Alkylation of 2,3,6,11-tetrahydroanthra[2,1-d]isothiazole-3,6,11-trione and its S-oxide

The reactions of 2,3,6,11-tetrahydroanthra[2,1-d]isothiazole-3,6,11-trione with dimethyl sulfate, benzyl chloride, and allyl bromide afforded the corresponding 2-alkyl-2,3,6,11-tetrahydroanthra[2,1-d]isothiazole-3,6,11-triones and 3-(alkoxy)-6,11-dihydroanthra[2,1-d]isothiazole-6,11-diones. The reactions of 2,3,6,11-tetrahydroanthra[2,1-d]isothiazole-3,6,11-trione and its S-oxide with a formaldehyde—secondary amine system yielded 2-[(alkylamino)methyl]-2,3,6,11-tetrahydroanthra[2,1-d]isothiazole-3,6,11-triones and 2-[(alkylamino)methyl]-3,6,11-trioxo-2,3,6,11-tetrahydroanthra[2,1-d]isothiazole 1-oxides, respectively.     

N-Bromoamides as versatile catalysts for aziridination of olefins using chloramine-T

N-Bromoamides catalyze effectively the aziridination of electron-deficient as well as electron-rich olefins using chloramine-T (N-chloro-N-sodio-p-toluenesulfonamide) as a nitrogen source under ambient conditions to afford the corresponding aziridines in good to excellent yields.     

Spectrofluorimetric Method for the Determination of Aluminum with Alizarin Red PS

 A simple and direct spectrofluorimetric method has been developed for the determination of aluminum using alizarin red PS (1,2,4-trihydroxy 9,10-anthraquinone-3-sulfonic acid). The method is based on the strong fluorescence (480/564 nm) of Al³⁺ and alizarin red. Experimental parameters such as pH, concentration of the ligand, ionic strength of the solution, reaction time and temperature were optimized in order to maximize the analytical signal. Interferences of several ions (anions and cations) were studied and evaluated. The linear range of the method extends from 3 to 100 μg L⁻¹. Limit of detection (3s_b) was 0.9 μg L⁻¹. The method was tested with a silicate certified reference material. Interferences were eliminated by a liquid extraction with cupferron. Author for correspondence. E-mail: aucelior@rdc.puc-rio.br Received September 10, 2002; accepted January 15, 2003 Published online May 5, 2003     

A quantum chemical study on structure of 1,2-bis(diphenylphosphinoyl)ethane and phenol cocrystal

The cocrystal of 1,2-bis(diphenylphosphinoyl)ethane (DPPEO) with phenol (1:1) were studied theoretically with AM1, PM3, MNDO and MINDO/3 semi-empirical methods to elucidate its structure. The bond lengths and angles from theoretical studies of molecule DPPEO/phenol (1:1) were found to be as expected. Theoretical results, concerning with intermolecular van der Waals forces in cocrystal, were compared with the previously obtained experimental data and AM1 results were found to be the best fit for bond lengths and angles of DPPEO/phenol.     

Optical absorption spectra of linear and cyclic thiophenes—selection rules manifestation

We theoretically study the size-dependent relation between absorption spectra of thiophene-based oligomers and the corresponding cyclothiophenes. In our approach based on a Frenkel exciton Hamiltonian, we demonstrate that the geometry and selection rules determine the observed relations between the spectra.     

Calculation of Normal Vibrations of Chlorin by the Method of Density Functionals

Using the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and the absolute band intensities in the IR spectra of the chlorin molecule and its four symmetric isotopomers have been calculated. Scaling of the force field by the Pulay method in independent and natural coordinates has been carried out. A method for obtaining effective force fields without using experimental data on the fundamental vibration frequencies is proposed. By comparing the vibration modes and constructing special matrices, complete assignment of the fundamental frequencies of porphin and chlorin has been carried out. It has been shown that the majority of porphin macroring vibrations upon pyrrolenine ring hydrogenation are frequency-characteristic and only 12 vibrations change considerably. A frequency correlation with regard for the mode transition between chlorin and all its isotopomers under consideration has been established. Comparative analysis of the force fields of porphin and chlorin in dependent natural coordinates has revealed the unique nonlocal character of the change in force constants of the macroring upon hydrogenation of one pyrrolenine ring. Modeling of the IR spectra of chlorin and its isotopomers has been performed. Assignment and interpretation of the normal vibrations of the molecules under consideration have been carried out.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.