An attempt on the calculation of relativistic potential energy curves: Noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF₂ may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF₂ and XeF₂ to within 2 eV.     

The Module Structure Theorem for Sobolev Spaces on Open Manifolds

We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.     

The continuation of the periodic table up to Z = 172. The chemistry of superheavy elements

The chemical elements up toZ = 172 are calculated with a relativistic Hartree-Fock-Slater program taking into account the effect of the extended nucleus. Predictions of the binding energies, the X-ray spectra and the number of electrons inside the nuclei are given for the inner electron shells. The predicted chemical behaviour will be discussed for all elements betweenZ = 104-120 and compared with previous known extrapolations. For the elementsZ = 121–172 predictions of their chemistry and a proposal for the continuation of the Periodic Table are given. The eighth chemical period ends withZ = 164 located below Mercury. The ninth period starts with an alkaline and alkaline earth metal and ends immediately similarly to the second and third period with a noble gas atZ = 172.

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Zusammenfassung Mit einem relativistischen Hartree-Fock-Slater Rechenprogramm werden die chemischen Elemente bis zur Ordnungszahl 172 berechnet, wobei der Einfluß des ausgedehnten Kernes berücksichtigt wurde. Für die innersten Elektronenschalen werden Voraussagen über deren Bindungsenergie, das Röntgenspektrum und die Zahl der Elektronen im Kern gemacht. Die voraussichtliche Chemie der Elemente zwischenZ = 104 und 120 wird diskutiert und mit bereits vorhandenen Extrapolationen verglichen. Für die ElementeZ =121–172 wird eine Voraussage über das chemische Verhalten gegeben, sowie ein Vorschlag für die Fortsetzung des Periodensystems gemacht. Die achte chemische Periode endet mit dem Element 164 im Periodensystem unter Quecksilber gelegen. Die neunte Periode beginnt mit einem Alkali- und Erdalkalimetall und endet sofort wieder wie in der zweiten und dritten Periode mit einem Edelgas beiZ = 172.

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Resumé Les éléments chimiques jusqu'áZ = 172 sont calculés à l'aide d'un programme Hartree-Fock-Slater relativiste en tenant compte de l'extension du noyau. On fournit des prédictions quant aux énergies de liaison, aux spectres X et au nombre d'électrons dans les noyaux pour les couches électroniques internes. Le comportement chimique prévu est discuté pour tous les éléments entreZ = 104–120 et comparé aux extrapolations connues auparavant. Pour les éléments Z =121–172 on effectue des prévisions de propriétés chimiques et l'on propose un prolongement du Tableau Périodique. La huitième période chimique se termine àZ = 164 sous le mercure. La neuviéme période débute avec un métal alcalin et alcalino-terreux et se termine comme la seconde et la troisième période avec un gaz rare àZ = 172.

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This work has been supported by the Bundesministerium für Wissenschaft und Bildung and by the Deutsche Forschungsgemeinschaft.     

Effect of the homogeneity of the column set on the performance of a simulated moving bed unit. I. Theory

Although it is impossible to manufacture identical columns for use in a simulated moving bed (SMB) process, theoretical studies assume that all the columns in an SMB unit have identical characteristics. In practice, calculations in modeling and optimization studies are made with the average values of each column parameter set. In this report, the effects on SMB process performance caused by column-to-column fluctuations of the parameters are discussed. As a first step, we show how the differences in porosity of the columns may be taken into account with a revised set of separation conditions. Reductions in the purity of the extract and the raffinate streams are quantitatively related to the column-to-column fluctuations of the retention times of the two components arising from these porosity differences. For the sake of simplicity, the discussion first addresses the case of a four-column SMB operating under linear conditions. Then, the scope is extended to the cases of SMB units incorporating several columns in each section and to SMB units operating under nonlinear conditions.     

Ground state correlation energy of the Be-sequence forZ=4–20 in MCDF approximation

The ground state (J=0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation forZ=4–20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.     

Darstellung und Charakterisierung von bindungsisomeren Hexakis(thiocyanato-isothiocyanato)-iridaten(III) und einiger Chloro-, Cyano-pentarhodanoiridate(III)

Preparation and Characterization of Bond-Isomeric Hexakis(thiocyanato-isothiocyanato)-iridates(III) and Some Chloro-, Cyano-pentarhodanoiridates(III) The evaporated ethanolic extract of the reaction product of K₃[IrCl₆] and HNO₃, refluxed with an aqueous KSCN solution yields a mixture of the bond isomers [Ir(NCS)_n(SCN)_6?n]^3?, n = 0–2 and small amounts of bond isomeric chloropentrahodanoiridates(III). By heating the tetrabutylammonium salts, N coordination of the ambident SCN^? is favoured forming compounds with n = 2–5 beside chloro- and cyanopentarhodanoiridates(III). With n = 2, 3 pairs of geometric isomers can be detected. The pure compounds are separated by ion exchange chromatography on diethylaminoethylcellulose. The trans/mer-complexes migrate 1.9 times faster than the cis/fac-isomers. Depending on S- or N-bonding the IR and Raman spectra show typical vibrations: ν_CN(N) and ν_CN(S): 2100–2175, ν_CS(N): 810–855, ν_CS(S): 690–710, δ_NCS: 470–480, δ_SCN: 420–470, ν_IrN: 300–325, ν_IrS: 255–313 cm^?1. Except the inner ligand vibrations the Rh? N and Rh? S valence frequencies are assigned according to the supposed point symmetries. By interaction of the trans-positioned ligands characteristic shifts are caused.     

Schwingungs- und Elektronenspektren der bindungsisomeren Hexakis(thiocyanato-isothiocyanato)-ruthenate(III)

Vibrational and Electronic Spectra of Bond-Isomeric Hexakis(thiocyanato-isothiocyanato)ruthenates(III) Well resolved IR, Raman, and Electronic spectra of the bond isomeric complexes (TBA)₃[Ru(NCS)_n(SCN)_6?n], n = 1–5, including the pairs of geometric isomers n = 2, 3, 4, are recorded at low temperatures (10 and 80 K). Characteristic vibrations of the N- or S-coordinated ambident ligand SCN^? occur as listed: ν_CS(N): 810–850, ν_CS(S): 690–710, δ_NCS: 450–490, δ_SCN: 420–450, ν_RuN: 300–350, ν_RuS: 270–295 cm^?1. The assignment of the complexes is based on stepwise increasing intensities of the ν_CS(N) modes with increasing number of N-coordinated ligands. Characteristic shifts and splittings in the spectra allow to distinguish the geometric bond isomers according to their different symmetries. Even the absorption spectra in the visible range show within the series of bond isomers and for the cis/trans pairs systematic alternations.     

Quantum-chemical approach to the elementary steps of plasma etching

We derive for the first time a mechanism of reactive plasma etching in the system Si/F by the quantum-chemical approach. SiF₂-like species at the surface play an important role. SiF₃ surface complexes also occur. The final etching product SiF₄ is formed with high probability in the gas phase.