Solving Problems with Semidefinite and Related Constraints Using Interior-Point Methods for Nonlinear Programming

 In this paper, we describe how to reformulate a problem that has second-order cone and/or semidefiniteness constraints in order to solve it using a general-purpose interior-point algorithm for nonlinear programming. The resulting problems are smooth and convex, and numerical results from the DIMACS Implementation Challenge problems and SDPLib are provided. Received: March 10, 2001 / Accepted: January 18, 2002 Published online: September 27, 2002 Key Words. semidefinite programming – second-order cone programming – interior-point methods – nonlinear programming Mathematics Subject Classification (2000): 20E28, 20G40, 20C20     

Flexible strategy for syntheses of spirooxindoles using palladium-catalyzed carbosilylation and Sakurai-type cyclization

The intramolecular carbosilylation of N-[2-(1,3-butenyl)aryl]carbamoyl chloride has been investigated. The reaction with hexamethyldisilane proceeds smoothly in the presence of a catalytic amount of [Pd(η(3)-allyl)Cl](2) to give oxindoles with an allylsilane functional group in good yield. The subsequent subjection of the products to a Sakurai-type reaction provides more advanced tricyclic spirooxindoles by controlling the stereochemistry of three contiguous stereogenic centers.     

Solubility and optical activity of Bi12SiO20 crystals

In this paper the solubility and optical activity of Bi₁₂SiO₂₀ (BSO) single crystals grown in aqueous NaOH under hydrothermal conditions were reported. BSO was found to have a positive solubility coefficient from 350 to 400 °C in 0.5–3 M NaOH, as well as a positive dependence on mineralizer concentration. The reason why additional SiO₂ should be introduced in the mineralizer to grow high quality BSO was analyzed. High quality and colorless BSO crystals were grown using 4 M NaOH as a mineralizer and additional 3 wt% SiO₂ introduced in the mineralizer. Results showed that the optical activity of hydrothermal colorless BSO was superior to that of BSO grown by the Czochralski (Cz) method.     

Crystallographic and Conformational Analysis of [(Z)-2-ethoxy-6-[(2-hydroxyphenylamino)methylene]cyclohexa-2,4-dienone]

Abstract  The single crystal X-ray diffraction analysis of the title compound, C₁₅H₁₅NO₃, shows that the structure is adopted to its NH tautomeric form and crystallizes in the orthorhombic space group P bcn with a = 21.2424(15) ?, b = 12.7696(9) ?, c = 9.3605(10) ?, Z = 8, V = 2539.1(4) ?³, D _c  = 1.346 g/cm³. The molecular conformation in the crystal is stabilized by an intramolecular H-bond and the crystal structure is stabilized by the bifurcated O–H···O type intermolecular H-bonds. In order to understand the effects on conformational flexibility of the title molecule, molecular energy profile was calculated as a function of the selected torsion angle by means of AM1 semi-empirical method. Index Abstract  Molecular and crystal structure of [(Z)-2-ethoxy-6-[(2-hydroxyphenylamino)methylene]cyclohexa-2,4-dienone], C₁₅H₁₅NO₃, have been determined by single crystal X-ray diffraction study, and conformational analysis of the title molecule with respect to the selected torsion angle has been achieved by AM1 semi-empirical calculations.      

Enhanced π‐back‐donation resulting in the trans labilization of a pyridine ligand in an N‐heterocyclic carbene (NHC) PdII precatalyst: a case study

The molecular structure of the benzimidazol‐2‐ylidene–PdCl₂–pyridine‐type PEPPSI (pyridine‐enhanced precatalyst, preparation, stabilization and initiation) complex {1,3‐bis[2‐(diisopropylamino)ethyl]benzimidazol‐2‐ylidene‐κC²}dichlorido(pyridine‐κN)palladium(II), [PdCl₂(C₅H₅N)(C₂₃H₄₀N₄)], has been characterized by elemental analysis, IR and NMR spectroscopy, and natural bond orbital (NBO) and charge decomposition analysis (CDA). Cambridge Structural Database (CSD) searches were used to understand the structural characteristics of the PEPPSI complexes in comparison with the usual N‐heterocyclic carbene (NHC) complexes. The presence of weak C—H…Cl‐type hydrogen‐bond and π–π stacking interactions between benzene rings were verified using NCI plots and Hirshfeld surface analysis. The preferred method in the CDA of PEPPSI complexes is to separate their geometries into only two fragments, i.e. the bulky NHC ligand and the remaining fragment. In this study, the geometry of the PEPPSI complex is separated into five fragments, namely benzimidazol‐2‐ylidene (Bimy), two chlorides, pyridine (Py) and the Pd^II ion. Thus, the individual roles of the Pd atom and the Py ligand in the donation and back‐donation mechanisms have been clearly revealed. The NHC ligand in the PEPPSI complex in this study acts as a strong σ‐donor with a considerable amount of π‐back‐donation from Pd to C_carbene. The electron‐poor character of Pd^II is supported by π‐back‐donation from the Pd centre and the weakness of the Pd—N(Py) bond. According to CSD searches, Bimy ligands in PEPPSI complexes have a stronger σ‐donating ability than imidazol‐2‐ylidene ligands in PEPPSI complexes.     

Characterization of nucleobases in sea buckthorn leaves: An HPTLC approach

The present study aims to establish a high-performance thin layer chromatography (HPTLC)-based comparative analysis, directed toward characterization of nucleobases in aqueous and alcoholic extracts of sea buckthorn leaves from three different varieties: Hippophae salicifolia, Hippophae rhamnoides mongolica, and Hippophae rhamnoides turkestanica. The alcoholic and aqueous leaf extracts from these sea buckthorn varieties were prepared using accelerated solvent extraction technique. A novel HPTLC method for separating and identifying six nucleobases, namely, guanosine, guanine, cytosine, adenine, uracil, and thymine were adopted. HPTLC analysis indicated the presence of one or more of these nucleobases in a total of six leaf extracts evaluated, their quantities varying from 0.23 to 7.76?µg nucleobase per mg of extract. Though a typical trend could not be observed in the values obtained, the extracts were found to be considerably rich with respect to nucleobase contents. The results acquired from HPTLC were subsequently validated by hyphenation with mass spectrometry and also by applying chemometric tools in form of heat maps, hierarchical cluster dendrograms, and principal component analysis. The presence of nucleobases in the leaf extracts was confirmed by HPLC as well but HPTLC proved to be a better approach for characterization of nucleobases in plant extracts, than high performance liquid chromatography (HPLC).     

PM3 semiempirical study and its comparison with X-ray crystal structure of 4-[2-Methyl-4-(4-methoxyphenylazo)] phenoxyphtalonitrile

  The molecular and crystal structures of the title compound, C₂₂H₁₆N₄O₂, were determined by single crystal X-ray diffraction technique. The title compound crystallizes in monoclinic space group P1 2 ₁ /n1, with a=12.7811(9) ?, b=8.2002(4) ?, c=17.8772(14) ?, Z=4, D _calc=1.3112(1) g/cm³, μ (Mo-K_α)=0.087 mm⁻¹. The structure was solved by direct methods and refined to a final R=0.056 for 1891 reflections with I > 2σ (I). The asymmetric unit in the crystal structure contains only one neutral molecule. The positions of nitrogen atoms in the azo groups were disordered. There is no classic hydrogen bond in the crystal structure. The molecules in the crystal structure are stacked by π–π stacking and one edge-to-face interactions. In order to determine conformational flexibility and crystal packing effects on the molecules, molecular energy profile of the title compound was obtained with respect to the selected torsion angle, which is varied from −180° to +180° in every 10° via PM3 semi-empirical method.     

Crystallographic and conformational analyses of zwitterionic form of (<Emphasis Type="Italic">E</Emphasis>)-2-methoxy-6-[(2-morpholinoethylimino)methyl]phenolate

The single crystal X-ray diffraction analysis of the title compound, C₁₄H₂₀N₂O₃, reveals that the structure is adapted to its zwitterionic form and centrosymmetric dimers are formed by N⁺–H···O⁻ type ionic weak hydrogen bonds in the crystal structure. The title compound crystallizes in the triclinic space group P−1 with a = 5.9255(13) ?, b = 9.853(3) ?, c = 12.248(3) ?, α = 101.793(19)°, β = 94.941(17)°, γ = 104.36(2)°, Z = 2, D_x = 1.308 g/cm³, μ (Mo-K_α) = 0.092 mm⁻¹. The structure was solved by direct methods and refined to a final R = 0.0371 for 2183 reflections with I > 2σ (I). The crystal structure is stabilized by N⁺–H···O⁻ type intra-molecular hydrogen bonds and N⁺–H···O⁻ type packing interactions referred to as weak hydrogen bonds. To elucidate conformational flexibility of the title molecule, the selected torsion angle is varied from −180° to +180° in every 10° separately and then molecular energy profile is calculated and construed. In addition, charge-population analysis of the crystallographically observed structure confirms its zwitterionic form.     

Mono-, di- and trinuclear copper(II) dioxime complexes; 3-{2-[2-(2-hydroxyimino-1-methylpropylideneamino)ethylamino]ethylimino}butan-2-one oxime

A new ligand incorporating a dioxime moiety, 3-{2-[2-(2-hydroxyimino-1-methylpropylideneamino)ethylamino]ethylimino}butan-2-one oxime, (H₂mdo), has been synthesized and its mono-, di- and trinuclear copper(II), and hetero-dinuclear copper(II)–manganese(II) complexes have been prepared and characterized by elemental analyses, magnetic moments, ¹H- and ¹³C-n.m.r., i.r. and mass spectral studies. A mononuclear copper(II) complex of H₂mdo was found to have a 1:1 metal:ligand ratio. Elemental analyses, stoichiometric and spectroscopic data of the metal complexes indicated that the metal ions are coordinated to the oxime and imine nitrogen atoms (C=N); the data support the proposed structure of H₂mdo and its complexes.