About Tracing Problems in Dynamic Geometry

Dynamic Geometry is the field of interactively performing geometric construction on a computer. In addition to simulating ruler-and-compass constructions we allow a drag mode. This drag mode allows to move geometric objects that have at least one degree of freedom. The remaining part of the construction should adjust automatically. Thus, during the motion, we have to trace the resulting paths of all geometric objects. This path tracking problem is known as the Tracing Problem from Dynamic Geometry. It combines the step-by-step procedure of doing geometric constructions with the continuous concept of motions. This study is based on the model for Dynamic Geometry used in the interactive geometry software Cinderella. We give a numerical solution to the Tracing Problem based on continuation methods and a reliable algorithm based on real and complex interval arithmetic. Degenerate situations like the intersection of two identical lines lead to critical points in the configuration space and are treated separately.     

Chemoselectivity of the Reactions of Diazomethanes with 5‐Benzylidene‐3‐phenylrhodanine

The reactions of 5‐benzylidene‐3‐phenylrhodanine ( 2 ; rhodanine=2‐thioxo‐1,3‐thiazolidin‐4‐one) with diazomethane ( 7a ) and phenyldiazomethane ( 7b ) occurred chemoselectively at the exocyclic C?C bond to give the spirocyclopropane derivatives 9 and, in the case of 7a , also the C‐methylated products 8 (Scheme 1). In contrast, diphenyldiazomethane ( 7c ) reacted exclusively with the C?S group leading to the 2‐(diphenylmethylidene)‐1,3‐thiazolidine 11 via [2+3] cycloaddition and a ‘two‐fold extrusion reaction’. Treatment of 8 or 9b with an excess of 7a in refluxing CH₂Cl₂ and in THF at room temperature in the presence of [Rh₂(OAc)₄], respectively, led to the 1,3‐thiazolidine‐2,4‐diones 15 and 20 , respectively, i.e., the products of the hydrolysis of the intermediate thiocarbonyl ylide. On the other hand, the reactions with 7b and 7c in boiling toluene yielded the corresponding 2‐methylidene derivatives 16, 21a , and 21b . Finally, the reaction of 11 with 7a occurred exclusively at the electron‐poor C?C bond, which is conjugated with the C?O group. In addition to the spirocyclopropane 23 , the C‐methylated 22 was formed as a minor product. The structures of the products (Z)‐ 8, 9a, 9b, 11 , and 23 were established by X‐ray crystallography.     

Stereochemistry of the Conversion of 2‐Phenoxyethanol into Phenol and Acetaldehyde by Acetobacterium sp.

The conversion of 2‐phenoxyethanol to phenol and acetate by the anaerobic bacterium Acetobacterium sp. strain LuPhet1 proceeds through acetaldehyde with concomitant migration of a H‐atom from C(1) to C(2) of the glycolic moiety. Separate feeding experiments with (R)‐ and (S)‐2‐phenoxy(1‐²H)ethanol, prepared via chemoenzymatic syntheses, indicate that the H‐atom involved in the 1,2‐shift is the pro‐S one of the enantiotopic couple of the alcohol function.     

Gold as a hydrogen sensing electrode forin situ measurement of dissolved H2 in supercritical aqueous fluid

Potentiometric studies of the Au-YSZ(Hg/HgO) (YSZ=yttrium stabilized zirconia) cell were conducted to investigate the suitability of gold as a sensing element forin situ determination of dissolved H₂ in aqueous fluids at 375–400°C and 400 bars. Experimental results indicate that the gold electrode responds rapidly and reversibly to variations in dissolved H₂, even at H₂<0.1 mmol-kg^?1. Nernstian response of the cell to dissolved H₂ was demonstrated at 400°C and 400 bars $$\Delta E = 0.9815 + 0.0668 \log m_{H_2 } $$ In fact, the performance of the gold electrode compares well to that of platinum. Considering the well known difficulties of using platinoid metals in H₂S-bearing fluids, however, the gold electrode holds great promise forin situ measurement of dissolved H₂ in chemically complex natural hydrothermal fluids. The results also suggest that the Au-YSZ(Hg/HgO) cell can be used to determine the solubility behavior of H₂ in aqueous fluid at temperatures and pressures in the vicinity of the critical point of water. At present, such data are lacking, which severely constrains knowledge of the effect of temperature and pressure on the Henry's law constant of H₂ in water.     

Homoleptic, sigma-bonded octahedral [M(CO)(6)](2+) cations of iron(II), ruthenium(II), and osmium(II). Part 1: Syntheses, thermochemical and vibrational characterizations, and molecular structures as [Sb(2)F(11)](-) and [SbF(6)](-) salts. A comprehensive, comparative study

Homoleptic octahedral, superelectrophilic sigma-bonded metal carbonyl cations of the type [M(CO)(6)](2+) (M = Ru, Os) are generated in the Bronsted-Lewis conjugate superacid HF/SbF(5) by reductive carbonylation of M(SO(3)F)(3) (M = Ru, Os) or OsF(6). Thermally stable salts form with either [Sb(2)F(11)](-) or [SbF(6)](-) as anion, just as for the previously reported [Fe(CO)(6)](2+) cation. The latter salts are generated by oxidative (XeF(2)) carbonylation of Fe(CO)(5) in HF/SbF(5). A rationale for the two diverging synthetic approaches is provided. The thermal stabilities of [M(CO)(6)][SbF(6)](2) salts, studied by DSC, range from 180 degrees C for M = Fe to 350 degrees C for M = Os before decarbonylation occurs. The two triads [M(CO)(6)][SbF(6)](2) and [M(CO)(6)][Sb(2)F(11)](2) (M = Fe, Ru, Os) are extensively characterized by single-crystal X-ray diffraction and vibrational and (13)C NMR spectroscopy, aided by computational studies of the cations. The three [M(CO)(6)][SbF(6)](2) salts (M = Fe, Ru, Os) crystallize in the tetragonal space group P4/mnc (No. 128), whereas the corresponding [Sb(2)F(11)](-) salts are monoclinic, crystallizing in space group P2(1)/n (No. 14). In both triads, the unit cell parameters are nearly invariant of the metal. Bond parameters for the anions [SbF(6)](-) and [Sb(2)F(11)](-) and their vibrational properties in the two triads are completely identical. In all six salts, the structural and vibrational properties of the [M(CO)(6)](2+) cations (M = Fe, Ru, Os) are independent of the counteranion and for the most part independent of M and nearly identical. Interionic C...F contacts are similarly weak in all six salts. Metal dependency is noted only in the (13)C NMR spectra, in the skeletal M-C vibrations, and to a much smaller extent in some of the C-O stretching fundamentals (A(1g) and T(1u)). The findings reported here are unprecedented among metal carbonyl cations and their salts.     

Social and antisocial [3 + 3] Schiff base macrocycles with isomeric backbones

Two new conjugated macrocycles have been prepared in high yield using Schiff base condensation. These are the first Schiff base macrocycles to incorporate phenanthrene, and they contain 66 and 78 atoms, respectively, in their smallest closed ring. Although the backbones of the two macrocycles have nearly the same constitution, one aggregates in chloroform while the other does not. This is rationalized based on the differential overlap of aromatic components in the dimers.     

Chronocoulometric and rotating disc electrode determination of the charge propagation current through poly-4-vinylpyridine films containing hexachloroiridate anions

Charge propagation currents through polymer films coated on electrodes which contain redox active sites are usually determined by potential step methods. The aim of this study was to compare the charge propagation current obtained from chronocoulometric measurements with charge transport through a poly-4-vinylpyridine/IrCl₆²⁻ film during the mediated oxidation of Fe²⁺ at a rotating disc electrode. The two methods gave identical results for the model system chosen.