A simple evaluation of a theta value,the Kronecker limit formula and a formula of Ramanujan

The Ramanujan Journal - We evaluate the classic sum $$\sum _{n\in {\mathbb {Z}}} e^{-\pi n^2}$$ . The novelty of our approach is that it does not require any prior knowledge about modular forms,...     

Complexes of copper(II) with sugar α-amino acids as ligands

Summary Complexes of Cu^II with 2-(benzylamino)-2-deoxy-d-glycero-d-talo heptonic acid (BnMa) and 2-(benzylamino)-2-deoxy-d-glycero-l-gluco heptonic acid (BnGa) were prepared and characterized by elemental analysis, thermal data, i.r., electronic and e.s.r. spectra, magnetic susceptibility measurements, and X-ray powder diffraction. The metal:ligand stoichiometry of these complexes is 12 and coordination around Cu^II seems to be octahedral, with the ligands bound through the N atom of the amino group and O atoms of the bridging carboxylate group.     

Effect of acetate on ferrihydrite crystallization

Mössbauer spectroscopy was used to follow the aging of ferrihydrite with different amounts of acetate, to achieve more crystalline products. Mössbauer spectra of fresh samples did not show any magnetic components. After two years aging, the solids presented crystalline fractions. Hematite formation was inhibited as acetate content increased in solids. For an acetate/iron molar ratio equal to 0.63 goethite was formed instead of hematite. X-ray diffraction confirmed these results. This work shows that synthetic samples can be used for elucidating the anti-hematitic effect of organic matter already detected in soils.     

Self-interaction-corrected electronegativities and hardness for atoms

Electronegativity χ and hardness η for 54 atoms and their positive and negative ions are calculated by means of self-interaction-corrected DFT including correlation terms. The exchange potential energy is treated by local spin density approximation corrected to account for self-interaction effects as suggested by Rae. The highest occupied orbital eigenvalues for ions are identified to the chemical potential μ^± for positive and negative charged atoms depending upon the developing charge process. Values of χ^±δ and η^± for the different ionic species are given for several values of δ. Average values for 〈χ〉 and 〈η〉 in the sense of Mulliken finite formula for neutral atoms are also tabulated and compared with Mulliken values from experimental data. The agreement among them is almost quantitative.     

Lead(II) thiocyanate complexes with bibracchial lariat ethers: an X-ray and DFT study

Compounds of formula [Pb(L2)(NCS)2] (1) and [Pb(L4)(SCN)2] (2) (where L2 is the lariat crown ether N,N'-bis(3-aminobenzyl)-4,13-diaza-18-crown-6 and L4 is the Schiff-base lariat crown ether N,N'-bis(3-(salicylaldimino)benzyl)-4,13-diaza-18-crown-6) were isolated and structurally characterized by X-ray diffraction analyses. The X-ray crystal structures of both compounds show the metal ion coordinated to the six donor atoms of the crown moiety, leaving the corresponding pendant arms uncoordinated. The coordination sphere of lead(II) is completed by two thiocyanate groups that coordinate either through their nitrogen (1) or sulfur (2) atoms. The organic receptor adopts a syn conformation in 1, while in 2 it shows an anti conformation. To rationalize these unexpected different conformations of the L2 and L4 receptors in compounds 1 and 2, as well as the different binding modes found for the thiocyanate ligands, we have carried out theoretical calculations at the DFT (B3LYP) level. These calculations predict the syn conformation being the most stable in both 1 and 2 complexes. So, the anti conformation found for 2 in the solid state is tentatively attributed to the presence of intermolecular pi-pi interactions between phenol rings, for which the dihedral angle between the least-squares planes of both rings amounts to 2.6 degrees and the distance between the center of both rings is 3.766 A. On the other hand, the analysis of the electronic structure has revealed that the Pb-ligand bonds present highly ionic character in this family of compounds. They also suggest a greater transfer of electron density from the NCS- ligands when they coordinate through the less electronegative S atom. The Pb-SCN covalent bond formation mainly occurs due to an effective overlap of the occupied 3p z orbitals of the S atoms and the unoccupied 6p z AO of the Pb atom, while the Pb-NCS bonding interaction is primarily due to the overlap of the 6s and 7s AO of Pb with sp(1.10) hybrids of the N donor atoms. Our electronic structure calculations can rationalize the different coordination of the thiocyanate groups in compounds 1 and 2: the simultaneous formation of two Pb-SCN bonds is more favorable for S-Pb-S angles close to 180 degrees , for which the overlap between the occupied 3p z orbitals of the S atoms and the unoccupied 6 pz AO of the Pb atom is maximized.     

Electrochemical and ESR study of 5-nitrofuryl-containing thiosemicarbazones antiprotozoal drugs

Cyclic voltammetry and electron spin resonance (ESR) techniques were used in the investigation of several potential antiprotozoal thiosemicarbazones nitrofurane derivatives. A self-protonation process involving the protonation of the nitro group due to the presence of an acidic proton in the thiosemicarbazone moiety was observed in the first step of a CEE(rev) reduction mechanism of these derivatives. ESR spectra of the free radicals obtained by electrolytic reduction were characterized and analyzed. AM1 methodology was used to obtain the optimized geometries and UB3LYP calculations were performed to obtain the theoretical hyperfine coupling constants. The theoretical study exhibited an unusual assignment of the spin densities showing a free radical centered in the thiosemicarbazone moiety rather than the nitro which are in agreement with the experimental hyperfine pattern.     

Interaction of Tb(III) and hydrolyzed polyacrylamides in solution as a gel and in the solid state

Formation of the HPAM-Tb³ complex in solution was observed in the intensification of Tb(III) fluorescence, viscosity, and light scattering. The interaction is dependent on the degree of hydrolysis of the copolymer and the pH of the solution. As the pH value increases, an intensification of the interaction and formation of a gel is observed. The latter was associated with the appearance of crosslinks in which terbium, or one of its hydrolysis products, works as a binding agent between chains. After drying, the characterization of the residues of the gels was effected by analytical determination (C, H, N, Cl, Tb), fluorescence, and infrared spectrophotometry. The analysis and fluorescence revealed the existence of particles of terbium hydroxide; the infrared spectrophotometry showed the binding of terbium (III) to carboxylate of the copolymer.     

A comparative analysis of various gradient methods for geometry optimization at the ab initio SCF-MO level

Various techniques, already suggested for improving the computational efficiency of the force relaxation method, have been applied here in conjunction with the variable metric algorithms suggested by Murtagh and Sargent and by Fletcher. Various tests have been performed to assess the computational efficiency of the resulting minimization procedures. In addition, procedures where the steps are defined in terms of a parabolic fitting of the forces in approximated normal coordinates have been tested. In all cases the forces are computed analytically.     

Reactivity of 2-halo-2H-azirines. 1. Reactions with nucleophiles.

Nucleophilic substitution reactions of 2-halo-2H-azirines 1a, 1b, 1d, and 1e with potassium phthalimide and aniline allowed the preparation of new substituted 2H-azirines 2-5. The reactions of 2-bromo-2H-azirine 1a with methylamine led to the synthesis of alpha-diimines 7 and 8. 2-Halo-2H-azirines were also established as building blocks for the synthesis of a range of heterocyclic compounds, namely, quinoxalines 10a-10d, 3-oxazoline 14, and 2H-[1,4]oxazines 18 and 20. X-ray crystal structures of alpha-diimine 7, 3-oxazoline 14, and 2H-[1,4]oxazine 18 are reported.