Die Hamiltonsche partielle Differentialgleichung als Ausgangspunkt für die Umkehrung des Variationsproblems und ihre damit zusammenhängende Bedeutung für die Integration der allgemeinen partiellen Differentialgleichungen erster Ordnung

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Pflanzenchemie

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The Crystal Structure of α-F2: Solving a 50 Year Old Puzzle Computationally

The cohesive energy of α-fluorine, with C2/c space group symmetry, was calculated at benchmark quality by applying the method of increments. The known experimental X-ray structure data needed to be refined, since the reported intramolecular bond length was unrealistically large. At the CCSD(T) level, including corrections for zero-point energy, the basis set superposition error, and extrapolated to the complete basis set limit, a cohesive energy of −8.72 kJ mol⁻¹ was calculated, which agrees well with the 0 K-extrapolated experimental value of −8.35 kJ mol⁻¹. 1 Comparison of the C2/c structure with a Cmca structure, isotypic to that of chlorine, bromine, and iodine reveals that the origin of the different structure of solid fluorine, compared to the heavier halogens, is the lack of significantly stabilizing σ-hole interactions. In addition, the wave numbers of the stretching mode in solid fluorine were calculated at coupled cluster level and compared to newly recorded Raman spectra of condensed fluorine. Both experiment and calculation indicate a slight up-shift for the stretching mode by 2 or 5 cm⁻¹, respectively, with respect to a free F₂ molecule in the gas phase.     

Thermal Properties of Oligo(2-ethyl-2-oxazoline) Containing Comb and Graft Copolymers and their Aqueous Solutions

Summary: The cationic ring opening polymerization of 2-ethyl-2-oxazoline (EtOx) was applied for the synthesis of methacrylate end-functionalized well-defined macromonomers that could be polymerized in a controlled manner using reversible addition-fragmentation chain transfer polymerization. The obtained comb polymers revealed lower critical solution temperature behavior in aqueous solution. The cloud points of these solutions could be tuned in a range from 35 °C to 85 °C by the incorporation of hydrophobic methyl methacrylate comonomer in varying amounts into the graft copolymers whereas copolymerization with methacrylic acid rendered temperature and pH sensitive copolymers. Thermo-gravimetric analysis showed a two-step decomposition of the graft copolymers and differential scanning calorimetry revealed glass transition temperatures that are significantly lowered in comparison to linear PEtOx.