Evaluation of quadrature schemes for the discrete ordinates method

After reviewing the presently available quadrature schemes for the discrete ordinates method, the accuracy of different schemes is analyzed and evaluated. It is shown from a comprehensive error analysis that the moment conditions have to satisfied not only for the principal coordinates directions, as it is mostly carried out, but for any arbitrary test direction. Among the schemes with approximately 50 discrete ordinates the DCT-020-2468 quadrature was found to give the best accuracy. The highest accuracy among all schemes is achieved by the LC-11 quadrature which requires 96 discrete ordinates. This scheme is rarely used up to date and deserves more attention for high accuracy predictions.     

The onset of deconfinement inSU(2) lattice gauge theory

InSU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeN _σ ³ ×4,N _σ=8, 12, 18 and 26, we calculate the quantityΔ≡(ε?3P)/T ⁴. It increases sharply just aboveT _c , peaks atT/T _c =1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just aboveT _c , the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.     

S=N versus S+-N-: an experimental and theoretical charge density study

To elucidate the bonding situation in the widely discussed hypervalent sulfur nitrogen species, the charge density distributions rho(r) and related properties of four representative compounds, methyl(diimido)sulfinic acid H(NtBu)(2)SMe (1), methylene-bis(triimido)sulfonic acid H(2)C[S(NtBu)(2) (NHtBu)](2) (2), sulfurdiimide S(NtBu)(2) (3), and sulfurtriimide S(NtBu)(3) (4), were determined experimentally by high-resolution low-temperature X-ray diffraction experiments (T = 100 K). This set of molecules represents an ideal frame of reference for the comparison of SN bonding modes, because they contain short formal S=N double bonds as well as long S-N single bonds, some of them influenced by inter- or intramolecular hydrogen bonds. For comparison, the gas-phase ab initio calculations of the four model compounds, H(NMe)(2)SMe, H(2)C[S(NMe)(2)(NHMe)](2), S(NMe)(2), and S(NMe)(3), were performed. The topological features were found to be not particularly sensitive with respect to different substituents R (R = H, Me, tBu). In this paper, it is documented that theory and experiment differ in the eigenvalues of the Hessian matrix because of systematically differing positions of the bond critical points but agree very well concerning the spatial Laplacian distribution and the distinct polarization of all investigated sulfur-nitrogen bonds. Both recommend the S(+)-N(-) formulation of sulfur nitrogen bonds in 1 and 2 since all nitrogen atoms are found to be sp(3) hybridized. The planar SNx (x = 2, 3) units in the diimide 3 and the triimide 4 reveal characteristics of m-center-n-electron systems. For none of the investigated S-N bonds, a classical double bond formulation can be supported. This is further substantiated by the NBO/NRT approach. Valence expansion to more than eight electrons at the sulfur atom can definitely be excluded to explain the bonding.     

Zur Kenntnis der μ-Peroxo-bis(pentacyanokobaltate(III)). Neuartige Darstellung,Beschreibung eines μ-Hydroperoxo-komplexes K5[Co2OOH(CN)10] · 2 H2O und eines μ-Peroxo-Carbonato-Komplexes K6[Co2CO4(CN)10] · 2 H2O

Investigations on Metal Catalysts. XXII. Chemisorption of Hydrogen on Pt? Ru and η-Al₂O₃ Supported Pt? Ru Catalysts Measurements of the H₂ chemisorption by volumetric method were carried out on several series of Pt? Ru and η-Al₂O₃ supported Pt? Ru catalysts. Addition of Ru to Pt and vice versa effects a remarkable influence on the sorption behaviour of the starting samples. For mixtures of carrier-free catalysts and η-Al₂O₃ as well as Pt? Ru/η-Al₂O₃ catalysts a hydrogen-spillover effect was found.