Half-flat structures on S^3\times S^3

We describe left-invariant half-flat $ \mathrm{SU }(3) $ -structures on $ S^3\times S^3$ using the representation theory of $ \mathrm SO (4) $ and matrix algebra. This leads to a systematic study of the associated cohomogeneity one Ricci-flat metrics with holonomy $ \mathrm G _2$ obtained on $ 7 $ -manifolds with equidistant $ S^3\times S^3$ hypersurfaces. The generic case is analysed numerically.     

Expansion of analytic functions in q-orthogonal polynomials

A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey–Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.      

Stereocontrolled Photooxygenations–A Valuable Synthetic Tool§

The stereochemical course of the singlet-oxygen ene reaction with acyclic olefins may be controlled if in the substrate conformational fixation (1,3-allylic strain) an allyl-ic substituent for interaction with the attacking oxygen enophile aligns. Various substrates were chosen to elucidate the features of the olefin that are necessary to control the sense (threo versus erythro) and the extent of the ii-facial preference of the singlet-oxygen attack. Depending on the electronic properties of the double bond and the nature of the allylic substituent, threo or erythro selectivity may be imposed through hydrogen bonding, electrostatic and steric effects and stereoelectronic alignment. Such directing properties, especially that of the hydroxy group, were also confirmed in the other reaction modes of singlet oxygen, namely the [4+2] cycloaddition to chiral naphthylenic alcohols and the [2+2] cycloaddition to an adamantylidene-substituted allylic alcohol. The syntheses of the natural products Merucathin and Iso-dihydromahubanolide B are two examples in which such stereocontrolled photooxygenations have been used as key steps to build up the required chirality diastereose-lectively.     

Effect of the alkylaluminum cocatalyst on ethylene polymerization by a nickel–diimine complex

Different chlorine-free alkylaluminum compounds were active cocatalysts for ethylene polymerization in the presence of 1,4-bis(2,6-diisopropylphenyl)-acenaphthenediimine-dichloronickel (II) (1). The combination of 1 with trimethylaluminum or triisobutylaluminum produced catalytically active species that polymerized ethylene with productivities up to 469 kg_polymer/(mol_Ni · h). The activity of the catalytic system and the properties of the polymeric materials were influenced strongly by the reaction temperature. The polymers had a high molecular weight (up to 642 × 10³ g · mol⁻¹), and the molecular weight increased with the reaction time. The polyethylenes were branched, and the branching could be modulated by the proper choice of reaction parameters. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4656–4663, 1999     

Bis(dichlorosilyl)methylamine – Synthesis,Crystal Structure,and Conformational Analysis in the Gas Phase

A straightforward preparation has been found for bis(dichlorosilyl)methylamine, (SiHCl₂)₂NMe ( 1 ), involving reaction between H₂NMe and an excess of SiHCl₃, dissolved either in pentane or THF at 253 K. 1 and a side‐product, 1,3,5‐trichloro‐2,4,6‐trimethylcyclotrisilazane, (–SiHCl–NMe–)₃ ( 2 ), were identified by elemental analysis, mass spectrometry and ¹H‐NMR‐spectroscopy. Some physical, NMR‐ and IR spectroscopical properties of 1 were determined. The molecular and crystal structure of 1 was investigated by single crystal X‐ray diffraction. Selected structural parameters: r(Si–N) 169.7(5), r(Si–Cl) 203.1(2)–204.4(2), r(C–N) 150.0(8) pm; a(SiNSi) 123.6(3), a(SiNC) 118.3(4)/118.0(4)°. Ab initio force field data and infrared intensities were calculated for four conformers of 1 . Comparison of the observed and calculated IR spectra favours the two structures found ab initio provided that their actual abundancies are different from those calculated.     

Stereoselective Synthesis of Functionalized Pyrrolidines by the Diverted N−H Insertion Reaction of Metallocarbenes with β‐Aminoketone Derivatives

A highly stereoselective route to functionalized pyrrolidines by the metal‐catalyzed diverted N?H insertion of a range of diazocarbonyl compounds with β‐aminoketone derivatives is described. A number of catalysts (rhodium(II) carboxylate dimers, copper(I) triflate, and an iron(III) porphyrin) are shown to promote the process under mild conditions to give a wide range of highly substituted proline derivatives. The reaction starts as a metallocarbene N?H insertion but is diverted by an intermolecular aldol reaction.     

The putative Diels-Alderase macrophomate synthase is an efficient aldolase

We find that the putative Diels-Alderase macrophomate synthase (MPS) catalyzes the addition of pyruvate enolate, generated by decarboxylation of oxaloacetate, to a variety of aldehydes. Alkyl, aryl, and heteroaryl aldehydes are accepted as substrates, providing gamma-hydroxy-alpha-ketoacids in 35-95% yield with modest levels of stereochemical control. These aldol products, which are difficult to synthesize by other methods, are formed with efficiency comparable to that of macrophomate. Our results thus provide evidence that a two-step Michael-aldol pathway is a plausible alternative to the postulated [4 + 2] cycloaddition in the MPS-catalyzed addition of pyruvate enolate to 2-pyrones. They are also relevant to understanding the divergent evolution of type II pyruvate aldolases.     

Increasing molecular weight parameters of a helical polymer through polymerization in a chiral solvent

In this communication, we will demonstrate that polymerization in a chiral solvent can affect the molecular weight distribution of the product by perturbing the balance of the P and M helical screw senses of the growing chains. Specifically, for the Wurtz-type synthesis of polymethylphenylsilane (PMPS) in either (R) or (S)-limonene, the weight-average molecular weight of the products (average Mw = 80 000) was twice that of PMPS synthesized in (R/S)-limonene (average Mw = 39 200). Peturbation of the helical segmentation along the polymer chains leads to a reduction in the rate of occurrence of a key termination step. This the first time that a chiral solvent has been demonstrated to have such an effect on a polymerization process in affecting molecular weight parameters in contrast to affecting tacticity.     

Interplay between intramolecular resonance-assisted hydrogen bonding and aromaticity in o-hydroxyaryl aldehydes

In this work, we analyze a series of o-hydroxyaryl aldehydes to discuss the interrelation between the resonance-assisted hydrogen bond (RAHB) formation and the aromaticity of the adjacent aromatic rings. As compared to the nonaromatic reference species (malonaldehyde), the studied compounds can be separated into two groups: first, the set of systems that have a stronger RAHB than that of the reference species, for which there is a Kekulé structure with a localized double CC bond linking substituted carbon atoms; and second, the systems having a weaker RAHB than that of the reference species, for which only pi-electrons coming from a localized Clar pi-sextet can be involved in the RAHB. As to aromaticity, there is a clear reduction of aromaticity in the substituted ipso ring for the former group of systems due to the formation of the RAHB, while for the latter group of species only a slight change of local aromaticity is observed in the substituted ipso ring.