On the geometry of conjugacy classes in classical groups

Summary We study closures of conjugacy classes in the Lie algebras of the orthogonal and symplectic groups and determine which ones are normal varieties. Furthermore we give a complete classification of the minimal singularities which arise in this context, i.e. the singularities which occur in the open classes in the boundary of a given conjugacy class. In contrast to the results for the general linear group ([KP1], [KP2]) there are classes with non normal closure; they are branched in a class of codimension two and give rise to normal minimal singularities. The methods used are (classical) invariant theory and algebraic geometry. Supported in part by the SFB Theoretische Mathematik, University of Bonn, and by the University of Hamburg     

Gravitational geometric phase in the presence of torsion

We investigate the relativistic and non-relativistic quantum dynamics of a neutral spin-1/2 particle subject to an external electromagnetic field in the presence of a cosmic dislocation. We analyze the explicit contribution of the torsion in the geometric phase acquired in the dynamics of this neutral spinorial particle. We discuss the influence of the torsion in the relativistic geometric phase. Using the Foldy–Wouthuysen approximation, the non-relativistic quantum dynamics is studied and the influence of the torsion on the Aharonov–Casher and He–McKellar–Wilkens effects are discussed. An erratum to this article can be found at     

Environmentally friendly sonocatalysis promoted preparation of 1-thiocarbamoyl-3,5-diaryl-4,5-dihydro-1H-pyrazoles

An efficient and green synthesis of thiocarbamoyl-3,5-diaryl-4,5-dihydro-1H-pyrazoles via the condensation of chalcones with thiosemicarbazide in ethanol and KOH under ultrasound irradiation is reported. The products were isolated in good yields after short reaction times.     

Preparation of a new chiral non-racemic sulfur-containing diselenide and applications in asymmetric synthesis

The synthesis of the new chiral non-racemic sulfur-containing diselenide, di-2-methoxy-6-[(1S)-1-(methylthio)ethyl]phenyl diselenide, is described. When treated with ammonium persulfate this diselenide is transformed into the corresponding selenenyl sulfate, which acts as a strong electrophilic reagent and adds to alkenes, in the presence of methanol or water, to afford the products of selenomethoxylation or selenohydroxylation, respectively, with excellent diastereoselectivities. Starting from alkenes containing internal nucleophiles, asymmetric cyclofunctionalization reactions also resulted in good chemical yields, complete regioselectivities, and high diastereoselectivities. This sulfur-containing diselenide can also be used in catalytic amounts to promote one-pot selenenylation-deselenenylation processes, from which several types of products can be obtained in high yield and with good enantiomeric excess.     

Influence of surface composition on hydrogen peroxide decomposition catalyzed by Co(II) aminopyridine-supported compounds on amorphous silica gel

Cobalt compounds supported on 2-, 3-, and 4-aminopyridine-modified silica surfaces, named Sil2Co, Sil3Co, and Sil4Co, respectively, were used to catalyze the decomposition of hydrogen peroxide on ethanolic solutions at 293, 298, and 303 K. The calculated k values (x10(-4) s(-1)) for Sil2Co, Sil3Co, and Sil4Co are 0.65, 1.24, and 4.78 (293 K); 1.23, 1.87, and 6.33 (298 K); and 1.80, 2.80, and 10.30 (303 K), respectively. All obtained results evidence that such decomposition is a first-order reaction. Zinc-, nickel-, and copper-supported compounds were also tested, but exhibited a very low catalytic activity. By using the k values at 298 and 303 K, and employing the equation ln (k1/k2) = E(a)/R(1/T2-1/T1), the activation energy values for the considered reaction were Sil2Co = 57.20, Sil3Co = 60.60, and Sil4Co = 73.10 kJ mol(-1), respectively. The low values calculated for E(a) are in agreement with a free-radical mechanism.     

Conformational studies by dynamic NMR. 86. Structure, stereodynamics, and cryogenic enantioseparation of the stereolabile isomers of o-dinaphthylphenyl derivatives

Static and dynamic stereochemistry of the hydrocarbon comprising a phenyl ring bearing two alpha-naphthyl substituents in the ortho positions, i.e., 1,2-di-(4-methyl-naphth-1-yl)-benzene 1, has been studied by a combination of variable temperature NMR, cryogenic HPLC, and MM calculations. Whereas in solution both syn (meso) and anti (chiral) forms were observed and the corresponding interconversion barrier was determined (Delta G(++) = 19.5 kcal mol(-1)), only the diastereoisomer anti was found to be present in the crystalline state (X-ray diffraction). When the molecule is rendered asymmetric by introduction of a nitro group in the phenyl ring as in 1,2-di-(4-methyl-naphth-1-yl)-4-nitrobenzene 2, the chiral syn and anti diastereoisomers are simultaneously present both in solution and in the solid state, albeit in different proportions. Cryogenic chromatography on a HPLC chiral stationary phase at 20 degrees C allowed the stereolabile diastereoisomers and the corresponding enantiomers to be separated.     

The nature of superacid electrophilic species in HF/SbF(5): a density functional theory study

A density functional theory study at the B3LYP/6-31++G** + RECP(Sb) level of the HF/SbF(5) superacid system was carried out. The geometries of possible electrophilic species, such as H(2)F(+).Sb(2)F(11)(-) and H(3)F(2)(+).Sb(2)F(11)(-), were calculated and correspond with available experimental results. Calculations of different equilibrium reactions involving HF and SbF(5) allowed the relative concentration of the most energetically favorable species present in 1:1 HF/SbF(5) solutions to be estimated. These species are H(+).Sb(2)F(11)(-), H(2)F(+).Sb(2)F(11)(-), H(3)F(2)(+).Sb(2)F(11)(-), and H(4)F(3)(+).Sb(2)F(11)(-), which correspond to 36.9, 16.8, 36.9, and 9.4%, respectively. Calculations of the acid strength of the electrophilic species were also performed and indicated that, for the same anion, the acid strength increases with the solvation degree. The entropic term also plays a significant role in proton-transfer reactions in superacid systems.     

Intensity and polarization self-pulsations in vertical-cavity surface-emitting lasers

We implement a dynamic model that describes the polarization behavior in vertical-cavity surface-emitting lasers that contain an absorbing region surrounding the active zone. We find four regions of qualitatively different behavior: stable linearly polarized operation, intensity pulsations of a linearly polarized component, pulsations of both total-intensity and polarization components, and polarization self-pulsation with constant total intensity. We characterize the four regions by computing the polarization-resolved optical and power spectra. The predicted behavior agrees with recent experimental results.     

Surface integrals as symmetry generators in supergravity theory

It is shown that in asymptotically flat space the weakly vanishing Hamiltonian of supergravity theory has to be modified by adding to it certain surface integrals. The numerical value of the surface integrals yields the total energy-momentum, angular momentum and supercharge of the system. The surface integrals have well defined (Dirac) brackets only after the coordinates and supergauge are fixed. In that case they close according to the flat space supersymmetry algebra. If an internal symmetry is included, new surface integrals appear corresponding to the additional gauge charges.