Normal coordinate analysis and mean amplitudes of bis(2,2,6,6-tetramethylheptane-3,5-dionato)uranyl

A normal coordinate analysis has been performed for bis(2,2,6,6-tetramethylheptane-3,5-dionato)uranyl according to two simplified models: (i) a 35-atom model consisting of one tetramethylheptanedionate ligand attached to uranyl; symmetry C_2V and (ii) a 31-particle model of the whole complex, where the methyl groups are taken as point masses; symmetry D_2h. The construction of independent symmetry coordinates by the “method of fragments” is described. Calculated vibrational frequencies are reported along with mean amplitudes (l- values) and perpendicular amplitude coefficients (K- values) for selected interatomic distances.     

A gas electron diffraction study of the molecular structure of trans-stilbene

The molecular structure of trans-stilbene has been studied by the gas electron diffraction method. Unlike the approximately planar structure with C_i symmetry found for the solid state, the molecule in the gas phase was found to be non-planar and to possess C₂ symmetry. The phenyl groups were found to be rotated ca. 30° about the C-φ bonds. The non-planarity of the molecule is, however, not so large as to seriously influence the resonance energy.     

Compositions and structures of nanoparticles of trigonal symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>3<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

A method has been developed for the determination of the structure and number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group. The formulas for calculation of the number of particles of symmetry D _3d have been reported. It has been shown that the number of atoms in trigonal shells is determined by three structurally invariant numbers and the quantum number of the group order n. All possible nanostructures of symmetry D _3d have been classified: C_{θ + 6z} , z = 0, 1, 2, ..., where the basic shells are C_θ = C₆, C₈, and C₁₄. A sum rule has been obtained for the coordination numbers of the shell sites located on symmetry axes. Trigonal nanoparticles are parent ones for obtaining (3,0), (6,0), and (9,0) nanotubes of trigonal type. The general formulas of these nanotubes with icosahedral, dodecahedral, and cubic caps are N_{8 + 12p} , N_{20 + 24p} , and N_{60 + 36p} (p = 1, 2, ...), respectively. The graphical constructions of all classes of trigonal nanoparticles and nanotubes are reported.     

Infrared spectra of matrix-isolated gaseous ternary oxides: Part VI. The infrared spectra of lithium,cesium and thallium sulfates and indium and thallium molybdates

Infrared spectra of Li₂SO₄, Cs₂SO₄, Tl₂SO₄, In₂MoO₄ and Tl₂MoO₄ molecules isolated in nitrogen matrices at 12 K have been obtained. D_2d symmetry of these species is proposed. The splitting of the v₃(F₂) mode on passing from T_d to D_2d symmetry is briefly discussed.     

Vibrations of central oxygen in a high-symmetry tetranuclear metal cluster: A definitive assignment using isotopic substitution in a basic zinc carboxylate complex

The complex [Zn₄O(OOCC(CH₃)₃)₆] contains a tetrahedral oxo-centred metal cluster unit. Structures of this type have been characterised by X-ray diffraction, and in some cases exact tetrahedral symmetry has been found. However, crystal structures of high symmetry can conceal molecular structures of lower symmetry, averaged by static or dynamic disorder. The symmetry of this complex has therefore been checked over a short time-frame, in solution, by using vibrational spectroscopy with isotopic substitution. The antisymmetric vibration of the central oxide ion (t₂ symmetry in the T_d point group) has been located unambiguously and shown to be free of splitting by any symmetry lowering, and moreover to be essentially purely localised about the central oxygen.     

Stereoselective reductions with macrocyclic NADH models

Macrocyclic NADH models with two (C₂ symmetry) or four (D₂ symmetry) nicotinamide units comprised in a ring have been prepared and found to reduce activated carbonyl compounds in good yields and high enantiomeric excess. The roles of magnesium ions as a cocatalyst and the temperature have also been investigated. The smaller, C₂-symmetric macrocycle gave 96% ee upon reduction of ethyl benzoylformate whereas the best result with the larger D₂-symmetric model was 81% ee for the reduction of methyl benzoylformate.     

The i.r. and Raman spectra of tetraethylammonium hexafluoroantimonate (C2H5)4NSbF6

The vibrational spectra of (C₂H₅)₄NSbF₆ (I) at ambient temperature are compatible with cubic symmetry but there are signs that the symmetry of the crystal is lower than Fm3m-O⁵_h, the space group predicted from X-ray powder diffraction methods. Torsional modes of the methyl groups have been identified but could not be assigned unambiguously. A rotational barrier of approximately 2kcal/mol has been calculated for the threefold reorientational motions of these groups. These motions change very little when the phase transition temperature (∼26O K) is traversed. In (C₂H₅)₄NSbF₆ (II) most of the degenerate -CH₂, -CH₃, CC and SbF modes are split into two components. The interionic lattice modes reflect the disorder which exists in the crystal at ∼300 K but at lower temperatures in (C₂H₅)₄NSbF₆ (II) well-defined features have been observed.     

Spectroscopy at very high pressures: Part 27. Raman study of the second-order phase transitions in sodium nitrite and sodium nitrate

Raman spectra of NaNO₂ have been studied as a function of hydrostatic pressure to 40 kbar at 295 and 348 K. Slight changes in slope of mode frequency versus pressure plots support the view that a structural anomaly exists at 9 ± 1 kbar. The absence of qualitative changes in the Raman spectra allow the space group of NaNO₂ IV to be specified as one of P1, P2, B2, Pm or Bm. The Raman spectrum of NaNO₃ has been studied to 87 kbar. The changes observed are fully consistent with a second-order transition to a phase with symmetry C⁶_3v, as indicated by previous X-ray work, although the transition is sluggish.     

Normal coordinate analysis of malononitriles: I. G Matrix elements

The elements of the kinetic energy matrix G of CX₂(CN)₂ using several sets of internal symmetry coordinates have been calculated and discussed.     

Infrared spectra of matrix isolated and solid ethylene. Formation of ethylene dimers

Spectra of matrices with ethylene/argon ratios from 1/1 to 1/999 and a 1/24 ethylene/xenon matrix have been recorded in the temperature range 15–105 K. From relative i.r. intensities, frequency shifts and statistical calculations, the data are interpreted in terms of a monomer → dimer → aggregate → crystal scheme. It is proposed that the dimer, (C₂H₄)₂, has D_2d symmetry with a structure determined by quadruple hydrogen bonding and hydrogen-hydrogen repulsion. A method is described for calculation of the vibrational splitting due to interactions between the dimer molecular constituents.Solid ethylene has been studied between 15 and 85K. A transformation between two crystalline phases is characterized.     

Magnetic and thermodynamic properties of ferrimagnetic cyclic clusters and infinite chains with alternating spins of the [s-S]n Type: s = 1/2 and S = 3/2–7/2

Based on the method considering spin and spatial symmetry, numerical calculations of spin-level spectra have been performed for cyclic clusters and infinite chains with alternating spins of the [s-S]_n type, where s = 1/2 and S = 3/2–7/2. The temperature dependences of internal energy and magnetic susceptibility for ferrimagnetic systems of this type have been determined. The curves of the magnetic susceptibility as a function of temperature have been extrapolated to n → ∞. The theoretical curves are compared with experimental data.     

Compositions and structures of nanoparticles of pentagonal axial symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>5<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

The method of determination of the structure and the number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group has been developed. The formulas for the calculation of the number of particles with symmetry group D _5d are reported. The number of particles in these shells is determined by three structurally invariant numbers and the “quantum number” of the group order n. The classification of all possible nanostructures with symmetry group D _5d is given: C _θ+10z , z = 0, 1, 2, …, where the basic shells are C _θ = C ₂, C ₁₀, C ₁₂. The sum rule has been obtained for the coordination numbers of shell sites located at symmetry axes. Pentagonal axial nanoparticles are shown to be the initial shells for obtaining (5,5) and (10,10) armchair nanotubes or (5,0) and (10,0) zigzag nanotubes. The general formula of these nanotubes closed with icosahedral and dodecahedral caps is N _20+10p , N _60+10p (p = 1, 2, …). The graphical constructions of all classes of nanoparticles and nanotubes of the pentagonal axial type are reported.     

The Raman spectra of tetracoordinate CdCl3X2− halogenocadmate(II) anions in the solid state

Anionic halogenocadmate(II) complexes of the type CdCl₃X²⁻ have been prepared and characterized as salts of tetrapropylammonium. The Raman spectra of these crystalline solids have been interpreted in terms of a C_3v symmetry. The tetrachlorocadmate(II) anion also possesses such a symmetry in the solid state.     

Solid state NMR spectroscopy of metal carbonyls. The influence of site symmetry on the solid state spectrum of cis-(η5-C5H5)2Fe2(CO)4

Solid state carbon-13 NMR spectra of metal carbonyls are readily obtained using commercial instrumentation. The observed isotropic chemical shifts are in good agreement with solution values. Furthermore there is a one-to-one correspondence between crystallographically unique carbonyls and magnetically distinguishable carbonyls in the absence of accidental degeneracies. For cis-(η⁵-C₅H₅)₂Fe₂(CO)₄ the site symmetry is C₁ while the molecular symmetry is C_2ν. The lower solid state symmetry gives rise to more resonances in the solid spectrum than in solution. Magic angle tuning and chemical shifts were obtained using hexamethylbenzene as a standard.     

Magnetic and thermodynamic properties of Heisenberg chains and n-nuclear cyclic clusters: S i = 3/2 (n ≤ 11, n → ∞) and S i = 2 (n ≤ 10, n → ∞) systems

Based on the method considering spin and spatial symmetry, numerical calculations of the spin-level spectra have been performed for n-nuclear cyclic clusters with S _i = 3/2 (n ≤ 11) and S _i = 2 (n ≤ 10). The theoretical curves of the magnetic susceptibility, the magnetic contribution to the heat capacity, the internal energy, and the entropy as a function of temperature have been obtained. The theoretical curves of the magnetic susceptibility and the magnetic contribution to the heat capacity have been extrapolated to n → ∞ with a controlled accuracy.     

Nature of the hydrogen bridge in transition metal complexes: I. Molecular orbital calculations of binuclear carbonyls of Cr,Mo Fe and Ni with single hydrogen bridges

Determination of the electronic structure was performed by the parameter-free Fenske-Hall method for the complexes [(CO)₅MHM(CO)₅]⁻ with D_4h, C_2v and C₂ symmetries (wehre M = Cr, Mo) as well as for the complex [(CO)₃NiHNi(CO)₃]⁻ with C_2v and D_3h symmetries and for the complex [(CO)₄FeHFe(CO)₄]⁺ with a D_3h symmetry.The character and stability of the metalhydrogenmetal bridge bond in each of these complexes was compared. The effect of lowering the symmetry on the electronic structure of these complexes is also discussed. The influence of the bridging hydrogen atom on terminal ligands, i.e. its cis effect, was characterized.     

Coordination chemistry of benzoxazole-2-thione. Complexes of some transition metal acetates,tetrafluoroborates, sulphates and nitrates

Several complexes of cobalt(II), nickel(II), copper(II), copper(I), zinc(II), cadmium(II)and mercury(II) acetate, tetrafluoborate, sulphate and nitrate with benzoxazole-2-thione have been prepared and characterized by chemical analyses, ligand-field spectra, magnetic susceptibility measurements, molecular conductances and vibrational spectra (conventional and far i.r.). In the light of spectroscopic investigation it is possible to distinguish whether the anions present are coordinated to the transition metal ion or are present as free ions. Spectroscopic parameters of the cobbalt(II) and nickel(II) complexes are compared with similar chromophores containing sulphur, oxygen and nitrogen donor atoms. The evidence suggests that the sulphato- and nitrato-derivatives of cobalt and nickel are tetrahedral, the nickel tetrafluoroborato-derivative resulted octahedral, while the nickel acetato-complex and the complexes of the cobalt acetate and tetrafluoroborate resulted square planar and in predominantly planar environment respectively. The zinc, cadmium and mercury derivatives with a 1:2 and 1:3 metal:ligand molar ratio have a tetrahedral symmetry with the exception of[Znbot₂Ac₂] which resulted hexacoordinate with the acetato groups acting as symmetrical chelates. The complexes [ZnbotSO₄] and [CdbotSO₄] have a linear structure with the sulphate group acting as unidentate with a C_3ν symmetry, polymeric structures with the sulphate anion functioning probably as chelate and of symmetry lower than C_2ν being excluded from the i.r. evidence. Allocation for the possible metal-ligand and metal-anion modes have also been made.     

Vibrational spectra and structure of gaseous and solid dimethylboric anhydride

The Raman spectra of gaseous, liquid and solid dimethylboric anhydride (CH₃)₂BOB(CH₃)₂ have been recorded from 10–3500 cm^?1. The IR spectra from 4000–30 cm^?1 have also been recorded. The spectra of the gaseous phase have been interpreted in terms of C₂ symmetry implying a bent B-O-B skeleton with the B(CH₃)₂ groups twisted and consistent with a rather larger barrier to internal rotation about the B-O bonds. The spectra of the crystalline state, however, suggest that the molecular symmetry is altered upon solidification. Isotopic substitution of the oxygen atom by ¹⁸O confirmed that the B-O-B skeleton is linear in the solid state, and the spectra have been interpreted in terms of D_2h molecular symmetry.     

Structural stability and energetics of C,Si, and Ge microclusters: empirical many-body potential energy function calculation

The structural stability and energetics of carbon, silicon, and germanium microclusters containing 3?7 atoms have been investigated by using a recently developed empirical many-body potential energy function (PEF), which comprises two- and three-body atomic interactions. The PEF satisfies both bulk cohesive energy per atom and bulk stability exactly. It has been found that the most stable C_3?4 microclusters are linear withD _∞h symmetry but C_5?7 microclusters are planar withD _nh symmetry. Silicon and germanium microclusters show similar structural stability. TheX _n (X=Si, Ge;n=3?7) microclusters are found to be most stable in the following forms:X ₃ is triangular withD _3h symmetry,X ₄ is tetragonal withT _d symmetry,X ₅ is square pyramidal withD _4h symmetry,X ₆ is bipyramidal square withO _h symmetry, and finallyX ₇ is square pyramidal having two atoms underneath withD _2h symmetry.     

Geometrical and electronic structure of hydrated CH 5 + and CH 5 −

Different conformations of isolated and solvated CH ₅ ⁺ and CH ₅ ^? ions have been studied by CNDO method with Wiberg's parametrization. The anion has been found to have a most stable conformation ofD _3h symmetry both in the gas phase and in solution. AC _s symmetry conformation is the most stable one for the isolated cation, whereas a conformation withC _4v symmetry is energetically preferred in solution.