Structure of radical cations of saturated heterocyclic compounds with two heteroatoms as studied by electron paramagnetic resonance, electron-nuclear double resonance, and density functional theory calculations

The radical cations of piperazine, morpholine, thiomorpholine, and thioxane were investigated by electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy in a solid Freon matrix. Optimized geometry and magnetic parameters of the radical cations were calculated using a density functional theory (DFT)/Perdew-Burke-Ernzerhof (PBE) method. Both experimental and theoretical results suggest that all the studied species adopt chair (or distorted chair) conformations. No evidence for the boat conformers with intramolecular sigma-bonding between heteroatoms were obtained. In the cases of morpholine and thioxane, the oxygen atoms are characterized by relatively small spin populations, whereas a major part of spin density is located at N and S atoms, respectively. The thiomorpholine radical cation exhibits nearly equal spin population of N and S atoms. In most cases (except for thioxane), the calculated magnetic parameters agree with the experimental data reasonably well.     

Generation of optical vortex light beams by volume holograms with embedded phase singularity

Special features of the optical-vortex (OV) beams generated by thick holographic elements (HE) with embedded phase singularity are considered theoretically. The volume HE structure is based on the 3D pattern of interference between an OV beam and a standard reference wave with regular wavefront. The incident beam diffraction is described within the framework of a linear single-scattering model in which the volume HE is represented by a set of parallel thin layers with the “fork” holographic structure. An explicit integral expression is derived for the complex amplitude distribution of the diffracted paraxial beam with OV. The numerical analysis demonstrates that the HE thickness may essentially influence not only selectivity and efficiency of the OV beam generation but also the amplitude and phase profile of the diffracted beam as well as regularities of its propagation. We have studied the generated OV morphology and laws of its evolution; in particular, the possibility of obtaining a circularly symmetric OV beam regardless of the diffraction angle is revealed.     

Some properties of elements of the prime field

We obtain some properties of primitive roots in the groups of residue class modulo prime number, in particular, Fermat primes and Sophie Germain primes. We also obtain some formulas for computation of products of elements in some subsets of the prime field of positive characteristic.     

Influence of Binder and Dyes on the Mechanism of Tunnel Luminescence of AgBr(I) Microcrystals

Optics and Spectroscopy - It has been previously found that, in the AgBr(I) emulsion microcrystals (with a silver content corresponding to pBr 4), the centers responsible for tunnel recombination...