Nodal surfaces of Fourier series: Fundamental invariants of structured matter

Periodic Nodal Surfaces (PNS) of Fourier series are derived and classified as fundamental invariants of structured matter. Relationships to periodic minimal surfaces PMS and to periodic zero potential surfaces (POPS) are given. A basic set of cubic PNS is represented in arithmetic form. The special importance of the invariance of the zeros to the type of the potential is stressed.     

[2+2]-Photocycloaddition von Cyclohexen an 2-Acetyl-5,5-dimethyl-1,3-cyclohexandion und 3-Acetyl-1,5,5-trimethyl-2,4-pyrrolidindion

Summary Irradiation of solutions of excess cyclohexene and 2-acetyl-5,5-dimethyl-1,3-cyclohexanedione (1), and 3-acetyl-1,5,5-trimethyl-2,4-pyrrolidinedione (4) results mainly in the formation of 1,5-diones2 and5. These originate from intermediate cycloadducts of cyclohexene and theexo-enols of the cyclic 1,3-diketones. The yields decrease with increasing polarity of the solvent. In solution2 and5 are in equilibrium with the cyclic hemiacetales3 and6.

     

1.2-Bis(pentamethylcyclopentadienyl)tetrachlorodisilane and its reduction to decamethylsilicocene

Reaction of pentamethylcyclopentadienyl(pentachloro)disilane (2), prepared from hexachlorodisilane and potassium pentamethylcyclopentadienide (Cp^*K), with a further equivalent of Cp^*K leads selectively to the title compound Cp^* ₂ Si ₂ Cl ₄ (3) which was characterized by NMR and X-ray structural data. Dehalogenation of 3 with four equivalents of sodium naphthalenide offers an alternative route for the synthesis of decamethylsilicocene (1). Dedicated to Professor Mitsuo Kira on the occasion of being honoured with the Wacker Silicon Award 2005.     

Two types of intramolecular addition of an Al-N multiple-bonded monomer LAlNAr' arising from the reaction of LAl with N3Ar' (L = HC[(CMe)(NAr)]2, Ar' = 2,6-Ar2C6H3, Ar = 2,6-iPr2C6H3)

The reaction of beta-diketiminated aluminum(I) monomer LAl with a large bulky azide N3Ar' (L = HC(CMeNAr)2, Ar' = 2,6-Ar2C6H3, Ar = 2,6-iPr2C6H3) in the temperature range from -78 degrees C to room temperature affords two different isomers 2 and 3, which have been characterized by spectroscopic and X-ray structural analyses, as well as elemental analysis. The variable-temperature 1H NMR kinetic studies of this reaction indicate the existence of the monomer LAlNAr' (1) at low temperature and the thermal stability of the compounds increases in the order of 1 < 2 < 3.     

Über die Struktur von Bis-(dihydroxoboroxalendiamiddioximato)-nickel(II)-tetrahydrat

The space group of the sparingly soluble brown coloured bis-(dihydroxobor-oxalene-diamide-dioximato)-nickel(II)-tetrahydrate (C₄H₁₂N₈O₈B₂Ni · 4 H₂O) is P21/c with a = 9.25, b = 13.27, c = 6.61 Å and β = 92.7°. The structure was solved on single crystals. There are two molecules in the unit cell. Within the square planar complex the nickel atom is bonded to the four nitrogen atoms of the plane system of the two dioximato ligands (Ni? N = 1.84 ± 0.02 Å). Each of the boron atoms is tetrahedrally surrounded by two oxygen atoms belonging to the oxime groups and two hydroxyl groups (B? O = 1.50 ± 0.06 Å). Thus the complex has the conformation of a chair form. The water molecules participate in intermolecular hydrogen bonds. There is no interaction between Ni atoms.