The Computable Dimension of I-Trees of Infinite Height

We study computable trees with distinguished initial subtree (briefly, I-trees). It is proved that all I-trees of infinite height are computably categorical, and moreover, they all have effectively infinite computable dimension.     

Calculations of thermodynamic stability of CpCoC<Subscript>2</Subscript>B<Subscript>9</Subscript>H<Subscript>11</Subscript> cobaltacarborane isomers

Quantum-chemical calculations of the geometry and energies of nine possible isomers of 12-vertex cobaltacarborane CpCoC₂B₉H₁₁ (1) were carried out by the DFT method (PBEPBE/DGDZVP/DGA1). Thermodynamic stability of the isomers increases with increasing distance between the carbon atoms in the cage and is virtually independent of the position of the CpCo vertex. The relative stabilities of the 1,2,3-(17.57 kcal mol⁻¹), 1,2,4-(3.72 kcal mol⁻¹), and 1,2,9-isomers of 1 (0 kcal mol⁻¹) are similar to the corresponding values for the ortho (17.61 kcal mol⁻¹), meta (3.21 kcal mol⁻¹), and para isomers (0 kcal mol⁻¹) of carborane C₂B₁₀H₁₂. The results of the present study confirm a close similarity of the CpCo and BH fragments in metallacarborane chemistry. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1557–1559, July, 2005.     

Synthesis of cationic complexes [(C<Subscript>4</Subscript>Me<Subscript>4</Subscript>)CoL]<Superscript>+</Superscript> (L is naphthalene,phenanthrene, and anthracene)

Cationic arene complexes [Cb*Co(naphthalene)]⁺ (2, Cb* = C₄Me₄) and [Cb*Co(phenanthrene)]⁺ were synthesized by the reactions of [Cb*Co(MeCN)₃]⁺ with arenes. The [Cb*Co(anthracene)]⁺ complex was synthesized by the abstraction of the iodide ion from [Cb*CoI]₂ by TIBF₄ in the presence of anthracene. Complex 2 exchanges the naphthalene ligand for other arenes at room temperature. Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1861–1863, September, 2007.     

Iron and ruthenium triple-decker complexes with a central pentaphospholyl ligand

Thirty-electron triple-decker complexes with a central pentaphospholyl ligand [(η-C₅Me₅)Fe(μ-η:η-P₅)M(η-C₅R₅)]BF₄ (M=Fe, R=Me or M=Ru, R=H, Me) were synthesized by a stacking reaction of cationic 12-electron fragments [(η-C₅R₅)M]⁺ with (η-C₅Me₅)Fe(η-P₅). Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1625–1626, August, 1998.     

Photochemical arene exchange in the iron dicarbollide complex [(η-9-SMe2-7,8-C2B9H10)Fe(η-C6H6)]+

Visible light irradiation of the dicarbollide complex [(η-9-SMe₂-7,8-C₂B₉H₁₀)Fe(η-C₆H₆)]⁺ (2a) in the presence of the benzene derivatives in CH₂Cl₂/MeNO₂ resulted in cations [(η-9-SMe₂-7,8-C₂B₉H₁₀)Fe(η-C₆R₆)]⁺ (2b-g; arene is anisole (b), toluene (c), m-xylene (d), mesitylene (e), durene (f), and hexamethylbenzene (g)) due to the arene exchange. The structures of [2g]PF₆ and related tricarbollide complex [(η-1-Bu^tNH-1,7,9-C₃B₈H₁₀)Fe-(η-C₆H₆)]PF₆ (1) were confirmed by X-ray diffraction analysis. The nature of bonding in cations 1, 2a, and [CpFe(η-C₆H₆)]⁺ was analyzed by an energy decomposition analysis.     

Synthesis and structure of (tricarbollide)iodide iridium complex [(η-1-ButNH-1,7,9-C3B8H10)IrI2]2

Cyclooctadiene complex (η-1-Bu^tNH-1,7,9-C₃B₈H₁₀)Ir(cod) (1) was obtained by the reaction of [(7-Bu^tNH-7,8,9-C₃B₈H₁₀)]Tl with [(cod)IrCl]₂ in the presence of TlPF₆. The reaction of 1 with I₂ gave diiodide [(η-1-Bu^tNH-1,7,9-C₃B₈H₁₀)IrI₂]₂ (2a). According to the X-ray diffraction data, complex 2a has a dimeric structure with two bridging iodine atoms.     

Synthesis of cationic indenyl- and fluorenyl-arene complexes of ruthenium

Interaction of [Ru(-C ₆ H ₆ )Cl ₂ ] ₂ with indenyl- or fluorenyllithium in THF gives, together with cationic benzene complexes [Ru( ⁵ -C ₉ H ₇ )(-C ₆ H ₆ )]⁺ and [Ru( ⁵ -C ₁₃ H ₉ )(-C ₆ H ₆ )]⁺, the neutral cyclohexadienyl derivatives Ru( ⁵ -C ₉ H ₆ -C ₉ H ₇ ) and Ru( ⁵ -C ₁₃ H ₉ )( ⁵ -C ₆ H ₆ -C ₁₃ H ₉ ), respectively. Interaction of the cyclohexadienyl complexes with Al ₂ O ₃ , Ph ₃ C⁺, and CF ₃ CO ₂ H has been studied. Reaction of Ru( ⁵ -C ₁₃ H ₉ )( ⁵ -C ₆ H ₇ ) with CF ₃ CO ₂ H in the presence of an arene yields cationic cyclohexadienylarene complexes: [Ru( ⁵ -C ₁₃ H ₉ )( ⁶ -arene)]⁺ (arene=C ₆ H ₆ or 1,3,5-Me ₃ C ₆ H ₃ ).A. N. Nesmeyanov Institute of Organoelemental Compounds, Russian Academy of Sciences, 117813 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 699–706, March, 1992.     

Model of a polaron superconductor

This paper studies the mechanism of superconductivity in the case where the electrons are strongly coupled to lattice vibrations and, therefore, are in the state of small polarons. The consideration is based on the Holstein model with zero lattice-vibration dispersion and represents a consistent realization of the BCS approach (with no need arising for boson introduction). The ground state and the excitation spectrum are found. The current states are studied and the criterion of their stability is formulated. The superconducting transition temperature is shown to increase without limit with increasing electron-phonon coupling constant. This is accompanied by an exponential decrease in the critical current. Some fundamental properties of high-temperature superconductors are shown to follow directly from this model.     

The effect of radiation defects in silicon single crystal lattice on the characteristic states of the interstitial muonium atom

Radiation defects are shown experimentally to affect differently the normal and anomalous muonium states in silicon. This evidences essentially different mobilities of the two muonium states in the sample lattice.