G-invariante Morse-funktionen

If f is a Morse function on a smooth manifold M there exists a homotopy equivalence from M to a CW complex X such that the critical points of f with index are in a one-one correspondence to the -cells of X. In the equivariant case, a similar result holds for a special type of invariant Morse functions. In this paper we prove the existence of such special invariant Morse functions on compact smooth G-manifolds. As a consequence, any compact smooth G-manifold is homotopy equivalent to a G-CW complex. Other applications deal with the Euler number of the fixed point set and Morse inequalities in equivariant homology theory.     

On the stereospecific conversion of proximally-oxygenated trisubstituted vinyltriphenylstannanes into stereodefined trisubstituted alkenes

[reaction: see text] Allylically oxygenated vinyl alpha-triphenylstannanes such as 22 can be readily converted into vinyl iodides and thereafter stereodefined trisubstituted alkenes with retention of configuration.     

4-Amino-imidazole durchThorpe-Cyclisierung

The alkylation of arylaminomethylenecyanamides1 or cyano-imidothiocarbamates2 with -halogen carbonyl compounds followed by base catalysed cyclization yields substituted 4-amino-imidazoles4. Imidazo[4,5-d]pyrimidones5, 6 and imidazo[4,5-b]pyridines7 can be obtained from4.     

Formulas for \bar \beta parameters and their limitations

The operator relationship p=[r, h] between linear momentum, position vector and Hamiltonian is the basis for an investigation of formulas for ¦ atomic orbitals is discussed. Formulas for parameters useful in extended Hückel methods are presented.

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Zusammenfassung Die Operatorengleichung p=[r, h] zwischen Impuls, Ortsvektor und Hamiltonoperator ist die Grundlage für eine Untersuchung von Formeln für -Parameter in der erweiterten Hückel[1]- und CNDO [2]-Methode. Das Eichproblem dieser Gleichung in Verbindung mit abgebrochenen Entwicklungen für Matrixelemente ¦P¦ über Atomfunktionen wird diskutiert. Nützliche Formeln für die erweiterte Hückel-Methode werden abgeleitet.

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Résumé La relation entre opérateurs moment linéaire, position et hamiltonien: p=[r, h] sert de base à une étude de formules pour les paramètres dans les méthodes de type Hückel étendu [1] et CNDO [2]. Le problème de jauge de cette équation est discuté par rapport au développement limité des éléments de matrice ¦P¦ dans une base d'orbitales atomiques. Présentation de formules pour les paramètres utiles dans les méthodes Hückel étendu.

     

Synthesis and X-ray crystal structures of six [TeL4][MF6] salts, where L is ethylene- or trimethylene-thiourea, and M is Si, Ge or Sn. Five Te(II) complexes with a novel type of structure linked together by unusual N–HF hydrogen bonds

The complexes [Te(etu)₄][SiF₆] (1), [Te(etu)₄][SiF₆] · H₂O (2), [Te(trtu)₄][SiF₆] (3), [Te(etu)₄][GeF₆] · H₂O (4), [Te(trtu)₄][GeF₆] (5) and [Te(etu)₄][SnF₆] (6) (etu = ethylenethiourea, trtu = trimethylenethiourea) have been prepared and their crystal structures determined by X-ray crystallographic methods. The crystals of 1, 3 and 5 are tetragonal; space groups P4cc (No. 103) with Z = 4 for 1, P4nc (No. 104) with Z = 2 for 3, and I4 (No. 79) with Z = 2 for 5. The crystals of 2, 4 and 6 are orthorhombic, space group Pccn (No. 56) with Z = 8 for 2 and 4 and Z = 4 for 6; those of 2 and 4 being isomorphous. The cations contain square planar or slightly distorted square planar TeS₄ coordination groups. In 1, 3 and 5 the Te atoms are located on fourfold rotation axes; the cations have fourfold rotational symmetry and the four thiourea ligands extend to the same side of the TeS₄ plane. These are the first examples of [TeL₄]²⁺ conformers of this type. In 2 and 4 the Te atoms lie on general positions; the cations are distorted versions of those in 1, and also in these the four ligands extend to the same side of the TeS₄ plane. In 6 the Te atoms are located on twofold rotation axes, the conformation of the cations corresponds to the point group C₂ with two neighbouring ligands extending to one side of the coordination plane and the remaining two to the opposite side. In 1–5 each of the four ligands forms a N–HF bond to the same F atom in the counter ion. The crystals of 1–5 are red, and those of 6 are yellow. The red colour is attributed to interactions of Te and S lone electron pairs caused by ligand TeS₄/TeSC tilt angles markedly different from 90°.     

Iodine fluorosulfate reactions with fluorocarbons

Iodine monofluorosulfate has been found to react with fluoroolefins in the absence of a solvent to give the corresponding iodo alkyl fluorosulfates by addition of ?l and ?OSO₂F across the double bond. The observed products were ICF₂CF₂SO₃F, CF₃CFlCF₂SO₃F, and the isomer mixture ICF₂CFClSO₃F and ICFClCF₂SO₃F. Perfluorocyclobutene was unreactive. The iodine fluorosulfate used for this study was synthesized from the reactions of either I₂ or R_fI with ClSO₃F, with both reactions being new routes to this compound. These iodo fluorocarbon fluorosulfates are novel compounds and were characterized by spectroscopy and by formation of the derivatives CF₃CFICFO and ICF₂CFO.     

Stereochemie von Metallocenen, 40. Mitt.

Starting from optically active methylferrocene-- and--carboxylic acids (1 a and1 b) of known absolute configuration and enantiomeric purity about 15 chiral ferrocenes (of each isomeric series— and ) were obtained by suitable ligand transformations. Thereby (almost) all possible chiral combinations of the ligands CH₃, COOH (COO^–), COOCH₃, CN and NH₂ (NH₃ ⁺) were accessible which are necessary for a potential test of approximations of chirality functions for compounds with basic symmetry C_5v. The chiroptical properties of these disubstituted ferrocenes are recorded.Preliminary tests using a shortened Ansatz revealed large discrepancies between calculated () and found [M]_D-values. Possible reasons for this failure are discussed.

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61. Mitt. über Ferrocenderivate

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39. Mitt.:A. Meyer, H. Neudeck undK. Schlögl, Chem. Ber.110, 1403 (1977).

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60. Mitt.:V. Rapi, K. Schlögl undB. Steinitz, J. Organometal. Chem.94, 87 (1975).