s-strongly perfect cartesian product of graphs

The study of perfectness, via the strong perfect graph conjecture, has given rise to numerous investigations concerning the structure of many particular classes of perfect graphs. In “Perfect Product Graphs” (Discrete Mathematics, Vol. 20, 1977, pp. 177--186), G. Ravindra and K. R. Parthasarathy tried, but unfortunately without success, to characterize the perfectness of the cartesian product of graphs (see also MR No. 58--10567, 1979). In this paper we completely characterize the graphs that are both nontrivial cartesian products and s-strongly perfect.     

Influence of the Counterions on the Structures of Ternary Zn/Sn/Se Anions: Synthesis and Properties of [Rb10(H2O)14.5][Zn4(μ4‐Se)2(SnSe4)4] and [Ba5(H2O)32][Zn5Sn(μ3‐Se)4(SnSe4)4]

Reactions of rubidium or barium salts of the ortho‐selenostannate anion, [Rb₄(H₂O)₄][SnSe₄] ( 1 ) or [Ba₂(H₂O)₅][SnSe₄] ( 2 ) with Zn(OAc)₂ or ZnCl₂ in aqueous solution yielded two novel compounds with different ternary Zn/Sn/Se anions, [Rb₁₀(H₂O)_14.5][Zn₄(μ₄‐Se)₂(SnSe₄)₄] ( 3 ) and [Ba₅(H₂O)₃₂][Zn₅Sn(μ₃‐Se)₄(SnSe₄)₄] ( 4 ). 1 – 4 have been determined by means of single crystal X‐ray diffraction: 1 : triclinic space group lattice dimensions at 203 K: a = 8.2582(17) Å, b = 10.634(2) Å, c = 10.922(2) Å, α = 110.16(3)°, β = 91.74(3)°, γ = 97.86(3)°, V = 888.8(3) ų; R₁ [I > 2σ(I)] = 0.0669; wR₂ = 0.1619; 2 : orthorhombic space group Pnma; lattice dimensions at 203 K: a = 17.828(4) Å, b = 11.101(2) Å, c = 6.7784(14) Å, V = 1341.5(5) ų; R₁ [I > 2σ(I)] = 0.0561; wR₂ = 0.1523; 3 : triclinic space group ; lattice dimension at 203 K: a = 17.431(4) Å, b = 17.459(4) Å, c = 22.730(5) Å, α = 105.82(3)°, β = 99.17(3)°, γ = 90.06(3)°, V = 6563.1(2) ų; R₁ [I > 2σ(I)] = 0.0822; wR₂ = 0.1782; 4 : monoclinic space group P2₁/c; lattice dimensions at 203 K: a = 25.231(5) Å, b = 24.776(5) Å, c = 25.396(5) Å, β = 106.59(3)°, V = 15215.0(5) ų; R₁ [I > 2σ(I)] = 0.0767; wR₂ = 0.1734. The results serve to underline the crucial role of the counterion for the type of ternary anion to be observed in the crystal. Whereas Rb⁺(aq) stabilizes a P1‐type Zn/Sn/Se supertetrahedron in 3 like K⁺, the Ba²⁺(aq) ions better fit to an anionic T3‐type Zn/Sn/Se cluster arrangement as do Na⁺ ions. It is possible to estimate a radius:charge ratio for the stabilization of the two structural motifs.     

A Simplified version of the Pariser-Parr-Pople treatment of π-electron systems

The semi-empirical configuration interaction treatment due to Pariser and Parr and to Pople has been modified by reducing the set of electronic interaction integrals to ₁₁ and ₁₂ and by limiting the number of configurations to 10. Hückel MOs are used as basis functions. The dependence of the resonance integral _v on the interatomic distance R _v is simulated by making _v a quadratic function of the Hückel bond orders P _v .

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Zusammenfassung Eine Modifikation des semiempirischen CI-Verfahrens von Pariser, Parr und Pople wurde zur Behandlung von -Systemen herangezogen. Als Vereinfachung wurde der Grad der CI-Matrix auf zehn beschränkt und von den Elektronenwechselwirkungsintegralen nur ₁₁ und ₁₂ berücksichtigt. Hückel-MOs wurden als Basisfunktionen verwendet. Die Abhängigkeit des Resonanzintegrals _v vom interatomaren Abstand R _v wurde durch den Ansatz von _v als quadratische Funktion der Hückel-Bindungsordnung P _v angenähert.

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Résumé Le procédé semi-empirique de l'interaction de configuration selon Pariser, Parr et Pople a été modifié en réduisant l'ensemble des intégrales d'interaction électronique à ₁₁ et limitant le nombre des configurations à 10. Les fonctions de base sont des orbitales moléculaires selon Hueckel. La dépendance entre l'intégrale de résonance _v et la distance interatomique R _v est simulée en posant que _v est une fonction quadratique des ordres de liaisons P _v selon Hückel.

     

Reinigung des Wasserstoffgases zu analytischen Zwecken

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Linear and Star-Shaped Extended Di- and Tristyrylbenzenes: Synthesis,Characterization and Optical Response to Acid and Metal Ions

Two linear 1,4-distyrylbenzenes and five star-shaped 1,3,5-tristyrylbenzene derivatives ( L_2a and L_2b , Y₀–Y₃ and Y_NBu ) were synthesized and spectroscopically characterized. The photophysical properties, optical response to acid and metal ions were investigated. Upon backbone extension of linear distyrylbenzenes or the introduction of dibutylanilines, the electronic spectra are redshifted. Incorporation of electron-deficient pyridyl units does not significantly affect the optical properties. Variation of the number of pyridine rings and substitution pattern tune the fluorescence response to acids and metal ions. The novel arenes discriminate Al³⁺, Mn²⁺, Fe³⁺, Fe²⁺, Cd²⁺, Ag⁺ and Hg²⁺.     

Über Chinonschwefelimine

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