting due to the exchange interaction is discussed. Diffuse neutron-scattering intensity patterns are calculated for each collective angular momentum state, and the ground state is inferred by comparing with experiment.

NUCLEI WITH TETRAHEDRAL SYMMETRY

We discuss a point-group-theory based method of searching for new regions of nuclear stability. We illustrate the related strategy with realistic calculations employing the tetrahedral and the octahedral point groups. In particular, several nuclei in the Rare Earth region appear as excellent candidates to study the new mechanism.

Chemical Bonding in Octahedral XeF6 and SF6

Quantum chemical density functional theory calculations have been carried out for octahedral XeF6 and SF6 at the BP86/TZ2P level with relativistic effects included by the ZORA approximation. The energy decomposition analysis of XeF6 and SF6 using neutral and charged fragments EF5 + F and EF5+ + F− as well as E + F6 and E6+ + F66− indicates that the dominant E–F orbital interactions take place between σ-orbitals which have t1u symmetry in the octahedral point group. The contribution of the a1g orbitals is negligible in the 16 valence electron compound XeF6. The a1g contribution becomes larger in the 14 valence electron species SF6 but it is less important than the t1u term. The bonding between the neutral species comes mainly from covalent (orbital) interactions but the quasiclassical electrostatic attraction significantly contributes to the attractive interactions. The bonding which comes from the ΔEorb term is compensated by the Pauli repulsion ΔEPauli. The sum of ΔEorb and ΔEPauli is repulsive for XeF6 and SF6, which would not be stable molecules without quasiclassical electrostatic attraction.

Electronic states of nickel(ii) in spinel-type structures

—The electronic spectra of Ni II as the promoter of a hydrodesulfurization catalyst (NiO-MoO 3/γ-Al 2O 3) has been studied. On the basis of the positions and intensities of the maxima in electronic d-d transitions the presence of an octahedral point group symmetry (O h) of Ni II was established for the untreated sample and samples taken from the regenerated catalyst layers. In other cases, the distribution of d-d transition maxima indicated that in addition to the octahedral (O h) a tetrahedral (T d) coordination of Ni II was also present, suggesting the occurrence of a spinel-type structure. The experimental values obtained for the crystal field splitting parameter (10D q) enabled calculation of the electronic state energies, as well as the values of parameters of partially populated d-orbitals of Ni II. On the basis of these data, the effective values of ionization potential H dd were calculated and a most probable MO scheme was proposed.

Energy transfer by electric dipole-magnetic dipole interaction in cubic crystals

The energy transfer probability for an ion-ion cross relaxation process which involves an electric dipole vibronic transition at the donor ion site, and a magnetic dipole transition at the acceptor ion site, is shown to be zero for the case of lanthanide ions situated at octahedral point group symmetry sites in crystals.

Polymeric coordination complexes based on cobalt, nickel, and ruthenium that exhibit synergistic thermal properties

d-Block transition-metal-containing polymer blends which form coordination complexes are the focus of this research. The model compounds are Co chloride hexahydrate, Ni acetate tetrahydrate, and the dimer of dichlorotricarbonylruthenium (II). The ligand is poly (4-vinylpyridine), P4VP, or copolymers that contain 4-vinylpyridine repeat units. Differential scanning calorimetry suggests that the glass transition temperature (gtt) of the polymeric ligand(s) is enhanced by these d-block metal salts in binary and ternary blends. Co and Ni salts function as transition-metal compatibilizers for two immiscible copolymers of styrene with 4-vinylpyridine and butyl methacrylate with 4-vinylpyridine. At the molecular level, FTIR of P4VP-Ru precipitates reveals that the pyridine nitrogen lone pair coordinates to the metal center and strengthens Ru-carbonyl bonds in the polymeric complex. IR absorption frequencies of the CO ligands are consistent with {pi}-backbonding between the t{sub 2g} molecular orbitals of the metal in the octahedral point group and the {pi}* antibonding orbitals of CO. High-resolution C-13 solid-state NMR spectroscopy identifies at least two, and possibly three, carbonyl signals in the undiluted pseudooctahedral Ru dimer via the Bloch-decay pulse sequence. In the polymeric complex, carbonyl C-13 magnetization unique to the Ru salt is generated via intermolecular polarization transfer from the proton spin manifold of poly(4-vinylpyridine)more » using a cross-polarization thermal mixing time of 2 ms. Since there are no protons in the Ru dimer, the observation of energy-conserving H-1/C-13 spin diffusion between dissimilar molecules under matched Hartmann-Hahn spin-lock conditions argues convincingly that heteronuclear dipolar distances are small enough for the proposed polymeric complex to form. Thermodynamic interpretation of ligand field stabilization energies appropriate to tetrahedral Co complexes is employed to estimate the synergistic enhancement of the gtt.« less

Bond orientational order in the blue phases of chiral liquid crystals.

It is proposed to describe blue phases by two order parameters: the standard alignment tensor field ${\mathit{Q}}_{\mathrm{\ensuremath{\alpha}}\mathrm{\ensuremath{\beta}}}$(r) and a bond orientational tensor order parameter of octahedral point group symmetry scrO(432). The yet mysterious blue fog then emerges as a liquid of purely cubic bond orientational order. In the transition from the cubic blue phases to the blue fog the cubic space group symmetry is being reduced to its octahedral factor group. Because of the new order parameter the ${\mathit{scrO}}^{5}$(scrI432) structure, which in all previous calculations proved most stable, but never has been detected in experiment, is eliminated from the phase diagram.

Orbifold compactified superstring models with tetrahedral and octahedral point groups

For orbifolds with tetrahedral or octahedral point group and embedding of the complete space group in the gauge group, we study simultaneously the conditions for modular invariance to be satisfied, for complete generations of quarks and leptons to survive, and for realistic gauge symmetry breaking to occur either by “Wilson lines” alone or with additional intermediate scale breaking by a 27 + 27 . Models with four complete generations and a realistic gauge group are obtained.

Paramagnetic silver clusters in irradiated AgA molecular sieves

Three paramagnetic silver clusters have been detected in γ-irradiated 4A molecular sieve loaded with silver. These clusters are identified as Ag 2 +, Ag 3 2+, and Ag 6 +. Ag 3 2+ is triangular, 2A′ 1 in D 3 h symmetry, having equal hyperfine interactions with three silver nuclei. Ag 6 + belongs to the octahedral point group ( O h ) and shows 180 MHz hyperfine interactions with six equivalent 107Ag nuclei, and 13 MHz hyperfine interactions with a surrounding cube of eight 107Ag nuclei. It is concluded that the ground state of Ag 6 + is probably 4A 1u.

Vibrational Spectra of MoF6 and TcF6

Infrared spectra of gaseous MoF6 and TcF6 from 6–43 μ, the Raman spectrum of MoF6 gas, and an incomplete Raman spectrum of liquid TcF6 are reported. These are interpreted in terms of the octahedral point group 0h. The fundamental frequencies for MoF6 are 741(ν1), 643(ν2), 741(ν3), 264(ν4), 306(ν5), and 190(ν6). For TcF6 they are 705(ν1), 551(ν2), 748(ν3), 265(ν4), 255(ν5) and ν6 has not been determined. Differences between the spectra of MoF6 and TcF6 are explained as a consequence of orbital degeneracy in the ground state of the latter, in analogy with similar differences in the 5d series.

Vibrational Spectra of ReF6

The infrared-absorption spectrum from 6–43 μ and the Raman spectrum of ReF6 gas are reported. They are interpreted in terms of the octahedral point group 0h. The six fundamental frequencies are 755(ν1), 596(ν2), 715(ν3), 257(ν4), 246(ν5), and 193(ν6). Thermodynamic functions are calculated for the ideal gaseous state.

Vibrational Spectra of OsF6 and PtF6

Infrared absorption spectra of gaseous OsF6 and PtF6 from 6–50μ and the Raman spectrum of liquid OsF6 are reported. These are interpreted in terms of the octahedral point group Oh, and the six fundamental frequencies are determined. Their values and symmetry species are for OsF6 733 (a1g), 632 (eg), 720 (f1u), 268 (f1u), 252 (f2g), and 230 (f2u); for PtF6 655 (a1g), 601 (eg), 705 (f1u), 273 (f1u), 242 (f2g), and 211 (f2u). Thermodynamic functions, including electronic contributions, are calculated for the ideal gaseous state of both compounds. A comparison of the details of the vibrational spectra of eleven hexafluorides reveals certain characteristic features for OsF6 and ReF6. Since only these two molecules have appropriately degenerate electronic ground states these differences are interpreted as evidence of a Jahn-Teller effect.