Interaction of 1,2,5-chalcogenadiazole derivatives with thiophenolate: hypercoordination with formation of interchalcogen bond versus reduction to radical anion

According to the DFT calculations, [1,2,5]thiadiazolo[3,4-c][1,2,5]thiadiazole (4), [1,2,5]selenadiazolo[3,4-c][1,2,5]thiadiazole (5), 3,4-dicyano-1,2,5-thiadiazole (6), and 3,4-dicyano-1,2,5-selenadiazole (7) have nearly the same positive electron affinity (EA). Under the CV conditions they readily produce long-lived π-delocalized radical anions (π-RAs) characterized by EPR. Whereas 4 and 5 were chemically reduced into the π-RAs with thiophenolate (PhS(-)), 6 did not react and 7 formed a product of hypercoordination at the Se center (9) isolated in the form of the thermally stable salt [K(18-crown-6)][9] (10). The latter type of reactivity has never been observed previously for any 1,2,5-chalcogenadiazole derivatives. The X-ray structure of salt 10 revealed that the Se-S distance in the anion 9 (2.722 ?) is ca. 0.5 ? longer than the sum of the covalent radii of these atoms but ca. 1 ? shorter than the sum of their van der Waals radii. According to the QTAIM and NBO analysis, the Se-S bond in 9 can be considered a donor-acceptor bond whose formation leads to transfer of ca. 40% of negative charge from PhS(-) onto the heterocycle. For various PhS(-)/1,2,5-chalcogenadiazole reaction systems, thermodynamics and kinetics were theoretically studied to rationalize the interchalcogen hypercoordination vs reduction to π-RA dichotomy. It is predicted that interaction between PhS(-) and 3,4-dicyano-1,2,5-telluradiazole (12), whose EA slightly exceeds that of 6 and 7, will lead to hypercoordinate anion (17) with the interchalcogen Te-S bond being stronger than the Se-S bond observed in anion 9.     

Wetting on the microscale: shape of a liquid drop on a microstructured surface at different length scales

Describing wetting of a liquid on a rough or structured surface is a challenge because of the wide range of involved length scales. Nano- and micrometer-sized textures cause pinning of the contact line, reflected in a hysteresis of the contact angle. To investigate contact angles at different length scales, we imaged water drops on arrays of 5 μm high poly(dimethylsiloxane) micropillars. The drops were imaged by laser scanning confocal microscopy (LSCM), which allowed us to quantitatively analyze the local and large-scale drop profile simultaneously. Deviations of the shape of drops from a sphere decay at two different length scales. Close to the pillars, the amplitude of deviations decays exponentially within 1-2 μm. The drop profile approached a sphere at a length scale 1 order of magnitude larger than the pillars' height. The height and position dependence of the contact angles can be understood from the interplay of pinning of the contact line, the principal curvatures set by the topography of the substrate, and the minimization of the air-water interfaces.     

2‐Polyfluoroacylcycloalkanones in reactions with selected phosphorus(III) compounds

The reactivity of 2‐polyfluoroacylcycloalkanones and their O‐silylated derivatives towards phosphites and tris(trimethylsilyl)aminoiminophosphine has been investigated. From α‐polyfluoroalkyl substituted phosphonates, generated from tris(trimethylsilyl) phosphite and 1,3‐diketones, the respective phosphonic acids and their salts have been obtained. In one case, upon warming, a phosphonic acid underwent a ring closure to yield an oxaphospholene. 2‐Trifluoroacetylcycloalkanones and diethyl isocyanatophosphite furnished phosphoranes diastereospecifically, via addition of phosphorus at the trifluoroacetyl group and two additional heterocyclizations. Tris(trimethylsilyl)aminoiminophosphine formed very reactive trimethylsilylimino‐1,2λ⁵σ⁴‐phospholenes, which added hexafluoroacetone to give spirocyclic 1,3,2λ⁵σ⁵‐oxazaphosphetanes. The structures of the new compounds were determined by NMR spectroscopy and X‐ray single crystal analysis. © 2002 Wiley Periodicals, Inc. Heteroatom Chem 13:97–107, 2002; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/hc.10001     

First P-trifluoromethylated ylides

Trifluoromethylated phosphines R₂PCF₃ (R = NEt₂, Me, ¹Pr) were methylated by CH₄OSO₂CF₃, yielding the corresponding phosphonium salts [R₂P(CF₃)CH₃] [F₃CSO₃]. Treatment with LiN(SiMe₃)₂ at −80°C furnished the phosphorus ylides R₂P(CF₃) = CH₂ that could be trapped by use of hexafluoroacetone with formation of stable 1,2λ⁵σ⁵-oxaphosphetanes. The single-crystal X-ray structure determination of one of these oxaphosphetanes showed a distorted trigonal bipyramid at phosphorus with the P-CF₃ group in an axial position. © 1996 John Wiley & Sons, Inc.     

Some asymptotics for multimodality tests based on kernel density estimates

Summary A test due to B.W. Silverman for modality of a probability density is based on counting modes of a kernel density estimator, and the idea of critical smoothing. An asymptotic formula is given for the expected number of modes. This, together with other methods, establishes the rate of convergence of the critically smoothed bandwidth. These ideas are extended to provide insight concerning the behaviour of the test based on bootstrap critical values.