Substituent effects in trans‐p,p′‐disubstituted azobenzenes: X‐ray structures at 100 K and DFT‐calculated structures

The crystal and molecular structures of two para‐substituted azobenzenes with π‐electron‐donating –NEt₂ and π‐electron‐withdrawing –COOEt groups are reported, along with the effects of the substituents on the aromaticity of the benzene ring. The deformation of the aromatic ring around the –NEt₂ group in N,N,N′,N′‐tetraethyl‐4,4′‐(diazenediyl)dianiline, C₂₀H₂₈N₄, (I), may be caused by steric hindrance and the π‐electron‐donating effects of the amine group. In this structure, one of the amine N atoms demonstrates clear sp²‐hybridization and the other is slightly shifted from the plane of the surrounding atoms. The molecule of the second azobenzene, diethyl 4,4′‐(diazenediyl)dibenzoate, C₁₈H₁₈N₂O₄, (II), lies on a crystallographic inversion centre. Its geometry is normal and comparable with homologous compounds. Density functional theory (DFT) calculations were performed to analyse the changes in the geometry of the studied compounds in the crystalline state and for the isolated molecules. The most significant changes are observed in the values of the N=N—C—C torsion angles, which for the isolated molecules are close to 0.0°. The HOMA (harmonic oscillator model of aromaticity) index, calculated for the benzene ring, demonstrates a slight decrease of the aromaticity in (I) and no substantial changes in (II).     

Estimation of the breakthrough volume of selected steroids for C‐18 solid‐phase extraction sorbent using retention data from micro‐thin layer chromatography

SPE method is a very popular technique, and is commonly used for the prepurification, concentration, and isolation of different organic compounds from variable matrices. In this work, the optimization of SPE process was carried out. The breakthrough volume of solid sorbents based on octadecylsilane was determined and three methods were compared: (1) calculation one – the breakthrough volume was calculated using retention factor k determined with micro‐TLC method, frontal analysis – (2) breakthrough volume was determined as volume of whole elution peak, and (3) breakthrough volume was determined as the center of peak gravity. For calculation method, the k values of key estrogens and progestogens were derived from the micro‐TLC experiment reported previously. By combining these three methods, we can point the start of elution, the maximum concentration of analyte in eluate, and the whole eluent volume, which is necessary to achieve an appropriate selectivity and high extraction recovery. Proposed calculation method allows to estimate the beginning of the steroid peak, when the analyte appears in the eluate flowing from the sorbent. Such observation advances the SPE optimization protocol that was described before and was based on the correlation between raw k_SPE and k_micro‐TLC data.     

Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in the stable range there is a Kostant-Sekiguchi map such that the conjecture formulated in [6] holds. We also show that the conjecture cannot be true in general.     

Cis-coordination of the chromate anions in helical Co/Ni block-type polymeric systems. Structural and spectroscopic characteristics of catena(μ-CrO4-O,O′)[Co(HIm)3H2O] and catena(μ-CrO4-O,O′)[Co0.43Ni0.57(HIm)3H2O]

Two polymeric complexes: catena(μ-CrO₄-O,O′)[Co(HIm)₃H₂O] (1) and catena(μ-CrO₄-O,O′)[Co_0.43Ni_0.57(HIm)₃H₂O] (2) (where HIm=imidazole) with a cis-bridging coordination mode of the CrO₄ ²⁻ anion have been synthesized and characterized by X-ray and spectroscopic methods. These crystals were isolated from nine systems of varying reagent molar ratios and three excluding anions: Cl⁻, NO₃ ⁻ and SO₄ ²⁻ exclusively as mer [M(HIm)₃O₃]-type isomers. The unit cell of these isostructural complexes (monoclinic crystal system P2₁ /n) contains two independent helixes, left- and right handed, stabilized by intrahelical and interhelical hydrogen bonding and π–π interaction between pairs of the imidazole rings from neighbouring helixes. The Raman spectra at 77 K of 1 and 2 deconvoluted into lorentzian components revealed the block-type polymeric structure of the complexes. Moreover, the solution studies at millimolar concentrations of 1 and 2 indicated their complete decomposition in water. Four K electronic spectral analysis of the crystals (band deconvolution into gaussian components) enhanced with the data obtained in the polarized light allowed for assignment of the bands to the respective d–d transition (D_4h symmetry). It was found that the metallic centres are independently absorbing species, which supports the suggestion of a block-type structure of the polymers. The respective crystal field parameters for Co and Ni were calculated.     

The Oscillator Character Formula,for isometry groups of split forms in deep stable range

Let G˜ and G˜ ^′ be a reductive dual pair of the type mentioned in the title, with G˜ the smaller member. Let Π and Π′ be unitary representations of G˜,G˜ ^′ which occur in Howe’s correspondence. We express the distribution character of Π′ in terms of the character of Π via an explicit integral kernel operator. Oblatum 4-I-1995     

N‐Meth­yl‐N‐(2‐nitro­phen­yl)nitramine and N‐meth­yl‐N‐(3‐nitro­phen­yl)­nitramine

The structures of the two title isomeric compounds (systematic names: N‐meth­yl‐N,2‐dinitro­aniline and N‐meth­yl‐N,3‐di­nitro­aniline, both C₇H₇N₃O₄) are slightly different because they exhibit different steric hindrances and hydrogen‐bonding environments. The aromatic rings are planar. The –N(Me)NO₂ and –NO₂ groups are not coplanar with the rings. Comparison of the geometric parameters of the ortho, meta and para isomers together with those of N‐meth­yl‐N‐phenyl­nitramine suggests that the position of the nitro group has a strong influence on the aromatic ring distortion. The crystal packing is stabilized by weak C—H⋯O hydrogen bonds to the nitramine group.