Coherent States for the Legendre Oscillator

Two families of coherent states (the eigenstates of the annihilation operator and the Klauder–Gazeau temporally stable coherent states) are constructed for the Legendre oscillator defined in this paper. Bibliography: 14 titles.     

Asymptotic behavior of a functional Gaussian integral

Functional Gaussian integrals relative to a Wiener measure are considered, where both the integrand and the integration measure depend on some parameter . Asymptotic relations are obtained for such integrals for ^–1/2 ( is the deviation), when and tend to 0. Such relations are useful in the investigation of the asymptotic behavior of expressions of the partition function type tr exp (—tH) for t 0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 26–36, 1990.     

On the anomalous <Emphasis Type="Italic">A</Emphasis> dependence of the charge radii of heavy calcium isotopes

The charge radii of calcium isotopes are calculated within the self-consistent theory of finite Fermi systems based on the Fayans energy density functional. The fluctuating contribution of low-energy vibrations, i.e., phonons is taken into account approximately. As a result, an anomalous increase in the charge radii of neutron- rich calcium isotopes observed in a recent experiment has been reproduced.     

2-Phosphinothioyl- and 2-phosphinoylethylcyclopentadienyl zirconium and titanium complexes. Crystal structure of [η5:η1-C5H4CH2CH2P(O)Ph2]TiCl3

The intracomplex conversion of (2-diphenylphosphanoethyl)cyclopentadienyl zirconium and titanium complexes into the corresponding 2-phosphinothioyl and 2-phosphinoyl derivatives, viz., (η⁵-C₅H₅)[η ⁵-C₅H₄CH₂CH₂P(S)Ph₂]ZrCl₂, [η⁵-C₅H₄CH₂CH₂P(S)Ph₂]ZrCl₃, [η⁵:η¹C₅H₄CH₂CH₂P(O)Ph₂]ZrCl₃·THF, and [η⁵:η ¹-C₅H₄CH₂CH₂P(O)Ph₂]TiCl₃ (7), was performed. The NMR spectroscopy data revealed the following order of the coordination ability of the functional groups with respect to the Zr center: Ph₂P=O > Ph₂P > Ph₂P=S. An analogous order was found for the monodentate ligands (Ph₃P=O > Ph₃P > Ph₃P=S) with respect to (η⁵-C₅H₅)ZrCl₃. The molecular structure of complex 7 was established by X-ray diffraction analysis. Coordination of the Ph₂P=O group to the titanium atom was found retained both in the crystalline state and solution.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 116–122, January, 2005.     

空间受阻型Lewis酸碱对在小分子活化中的应用

作为一种新型的非金属有机催化剂,空间受阻型路易斯酸碱对由于具有的独特化学反应性,近年来在有机小分子活化和催化加氢领域的研究非常活跃。本文总结了近年来国外发表的有关空间受阻型路易斯酸碱对的研究报道,从其结构特征、有机小分子的活化、H₂活化机理的探讨及在催化领域应用的研究成果4个方面进行了详细的归纳整理。空间受阻型路易斯酸碱对对有机小分子的活化作用来源于其“分子间静电相互作用力”。这个在有机化学中早已熟知的概念却在2006年才被发现可活化有机小分子,并在之后受到广泛的关注。空间受阻型路易斯酸碱对化学的发展也扩展了有机化学反应研究的范畴,继续深入研究这种“分子间静电相互作用力”在其他未知领域的应用必将带来更大的发现。然而目前国内从事相关领域研究的报道很少,因此希望本文能够引起国内更多科研工作者对这个新兴领域产生研究兴趣。     

1,2-二甲基咪唑啉的合成及表征

对1,2-二甲基咪唑啉的合成进行了详细研究. 以甲胺水溶液和2-溴乙胺氢溴酸盐(1)为原料进行反应, 在两种原料物质的量之比为5∶1, 缓缓回流12 h的条件下, 得到N-甲基乙二胺(2), N-甲基乙二胺经过乙酸化得到N-甲基-N,N′-二乙酰基乙二胺(3), 然后, N-甲基-N,N′-二乙酰基乙二胺和氧化钙在高温下关环得到1,2-二甲基咪唑啉(4). 并对所得到的产物1,2-二甲基咪唑啉经元素分析, 1H NMR, IR和GC-MS得到了表征.     

Synthesis and photoinduced isomerization ofansa{·5,·5′-[1,1′-(1-silacyclopent-3-ene-1,1-diyl)bis(indenyl)]} dichlorozirconium The crystal structure of itsmeso form

ansa{·⁵,·⁵′-[1,1′-(1-silacyclopent-3-ene-1,1-diyl)bis(indenyl)]} dichlorozirconium (1a,b) was synthesized. The crystal structure ofmeso-[(1,4-CH₂CH=CHCH₂)Si(C₉H₆)₂ZrCl₂] (1b) was established by X-ray diffraction analysis. Photoinduced interconversion of the racemic (1a) andmeso forms was studied under various conditions. The photostationary state (rac: meso=55∶45) was established rapidly when solutions ofansa-zirconocene were irradiated with visible light. Deceased Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2351–2356, November, 1998.     

N-symmetric Chebyshev polynomials in a composite model of a generalized oscillator

We continue to study a composite model of a generalized oscillator generated by an N-periodic Jacobi matrix. The foundation of the model is a system of orthogonal polynomials connected to this matrix for N = 3, 4, 5. We show that such polynomials do not exist for N ?? 6.     

On the regioselectivity of alkylation of the (trimethylsilyl)tetramethylcyclopentadienide anion. A new approach to the synthesis of 1,2,3,4-tetramethylfulvene

The regioselectivity of alkylation of lithium (trimethylsilyl)tetramethylcyclopentadienide C₅Me₄SiMe₃ ⁻Li⁺ was studied by ¹H and ¹³C NMR spectroscopy using its reactions with MeI, MeOTs, ClCH₂CH₂Br, and ClCH₂CH₂I in different solvents as representative examples. Sterically non-hindered MeI and MeOTs presumably attack the C atom bonded to the silyl group giving 1,2,3,4,5-pentamethylcyclopentadienylsilane. For bulkier alkyl halides, such as ClCH₂CH₂Br and ClCH₂CH₂I, the regioselectivity of alkylation changes to form preferentially gem-dialkyl-substituted cyclopentadienes. The reaction of C₅Me₄SiMe₃ ⁻Li⁺ with formaldehyde affords 1,2,3,4-tetramethylfulvene in a high yield, providing an alternative synthetic approach to a number of ω-functionalized peralkylated cyclopentadienes. The quantum-chemical calculations of the C₅Me₄SiMe₃ ⁻ anion by the RHF and DFT (RMPW1PW91) methods in the valence-split 6-311+G(d,p) basis set are in good agreement with the experimental data.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2089–2093, October, 2004.