Vibrational and lifetime line broadenings in ESCA

The line profile of the narrow, symmetric 1s line from neon, recorded with the new ESCA instrument with X-ray monochromatization, is analyzed. The natural linewidth of this line is found to be 0.23 ± 0.02 eV, in good agreement with theoretical calculations of the oscillator strengths for Auger transitions and X-ray emission. Spectra from molecules show frequently asymmetric core electron lines under high resolution. This rules out previous explanations based on a chemical influence on the natural lifetime. Contrary to earlier assumptions, vibrational excitations are shown to be important in core electron spectra. For methane, the vibrational energy spacing is large enough to allow the vibrational lines to be partly resolved. Recent results from accurate PNO CI calculations on methane agree well with the experimental findings. The Franck-Condon transitions in the C1s and N1s lines from CO and N₂ are shown to be well described in the harmonic approximation and approximating the potential curves of the highly excited core hole states with the potential curve for the ground state of NO⁺, X¹ Σ⁺. Knowledge of vibrational excitations in core electron spectra is shown to be valuable in the analysis of high resolution X-ray emission spectra of free molecules.     

Oxoniobates Containing Metal Clusters

Metal clusters, discrete or condensed, are characteristic of the structures of many compounds which contain transition metals in low oxidation states. The highly reduced oxoniobates support the concept of condensed clusters. They contain Nb₆O₁₂ clusters which are either isolated or linked at the apices of the Nb₆ octahedra to form oligomeric chains or networks. The analysis of the bonding relationships allows the identification of different types of Nb atoms and thus the quantitative prediction of valence electron concentrations for finite or infinite structures composed of these condensed M₆X₁₂ clusters.     

Computing global minima to polynomial optimization problems using Gröbner bases

The local optimality conditions to polynomial optimization problems are a set of polynomial equations (plus some inequality conditions). With the recent techniques of Gröbner bases one can find all solutions to such systems, and hence also find global optima. We give a short survey of these methods. We also apply them to a set of problems termed with exact solutions unknown in the problem sets of Hock and Schittkowski. To these problems we give exact solutions.