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.     

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.     

Crystal structure of glycine phosphite C<Subscript>2</Subscript>H<Subscript>5</Subscript>NO<Subscript>2</Subscript>·H<Subscript>3</Subscript>PO<Subscript>3</Subscript>

Single crystal X-ray diffraction study of glycine phosphite C₂H₅NO₂·H₃PO₃ was performed (monoclinic, space group P2₁/c, a = 7.401(3) Å, b = 8.465(3) Å, c = 9.737(3) Å; β = 100.73(5)°, Z = 4). It has been found that one of hydrogen atoms is located at the centre of symmetry forming two strong hydrogen bonds to yield H₄P₂O ₆ ^?2 dimers, while another hydrogen atom is statistically disordered over two positions and organizes the dimers into an infinite corrugated chain. The ordering of this hydrogen atom position and/or displacement of the other one from the centre of symmetry will lead to the loss of symmetry centre and lowering of the point group symmetry from C_2h to piezo-active group C₂ or C _s .     

Preparation and Crystalline Structure of Dihydrate of <Emphasis Type="Italic">hemi</Emphasis>-(Diazonium-18-crown-6) Isocyanurate of Isocyanuric Acid

Crystalline dihydrate of hemi-(diazonium-18-crown-6) isocyanurate of isocyanuric acid, 0.5[H₂DA18K6]²⁺?(C₃H₂N₃O₃)^??C₃H₃N₃O₃?2H₂O, was prepared and investigated by X-ray crystallography. In the given structure the dication DA18K6 is center-symmetric and possesses crown conformation of approximate D_3h symmetry. Molecule of isocyanuric acid and its anion are nearly planer. This molecule possesses approximate D_3h symmetry and its anion possesses approximate C_2v symmetry. With sufficient precision were determined geometrical parameters (bond lengths, bond angles etc.) of ions and molecules and was determined their packing in the given crystalline structure in which there is developed system of intermolecular (interion) hydrogen bonds.     

Calculation of the thermodynamic characteristics of ions in vapor over sodium fluoride

The geometric parameters, normal vibration frequencies, and thermochemical characteristics of the ions present in vapor over sodium fluoride, Na₂F⁺, Na₃F ₂ ⁺ , NaF ₂ ^? , and Na₂F ₃ ^? , were calculated ab initio by the Hartree-Fock method and taking into account electron correlation. The main equilibrium configuration of all ions was found to be the linear configuration of D _∞h symmetry. Pentaatomic ions could also exist as two isomers, planar cyclic of C _2v symmetry and bipyramidal of D _3h symmetry. Their energies were higher than that of the D _∞h isomers, and their contents in vapor were negligibly low. The energies and enthalpies of dissociation of the ions with the elimination of the NaF molecule were calculated. The enthalpies of formation of the ions were obtained.     

Electronic absorption spectra of solutions of molecular chlorine in molten alkali metal chlorides

Electronic reflection absorption spectroscopy has been used for measuring the electronic spectra of chlorine solutions in molten alkali metal chlorides 2CsCl-NaCl, KCl-NaCl, and CsCl in the range 240–400 nm. Absorption bands of chloride melts are interpreted as electronic transitions in the molecular group Cl₂ and in the triatomic linear group Cl ₃ ^? of symmetry D _∞h and C _∞V .     

Intramolecular rearrangements of β-diketonates of metals. A non-emprical study of the structure of Y(MDA)<Subscript>3</Subscript> and La(MDA)<Subscript>3</Subscript> complexes

The structure of tris-complexes of yttrium and lanthanum with malonic dialdehyde (MDA = C₃O₂H₃) is studied by a non-empirical Hartree-Fock method and also with taking into account the electron correlation by the second order Möller-Plesset perturbation theory using the effective pseudo-potentials to describe the atomic cores and two-exponent valence basis sets supplemented with polarization functions. Three most probable geometrical configurations of the D ₃, D _3h , and C ₂ nuclei symmetry are considered for each molecule. The D ₃ structure corresponds to the minimum on the potential energy surface. The D _3h and C _2v configurations correspond to the transition states on the path of two most energetically favorable intramolecular rearrangements. Using the results of our previous calculations for the Sc(MDA)₃ molecule, regularities in the change in molecular parameter values of the series Sc(MDA)₃→Y(MDA)₃→La(MDA)₃ are analyzed. The theoretical and experimental structural and spectral data available in the literature are compared.     

Structure and Chemical Bonding of the B<Subscript>3</Subscript>S<Stack><Subscript>n</Subscript><Superscript>0/−</Superscript></Stack> (<Emphasis Type="Italic">n</Emphasis> = 2–4) Boron Sulfide Clusters: A Density Functional Theory Investigation

A density functional theory investigation on the structural and bonding properties of B₃S _n ^?/0 (n = 2–4) series has been performed. Based on B3LYP and CCSD(T) calculations, we present the linear D _∞h B₃S₂ ^? (1, ³Σ_g) and D _∞h B₃S₂ (2, ²Π_u), the Y-shaped C _2v B₃S₃ ^? (3, ¹A₁) and C _2v B₃S₃ (4, ²B₂), and perfectly planar structures C _2v B₃S₄ ^? (5, ¹A₁) and C _2v B₃S₄ (6, ²B₂) that contain rhombic B₂S₂ rings. The 1–6 ground-state structures are planar with linear “B–B–B” core, in which the first and the second S atoms prefer to bond terminally to the terminal B, and the third S atom bonds to the center B, however, when the third S atom is added with the fourth, the atoms tend to be in the bridging positions of two adjacent B atoms. The growth pattern of B₃S _n ^?/0 (n = 2–4) clusters helps to understand the structural properties of the other small boron sulfide clusters. Bonding analyses reveal that a dual or single three-center one-electron (3c–1e) π hypervalent bonds located over the “B–B–B” core of D _∞h B₃S₂ ^? (1) and B₃S₂ (2), respectively. While C _2v B₃S₄ ^? (5) and B₃S₄ (6) with rhombic B₂S₂ rings as the center with –BS and –S units all possess 4c–4e bonds (o-bonds) in the rhombic B₂S₂ rings.     

Maximum filling principle and sublattice characteristics for the atoms of period 4 elements

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) of A atoms (A = K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, or Kr) were determined. The sublattices contain chemically identical A atoms in the crystal structures of 136395 inorganic and organoelement compounds. Irrespective of the nature of period 4 element, the VDP of A atoms have most often 14 faces, the Fedorov cuboctahedron being the most abundant VDP type. In the crystals, A atoms were found to have, most often, C ₁ site symmetry (75% of cases) and also C _s , C _i , and C ₂ site symmetries (6 to 4%). Certain relationships were shown to exist between the nature of the A atom and the preferred symmetry of the site it occupies in the crystal structures.     

The inductive effect of a radical center and transferability of the properties of functional groups in <Emphasis Type="Italic">n</Emphasis>-alkyl radicals

Electron density distribution in n-alkyl radicals (from ethyl to n-octyl) was studied by the B3LYP/6-311++G(3df,3pd) DFT method. The theory of atoms in molecules was used to show that the inductive effect of a free valence extends to two neighboring CH₂ groups. The electronegativities χ(C^?H₂) > χ(CH₃) > χ(CH₂) of groups and χ(C^?) > χ(H) > χ(C) atoms were qualitatively determined. The group method for calculating the enthalpies of formation of n-alkyl radicals Δ_f H°(n-C _n H_{2n+ 1}, n > 5) was substantiated.     

Electron diffraction and quantum-chemical studies of the molecular structure of 2-methylbenzenesulfochloride

A combined electron diffraction and quantum-chemical (MP2/6-31G**) study of the molecular structure of 2-methylbenzenesulfochloride at 336(5) K was carried out. It was found that the gas phase contained only one conformer, C ₁. The following structural parameters were obtained: r _h1(C-H)_av = 1.095(8) Å, r _h1(C-C)_Ph = 1.402(4) Å, r _h1(C_Ph-C_meth) = 1.507(13) Å, r _h1(C_Ph-S) = 1.763(6) Å, r _h1(S=O) = 1.418(4) Å, r _h1(S-Cl) = 2.048(5) Å, ∠(H-C-H)_meth/av = 107.3(96)°, ∠(Cl-S-O)_av = 106.4(3)°, ∠C_Ph-S-Cl = 100.8(9), ∠O=S=O = 120.8(10)°. The C_C-C_S-S-Cl torsion angle that defines the position of the S-Cl bond relative to the plane of the benzene ring is 75.6(20)°. The B3LYP/6-311+G** calculated barriers of internal rotation of the methyl and sulfochloride groups are 1.2 kcal/mol and V ₀₁ = 10.2 (V ₀₂ = 4.1) kcal/mol, respectively.     

Theoretical prediction of the new high-density lithium boride LiB<Subscript>11</Subscript> with polymorphism and pseudoplasticity

We predict the possibility of existence of the new lithium boride LiB₁₁ with polymorphism. For energy reasons, the preferred type is α′-LiB₁₁ (trigonal space group R3m, a _h = 0.4982 nm, c _h = 1.1123 nm, z _h = 3, ρ = 2.63 g/cm³), with a framework built of tetrahedra and one-capped octahedra. α′-LiB₁₁ is pseudoplastic because of twinning via the high-symmetry state of α-LiB₁₁ (cubic space group \(F\bar 43m\), a = 0.6810 nm, z = 4, ρ = 2.65 g/cm³) and a bipolaron semiconductor. α → α′ transition is accompanied by the 0.0627-nm displacement of 1/11 B atoms. The β′ polymorph (tetragonal space group \(I\bar 4m2\), a = 0.4404 nm, c = 0.7708 nm, ρ = 2.80 g/cm³) is transformation hardened because of the transition to the α′ phase. We infer that LiB₁₁ formation is possible under high pressure.     

Quantum-chemical study of ytterbium fluorides and of complex F<Subscript>2</Subscript>YbF<Subscript>2</Subscript>CeF<Subscript>2</Subscript>

The structural parameters of the (²Σ⁺//C_∞v)-YbF, (¹A₁//C_2v)-YbF2, (²A₂^′//D_3h)-YbF₃, (¹Ag//D_2h)-YbF₂Yb, (¹Ag//C_2h)-FYbF₂YbF, (¹A₁//C_2v)-FYbF₂YbF, (¹A₁//C_2v)-YbF₂YbF₂, (³B_3u//D_2h)-F₂YbF₂YbF₂, (²A′//C_s)-FYbF₂YbF₂, and (³B₂//С_2v)-F₂YbF₂CeF₂ molecules have been determined. Disproportionation of ytterbium monofluoride (2YbF → YbF₂ + Yb + 0.46 eV) is less exothermic than dimerization (2YbF → YbF₂Yb + 2.10 eV). The bond energy of the ytterbium difluoride molecules in the trans dimer (2.93 eV) exceeds those in the cis dimer (2.86 eV) and the coaxial dimer (1.66 eV). Ytterbium trifluoride dimerizes exothermically (2.95 eV) without spin pairing. The dipole and quadrupole moments of the molecules as well as the charges and spin populations of the atoms and the valence electron configurations of the lanthanides have been calculated.     

(Dibenzo-18-Crown-6)ammonium bromide tetrahydrofuran solvate: Synthesis and crystal structure

A new compound, (dibenzo-18-crown-6)ammonium bromide tetrahydrofuran solvate [NH₄(Db18C6)]⁺ · Br^? · THF (I), is synthesized and studied by X-ray diffraction analysis. The crystals of compound I are triclinic: a = 8.848 Å, b = 9.696 Å, c = 16.023 Å, α = 73.75°, β = 86.93°, γ = 78.06°, Z = 2, space group P \(\bar 1\). The structure of compound I is solved by a direct method and refined by full-matrix least squares in the anisotropic approximation to R = 0.095 by 5624 independent reflections (CAD-4 automated diffractometer, γMoK _α). The Db18C6 molecule in structure I has a butterfly conformation with approximate symmetry C _2v . The NH ₄ ⁺ cation where three disordered H atoms form hydrogen bonds with all six O atoms of the Db18C6 molecule is situated in the center of the cavity of the eighteen-membered macrocycle of the Db18C6 molecule. One ordered H atom of the NH ₄ ⁺ cation forms a strong hydrogen bond with the Br^? anion.     

Structure and energetics of β-diketonates. XVI. Molecular structure and vibrational spectrum of zinc acetylacetonate according to gas-phase electron diffraction and quantum-chemical calculations

The molecular structure of zinc acetylacetonate was studied in a simultaneous electron diffraction and mass spectrometric experiment at 376(7) K and by quantum-chemical calculations. The Zn(acac)₂ molecule has a structure of D _2d symmetry with the chelate rings lying in mutually perpendicular planes. The main geometrical parameters of the molecule are r _h1(Zn-O) = 1.942(4) Å, r _h1(C-O) = 1.279(3) Å, r _h1(C-C_r) = 1.398(3) Å, r _h1(C-C _m ) = 1.504(5) Å, ∠(O-Zn-O) = 93.2(7)°, ∠(Zn-O-C) = 125.9(7)°, ∠(C-C_r-C) = 125.8(14)°, ∠(O-C-C _m ) = 115.2(9)°. The effective rotation angle of methyl groups is close to 30°, which is indicative of the free rotation of these groups. The vibration frequencies were obtained by quantumchemical calculations, and the IR spectrum of the Zn(acac)₂ molecule was interpreted.     

Supramolecular architecture of catechol and its 2:1 complex with dimethylsulfoxide

The crystal structures of catechol (o-dihydroxybenzene) and its 2:1 complex with dimethylsulfoxide are determined at T = 150 K. Crystal data: C₁₄H₁₈O₅S, M = 298.37, triclinic, space group P \(\bar 1\), unit cell parameters: a = 7.7285(13) Å, b = 9.9924(17) Å, c = 10.3188(18) Å, α = 89.963(4)°, β = 89.968(4)°, γ = 69.076(5)°, V = 744.3(2)ų, Z = 2, D _x = 1.331 g/cm³, R1 = 0.048; C₆H₆O₂, M = 110.11, monoclinic, space group P2₁/n, a = 9.8206(6)Å, b = 5.5903(3)Å, c = 10.4439(6)Å, β = 114.952(2)°; V = 519.85(5) ų, Z = 4, D _x = 1.407 g/cm³, R1 = 0.0289. In the 2:1 complex the molecules are joined in a supramolecular ensemble by D-H...A hydrogen bonds (D = O, C; A = O, π); in catechol they are bonded only by O-H...O. The state diagram of the catechol-dimethylsulfoxide system is examined by DTA.     

<Emphasis Type="Italic">Ab initio</Emphasis> study of scandium fluoride molecules: ScF,ScF<Subscript>2</Subscript>, AND ScF<Subscript>3</Subscript>

Equilibrium geometric parameters, normal mode frequencies and intensities in IR spectra, atomization enthalpy, and relative energies of low-lying electronic states of scandium fluoride molecules (ScF, ScF₂, and ScF₃) are calculated by the coupled-cluster method (CCSD(T)) in triple-, quadruple, and quintuple-zeta basis sets with the subsequent extrapolation of the calculation results to the complete basis set limit. The ScF molecule is also studied by the CCSDT technique. The error in the approximate calculation of triple excitations in the CCSD(T) method does not exceed 0.002 Å for the equilibrium internuclear distance R _e, 4 cm^?1 for the vibrational frequency, and 0.2 kcal/mol for the dissociation energy of the molecule. In the ground electronic state \(\tilde X^2 \) A ₁(C _2ν ) of ScF₂ molecules, R _e(Sc-F) = 1.827 Å and α_e(F-Sc-F) = 124.2°; the energy barrier to bending (linearization) h = E _min(D _g8h ) ? E _min(C_2ν) = 1652 cm^?1. The relative energies of Ã²Δ _g and \(\tilde B^2 \)Π _g electronic states are 3522 cm^?1 and 14633 cm^?1 respectively. The bond distance in the ScF₃ molecule (\(\tilde X^1 \) A′₁, D _3h ) is refined: R _e(Sc-F) = 1.842 Å. The atomization enthalpies Δ_at H ₂₉₈ ⁰ of ScF _k molecules are 139.9 kcal/mol, 289.0 kcal/mol, and 444.8 kcal/mol for k = 1, 2, 3 respectively.     

Structure and energy study of β-diketonates. XV. Composition of superheated vapors and structure of monomeric molecules of <Emphasis Type="Italic">tris</Emphasis>-hexafluoroacetylacetonates of dysprosium,holmium, erbium,and ytterbium

The molecular structure of tris-hexafluoroacetylacetonates of dysprosium, holmium, erbium, and ytterbium (M(hfa)₃, M = Dy, Ho, Er, Yb) is studied in the framework of synchronous electron diffraction and massspectrometric experiment and also quantum-chemically. For all M(hfa)₃ complexes structural parameters r _a , r _g , and r _h1 are found. It is established that the coordination polyhedron LnO₆ has a configuration of D ₃ symmetry. In experiments on superheated vapors of Dy(hfa)₃, Ho(hfa)₃, and Yb(hfa)₃ the molecular forms present in the vapor at different degrees of superheat are determined.     

Synthesis,crystal structure,and fluorescence properties of a two-dimensional copper(II) complex with Schiff base

A new Schiff base ligand C₁₉H₁₃NO₅(H₂L) was synthesized using 2-aminoterephthalic acid and 2-hydroxy-1-naphthaldehyde. A complex of this ligand [Cu(C₁₉H₁₁NO₅)(C₂H₆O)] _n was synthesized and characterized by IR, UV, fluorescence spectroscopy and X-ray diffraction single-crystal analysis. The crystal crystallizes in the monoclinic system, space group Pbca with a = 8.7745(18), b = 18.613(4), c = 24.644(5) Å, V = 4024.9(14) ų, Z = 8, F(000) = 1816, S = 1.009, ρ _calcd = 1.462 g cm^?3, μ = 1.122 mm^?1, the final R = 0.0477 and wR = 0.1594 for 4609 observed reflections (I > 2σ(I)). The Cu(II) is five-coordinated by one N atom and two O atoms from the Schiff base ligand and two carboxylate O atoms from another two ligands to form a distorted square-pyramidal geometry. Each ligand serves as a bridging ligand to link Cu²⁺ ions, leading to a two-dimensional coordination polymer. The fluorescence properties of the ligand and complex were also studied. The ligand shows strong fluorescence, and the fluorescence intensity is weakened after the Cu(II) complex formed.     

Synthesis and Crystal Structure of (18-Crown-6)(nitrato)(triphenylphosphine oxide)potassium

A new complex (18-crown-6)(nitrato)(triphenylphosphine oxide)potassium (I) is synthesized, and its crystal structure is studied by X-ray diffraction analysis (space group R3m, a = 14.336 Å, c = 13.776 Å, Z = 3). The structure is solved by the direct method and refined by the full-matrix least-squares method in the anisotropic approximation to R = 0.034 for 1122 independent reflections (CAD4 automated diffractometer, λ MoK_α radiation). Structure I contains a complex host-guest molecule [K(NO₃)(18-crown-6)(Ph₃PO)] with crystallographic symmetry 3m (three planes m contain three Ph rings of the Ph₃PO ligand and all O atoms of the crown ligand). The coordination polyhedron of the K⁺ cation is a distorted hexagonal bipyramid with all the six O atoms of the crown ligand in the base, the O atoms of the Ph₃PO ligand, and one (or two) O atoms of a disordered NO ₃ ^? ligand in the axial positions.