[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.

     

Domination number in graphs with minimum degree two

A set D of vertices of a graph G = （V, E） is called a dominating set if every vertex of V not in D is adjacent to a vertex of D. In 1996, Reed proved that every graph of order n with minimum degree at least 3 has a dominating set of cardinality at most 3n/8. In this paper we generalize Reed＇s result. We show that every graph G of order n with minimum degree at least 2 has a dominating set of cardinality at most （3n ＋IV21）/8, where V2 denotes the set of vertices of degree 2 in G. As an application of the above result, we show that for k ≥ 1, the k-restricted domination number rk （G, γ） ≤ （3n＋5k）/8 for all graphs of order n with minimum degree at least 3.     

Analysis of the contribution of skeletal vibrations to the heat capacity of linear macromolecules in the solid state

Automatic computer programs are developed to calculate one- two-, and three-dimensional Debye functions. Prior tables of these functions are critically reviewed. Also, strategies are derived to calculate Debye temperatures from heat capacities. Both, simple three-dimensional Debye analyses and Tarasov analyses were carried out on 35 linear macromolecules. The experimental heat capacities for these analyses were collected in the ATHAS data bank. It is shown that the skeletal heat capacity of linear macromolecules is often best represented by only two vibrations per chain atom. For most of the all-carbon chain macromolecules the intramolecular skeletal heat capacity can be given by C_vs=D₁[520 (28/MW)^1/2] whereMW is the molecular mass andD ₁ represents the one-dimensional Debye function. Polyoxides show a higher intramolecular theta temperature, but a lower intermolecular theta temperature. Double bonds and phenylene groups in the chain increase the intramolecular theta temperature.Dedicated to Prof. Dr. F. H. Müller.On leave from the Lumumba Peoples' Friendship University, Moscow, USSR.     

On theC p toC v conversion of solid linear macromolecules II

A modification is proposed for the Nernst-Lindemann equation that is used to convert calculated heat capacities at constant pressure (C _p ) to heat capacities at constant volume (C _v ) for solid, linear macromolecules. the constant A₀ per mole of repeating unit in this equation is derived by taking into account the variable number of vibrators excited at different temperatures. With the new equation it is possible to calculateC _p for solid polymers over a wider temperature range. The constant is calculated for solid polymers from experimental thermal expansivity, isothermal compressibility and heat capacity data obtained from the literature. An average value of (3.9±2.4)×10^–3(K mol)/J was obtained for A₀ (new) from data on 22 solid polymers. This average value may be used as a universal constant in case no experimental data on compressibility and expansivity are available for computation ofA ₀. The remaining variation of A₀ (new) with temperature is discussed and example calculations are shown for polyethylene. Effects of premelting and possibly large-amplitude motion are discovered for polyethylene in the temperature range 290 to 410 K.

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Zusammenfassung Es wurde eine Abänderung der Nernst-Lindemann Gleichung vorgeschlagen, mit deren Hilfe für feste, lineare Makromoleküle errechnete Wärmekapazitäten bei konstantem Druck (C _p ) in Wärmekapazitäten bei konstantem Volumen (C _p ) umgerechnet werden können. Zur Ableitung der molaren Konstanten A₀ in dem sich wiederholenden Teil der Gleichung wurde die variable Anzahl der erregten Schwinger bei verschiedenen Temperaturen berücksichtigt. Mit der neuen Gleichung wird es möglich, dieC _p fester Polymere für einen breiten Temperaturbereich zu errechnen. Die Konstante wurde für die festen Polymere auf Grund des ermittelten thermischen Ausdehnungsvermögens und der isothermen Kompressibilität sowie der der Literatur entnommenen Wärmekapazitätsangaben berechnet. Aus Angaben von 22 festen Polymeren wurde für A₀(neu) ein Durchschnittswert von (3,9±2,4)×10^–3 (K mol)/J erhalten. Verfügt man zur Berechnung von A₀ über keine experimentellen Werte für Kompressibilität und Ausdehnungsvermögen, so kann dieser durchscnittswert als universale Konstante angewendet werden. Die verbleibende Temperaturabhängigkeit von A₀(neu) wird besprochen und Beispielrechnungen für Polyäthylen gegeben. Für Polyäthylen wurden im Temperaturbereich 290 bis 410 K Effekte durch Vorschmelzen und Bewegungen mit großer Amplitude festgestellt.

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-, (C _p ) (C _v ) , . A ₀ , . C _p . A ₀ , , . 22 , A ₀ () (3,9±2,4)· 10^–3 ·/. A ₀ . A ₀ , . 290–410 .

     

Tetracyanoborate salts M[b(CN)4] with M = singly charged cations: properties and structures

A series of tetracyanoborate salts M[B(CN)4] with the singly charged cations of Li+, Na+, Rb+, Cs+, [NH4]+, Tl+, and Cu+ as well as the THF solvate tetracyanoborates Na[B(CN)4] x THF and [NH4][B(CN)4] x THF were synthesized and their X-ray structures, vibrational spectra, solubilities in water, and thermal stabilities determined and compared with already known M[B(CN)4] salts. Crystallographic data for these compounds are as follows: Na[B(CN)4], cubic, Fd3m, a = 11.680(1) A, Z= 8; Li[B(CN)4], cubic, P43m, a = 5.4815(1) A, Z= 1; Cu[B(CN)4], cubic, P43m, a = 5.4314(7) A, Z= 1; Rb[B(CN)4], tetragonal, /4(1)/a, a = 7.1354(2) A, c= 14.8197(6) A, Z= 4; Cs[B(CN)4], tetragonal, /4(1)/a, a = 7.300(2) A, c = 15.340(5) A, Z= 4; [NH4][B(CN)4], tetragonal, /4(1)/a, a = 7.132(1) A, c = 14.745(4) A, Z= 4; Tl[B(CN)4], tetragonal, /4(1)/a, a = 7.0655(2) A, c = 14.6791(4) A, Z= 4; Na[B(CN)4] x THF, orthorhombic, Pnma, a = 13.908(3) A, b = 9.288(1) A, c = 8.738(1) A, Z= 4; [NH4][B(CN)4] x THF, orthorhombic, Pnma, a = 8.831(1) A, b = 9.366(2) A, c = 15.061(3) A, Z= 4. The cubic Li+, Na+, and Cu+ salts crystallize in a structure consisting of two interpenetrating independent tetrahedral networks of M cations and [B(CN)4]- ions. The compounds with the larger countercations (Rb+, Cs+, Tl+, and [NH4]+) crystallize as tetragonal, also with a network arrangement. The sodium and ammonium salts with the cocrystallized THF molecules are both orthorhombic but are not isostructural. In the vibrational spectra the two CN stretching modes A1 and T2 coincide in general and the band positions are a measure for the strength of the interionic interaction. An interesting feature in the Raman spectrum of the copper salt is the first appearance of two CN stretching modes.     

Kombinierte Gas-Chromatographie-KMR-Technik

Ohne Zusammenfassung     

The 7‐bromo derivative of 2‐amino‐2′‐deoxytubercidin fluorinated at the sugar moiety

The title compound, 2,4‐diamino‐5‐bromo‐7‐(2‐deoxy‐2‐fluoro‐β‐d ‐arabinofuranosyl)‐7H‐pyrrolo[2,3‐d]pyrimidine, C₁₁H₁₃BrFN₅O₃, shows two conformations of the exocyclic C4′—C5′ bond, with the torsion angle γ (O5′—C5′—C4′—C3′) being 170.1 (3)° for conformer 1 (occupancy 0.69) and 60.7 (7)° for conformer 2 (occupancy 0.31). The N‐glycosylic bond exhibits an anti conformation, with χ = −114.8 (4)°. The sugar pucker is N‐type (C3′‐endo; ³T₄), with P = 23.3 (4)° and τ_m = 36.5 (2)°. The compound forms a three‐dimensional network that is stabilized by several intermolecular hydrogen bonds (N—H...O, O—H...N and N—H...Br).