Compositions and structures of nanoparticles of tetrahedral symmetry

The formulas for calculation of the composition of nanoparticles with symmetry group T _d are reported. The numbers of atoms in the shells of tetrahedral symmetry are determined by three structurally invariant numbers and the “quantum number” of the group order n. Four classes of all possible nanostructures with symmetry group T _d are revealed: C _{? + 12z} , where z = 0, 1, 2, ..., and C _? is C ₄, C ₆, C ₈, C ₁₀, or C ₁₄. The sum rule for the coordination numbers of the shell sites located on the axes of symmetry is obtained. The six-shell periodicity of the number of occupied sites located on the symmetry axes and in symmetry planes is revealed.     

Infrared spectra of Ag2BrNO3 and Ag2ClNO3

The infrared spectra of Ag₂BrNO₃ and Ag₂ClNO₃ are reported. Vibration assignments are proposed on the basis of the group theoretical analysis and D_2h symmetry. Factor group, site and TO-LO splittings are observed. The internal and external mode frequencies are correlated with those of AgNO₃ and KNO₃(II).     

Structures of two polymorphic modifications of tris(p-chlorophenyl)arsinoxide and comparison with the structure of tris(p-chlorophenyl)arsinsulfide

A full X-ray structure analysis of two polymorphic modifications of tris(p-chlorophenyl)arsinoxide, C₁₈H₁₂AsOCl₃, has been performed. Modification I is triclinic, space group P$\text{1}$, Z = 4; modification II is hexagonal, space group P6₃, Z = 2. The geometrical parameters of the molecules in the two polymorphs are similar; the mean values for the bond distances and angles are: AsO 1.641, AsC 1.928, CCl 1.736 Å; CAsC 107.3, CAsO 111.6°. The packing modes in I and II are significantly different: in I supersymmetrical relationships between the molecules independent of space-group symmetry are found: in II cylindrical cavities of diameter ca. 5 Å are present along the 6₃ axes. The structures of the molecules in I and II are compared with that of tris(p-chlorophenyl)arsinsulfide, C₁₈H₁₂AsSCl₃ (III, space group P2₁/b, Z = 4).     

Infrared and Raman spectra of lithium trihorate: Vibrational assignments and a correlation with its nonlinear optical activity

Infrared and polarized single crystal Raman spectra of lithium triborate (LBO; LiB₃O₅) are reported and analysed. All four (A₁, A₂, B₁ and B₂) symmetry species of the C_2v, point group isomorphic to the C_2v⁹(Pna2₁) space group are Raman active in distinct crystal polarization experiments. A complete set of symmetry assignments based on a factor group analysis is presented. The internal and external vibrations are separated on the basis of frequency and the observation that the magnitude of the correlation splitting for the internal modes is very small. A comparison of the internal frequencies of various borate species suggests a correlation between the B-O stretching frequency and the nonlinear optical efficiency of the material.     

Compositions of nanoparticles of hexagonal symmetry

The formulas for calculation of the number of atoms in nanoparticles with symmetry group D _6h are reported. The numbers of atoms are determined by six structurally invariant numbers and the “quantum number” of the group order n. Eight classes of nanostructures with symmetry group D _6h are revealed: C _{? + 12z} , where z = 0, 1, 2, …, and C _? is C ₂, C ₆, C ₈, or C ₁₄. The sum rule for the coordination numbers of all atoms of subshells related to symmetry elements is established. Two-dimensional nanoparticles are considered.     

Low-temperature phases of the solid electrolyte Ag26I18W4O16

Single crystal X-ray diffraction photographs taken with a Buerger precession camera, at temperatures 250, 214, and 122 K, corroborate the existence of three low-temperature phases of Ag₂₆I₁₈W₄O₁₆. These phases are labeled α′, β, and γ in order of decreasing temperature. The α′ phase is monoclinic, space group P2₁, Z = 2; the β phase is triclinic, space group $\text{P}\text{1}$ or P1, Z = 2; and the γ phase is triclinic, space group P1, Z = 1. Lattice constants at the aforementioned temperatures are given. Twins in the β and γ phases are related by the albite and pericline laws, as are twins in the feldspars. The highest symmetry known to be attained by the (W₄O₁₆)^8? entity is 2(C₂), which, strictly, it must lose at the transition to the α′ phase.     

Bis-μ-hydroxo-bis(π-cyclopentadienyldinitratozirkonium-(IV))tetrahydrofuran(12), ein zweikerniger organozirkonium(IV)-komplex mit siebenfach koordinierten metallzentren

Cp₂ZrCl₂ reacts with nitric acid in CHCl₃ to yield a dinuclear, doubly OH-bridged complex which can be isolated together with tetrahydrofuran of crystallization: [π-C₅H₅Zr(NO₃)₂(μ-OH)]₂ · 2THF (B). The crystal data of B are as follows: space group P2₁/c, a 8.825(2), b 12.137(3), c 13.018(2) Å, β 97.61(2)°. The unit cell contains two dinuclear centrosymmetric metal complexes and four molecules of tetrahydrofuran of crystallization. The Zr atom has a pentagonal-bipyramidal coordination geometry with the Cp group occupying an axial position, two chelating NO₃ ligands and one OH bridging group in the equatorial plane, and one OH group in the other axial position.     

Conformational studies of some 2-phenylpropyl derivatives by NMR spectroscopy and use of lanthanide shift reagents

The conformational distribution of CH₃CH(Ph)CH₂X (X = OH, OCH₃, NH₂ Cl) has been studied by NMR and IR spectroscopy. The results are interpreted in favour of the conformers with methoxy- or chloro-groups anti to the phenyl group, but the amino group anti to the methyl group. For the alcohol both forms are about equally populated. It is suggested that intra-molecular hydrogen bonding might be affecting the conformational equilibria when X = OH, NH₂.     

Lattice dynamical properties of TcB2 compound

The structural, lattice dynamical, and some thermodynamical properties of TcB₂ in hexagonal AlB₂-type structure (Hex-I) (space group P6/mmm), hexagonal ReB₂-type structure (Hex-II) (space group P63/mmc) are investigated using first-principles calculations. The phonon dispersion curves are derived from the direct method. The present results show that this compound is dynamically stable for considered structures. The temperature-dependent behavior of thermodynamical properties such as internal energy, free energy, entropy, and heat capacity are also presented and trends are discussed.     

Infrared spectra of KNaSO4 and K3Na(SO4)2

The infrared spectra, transmittance and polarized reflectance, of KNaSO₄ and K₃Na(SO₄)₂ are reported. Group theoretical analysis was carried out and a vibrational assignment proposed on basis of C_3v and D_3d symmetries. Factor group and site effects are discussed.     

Theoretical study of the static Jahn-Teller effect—III. Type of vibronic coupling in hexahalo complexes

Three types of vibronic coupling in hexacoordinate complexes are compared: the T_ig−(a_1g + e_g) type in the group O_h, the E_g−(α_1g + e_g) type in the group D_3d, and the E_g−(α_1g + b_1g) type in the group D_4h. It is shown that the group with the highest symmetry (O_h) does not imply the best model of vibronic coupling. Numerical applications were obtained for 29 complexes of the MX^q₆ type having a triply degenerate electronic state in an octahedral geometry on the CNDO-UHF level of the MO-LCAO-SCF method. Characteristics of these Jahn-Teller active systems are calculated and discussed.     

Structural studies on bulky phosphines: X-ray crystal structures of [2,4,6-(t-Bu)3C6H2P(SiMe3)2] and

The crystal and molecular structures of two bulky phosphines containing the 2,4,6-(t-Bu)₃C₆H₂ group are reported. Compound1, [2,4,6-(t-Bu)₃C₆H₂P(SiMe₃)₂], crystallizes in the monoclinic space group P2₁/c; a = 9.450(8), b = 17.154(6), c = 17.790(5)Å, β = 101.19(5)°. Compound2,

, also crystallizes in the monoclinic space group P2₁/c: a = 18.224(5), b = 9.394(2), c = 12.321(2)Å, β = 107.28(2)°. Structural features resulting as a consequence of the bulky 2,4,6-(tBu)₃C₆H₂ group, in particular the geometry at phosphorus, are discussed.     

Crystal structures of phosphomolybdyl salts: Pb(MoO2)2(PO4)2 and Ba(MoO2)2(PO4)2

Crystal structures of Pb(MoO₂)₂(PO₄)₂ and Ba(MoO₂)₂(PO₄)₂ were determined. Both compounds contain the molybdyl group MoO₂. The monoclinic unit-cell parameters are a = 6.353(7), b = 12.289(4), c = 11.800 Å, β = 92°56(6), and Z = 4 for the lead salt and a = 6.383(8), b = 7.142(7), c = 9.953(8) Å, β = 95°46(8), and Z = 2 for the barium salt. $\text{P2}{}_1\text{c}$ is the common space group. The R values are respectively R = 0.027 and R = 0.031 for 1964 and 1714 independent reflections. The frameworks built up by a three-dimensional network of monophosphate PO₄ and molybdyl MoO₂ groups are similar, characterized mainly by corner-sharing PO₄ and MoO₆ polyhedra. Two oxygen atoms of each MoO₆ group are bonded to the molybdenum atom only as in other molybdyl salts.     

Some new observations on the luminescence of PbMoO4 and PbWO4

We report on the luminescence of doped and undoped PbMoO₄ and PbWO₄ single crystals; a red emission is found for the first time for PbMoO₄. The degree of polarization of both the emissions of PbWO₄ and of the shorter-wavelength emission of PbMoO₄ is measured. The shorter-wavelength emissions are assigned to the ³T₁¹A₁ transition in the tetrahedral MoO₄^2?(WO₄^2?) group. It is assumed that the ³T₁ level is split due to spin-orbit coupling. The longer-wavelength emissions are assigned to a transition in a molybdate (tungstate) group lacking an oxygen ion, i.e., a MoO₃(WO₃) group.     

Metals in Biochemistry : P.M. Harrision and R.J. Hoare. Publ. Chapman & Hall,London and New York 1980, 78 pp + index. Price £2.45

The complex H₂Os₃(μ₃-NCH₃)(CO)₁₂ in decalin at 198°C in 35% yield. Crystal data for the former obtained at ?158°C are: orthorhombic, space group Pmcn, a 14.113(2), b 6.605(1), c 17.683(4) », Z = 4, D_c 3.44 g cm^?3. The hydrogen atoms are related by symmetry. The position of the unique hydrogen atom has been refined. It is observed asymmetrically bridging (closer to the unique Os atom) the longer edge of the isosceles triosmium triangle. The hydrogen atoms are out of the trimetal plane away from the triply-bridging nitrogen atom.Crystal data for the tetraosmium complex at 25°C are: monoclinic, space group C2/c a 30.818(9), b 8.463(2), c 16.621(2), », β 108.90(2)°, Z = 8, D_c 3.75 g cm^?3. The four osmium atoms form a distorted tetrahedral framework capped by the nitrogen atom of the methylnitrene group on the face containing the three longer OsOs separations.     

Electrostatic energies of the {CoNO}8 group in ligand fields

The qualitative features of the electronic states of the {CoNO}⁸ group are investigated by calculating the electrostatic energies of the (d _z2, d _xz, d _yz)², (d _xz, d _yz)², and (d _z2)² electron configurations in D′₄ symmetry. The geometries of the {CoNO}⁸ group are correlated with the behavior of the singlet electronic states in the D′₄ ligand field.     

Über metall-alkyl-verbindungen: XIV. Die kristallstrukturen von K[In(CH3)4], Rb[In(CH3)4] und Cs[In(CH3)4]

The crystal structure of KInMe₄ and CsInMe₄ have been determined from single crystal diffractometer data. Lattice parameters of RbInMe₄ obtained by powder methods are given. KInMe₄ and RbInMe₄ are isostructural (space group I4₁/amd), containing four formula units in the unit cell. CsInMe₄ belongs to space group P4? 2m with one formula unit per unit cell. Lattice parameters in Å: KInMe₄:a=9.904(2), c=8.132(2); RbInMe₄:a=10.208(2), c=8.146(2); CsInMe₄:a=7.459(1), c=4.163(1). All compounds consist of isolated alkali cations and tetrahedral InMe₄-anions. InC distances are 2.239(3) in KInMe₄ and 2.26(2) in CsInMe₄. The appearance of three different structure types of alkali metal tetramethyl indates is explained by the increasing alkali ion radii.     

Crystal Structures of Three Framework Alkali Metal Uranyl Phosphate Hydrates

Three homeotypic hydrated alkali metal uranyl phosphates, A₂(UO₂)[(UO₂)(PO₄)]₄(H₂O)₂, A=Cs (CsUP), Rb (RbUP), K (KUP), were synthesized by hydrothermal methods. Intensity data were collected at room temperature using MoKα radiation and a CCD-based area detector. Their crystal structures were solved by Patterson (CsUP) and direct (RbUP, KUP) methods and refined by full-matrix least-squares techniques to agreement indices (CsUP, RbUP, KUP) wR₂=0.048, 0.230, 0.072 for all data, and R1=0.023, 0.078, 0.038 calculated for 5338, 4738, 4514 unique observed reflections (∣F_o∣≥4σ_F), respectively. The compound CsUP is orthorhombic, space group Cmc2₁, Z=4, a=14.854(1), b=13.879(1), c=12.987(1) Å, V=2677.5(3) ų. Both RbUP and KUP are monoclinic, space group Cm, but are presented in the unconventional pseudo-orthorhombic space group Fm11 to facilitate comparison with CsUP and to allow a model for RbUP that includes the effects of pseudo-merohedral twinning. RbUP is monoclinic, space group Fm11, Z=4, a=15.72(2), b=13.84(1), c=13.05(1) Å, α=90.39°(2), V=2839(5) ų; KUP is monoclinic, space group Fm11, Z=4, a=15.257(1), b=13.831(1), c=13.007(1) Å, α=91.760°(1), V=2743.4(3) ų. The structures consist of sheets of phosphate tetrahedra and uranyl pentagonal bipyramids, with composition [(UO₂)(PO₄)]⁻, that are topologically identical to the uranyl silicate sheets in uranophane-beta. These sheets are connected by a uranyl pentagonal bipyramid in the interlayer that shares corners with two phosphate tetrahedra on each of two adjacent sheets and whose fifth equatorial vertex is an H₂O group, resulting in an open framework with alkali metal cations in the larger cavities of the structures. Where CsUP and RbUP have two alkali metal positions and a H₂O group in these cavities, KUP has four K atoms and two H₂O groups, all of which are partially occupied, in the interstitial sites.