Embeddings of SL(2; ?) into the cremona group

Geometric and dynamic properties of embeddings of SL(2; ℤ) into the Cremona group are studied. Infinitely many nonconjugate embeddings that preserve the type (i.e., that send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many nonconjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2; ℤ), preserves an elliptic curve and all its elements of infinite order are hyperbolic.     

Solubility of <Emphasis Type="Italic">d</Emphasis>-element salts in organic and aqueous–organic solvents: II. Effect of halocomplex formation on solubility of cobalt bromide and chloride and nickel chloride

Solubility of salts in the systems MCl₂–H₂O–Solv (M = Co, Ni) and CoBr₂–H₂O–Solv (Solv = dimethyl sulfoxide, dimethyl formamide, and dimethyl acetamide) at 25°C was measured experimentally. Dominating species of cobalt and nickel halides existing in various concentration regions were identified by analysis of electron absorption spectra. It was shown that the major factor defining solubility is the interaction of halocomplexes of metal ions with solvent molecules.     

Influence of acido ligands on the structure of copper dihalide solvates with dimethyl sulfoxide and <Emphasis Type="Italic">N,N</Emphasis>-dimethylformamide

Structures of copper dihalide solvates with dimethyl sulfoxide (DMSO) and N,N-dimethylformamide (DMF) were determined by XRD single crystal analysis. The existence of two DMSO solvates with CuBr₂, but only one with CuCl₂, was attributed to a lower Cu-Br bond strength in comparison with Cu-Cl, and, as a consequence, by its easier breaking to form a bond with a solvent molecule. Fundamentally different structures of CuX₂·2DMF (X = Br, Cl) solvates are caused by different donor power of the acido ligands.     

Crystal structure and vibrational spectra of M[VO<Subscript>2</Subscript>(SeO<Subscript>4</Subscript>)(H<Subscript>2</Subscript>O)<Subscript>2</Subscript>]·H<Subscript>2</Subscript>O (M = K,Rb, NH<Subscript>4</Subscript>)

By the hydration of MVO(SeO₄)₂ with saturated water vapors at room temperature a series of isostructural complex compounds of vanadium(V) of the composition M[VO₂(SeO₄)(H₂O)₂]·H₂O (K, Rb, NH₄) are synthesized and their physicochemical properties are studied. Based on the X-ray and neutron diffraction data, it is found that their crystal structure is composed of VO₆ octahedra linked in infinite chains by bridging SeO₄ tetrahedra. Each of the VO₆ octahedra has two short terminal V-O bonds forming a bent dioxovanadium group VO₂⁺. Two water molecules are coordinated by vanadium and one molecule is out of the first coordination sphere in the interchain space. The vibrational spectra of the studied compounds are completely consistent with their structural features.     

Metal-metal bonding in tetracyanometalates (M=PtII, PdII, NiII) of monovalent thallium. Crystallographic and spectroscopic characterization of the new compounds Tl2Ni(CN)4 and Tl2Pd(CN)4

The new crystalline compounds Tl2Ni(CN)4 and Tl2Pd(CN)4 were synthesized by several procedures. The structures of the compounds were determined by single-crystal X-ray diffraction. The compounds are isostructural with the previously reported platinum analogue, Tl2Pt(CN)4. A new synthetic route to the latter compound is also suggested. In contrast to the usual infinite columnar stacking of [M(CN)4]2- ions with short intrachain M-M separations, characteristic of salts of tetracyanometalates of NiII, PdII, and PtII, the structure of the thallium compounds is noncolumnar with the two TlI ions occupying axial vertices of a distorted pseudo-octahedron of the transition metal, [MTl2C4]. The Tl-M distances in the compounds are 3.0560(6), 3.1733(7), and 3.140(1) A for NiII, PdII, and PtII, respectively. The short Tl-Ni distance in Tl2Ni(CN)4 is the first example of metal-metal bonding between these two metals. The strength of the metal-metal bonds in this series of compounds was assessed by means of vibrational spectroscopy. Rigorous calculations, performed on the molecules in D4h point group symmetry, provide force constants for the Tl-M stretching vibration constants of 146.2, 139.6, and 156.2 N/m for the NiII, PdII, and PtII compounds, respectively, showing the strongest metal-metal bonding in the case of the Tl-Pt compound. Amsterdam density-functional calculations for isolated Tl2M(CN)4 molecules give Tl-M geometry-optimized distances of 2.67, 2.80, and 2.84 A for M = NiII, PdII, and PtII, respectively. These distances are all substantially shorter than the experimental values, most likely because of intermolecular Tl-N interactions in the solid compounds. Time-dependent density-functional theory calculations reveal a low-energy, allowed transition in all three compounds that involves excitation from an a1g orbital of mixed Tl 6pz-M ndz2 character to an a2u orbital of dominant Tl 6pz character.     

Solution-solid phase equilibrium in the systems MBr<Subscript>2</Subscript>-NR<Subscript>4</Subscript>Br-H<Subscript>2</Subscript>O (M = Cd,Cu, Co; R = Me,Et, Bu) at 25°C

The solubility diagrams in ternary MBr₂-NR₄Br-H₂O systems (M = Cd, Co; R = Me, Et, Bu) at 25°C were determined by isothermal saturation. The composition and crystallization range of solid compounds occurring in equilibrium with the liquid phase were found. The effects of ion hydration, association of tetraalkylammonium salts, and complex formation with d-elements on the solution-solid phase equilibrium were estimated.     

Effect of Alkali Metal Chlorides on the Solubility in Ternary Water-Salt Systems Containing Copper Monochloride

Solubility in the systems of CuCl-LiCl-H₂O and CuCl-CsCl-H₂O at 25°C was studied by the method of isothermal removal of oversaturation. The results were examined in terms of the competition between hydration and complex formation processes in water-salt systems.     

Description of evaporation of a spherical liquid drop by a non-Markovian random process based on integral stochastic equations

Processes of evaporation (condensation) of vapor particles from the surface of a spherical drop and processes of their diffusion into surrounding volume are considered. Special features of evaporation are investigated taking into account vapor particle fluctuations caused by random changes in the temperature, concentration, etc. Statistical characteristics of fluctuations of the corresponding quantities, including the mass flow through the liquid-vapor boundary and concentration on the liquid surface, are presented. The distribution of completely evaporated drop number versus time is presented.     

Potassium ion-mediated non-covalent bonded coordination polymers

Crystal structures and vibrational spectra of three related network-forming coordination complexes have been studied. Two novel thermodynamically stable pseudo-polymorphic solvated rhodium chloro compounds, [cis-RhCl(4)(DMSO-κS)(2)K](n), 1, and [cis-RhCl(4)(DMSO-κS)(2)K·3H(2)O](n), 2, and one metastable compound [trans-RhCl(4)(DMSO-κS)(2)K·0.25H(2)O](n), 3, crystallize at ambient temperature in the orthorhombic space group P2(1)2(1)2(1) for 1, and the monoclinic space groups P2(1)/n and P2(1)/c for 2 and 3, respectively. All three structures contain [RhCl(4)(DMSO-κS)(2)](-) complexes in which the rhodium(III) ions bind to two dimethyl sulfoxide (DMSO) sulfur atoms and four chloride ions in distorted octahedral coordination geometries. The complexes are connected in networks via potassium ions interacting with the Cl(-) and the DMSO oxygen atoms. As the sum of Shannon ionic radii of K(+) and Cl(-) exceeds the K-Cl distances in compounds under study, these compounds can be described as Rh-Cl-K coordination polymers with non-covalent bonding, which is not common in these systems, forming 1- and 2-D networks for 1/2 and 3, respectively. The 2-D network with nano-layered sheets for compound 3 was also confirmed by TEM images. Further evaluation of the bonding in the cis- and trans-[RhCl(4)(DMSO-κS)(2)](-) entities was obtained by recording Raman and FT-IR absorption spectra and assigning the vibrational frequencies with the support of force-field calculations. The force field study of complexes reveals the strong domination of trans-effect (DMSO-κS > Cl) over the effect of non-covalent bonding in coordination polymeric structures. The comparison of calculated RhCl, RhS and SO stretching force constants showed evidence of K(+)-ligand interactions whereas direct experimental evidences of K(+)-Cl(-) interaction were not obtained because of strong overlap of the corresponding spectral region with that where lattice modes and Rh-ligand bendings appear.