Crystal structure of a (25R)-2α,3α-epoxy-5α-spirostan-6, 23-dione hemi-ethyl acetate solvate

The compound (25R)-2,3-epoxy-5-spirostan-6,23-dione, crystallizes as a hemi-ethyl acetate solvate, having two host molecules of similar conformation per molecule of ethyl acetate, in the asymmetric unit. The O atom of the epoxy group is -oriented. The presence of the epoxy group disturbs the chair conformation in the ring A of the steroidal nucleus. Ring A has a C5,C10 half-chair conformation. The six-membered rings B, C, and F have chair conformation as expected. The D ring adopts a C14-envelope conformation and the E ring is midway between a C22,O3 half-chair and a C22-envelope conformations. The A/B, B/C, and C/D ring junctions are trans. Crystal data: C₂₇H₃₈O₅·1/2C₄H₈O₂, Monoclinic, space group P2₁, a = 7.7363(18) b = 28.769(12) c = 12.038(6) Å, = 90.88(5), V = 2679.0(10) ų, Z = 4. The packing of the molecules is assumed to be dictated by van der Waals interactions and by intermolecular C—H ··· O hydrogen bonds.     

Exact correlated kinetic energy related to the electron density for two-electron model atoms with harmonic confinement

For arbitrary interparticle interaction u(r₁₂), the model two-electron atom in the title is shown to be such that the ground-state electron density ρ(r) is determined uniquely by the correlated kinetic energy density t_R(r) of the relative motion. Explicit results for t_R(r) are presented for the Hookean atom with force constant k=1/4, and also for . Possible relevance of the Hookean atom treatment to the ground state of the helium atom itself is briefly discussed.     

Methyl carbon chemical shifts of methylbenzoic acids and methylbenzoate anions

Methyl carbon chemical shifts have been assigned for methylbenzoic acids dissolved in CDCl₃, and for methylbenzoate anions obtained by dissolving these acids in aqueous NaOH solution. Chemical shifts have been interpreted by means of additive substituent parameters which reflect conformational features existing between adjacent substituents. Barriers to rotation of a methyl group adjacent to a carboxyl or carboxylate group have been estimated to differ by less than 2 kJ mol^?1 from the barrier of a methyl group in o-xylene.     

Mean field kinetic theory of a classical electron gas in a periodic potential. II. Qualitative analysis of the mean-field solution in one dimension

A qualitative analysis is made of the static and dynamic behavior of a one-dimensional classical electron gas in a periodic potential in the framework of a mean-field kinetic theory. The mean-field equations have been formally solved elsewhere in terms of the trajectories of one electron in the mean-field equilibrium potential, which determines the local electronic density. Taking advantage of the relative simplicity of the mean-field expressions in one dimension, we study the effects of the temperature upon the local electronic density, the static structure factor, and the spectrum of the fluctuations in the long-wavelength limit. At high temperatures, the system tends to behave like a homogeneous electron gas; however, the collective plasmon mode at zero wavenumber is damped and shifted below the plasma frequency. At low temperatures, the system behaves as an ensemble of independent electrons strongly localized in the neighborhood of the fixed ions that create the periodic potential; the plasmon mode then vanishes. We consider the physical relevance of these predictions. They turn out to be quite reasonable, despite the failure of meanfield theory to predict the phase of the model.     

On the Gauss map of B-scrolls in 3-dimensional Lorentzian space forms

In this note we show that B-scrolls over null curves in a 3-dimensional Lorentzian space form are characterized as the only ruled surfaces with null rulings whose Gauss maps G satisfy the condition being a parallel endomorphism of .     

Ultrasonic reflection from randomly distributed cylindrical cavities

The propagation of steady-state time-harmonic waves in an elastic solid containing cylindrical cavities that are randomly distributed in a slab region is investigated. When an antiplane wave is normally incident on the cavities, the amplitudes of the coherent reflected and transmitted waves outside the slab are evaluated and plotted as functions of frequency and porosity.     

A New Class of Task-Specific Imidazolium Salts and Ionic Liquids and Their Corresponding Transition-Metal Complexes for Immobilization on Electrochemically Active Surfaces

Adding to the versatile class of ionic liquids, we report the detailed structure and property analysis of a new class of asymmetrically substituted imidazolium salts, offering interesting thermal characteristics, such as liquid crystalline behavior, polymorphism or glass transitions. A scalable general synthetic procedure for N-polyaryl-N’-alkyl-functionalized imidazolium salts with para-substituted linker (L) moieties at the aryl chain, namely [LPh_mIm^HR]⁺ (L=Br, CN, SMe, CO₂Et, OH; m=2, 3; R=C₁₂, PEG_n; n=2, 3, 4), was developed. These imidazolium salts were studied by single-crystal X-ray diffraction (SC-XRD), NMR spectroscopy and thermochemical methods (DSC, TGA). Furthermore, these imidazolium salts were used as N-heterocyclic carbene (NHC) ligand precursors for mononuclear, first-row transition metal complexes (Mn^II, Fe^II, Co^II, Ni^II, Zn^II, Cu^I, Ag^I, Au^I) and for the dinuclear Ti-supported Fe-NHC complex [(OPy)₂Ti(OPh₂ImC₁₂)₂(FeI₂)] (OPy=pyridin-2-ylmethanolate). The complexes were studied concerning their structural and magnetic behavior via multi-nuclear NMR spectroscopy, SC-XRD analyses, variable temperature and field-dependent (VT-VF) SQUID magnetization methods, X-band EPR spectroscopy and, where appropriate, zero-field ⁵⁷Fe Mössbauer spectroscopy.     

Reflection and transmission of antiplane surface waves by a surface-breaking crack in a layered elastic solid

The reflection and transmission of antiplane surface waves (Love waves) by a surface-breaking crack in a layered elastic solid is investigated. The crack is normal to the free surface, and breaks into the lower half-space solid. The formulation of the problem is reduced to a singular integral equation of the Cauchy type. In this equation, the unknown function, which is the slope of the crack-face displacement, is discontinuous at the interface between the two solids. It is shown that the magnitude of the discontinuity is related to the ratio of the shear moduli. A Gaussian numerical method is used to obtain the solution of the singular integral equation. At some distance from the plane of the crack, the wave motion is the superposition of a finite number of Love-wave modes. The amplitudes of these modes are readily evaluated in terms of the slope of the crack-face displacement. Curves are presented for the reflection coefficients corresponding to the first three modes and for the transmission coefficient as functions of the dimensionless frequency.