On Unicycle Graphs with Maximum and Minimum Zeroth-order Genenal Randić Index

Let G be a graph and d _v denote the degree of the vertex v in G. The zeroth-order general Randić index of a graph is defined as R _α⁰(G) = ∑ _v∈V(G) d _v ^α where α is an arbitrary real number. In this paper, we obtained the lower and upper bounds for the zeroth-order general Randić index R _α⁰(G) among all unicycle graphs G of order n. We give a clear picture for R _α⁰(G) of unicycle graphs according to real number α in different intervals.     

Molecular Structure of Neodymium Diiodide

The molecular structure of neodymium diiodide was investigated in an electron diffraction study at T _exp = 795(10) K. The molecule has C_2v symmetry; the internuclear distance R_g(Nd–I) is 297.3(3) pm and _g = 132(3)°. The vibration frequencies were estimated from the experimental values of the root-mean-square vibration amplitudes.     

Geometrical structure of the molybdenum tetrabromide molecule is nontetrahedral

Molecular structure of molybdenum tetrabromide has been studied by electron diffractometry. The geometrical configuration of MoBr ₄ has been shown to be of C _2v symmetry. The following values of structural parameters have been obtained: R_g(MoBr ₁ )=233.9(6) pm, R_g(MoBr ₂ )=244.5(6) pm, (Br ₁ MoBr ₂ )=106(1)^o, and (Br ₂ MoBr ₃ )=86(2)^o. The frequency values of the vibrational spectrum have been estimated.Institute of High Temperatures, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 3, pp. 47–50, May–June 1993.Translated by L. Smolina     

Molecular Structure of Samarium Dibromide

The molecular structure of samarium dibromide has been studied by electron diffraction at T _exp = 1250(50) K. The molecule has C_2v symmetry; the internuclear distance R_g(Sm–Br) = 274.5(5) pm; _g =131(6)°. The vibration frequencies were estimated from the experimental values of the mean square vibration amplitudes.     

Kinetic of decomposition of some complexes under non-isothermal conditions

Kinetics of thermal decomposition of three structurally similar complexes Co₂Cu(C₂O₄)₃ (R-diam)₂, where R is ethyl, 1,2-propyl or 1,3-propyl, was studied under non-isothermal conditions and nitrogen dynamic atmosphere at heating rates of 5, 7, 10, 12 and 15 K min⁻¹. For data processing the Flynn-Wall-Ozawa and a modified non-parametric kinetic methods were used. By both methods the activation energy are in the range of 97–102 kJ mol⁻¹. The formal kinetic is r=kα(1−α)². Also a compensation effect between lnA and E was evidenced. The kinetic analysis lead to the conclusion of an identic decomposition mechanism by a single step process.     

Synthesis, crystal structure and magnetic properties of bimetallic complex of Ni2Co(TTHA)·12H2O

The bimetallic complex of Ni₂Co(TTHA)·12H₂O (TTHA = triethylene tetraminehexaacetic acid) was synthesized and characterized structurally and magnetically. The title complex crystallizes in the triclinic space group P ī with a = 0.7316(2), b = 0.8624(2), c = 1.5041(4) nm; α = 73.38(2), β = 83.97(2), γ = 70.50(2)°. The crystal structure is built up of [Ni₂(TTHA)(H₂O)₂]²⁻, Co(H₂O)₆²⁺ and water molecules. The variable magnetic measurement shows that there is strong antiferromagnetic interaction between two Ni(II) ions in [Ni₂(TTHA) (H₂O)₂]²⁻ with J _Ni−Ni = −141.64 cm⁻¹, g _Ni = 2.21 and that the constant of spin-orbit coupling of Co(II) ion is −134.8 cm⁻¹. __________ Translated from Acta Scientiarum Naturalium Universitatis Nankaiensis, 2007, 40(1): 6–10 [译自: 南开大学学报(自然科学版)]     

两个三维柱层式单一手性配位化合物:合成、结构和性质（英文）

在溶剂热合成条件下得到2个单一手性配位聚合物,即[Cd3((R)-CIA)2(bipy)2.5(H2O)2]·xGuest(1)和[Zn3((R)-CIA)(bmib)2(H2O)2 Cl]·H2O·xGuest(2)((R)-H3CIA=(R)-5-(1-羧基乙氧基)间苯二甲酸,bipy=4,4′-联吡啶,bmib=1,4-双(2-甲基-1H-咪唑-1-基)苯)。X射线单晶结构分析揭示配合物1和2都是柱层式结构的三维框架。从拓扑分析的角度看,配位物1具有(3,3,3,6,6)-连接的网络,拓扑符号为(4.5^2)2(4.8^2)2(42.6^8.8^3.10^2)(4^2.6^8.8^3.9^2)(5.8.9)2,而配合物2是(3,4,4)-连接的网络,拓扑符号为(6·7^2)2(6·7^5)2(6^2·7^4)。此外,对上述配合物的热稳定性、圆二色谱和荧光性质也做了研究。     

Ionization potentials of non-metal monosulfides. Conjugation in radical cations containing Group IV elements

The first vertical ionization potentialsI(n_s) of 69 monosulfides XSY (X, Y=H, Hal, organic, or heteroorganic substituent) are related to the inductive σ_I resonance (σ _R ⁺ ) and polarizability (σ_α) constants of the substituents by dependences of theI(n_S)=a+bΣσ_I+bΣσ_R+bΣσ_α type. TheI(n_s) values are also affected by hyperconjugation which increases on going from XSH to XSY (Y≠H) compounds. The first calculations of the σ _R ⁺ parameters characterizing the conjugation of Si-, Ge-, Sn-, and Pb-containing substituents with the S^.+ radical cation center are reported. The reasons for weakening of resonance donor properties of heteroorganic substituents of the +M-type in the systems studied as compared to those of the same substituents in the corresponding aromatic radical cations are considered. Translated fromIzvestiya Akademii Nauk. Seriya Khmicheskaya, No. 1, pp. 25–31, January, 2000.     

Kinetic characterization of the reduction of silica supported cobalt catalysts

Abstact  The reduction process of silica supported cobalt catalyst was studied by thermal analysis technique. The reduction of the catalyst proceeds in two steps:

Electron diffraction study of the structure of the NbOF3 molecule

Simultaneous electron diffraction and mass spectrometric study of vapor over hydrolyzed NbF₅ was carried out. Conditions providing the presence of niobium oxytrifluoride in the gas phase have been revealed, and structural parameters of the NbOF₃ molecule, corresponding to the r_α configuration of C_3v symmetry, have been determined: r_α(Nb=O) 1.688(7), Å; r_α(Nb-F) 1.861(4) Å; r_α(O-F) 2.857(23) Å; r_α(F-F) 3.079(22) Å; ∠_α(O-Nb-F) 107.1(1.5)^o; ∠_α(F-Nb-F) 111.6(1.4)^o. Ivanovo State Chemical Technological Academy. Ivanovo State University. Translated fromZhumal Struktumoi Khimii, Vol. 37, No. 4, pp. 708–715, July–August, 1996. Translated by L. Smolina     

Ionization potentials of non-metal monosulfides. Conjugation in radical cations containing Group IV elements

The first vertical ionization potentialsI(n_s) of 69 monosulfides XSY (X, Y=H, Hal, organic, or heteroorganic substituent) are related to the inductive σ_I resonance (σ _R ⁺ ) and polarizability (σ_α) constants of the substituents by dependences of theI(n_S)=a+bΣσ_I+bΣσ_R+bΣσ_α type. TheI(n_s) values are also affected by hyperconjugation which increases on going from XSH to XSY (Y≠H) compounds. The first calculations of the σ _R ⁺ parameters characterizing the conjugation of Si-, Ge-, Sn-, and Pb-containing substituents with the S^.+ radical cation center are reported. The reasons for weakening of resonance donor properties of heteroorganic substituents of the +M-type in the systems studied as compared to those of the same substituents in the corresponding aromatic radical cations are considered. Translated fromIzvestiya Akademii Nauk. Seriya Khmicheskaya, No. 1, pp. 25–31, January, 2000.     

Synthesis, crystal structure and characterization of a 2-D network organic-inorganic hybrid polymer with [α-BW12O40]5? as building blocks

A two-dimensional network compound [Ce(DMF)₄(H₂O)][α-BW₁₂O₄₀]·H₂O·(HDMA)₂ (HDMA = protoned dimethylamine, DMF = N,N-dimethylformamide) was synthesized from α-H₅BW₁₂O₄₀·nH₂O, Ce(NO₃)₃·6H₂O and DMF and characterized by IR, UV spectra and TG-DTA. The result of the X-ray single crystal diffraction indicates that the crystal is monoclinic, space group P2₁/n, with unit cell dimensional: a = 1.1983(3), b = 2.4216(5), c = 1.9517(4) nm, β = 92.91(3)°, Z = 4, R ₁ = 0.07710, wR ₂ = 0.1416. Structural analysis indicates that every [Ce(DMF)₄(H₂O)]³⁺ building block is surrounded by three adjacent [α-BW₁₂O₄₀]⁵⁻ polyanions, meanwhile, every [α-BW₁₂O₄₀]⁵⁻ polyanion interconnects with three neighboring [Ce(DMF)₄(H₂O)]³⁺ subunits, by making use of which two-dimensional network structure can be constructed. The result of thermogravimetric analysis manifests that the title compound has two-stage weight loss and the decomposition temperature of the title polyanionic framework is 560°C. The electrochemical analysis shows the title polyanion has three-step redox processes in the pH = 4–7 media.     

Crystal structure of [Mn(1,10-C12H8N2)3](B6H7)2

A new compound [MN^II(Phen)₃]²⁺(B₆H₇)₂⁻ is synthesized; its crystal structure is studied by XRD at 100 K. Crystallographic data: C₃₆H₃₈B₁₂N₆Mn, M = 739.39, triclinic symmetry, space group P , unit cell parameters: a = 10.3131(3) ?, b = 13.4839(4) ?, c = 15.1132(4) ?; α = 97.696(1)°, β = 108.324(1)°, γ = 102.211(1)°; V = 1903.9(1) ?³, Z = 2, d _calc = 1.290 g/cm³. The structure is solved by direct and Fourier methods and refined by full-matrix LSM in the anisotropic (isotropic for hydrogen atoms) approximation to the final factor R ₁ = 0.036 for 10169 I _hkl ≥ 2σ _I (Bruker-Nonius X8 APEX CCD diffractometer, λMoK _α). The structure contains two crystallographically different anions. Original Russian Text Copyright ? 2009 by T. M. Polyanskaya, M. K. Drozdova, V. V. Volkov, and K. G. Myakishev __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 50, No. 2, pp. 381–385, March–April, 2009.     

Solubility Measurements of Crystalline NiO in Aqueous Solution as a Function of Temperature and pH

Results of solubility experiments involving crystalline nickel oxide (bunsenite) in aqueous solutions are reported as functions of temperature (0 to 350 °C) and pH at pressures slightly exceeding (with one exception) saturation vapor pressure. These experiments were carried out in either flow-through reactors or a hydrogen-electrode concentration cell for mildly acidic to near neutral pH solutions. The results were treated successfully with a thermodynamic model incorporating only the unhydrolyzed aqueous nickel species (viz., Ni²⁺) and the neutrally charged hydrolyzed species (viz., Ni(OH)₂⁰)\mathrm{Ni(OH)}_{2}^{0}). The thermodynamic quantities obtained at 25 °C and infinite dilution are, with 2σ uncertainties: log₁₀K_s0^o = (12.40 ±0.29),\varDelta_rG_m^o = -(70. 8 ±1.7)\log_{10}K_{\mathrm{s0}}^{\mathrm{o}} = (12.40 \pm 0.29),\varDelta_{\mathrm{r}}G_{m}^{\mathrm{o}} = -(70. 8 \pm 1.7) kJ⋅mol⁻¹; \varDelta_rH_m^o = -(105.6 ±1.3)\varDelta_{\mathrm{r}}H_{m}^{\mathrm{o}} = -(105.6 \pm 1.3) kJ⋅mol⁻¹; \varDelta_rS_m^o = -(116.6 ±3.2)\varDelta_{\mathrm{r}}S_{m}^{\mathrm{o}} =-(116.6 \pm 3.2) J⋅K⁻¹⋅mol⁻¹; \varDelta_rC_p,m^o = (0 ±13)\varDelta_{\mathrm{r}}C_{p,m}^{\mathrm{o}} = (0 \pm 13) J⋅K⁻¹⋅mol⁻¹; and log₁₀K_s2^o = -(8.76 ±0.15)\log_{10}K_{\mathrm{s2}}^{\mathrm{o}} = -(8.76 \pm 0.15); \varDelta_rG_m^o = (50.0 ±1.7)\varDelta_{\mathrm{r}}G_{m}^{\mathrm{o}} = (50.0 \pm 1.7) kJ⋅mol⁻¹; \varDelta_rH_m^o = (17.7 ±1.7)\varDelta_{\mathrm{r}}H_{m}^{\mathrm{o}} = (17.7 \pm 1.7) kJ⋅mol⁻¹; \varDelta_rS_m^o = -(108±7)\varDelta_{\mathrm{r}}S_{m}^{\mathrm{o}} = -(108\pm 7) J⋅K⁻¹⋅mol⁻¹; \varDelta_rC_p,m^o = -(108 ±3)\varDelta_{\mathrm{r}}C_{p,m}^{\mathrm{o}} = -(108 \pm 3) J⋅K⁻¹⋅mol⁻¹. These results are internally consistent, but the latter set differs from those gleaned from previous studies recorded in the literature. The corresponding thermodynamic quantities for the formation of Ni²⁺ and Ni(OH)₂⁰\mathrm{Ni(OH)}_{2}^{0} are also estimated. Moreover, the Ni(OH)₃ ^-\mathrm{Ni(OH)}_{3}^{ -} anion was never observed, even in relatively strong basic solutions (m_{OH ^-} = 0.1m_{\mathrm{OH}^{ -}} = 0.1 mol⋅kg⁻¹), contrary to the conclusions drawn from all but one previous study.     

Synthesis and structures of nine-coordinate K[SmIII (Edta)(H2O)3] · 2H2O and Ten-Coordinate K2[SmIII(Pdta)(H2O)2]2 · 4.5H2O complexes

The title complexes, K[Sm^III(Edta)(H₂O)₃] · 2H₂O(I)(H₄Edta = ethylenediamine-N,N,N′,N′-tetraacetic acid) and K₂[Sm^III(Pdta)(H₂O)₂]₂ · 4.5H₂O (II) (H₄Pdta = propylenediamine-N,N,N′,N′-tetraacetic acid), were prepared and their compositions and structures were determined by elemental analyses and single-crystal X-ray diffraction techniques, respectively. Complex I has a mononuclear structure, and the Sm³⁺ ion is nine-coordinated by an Edta ligand and three water molecules, yielding a pseudo-monocapped square antiprismatic conformation, and the complex crystallizes in the orthorhombic crystal system with space group Fdd2. The crystal data are as follows: a = 19.84(5), b = 35.58(9), c = 12.15(3) ?, V = 8580(38) ?³, Z = 16, ρ _c = 1.925 g/cm³, μ = 3.010 mm⁻¹, F(000) = 4976, R = 0.0252, and wR = 0.0560 for 3510 observed reflections with I ≥ 2σ(I). Complex II has a binuclear structure and the Sm³⁺ ion is ten-coordinated by a Pdta ligand, two oxygen atoms from a carboxylic group of adjacent Pdta ligand and two water molecules, yielding a distorted bicapped square antiprismatic prism. The complex crystallizes in the triclinic crystal system with space group P $ \bar 1 $ \bar 1 . The crystal data are as follows: a = 8.9523(15), b = 10.7106(15), c = 11.6900(19) ?, α = 80.613(5)°, β = 80.397(5)°, γ = 76.530(4)°, V = 1065.7(3) ?³, Z = 1, ρc = 1.970 g/cm³, μ = 2.532 mm⁻¹, F(000) = 1620, R = 0.0332 and wR = 0.0924 for 5390 observed reflections with I ≥ 2σ(I).     

Cyclotron production of <Superscript>211</Superscript>At/<Superscript>211g</Superscript>Po by <Superscript>209</Superscript>Bi(α,2n) reaction

Astatine-211 (T _1/2 = 7.214 h) is an α-emitter at secular equilibrium by EC with its ultra-short-lived α-emitting daughter, polonium-211g (T _1/2 = 0.516 s), with a high Linear Energy Transfer (LET — 130 eV·nm⁻¹) and a half-life suitable for metabolic radiotherapy; the overall α branching of the ²¹¹At/^211gPo system is 100%. The direct production of ²⁰⁹Bi(α,2n)²¹¹At/^211gPo seems the most satisfactory method; Bi targets were irradiated at JRC-Ispra Cyclotron of European Commission, EC, using α-energy higher than 28.61 MeV in order to produce, via ²⁰⁹Bi(α,3n) reaction, small amounts of the γ-emitter ²¹⁰At (used as internal spike).     

Crystal structure of a new mononuclear complex of Mn(II) with a bbbi ligand (bbbi = 1,4-bis(benzimidazol-1-yl)-2-butene)

A new mononuclear complex Mn(bbbi)₂(H₂O)₄(ClO₄)₂·(bbbi)₂·(H₂O)₂ 1 (bbbi = 1,4-bis(benzimidazol-1-yl)-2-butene) is synthesized under hydrothermal conditions and characterized by IR spectroscopy, elemental analysis, and single crystal X-ray structural analysis. Crystal data for 1: triclinic, , a = 8.8478(7) ?, b = 15.0550(11) ?, c = 16.4310(12) ?, α = 108.657(7)°, β = 104.044(7)°, Γ = 99.317(7)°, V = 1942.2(3) ?³, Z = 1, final R = 0.0621. Each manganese atom is octahedrally coordinated by four aqua ligands and two nitrogen atoms of two distinct bbbi ligands. The molecule is stabilized by hydrogen bonding and π…π interactions.     

Influence of solvent on the yield of singlet oxygen upon the chloride ion-catalyzed decomposition of dimethyldioxirane

The excitation yield of the singlet molecular oxygen ¹Δ _g [φ(¹O₂)] in the reaction of the dimethyldioxirane with the chloride ion in benzene, acetone, methylene chloride, and acetonitrile solutions has been determined. The φ(¹O₂) value depends on the solvent nature and is in the range 50–84%. Correlation between the value of the singlet oxygen yield and the Kamlet-Taft parameter (α) characterizing the acidity of the solvent as a hydrogen bond donor has been established: the higher the α value, the higher the ¹O₂ yield.     

A criterion for the confluence of two seams of conical intersection in triatomic molecules

It is shown that the cross product t ^{I J} (R _x )≡g ^{I J} (R _x )×h ^{I J} (R _x ), where g _τ ^{I J} (R)=(c ^I (R _x )−c ^J (c ^I (R _x )+c ^J (R _x )), h _τ ^{I J} (R)=c ^I (R _x )^† c ^J (R _x ), τ is an internal nuclear coordinate, the c ^I (R) satisfy [H(R)−E _I (R)]c ^I (R)=0 and H(R) is the electronic Hamiltonian matrix, is a unique property of a conical intersection at R _x . t ^{I J} (R _x )=0 when R _x is located at the intersection of two (or more) seams of conical intersection. This criterion for an intersection of two seams of conical intersection has important implications for algorithms that seek to locate such points. Here it␣is␣used to analyze the trifurcation of a generic C_2v ^2S+1 A−^2S+1 B seam of conical intersection, analogous to those recently found in AlH₂ and CH₂. Received: 31 July 1997 / Accepted: 27 August 1997     

The molecular structure and conformation of acetamides in the vapour phase: Part III. Thioacetamide (ethanethioamide)

Thioacetamide has been studied by electron diffraction in the gas phase, utilizing a new nozzle construction and using a broad electron beam. The molecule has C_s symmetry, and one C-H bond eclipses the CS bond. The most important structural parameters are: r_g(C-N) = 135.6(3) pm, r_g(C—C) = 151.2(4) pm, r_g(CS) = 164.7(3) pm,∠_αCCS = 122.9(3)° and ∠_αCCN = 114.8(4)°. Parenthesized values are one standard deviation where correlation among data and uncertainty in the electron wavelength have been included. The methyl barrier, V₃, is found from the electron diffraction data to be 4.56 kJ mol^?1. This corresponds to a torsional frequency of 131 cm^?1.