The Photochemistry of 2-Cyclopentenyl Methyl Ketones

2-Cyclopentenyl and 3-phenyl-2-cyclopentenyl methyl ketones (15–18, 30, 31) undergo a 1,3-acetyl shift on direct irradiation, and the oxa-di-π-methane rearrangement to photochemically non-interconverting endo and exo bicyclo-[2.1.0]pentyl methyl ketones on triplet sensitization. Exceptions include the 2-methyl-3-phenyl-2-cyclopentenyl methyl ketone 32 and the 1-phenyl-2-cyclo-pentenyl methyl ketone 44 which are unreactive on direct irradiation and on triplet sensitization, respectively, and the 2-phenyl-2-cyclopentenyl methyl ketones 42 and 43 which do not react under either condition. The reactive triplet of the 3-phenyl-2-cyclopentenyl methyl ketone 30 has been identified as the localized styrene π,π*-state of E_T=59 kcal/mol by comparison of its phosphorescence at 77K in rigid glasses with that of 1-phenyl-cyclopentene, and by the independence of the quantum yield on sensitizer energy in the range of 61–74 kcal/mol.     

Conformational analysis of 1,1,2,2-tetraaryl-disilanes

A study of the static stereochemistry of 1,1,2,2-tetraphenyldisilane (1) and 1,1,2,2-tetramesityldisilane (2) by empirical force field calculations, X-ray diffraction, and ¹H NMR reveals that the preference for the anti conformation, exhibited by the unclamped 1,1,2,2-tetraarylethanes, is sustained in the analogous disilanes, although in somewhat attenuated form. This anti preference stands in contrast to the gauche preference of 1,1,2,2-tetraalkyldisilanes. Examination of ³J_HH coupling constants for R₂HSiSiHR₂; (R = phenyl, mesityl, 2,6-dimethyl-phenyl, t-butyl, cyclohexyl) suggests the existence of a Karplus relation for H-Si-Si-H systems.     

Synthesis of 2,3-dihydro-1H-imidazo[1,2-b]pyrazoles

Two novel 2,3-dihydro-1H-imidazo[1,2-b]pyrazole derivatives 7 and 8 have been prepared by hydrazinolysis with 2,4-dinitrophenylhydrazine of 1-(benzylideneamino)-2-(2-ethoxycarbonyl-2-nitromethylidene)-imidazolidine 4 . The precursor 4 was conveniently prepared from ethyl nitroacetate and 1-(benzylidene-amino)-2-(methylthio)imidazoline 3 . Two examples are presented in which ethyl aceto(and trifluoroaceto)acetate 2-nitrophenyl-hyrazone, 9 and 10 , both of which also feature the β-hydrazinoacrylate arrangement, are refluxed in ethanol containing hydrochloric acid and thereby converted into pyrazolones 11 and 12 , pyrazoles 13 and 14 , and ketone 2-nitrophenylhydrazones 15 and 16 , respectively.     

{2,2′‐[1,1′‐(4‐Aza­heptane‐1,7‐diyl­dinitrilo)diethyl­idyne]­diphenolato}­copper(II)

The quinquedentate ligand 2,2′‐[1,1′‐(4‐aza­heptane‐1,7‐diyl­dinitrilo)diethyl­idyne]diphenol in the title compound, [Cu(C₂₂H₂₇N₃O₂)], furnishes an N₃O₂ donor set, which results in a distorted square‐pyramidal coordination; the two O and two imine N atoms lie in the basal plane, while the secondary amine N atom of the ligand occupies the axial position. The axial Cu—N bond is 0.33 Å longer than the average of the equatorial bonds, and the O atoms are trans. The symmetry of the mol­ecule is lowered by the twist–boat and chair conformations adopted by the two CuNN chelate rings. The complex contains two intra­molecular C—H⋯O inter­actions, and two mol­ecules of the complex are linked into a dimer by means of moderate N—H⋯O hydrogen bonds. Spectroscopic evidence supports the presence of hydrogen bonds.     

Algorithms for cardinal interpolation using box splines and radial basis functions

Summary We describe an algorithm for (bivariate) cardinal interpolation which can be applied to translates of basis functions which include box splines or radial basis functions. The algorithm is based on a representation of the Fourier transform of the fundamental interpolant, hence Fast Fourier Transform methods are available. In numerical tests the 4-directional box spline (transformed to the characteristical submodule of ²), the thin plate spline, and the multiquadric case give comparably equal and good results.     

Condensation of a one-dimensional lattice gas

We consider a one-dimensional lattice gas in the canonical ensemble with interaction energy 1/r , 1<2. Using an energy-entropy argument we show that the gas condenses at sufficiently low temperatures meaning that the gas has a non-uniform density in the thermodynamic limit.Research supported by the Swedish research councils NFR and STUF     

Monte Carlo simulation of phase separation and clustering in the ABV model

As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump rates _A and _B, respectively. For a small concentration of vacancies (c _v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk ₁(t),k ₂ ² (t) is studied during the early stages of phase separation, for several choices of concentrationc _B of B atoms. Forc _B=0.18 also the time evolution of the cluster size distribution is studied. Apart from very early times, the mean cluster sizel(t) as well as the moments of the structure function depend on timet and the ratio of the jump rates (= _B/ _A) only via a scaled timet/(). Qualitatively, the behavior is very similar to the direct exchange model containing no vacancies. Consequences for phase separation of real alloys are briefly discussed.     

Bianchi type V perfect fluid cosmologies

Bianchi type V solutions of the Einstein equations are studied using the Hamiltonian approach. Explicit expressions depending on a single quadrature are given for the metric components in the general orthogonal perfect fluid case. It is shown that the quadrature can be evaluated in terms of elementary or elliptic integrals when the parameter in the equation of statep=(–1) takes the values 1, 10/9, 4/3, 14/9, 5/3, 2.     

Die Kristallstruktur von Rb6Si10O23

Zusammenfassung Die Kristallstruktur der Verbindung Rb₆Si₁₀O₂₃ (bisher als Rb₂Si₄O₉ beschrieben) wurde mit Hilfe dreidimensionaler Röntgendaten bestimmt und bis zu einemR-Wert von 0,078 verfeinert. Die Gitterparameter der rhombischen Elementarzelle (C2mm-C _2v ¹⁴ ) betragen:a=9,348,b=16,290 undc=8,055 Å. Die Struktur besitzt ein dreidimensionales Gerüst aus [SiO₄]-Tetraedern, die sowohl über 4 als auch über 3 Ecken vernetzt vorliegen. Die Anordnung der Tetraeder kann aus der Tridymitstruktur abgeleitet werden und zeigt noch deutlich pseudohexagonale Symmetrie. Bei 500 °C geht die Verbindung in eine Hochtemperaturform mit hexagonaler Symmetrie über (a=9,48 undc=8,16 Å bei 500 °C).

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The crystal structure of Rb₆Si₁₀O₂₃

The crystal structure of the compound Rb₆Si₁₀O₂₃ (identical with Rb₂Si₄O₉) has been determined by means of three-dimensional X-ray data resulting anR-value of 0.078. The lattice parameters of the orthorhombic unit cell (C2mm-C _2v ¹⁴ ) are:a=9.348,b=16.290 andc=8.055 Å. The structure consists of a three-dimensional framework built up by [SiO₄] tetrahedra sharing 4 as well as 3 corners. The arrangement of tetrahedra can be derived from tridymite structure and exhibits pseudohexagonal symmetry. The compound transforms to a high-temperature modification with hexagonal symmetry at 500 °C (a=9.48 andc=8.16 Å).

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Mit 3 Abbildungen     

A new perspective on beta-sheet structures using vibrational Raman optical activity: from poly(L-lysine) to the prion protein

The vibrational Raman optical activity (ROA) spectrum of a polypeptide in a model beta-sheet conformation, that of poly(l-lysine), was measured for the first time, and the alpha-helix --> beta-sheet transition monitored as a function of temperature in H(2)O and D(2)O. Although no significant population of a disordered backbone state was detected at intermediate temperatures, some side chain bands not present in either the alpha-helix or beta-sheet state were observed. The observation of ROA bands in the extended amide III region assigned to beta-turns suggests that, under our experimental conditions, beta-sheet poly(L-lysine) contains up-and-down antiparallel beta-sheets based on the hairpin motif. The ROA spectrum of beta-sheet poly(L-lysine) was compared with ROA data on a number of native proteins containing different types of beta-sheet. Amide I and amide II ROA band patterns observed in beta-sheet poly(L-lysine) are different from those observed in typical beta-sheet proteins and may be characteristic of an extended flat multistranded beta-sheet, which is unlike the more irregular and twisted beta-sheet found in most proteins. However, a reduced isoform of the truncated ovine prion protein PrP(94-233) that is rich in beta-sheet shows amide I and amide II ROA bands similar to those of beta-sheet poly(L-lysine), which suggests that the C-terminal domain of the prion protein is able to support unusually flat beta-sheets. A principal component analysis (PCA) that identifies protein structural types from ROA band patterns provides a useful representation of the structural relationships among the polypeptide and protein states considered in the study.