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.     

Natural states of interacting systems and their use for the calculation of intermolecular forces. II. Natural states in the asymptotic 1/R expansion

The asymptotic natural states i.e. the natural states of the subsystems in the various terms of the asymptotic expansion of the primitive wavefunction of the supersystem are defined. Integro-differential equations are derived that allow the direct calculation of these asymptotic natural states and from them, the terms C₆, C₈ etc. in the asymptotic 1/R expansion of the interaction energy. A pictorial interpretation of these states is given and the rapid convergence of the expansion in natural states is explained. The transferability of certain matrix elements is demonstrated and a virtually exact combination rule for the calculation of the C_k coefficients between different atoms from those for like atoms is obtained- The effects of intraatomic electron correlation on the C_k as well as the justification of a core-valence separation are discussed.     

Dispersion coefficients for Li+–H and Li+–He systems with coulomb and screened coulomb potentials

Exploiting powerful computational aspects and highly correlated exponential wave functions for two‐electron atoms, we have investigated the effects of screened Coulomb interaction on the hexadecapole polarizability of Li⁺(1¹S), and the dispersion coefficients C₆, C₈, C₁₀, and C₁₂ for interaction of Li⁺ with H and He atoms in their ground states. The dispersion coefficients and hexadecapole polarizability for different screening parameters ranging from 0 to 1.0 a are reported. In the unscreened case, the hexadecapole polarizability of Li⁺, and the dispersion C₁₂ coefficients for Li⁺–H and Li⁺–He system are reported for the first time in the literature. The C₆, C₈, and C₁₀ coefficients for the unscreened cases are comparable with the reported results. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The non-empirical calculation of second-order molecular properties by means of effective states. II. Effective TDCHF spectra for NO+ CO,CO2, and C2H2

Time-dependent coupled Hartree-Fock calculations have been performed in the large bases molecules NO⁺, CO. CO₂ and C₂H₂. Some first- and second-order properties are presented, in particular the isotropic dispersion interaction coefficients C₆⁰⁰⁰, C₈⁰⁰⁰ and C₁₀⁰⁰⁰ for all possible van der Waals dimers consisting of these monometers. These coefficients, and also the corresponding long-range anisotropic interaction coefficients, can be calculated easily for any of these dimers using the effective TDCHF multipole spectra presented in this paper. Formulas to this end are given.     

Basicity of bisperhalophenyl aurates toward closed-shell metal ions: metallophilicity and additional interactions

The interaction of bisperhalophenyl aurates [AuR₂]^? (R?=?C₆F₅, C₆F₃Cl₂, and C₆Cl₅) with the closed-shell Ag⁺, Cu⁺, and Tl⁺ ions has been studied theoretically and compared with the experimentally known X-ray diffraction crystal structures. Initially, the aurates have been fully optimized at MP2 level of theory in a D _2h symmetry. The analysis of the basicity of the three aurates [AuR₂]^? (R?=?C₆F₅, C₆F₃Cl₂ and C₆Cl₅) against Ag⁺ ions in a C _2v symmetry has been calculated in point-by-point bsse-corrected interaction energy analysis at HF and MP2 levels of theory. Taking into account the experimental observation of additional interactions between the heterometals and C _ipso atoms at the perhalophenyl rings or halogen atoms at the ortho position of the perhalophenyl rings, dinuclear models of the type [AuR₂]^?···Ag⁺ (R?=?C₆Cl₅, and C₆F₅); [AuR₂]^?···Cu⁺ (R?=?C₆F₅, and C₆Cl₅) and [AuR₂]^?···Tl⁺ (R?=?C₆F₅, and C₆Cl₅) with a C _2v , C ₂ , and C _s symmetries have been optimized at DFT-B3LYP level. The interaction energies have been computed through bsse-corrected single point HF and MP2 calculations. The energy stabilization provided and the heterometal preference have been analyzed and compared with the experimental results.     

Isolierung und struktur des dreikernigen hexamethylbenzolzirkonium-komplexes [(Me6C6)3Zr3Cl6]2+ [(Al2Cl7)−]2

Crystals of the trinuclear complex [(Me₆C₆)₃Zr₃Cl₆][Al₂Cl₇]₂ have been obtained from the reaction of ZrCl₄, hexamethylbenzene, AlCl₃, and Al in benzene. They are monoclinic, space group C2/2, with Z  4 and lattice parameters a 14.167(3), b 27.779(7), c 15.721(3) Å and β 94.27(4)°. The Zr atoms form a regular triangle. Each pair of Zr atoms is bridged by two Cl atoms. The fifth coordination site of each Zr atom is occupied by a h⁶-Me₆C₆ group. The cation is almost isostructural with the known trinuclear cation [(Me₆C₆)₃Nb₃Cl₆]²⁺. Important distances are: ZrZr 3.35, ZrCl 2.56, and Zrcenter of C₆ ring 2.17 Å. One of the two independent [Al₂Cl₇]^? anions occurs in a staggered conformation and one occurs in an eclipsed conformation.     

The thiolate anion as a nucleophile Part III. Reactions with various fluorobenzenes

The reactions of the fluorobenzenes, C₆F₅H, o-C₆H₂F₄, m-C₆H₂F₄, p-C₆H₂F₄, 1,3,5-C₆F₃H₃, 1,2,4-C₆F₃H₃, o-C₆F₂H₄, m-C₆F₂H₄, p-C₆F₂H₄ and C₆F₅H with thiolate anion nucleophiles RS^? (primarily MeS^?), have been studied in ethylene glycol/pyridine mixtures as a solvent. Multiple replacement of fluorine atoms was observed in the more highly fluorinated compounds, but in all cases two aromatic fluorine atoms were not replaced. Difluorobenzene and fluorobenzene did not react. The product orientations have been deduced from their NMR spectra. The mass spectra of the isomeric products C₆F₂H₃(SMe), C₆F₃H₂(SMe) and C₆F₂H₂(SMe)₂ have been examined.     

Dipole oscillator strength distributions,sums, and dispersion energy coefficients for CO and CO2

Globally reliable dipole oscillator strength distributions (DOSDs) have been constructed for ground state CO and CO₂ molecules; the DOSD for CO corresponds to photon energies greater than the electronic absorption threshold while that for CO₂ includes the infrared part of the spectra as well. The recommended DOSDs are used to evaluate the isotropic dipole—dipole dispersion energies for the COCO, COCO2 and CO2CO2 interactions as well as the molar refractivities, as a function of wavelength, and the dipole sums, S_k, k = 2(?1) -4, -6, -8, -10, for the two molecules. Pseudo-DOSD representations of the recommended DOSDs are provided which allow the efficient accurate evaluation of the dispersion energy coefficients C₆ for the interaction of CO or CO₂ with a variety of other atoms and molecules. Previous results for C₆ are found to be in disagreement with our recommended results for interactions involving CO₂. The results of this paper are used to give a reasonably general discussion of the difficulties associated with obtaining reliable results for C₆ by using Padé approximant bounding methods.     

Binuclear dinitrogen complexe of aryl- and benzyldicyclopentadienyltitanium(III) compounds

The preparation of the deep-blue diamagnetic dinitrogen complexes (Cp₂TiR)₂N₂ with R=C₆H₅, o-, m-, p-CH₃C₆H₄, C₆F₅, CH₂C₆H₅ is described. Their chemical and physcial properties confirm the formulation in which the R groups are σ-bonded to the Cp₂Ti moiety, and the two nitrogen atoms are equivalent. The heats of formation of the complexes from Cp₂TiR and N₂ in toluene have been determined from spectrophotometric data; for R=C₆H₅, o-, m-, p-CH₃C₆H₄, C₆F₅, CH₂C₆H₅, the values are ?18, ?9, ?17, ?20, ?17 and ?14 kcal·mol^?1, respectively. The solid complexes vary markedly in thermal stability, and are extremely air sensitive. The complexed nitrogen can be completely reduced with sodium naphthalene; after hydrolysis of the products, NH₃ and N₂H₄ are obtained. In the thermolysis of the solids, some of the nitrogen is reduced.     

Distribution de la densite des electrons de valence dans Cu2As

The distribution of valency electron density in Cu₂As (C38) has been determined by Fourier synthesis using as coefficients the values ΔF = F_obs ? F_core (F_core corresponds to the structure factors of the inner orbitals). The bonding between the pyramidal-site copper atoms and the arsenic atoms is exposed, as well as the bonding between tetrahedral-site and pyramidal-site copper atoms.The structural evolution of the unit cell from the Cu₂Sb-type (C38) to the Fe₂P-type (C22) and Co₂P-type (C23) can be related to the metal-metalloid interaction. This interaction mainly involves the pyramidal-site metal atoms in the Cu₂Sb-type, and the tetrahedral-site metal atoms in the Fe₂P- and Co₂P-types.     

Crystal structure of potassium 2-thiobarbiturate

The crystal and molecular structure of potassium thiobarbiturate C₄H₃KN₂O₂S (C₄H₄N₂O₂S-2-thiobarbituric acid, H₂TBA) is determined. Crystallographic data for KHTBA are as follows: a = 11.2317(17) Å, b = 3.8687(6) Å, c = 14.557(2) Å, β = 97.448(4)°, V = 627.18(17) ų, space group P2/c, Z = 4. Each potassium ion is linked with four oxygen atoms and two S atoms forming a distorted octahedron. N-H…O and C-H…S hydrogen bonds form a branched three-dimensional network. The structure is also stabilized by the π-π interaction of heterocyclic HTBA^? ions.     

A complex of cadmium(II) iodide with 4-cyanopyridine: Synthesis,crystal structure,and luminescent properties

The complex [CdI₂(4-CNPy)₂] (I) was obtained by a reaction of CdI₂ with 4-cyanopyridine (4-CNPy, C₆H₄N₂) and structurally characterized (CIF file CCDC no. 983377). The crystals of complex I are monoclinic, space group C2, a = 24.698(5) Å, b = 4.127(1) Å, c = 7.597(2) Å, β = 96.05(1)°, V = 770.0(3) ų, ρ_calcd = 2.477 g/cm³, Z = 2. In structure I, iodine atoms serve to unite complex molecules into the polymer chains [CdI₂(4-CNPy)₂]_∞ along the direction [010]. The Cd(1) atom lying on a twofold axis has a slightly distorted octahedral environment made up of four bridging iodine atoms and two nitrogen atoms of two ligands 4-CNPy (Cd-I_av, 2.947(2) and Cd-N(1), 2.410(6) Å). Within each chain, cadmium atoms are spaced apart at 4.13 Å. Complex I exhibits photoluminescence.     

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.     

Probes for narcotic receptor mediated phenomena. Part 31: Synthesis of rac-(3R,6aS,11aS)-2-methyl-1,3,4,5,6,11a-hexahydro-2H-3,6a-methanobenzofuro[2,3-c]azocine-10-ol, and azocine-8-ol, the ortho-c and the para-c oxide-bridged phenylmorphan isomers

Two of the 12 possible oxide-bridged phenylmorphans, were synthesized, rac-(3R,6aS,11aS)-2-methyl-1,3,4,5,6,11a-hexahydro-2H-3,6a-methanobenzofuro[2,3-c]azocine-10-ol (7) (the ortho-c compound), and rac-(3R,6aS,11aS)-2-methyl-1,3,4,5,6,11a-hexahydro-2H-3,6a-methanobenzofuro[2,3-c]azocine-8-ol (8) (the para-c compound). Single-crystal X-ray diffraction studies indicated that the dihedral angle between the least squares planes through the phenyl ring and the atoms C₁, C_11a, C₁₂, and C₃ in the piperidine ring in both 7·CHCl₃ and 8·HBr was 6.9°. The C₁₂-C_6a-C_6b-C_10a torsion angle was found to be 139.3° for both compounds. The angular relationship between the phenolic ring and the piperidine ring in phenylmorphans that interact with specific opioid receptors as agonists or antagonists is of considerable theoretical interest.     

Crystal structure of L-leucinium tetrafluoroantimonate(III)

The crystal structure of L-leucinium tetrafluoroantimonate(III) of the composition (C₆H₁₄NO₂)SbF₄ (orthorhombic symmetry: a = 6.1459(6) Å, b = 14.994(1) Å, c = 24.789(2) Å, Z = 8, P 2₁2₁2₁ space group) synthesized for the first time is determined. The (C₆H₁₄NO₂)SbF₄ structure represents a new structure type of tetrafluoroantimonate(III). It is formed by (C₆H₁₄NO₂)+ cations and chain complex [Sb₂F₈]_n ²ⁿ anions composed of Sb₂F₈ dimers linked into chains by bridging F atoms. The Sb₂F₈ dimers consist of SbF₃ and SbF₅ groups bound by bridging fluoride atoms of the SbF₅ group. Chains in the structure are linked by N-H…F, N-H…O, and O-H…F hydrogen bonds into a three-dimensional framework.     

The crystal and molecular structure of 5,5-diphenyloctafluorogermanthrene, (C6H5)2GeC12F8

F---F steric interaction between the two 6,6′-fluorines of the C₆F₄ rings in C₁₂F₈Ge(C₆H₅)₂ cause quite distortions in the molecule as these two fluorine atoms are forced to within 2.419 Å of each other (Van der Waals distance ⋍ 2.7 Å). Crystal data: C₁₂F₈Ge(C₆H₅)₂, M_r 522.89, C2/c, a 29.065(2), b 8.066(2), c 23.000(3) Å, β 129.85°, U 4139.63 ų, Z = 8, D_x 1.678 Mg m⁻³, Mo-K_α, λ 0.7107 Å, μ 15.58 cm⁻¹, F(000) = 2064, T 293 K, R = 0.044 for 2264 reflections with I > 3σ(I); Δϱ ± 0.5 e⁻     

Maximum filling principle and sublattice characteristics for the atoms of period 6 elements

The most important characteristics of the Voronoi-Dirichlet polyhedra (VDP) were determined for the 88223 crystallographically different A atoms (A = Cs, Ba, La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, or Bi) in sublattices containing chemically identical atoms in the crystal structures of 52370 inorganic and organoelement compounds. Irrespective of the nature of the A element, the VDP have most often 14 faces, the Fedorov cuboctahedron being the most abundant VDP type. The metal atoms A were found to have, most often, C ₁ site symmetry (76% of cases) and also C _s , C ₂, C _i , and C _2v site symmetries (7 to 2%). Certain relationships were shown to exist between the nature of the metal atom and the preferred symmetry of the sites it occupies in the crystal structures.     

Nickel(II) complex with 4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dione and dimethyl sulfoxide: Crystal and molecular structures

A nickel(II) complex with 4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dione and dimethyl sulfoxide, [Ni(C₈H₄F₃O₂S)₂(C₂H₆OS)₂], was obtained and examined by X-ray diffraction. The crystals are monoclinic: a = 7.557(2) Å, b = 17.854(3) Å, c = 10.470(2) Å, β = 106.412(3)°, V = 1355.1(4) ų, ρ_calcd = 1.611 g/cm³, Z = 2, space group P2₁, R = 0.032. The coordination polyhedron of the nickel atom is a distorted octahedron consisting of four equatorial O atoms of two β-diketonate ligands and two axial O atoms of DMSO. The average Ni-O_ax and Ni-O_eq distances are 2.083(2) and 2.019(2)Å, respectively. The crystal structure is built from the discrete mononuclear complexes [Ni(C₈H₄F₃O₂S)₂(C₂H₆OS)₂] linked only by van der Waals contacts.     

The crystal structure of U5Re3C8

U₅Re₃C₈ crystallizes tetragonal in space group P4/mbm with the lattice constantsa=1 131.3(1) pm,c=330.29(7) pm,V=0.4227 nm³ andZ=2 formula units per cell. The structure was determined from single-crystal counter-data and refined to a residual ofR=0.032 for 649 structure factors and 24 variable parameters. It is of a new type with carbon atoms on three different sites with approximately octahedral environment of five uranium and one rhenium or four uranium and two rhenium atoms. The positions of the metal atoms correspond to those of a (slightly distorted) cubic body centered structure as is also found for Ho₂Cr₂C₃, UCr₄C₄, UMoC₂, YCoC, and U₂IrC₂.