Photochemistry of β-(4-sydnonyl)-o-divinylbenzene: competitive cis-trans isomerization and photolysis

New cis- and trans-3-aryl-4-[2-(2-vinylphenyl)ethenyl]sydnones 2, aryl = phenyl, p-tolyl were prepared and transformed on irradiation in the presence of acrolein to a pyrazoline derivative that aromatized during isolation to trans-1-tolyl-3-[2-(2-vinylphenyl)ethenyl]pyrazole 7 and trans-5-formyl-1-tolyl-3-[2-(2-vinylphenyl)ethenyl]pyrazole 8.     

Synthesis and photochemistry of beta,beta'-di(2-furyl)-substituted o-divinylbenzenes: intra- and/or intermolecular cycloaddition as an effect of annelation

New heteroaryl-substituted o-divinylbenzenes, 2,2'-(1,2-phenylenedivinylene)difuran (9), 2,2'-(1,2-phenylenedivinylene)bisbenzo[b]furan (10), and 2,2'-(1,2-phenylenedivinylene)bisnaphtho[2,1-b]furan (11), were prepared and irradiated at various concentrations; intramolecular photocycloaddition and intermolecular [2+2] twofold photoaddition reactions took place to give bicyclo[3.2.1]octadiene derivatives 12-14 and cyclophane derivatives 15-17, respectively. Compound 11 was the most selective of these o-divinylbenzenes, which, owing to pi-pi intra- or intermolecular complexation, gave only the exo-bicyclo[3.2.1]octadiene derivative 14 at low concentrations, and only the cyclophane derivative 17 at high concentrations.     

Supramolecular structural variations with changes in anion and solvent in silver(I) complexes of a semirigid, bitopic tris(pyrazolyl)methane ligand

The bitopic ligand p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2) (pz = pyrazolyl ring) that contains two tris(pyrazolyl)methane units connected by a semirigid organic spacer reacts with silver(I) salts to yield [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgX)(2)]( infinity ), where X = CF(3)SO(3)(-) (1), SbF(6)(-) (2), PF(6)(-) (3), BF(4)(-) (4), and NO(3)(-) (5). Crystallization of the first three compounds from acetone yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgCF(3)SO(3))(2)]( infinity ) (1a), [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))(2)[(CH(3))(2)CO](2)]( infinity ) (2b), and [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)AgPF(6)]( infinity ) (3a), where the stoichiometry for the latter compound has changed from a metal:ligand ratio of 2:1 to 1:1. The structure of 1a is based on helical argentachains constructed by a kappa(2)-kappa(1) coordination to silver of the tris(pyrazolyl)methane units. These chains are organized into a tubular 3D structure by cylindrical [(CF(3)SO(3))(6)](6)(-) clusters that form weak C-H...O hydrogen bonds with the bitopic ligand. The same kappa(2)-kappa(1) coordination is present in the structure of 2a, but the structure is organized by six different tris(pyrazolyl)methane units from six ligands bonding with six silvers to form a 36-member argentamacrocycle core. The cores are organized in a tubular array by the organic spacers where each pair of macrocycles sandwich six acetone molecules and one SbF(6)(-) counterion. The structure of 3a is based on a kappa(2)-kappa(0) coordination mode of each tris(pyrazolyl)methane unit forming a helical coordination polymer, with two strands organized in a double stranded helical structure by a series of C-H...pi interactions between the central arene rings. Crystallization of 2-4 from acetonitrile yields complexes of the formula [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)[(AgX)(2)(CH(3)CN)(n)]]( infinity ) where n = 2 for X = SbF(6)(-) (2b), X = PF(6)(-) (3b) and n = 1 for X = BF(4)(-) (4b). All three structures contain argentachains formed by a kappa(2)-kappa(1) coordination mode of the tris(pyrazolyl)methane units linked by the organic spacer and arranged in a 2D sheet structure with the anions sandwiched between the sheets. Crystallization of 5 from acetonitrile yields crystals of the formula [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgNO(3))(2)(CH(3)CN)(4)]( infinity ), where the nitrate is bonded to the silver. The argentachains, again formed by kappa(2)-kappa(1) coordination, are arranged in W-shaped sheets that have an overall configuration very different from 2b-4b. Treating [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))(2)]( infinity ) with a saturated aqueous solution of KPF(6) or KO(3)SCF(3) slowly leads to complete exchange of the anion. Crystallization of a sample that contains an approximately equal mixture of SbF(6)(-)/PF(6)(-) from acetonitrile yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)[Ag(2)(PF(6))(0.78(1))(SbF(6))(1.22(1))(CH(3)CN)(2)][(CH(3)CN)(0.25) (C(4)H(10)O)(0.25)]]( infinity ), a compound with a sheet structure analogous to 2b-4b. Crystallization of the same mixture from acetone yields [p-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2)(AgSbF(6))[(CH(3))(2)CO](1.5)]( infinity ), where the metal-to-ligand ratio is 1:1 and the [C(pz)(3)] units are kappa(2)-kappa(0) bonded forming a coordination polymer. The supramolecular structures of all species are organized by a combination of C-H...pi, pi-pi, or weak C-H-F(O) hydrogen bonding interactions.     

Decomposing total IR spectra of aqueous systems into solute and solvent contributions: a computational approach using maximally localized Wannier orbitals

The theoretical principles underpinning the calculation of infrared spectra for condensed-phase systems in the context of ab initio molecular dynamics have been recently developed in literature. At present, most ab initio molecular dynamics calculations are restricted to relatively small systems and short simulation times. In this paper we devise a method that allows well-converged results for infrared spectra from ab initio molecular dynamics simulations using small systems and short trajectories characteristic of simulations typically performed in practice. We demonstrate the utility of our approach by computing the imaginary part of the dielectric constant epsilon"(omega) for H2O and D2O in solid and liquid phases and show that it compares well with experimental data. We further demonstrate that maximally localized Wannier orbitals can be used to separate the individual contributions of different molecular species to the linear spectrum of complex systems. The new spectral decomposition method is shown to be useful in present-day ab initio molecular dynamics calculations to compute the magnitude of the "continuous absorption" generated by excess protons in aqueous solutions with good accuracy even when other species present in the solutions absorb strongly in the same frequency window.     

Sums of reciprocals of certain additive functions

We obtain sharp estimates for sums of reciprocals and sums of quotients of certain non-negative integer-valued additive arithmetical functions.Research financed by the Mathematical Institute of Belgrade and Republika Zaj. of Serbia     

Interdisciplinary study on pottery experimentally impregnated with wine

Experimentally developed ceramic pots, with two different sizes of grain, were half-filled with wine and subjected to thermal alteration at constant elevated temperature ((60 ± 2)°C) in darkness for 12 weeks. This work sought to characterise the samples thereby obtained from chemical and mineralogical perspectives using scanning electron microscopy and an energy-dispersive X-ray microanalysis system (SEM-EDX), Fourier transform infrared spectroscopy (FTIR) and capillary electrophoresis (CE) with UV detection as an alternative to chromatographic methods, due to its good resolution, automation, simplicity, high speed, low consumption of chemicals and short time required for sample preparation. The capillary electrophoresis method was used for the detection of five wine biomarkers: succinic acid, malic acid, tartaric acid, citric acid and lactic acid. In general, it was noted that the fine-grained ceramic assortment retained the organic material better than the coarser-grained ceramics. An interesting observation derived from this study was that not only could tartaric acid be considered as a biomarker for wine residues in archaeological pottery, but malic acid could also act similarly for white wine and lactic acid for red wine.     

Chain rules for linear openness in metric spaces and applications

In this work we present a general theorem concerning chain rules for linear openness of set-valued mappings acting between metric spaces. As particular cases, we obtain classical and also some new results in this field of research, including the celebrated Lyusternik–Graves Theorem. The applications deal with the study of the well-posedness of the solution mappings associated to parametric systems. Sharp estimates for the involved regularity moduli are given.     

Review of AdS/CFT Integrability,Chapter V.1: Scattering Amplitudes: A Brief Introduction

Letters in Mathematical Physics - We review current efficient techniques for the construction of multi-leg and multi-loop on-shell scattering amplitudes in supersymmetric gauge theories. Examples...