Bound states of light and heavy quarks in hot hadronic matter

The correlators of currents \(\bar q\) Q,γ _v γ ₅ Q,q andQ being correspondingly light and heavy quark fields, in hot hadronic matter are investigated by means of finite temperature QCD sum rules. AtT? 100 MeV the modification of the effective spectrum parameters takes place, similar to that found earlier in the correlators of light quark currents. AtT?150 MeV the form of the spectrum is obtained, which indicates an appearance in hadronic matter of quasifree quarks with nonzero mass being fixed by the value of the quark condensate 〈 \(\bar q\) q〉 (T).     

Diastereoselective formation of calcium and ytterbium ansa-metallocenes via recombination of guaiazulene (Gaz) radical anions. Molecular structure of ansa-(η5-Gaz)2Ca(THF)2 and ansa-(η5-Gaz)2Yb(Py)2 (Gaz = 1,4-dimethyl-7-isopropylazulene) complexes

ansa-Metallocene derivative (⁵-Gaz)₂Ca(THF)₂ (1) (Gaz = 1,4-dimethyl-7-isopropylazulene) was synthesized by the reaction of CaI₂(THF)₂ with two equivalents of potassium and two equivalents of guaiazulene in THF. The ytterbium analog ansa-(⁵-Gaz)₂Yb(THF)₂ (2a) was synthesized by the reduction of guaiazulene with ytterbium naphthalenide in THF. The recrystallization of 2a from pyridine leads to the exchange of the coordinated solvent molecules and gives ansa-(⁵-Gaz)₂Yb(NC₅H₅)₂ (2b). The molecular structures of 1, 2a, and 2b were determined by X-ray diffraction analysis. The crystals of 1, 2a, and 2c consist of a racemic mixture of both R,R- and S,S-enantiomers. The calcium and ytterbium atoms ⁵-coordinate the five-membered rings of the guaiazulene ligands. The ¹H NMR spectroscopic and X-ray diffraction data unambiguously confirm the exclusive formation of N₂-symmetric ansa-metallocenes in these reactions. The reaction of compound 1 with Me₃SiCl in THF occurs with retention of the N—N bond between two guaiazulene moieties and affords bis(1,4-dimethyl-3-trimethylsilyl-7-isopropylazulene) (3) in high yield.     

Synthesis and crystal structure of the Sm(ButNCHCHNBut)2(bpy) complex

Reaction of Sm(bpy)₄ (bpy is 2,2′-bipyridyl) with di-tert-butyldiazabutadiene (dad) in tetrahydrofuran (THF) affords the mixed-ligand complex Sm(dad)₂(bpy) (1). Complex1 was isolated as black paramagnetic crystals readily soluble in THF, 1,2-dimethoxyethane (DME), toluene, and ether. Compound1 was characterized by IR and ESR spectroscopy, X-ray diffraction analysis, and by the results of magnetic measurements. Based on the difference between the Sm−N bond lengths and on the data of IR spectroscopy, the following formal charge distribution in the molecule of complex1 was proposed: Sm³⁺(dad)²⁻(dad)¹⁻(bpy)⁰. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1860–1862, October. 1997.     

Reaction of neodymium diiodide with methanol in acetonitrile. Structure of the cluster [Nd4(μ2-I)1.1(μ3-I)(μ2-OMe)4.9(μ4-O)(MeCN)12]I3

The reaction of neodymium diiodide NdI₂ with excess methanol in acetonitrile produced the tetranuclear neodymium cluster [Nd₄(μ₂-I)_1.1(μ₃-I)(μ₂-OMe)_4.9(μ₄-O)(MeCN)₁₂]I₃ (1). In the latter, the isomorphic substitution of one methoxy group by an I⁻ anion with site occupancies (%) of 90 and 10, respectively, was observed. Due to the isomorphic substitution in the crystal, cluster 1 can be considered as a superposition of two complexes, [Nd₄(μ₂-I)(μ₃-I)(μ₂-OMe)₅(μ₄-O)(MeCN)₁₂]I₃ and [Nd₄(μ₂-I)₂(μ₃-I)(μ₂-OMe)₄(μ₄-O)(MeCN)₁₂]I₃. The characteristic feature of cluster 1 is that the center of the Nd₄ cage is occupied by the μ₄-coordinated O²⁻ anion, which is indicative of the partial O-C bond cleavage in methanol. The reaction of NdI₂ with an equimolar amount of MeOH in an acetonitrile solution produced methoxide NdI₂(OMe)(MeCN)₄ in 49% yield. Dedicated to Professor W. J. Evans on the occasion of his 60th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1894–1897, October, 2007.     

Pentafluorophenylgermylbismuth compounds

Triethylbismuth reacts with (C₆F₅)₃GeH to give (C₆F₅)₃GeBiEt₂ and [(C₆F₅)₃Ge]₂BiEt and with (C₆F₅)₂GeH₂ to give [(C₆F₅)₂GeBiEt]₂. The presence of C₆F₅ radicals does not increase the stability of

compounds (M = Ge, Sn). Their reactivity in the transmetallation reaction with mercury has been studied.     

ESR study of reversible complex formation between bis(η5-cyclopentadienyl)vanadium and fullerene C60 in solution

Using the ESR method, equilibrium complex formation of fullerene C₆₀ with bis-(⁵-cyclopentadienyl)vanadium in solutions in aromatic solvents was found to occur. Based on an analysis of isotropic (g _i = 2.0008;A _i ,(V⁵¹)=–45.7 mT) and anisotropic (g _i =1.9808;g ₂ = 2.0135; <g ₃> = 2.0060;A ₁(⁵¹V)=–7.85 mT;A ₂(⁵¹V) = –6.50 mT; <A ₃(⁵¹V)> = 0.61 mT) ESR spectra parameters, it was established that the complex formed, Cp₂V(²-C₆₀), corresponds to vanadocene d¹-complexes with ²-bonded ligands.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1945–1947, November, 1994.     

Synthesis of trinuclear silicon-, germanium-, and tin-containing tungsten carbene complexes [(ButO)2(Cl)2W=CH]2EPh2 (E = Si, Ge, or Sn). Crystal structure of [(ButO)2(Cl)2W=CH]2SiPh2 complex

New trinuclear organosilicon, organogermanium, and organotin-containing tungsten carbene complexes Ph₂E[CH=WCl₂(OBu^t)₂]₂ (E = Si, Ge, or Sn) were synthesized by the reaction of the trinuclear carbyne complexes Ph₂E[C≡W(OBu^t)₃]₂ with HCl. The tin-containing carbene complex is thermally unstable and was identified in solution by ¹H and ¹³C NMR spectroscopy. The silicon-and germanium-tungsten carbene complexes were isolated in high yields as individual crystals and were characterized by elemental analysis, IR spectroscopy, and ¹H and ¹³C NMR spectroscopy. The structure of the silicon-containing complex Ph₂Si[CH=WCl₂(OBu^t)₂]₂ was established by X-ray diffraction. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2424–2427, November, 2005.     

A generalization of Kolmogorov’s theorem to biorthogonal systems

The fundamental Kolmogorov’s theorem about divergent trigonometric Fourier series is generalized to bounded biorthonormal systems defined on a separable metric space with Borel regular outer measure. Sharp lower bounds at points and on sets of positive measure are obtained for the arithmetic means of the symmetrized Lebesgue functions of biorthonormal systems defined on an arbitrary measure space. Earlier, similar results were obtained by the author for orthogonal systems on an interval.