Extensions of Szegö's theory of orthogonal polynomials,III

Let {ø _n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior ofø _n (dμ) when logμ′∈L ¹. In what follows we will discuss the asymptotic behavior of the ratioø _n (dμ ₂)/ø _n (dμ ₁) on the unit circle whendμ ₁ anddμ ₂ are close in a sense (e.g.,dμ ₂=gdμ ₁, where g≥0 is such thatQ(e ^it )g(t) andQ(e ^it )/g(t) are bounded for a suitable polynomialQ) and μ ₁ ^′ >0 almost everywhere or (a somewhat weaker requirement) lim _n→∞Φ _n (dμ ₁,0)=0 for the monic polynomial Φ _n . The asymptotic behavior of the same fraction outside the unit circle was discussed in an earlier paper.     

Cyclic sulfonium salts with S ... O interactions 2. Molecular structures with six-membered rings

1-[2-(N-methylcarbamoyl)phenyl]-3H-2,1-naphto-(1,8-d,e)-oxathiin-1-ium chloride (2), 1-[2-(N-methylcarbamoyl)-phenyl]-2-methyl-3-oxo-3H-1, 2-naphto-(1,8-d,e)-thiazin-1-ium chloride (3), 1-[8-(N-methylcarbamoyl)naphtyl]-2-methyl-3-oxo-3H-1, 2-naphto-(1,8-d,e)-thiazin-1-ium chloride (4) and 1-(8-carboxylatonaphtyl)-2-methyl-3-oxo-3H-1,2-naphto-(1,8-d,e)-thiazin-1-ium dipolar ion (5) cyclic sulfonium salts were prepared and their chemical properties investigated (spirosulfurane-formation, hydrolysis). The molecular structures obtained from x-ray diffraction can be described with a considerably distorted trigonal bipyramidal arrangement of the ligands about the sulfonium center, with O/N—S ... O=apical angles of 173.9, 164.9, 156.6, and 159.0°, as well as with S—O/N apical bond lengths of 1.648, 1.671, 1.664, and 1.682 Å. The structures exhibit relatively short S ... O close contacts with interatomic distances of 2.253, 2.448, 2.795, and 2.619 Å.     

On the reaction of dithiocarbamates with nitrogen-containing derivates of oxalic acid

Summary The action of bisimidochlorides of oxalic acid on dithiocarbamates produces 2-thioxo-3-aryl(alkyl)-4,5-diiminothiazolidines by cycloacylation. The molecular structure of 2-thioxo-3-(4-methoxyphenyl)-4,5-bis(phenylimino)-thiazolidine is confirmed by X-ray crystal structure analysis.

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Zur Reaktion von Dithiocarbaminaten mit stickstoffhaltigen Derivaten der Oxalsäure

Zusammenfassung Bei der Einwirkung von Bisimidchloriden der Oxalsäure auf Dithiocarbaminate entstehen durch Cycloacylierung 2-Thioxo-3-aryl(alkyl)-4,5-diiminothiazolidine. Die Molekülstruktur von 2-Thioxo-3-(4-methoxyphenyl)-4,5-bis(phenylimino)thiazolidin wird durch Röntgenkristallstrukturanalyse bestätigt.

     

Ab initio crystal orbital studies on linear chains of H atoms

Anab initio crystal orbital method is used to calculate the energies of an infinite chain of H atoms and of linear arrangements of H₂ molecules with different interatomic distances. The H₂ arrangements are not stable in respect to isolated molecules. The cohesive energy of an optimized arrangement of H atoms chain is 0.0354 a.u.     

Structure and electronic structure of polyacene

It is shown that infinite long polyacene chains may have three energetically close but structurally distinct isomers (a symmetrical, sym, form and two lower symmetry forms: one with double bonds in a trans and another isomer with double bonds in a cis pattern). The energetics is based on solid state MNDO theory. We discuss that the symmetrical form has a substantial energy gap E_g in the Hartree–Fock approach owing to exact exchange terms, which are nonlocal. Broken symmetry Hartree–Fock (HF ) solutions for polyacene are also described. An angularly distorted structure suggested earlier on Jahn–Teller grounds is found to be energetically not favorable.