Macdonald polynomials from Sklyanin algebras: A conceptual basis for thep-adics-quantum group connection

We establish a previously conjectured connection betweenp-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which interpolate between the zonal spherical functions of related real andp-adic symmetric spaces. The elliptic quantum algebras underlie theZ _n -Baxter models. We show that in then limit, the Jost function for the scattering offirst level excitations in the 1+1 dimensional field theory model associated to theZ _n -Baxter model coincides with the Harish-Chandra-likec-function constructed from the Macdonald polynomials associated to the root systemA ₁. The partition function of theZ ₂-Baxter model itself is also expressed in terms of this Macdonald-Harish-Chandrac-function, albeit in a less simple way. We relate the two parametersq andt of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular thep-adic regimes in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of q-deforming Euler products.Work supported in part by the NSF: PHY-9000386     

Analysis of bonding properties in molecular ground and excited states by a Cohen-type bond order

We propose a Cohen-type bond order analysis in terms of orthogonalized atomic basis functions which can be used to analyze NDO wave functions of large organic and metal–organic molecules. It is shown that for small molecules the results gained with this method are in excellent agreement with the same analysis based on ab initio STO -3G wavefunctions. For large planar aromatic systems these all-valence electron bond orders are found to be a consistent generalization of the π-bond order. A simple relation between these bond orders and the corresponding covalent bond energies is established. The method can be easily extended to study excited state multiconfiguration wave functions. We present calculations for C₂H₂, C₂H₄, C₂H₆, and Mn₂(CO)₁₀. The results indicate that the method can be used to discuss the photochemistry of organic and metal–organic compounds.     

NEXAFS measurements of the molecular ordering in the boundary layers of liquid crystalline free standing films

By near edge X-ray absorption fine-structure (NEXAFS) spectroscopy a finite molecular tilt angle in the surface layer of a free standing film in the liquid crystalline smectic A phase of C7 was directly detected. Analysis of the angular dependent intensities of the oxygen K edge NEXAFS spectra leads to an average tilt angle of the molecules in the surface layer of about 34°, which is characteristic for the bulk smectic C* phase of C7.     

Umbilic point screening in random optical fields

Umbilic points--singular points of curvature characterized by a fractional topological charge q=+/-1/2--are the most numerous of all special points in the landscape of random optical fields (speckle patterns), outnumbering maxima, minima, saddle points, and optical vortices. To the best of our knowledge, we present the first experimental evidence that positive and negative umbilic points screen one another. Theory predicts that in the absence of screening the charge variance in a bounded region is proportional to the area of the region, whereas in the presence of screening the variance is drastically reduced and is proportional to the perimeter. Our data confirm this latter prediction and provide the first estimates of the screening lengths for umbilic points of the intensity and of the amplitude (field modulus).     

Click Chemistry in Ultra-high Vacuum – Tetrazine Coupling with Methyl Enol Ether Covalently Linked to Si(001)

The additive-free tetrazine/enol ether click reaction was performed in ultra-high vacuum (UHV) with an enol ether group covalently linked to a silicon surface: Dimethyl 1,2,4,5-tetrazine-3,6-dicarboxylate molecules were coupled to the enol ether group of a functionalized cyclooctyne which was adsorbed on the silicon (001) surface via the strained triple bond of cyclooctyne. The reaction was observed at a substrate temperature of 380 K by means of X-ray photoelectron spectroscopy (XPS). A moderate energy barrier was deduced for this click reaction in vacuum by means of density functional theory based calculations, in good agreement with the experimental results. This UHV-compatible click reaction thus opens a new, flexible route for synthesizing covalently bound organic architectures.     

Interaction of Hydrogen with Ceria: Hydroxylation,Reduction, and Hydride Formation on the Surface and in the Bulk

The study reports the first attempt to address the interplay between surface and bulk in hydride formation in ceria (CeO₂) by combining experiment, using surface sensitive and bulk sensitive spectroscopic techniques on the two sample systems, i.e., CeO₂(111) thin films and CeO₂ powders, and theoretical calculations of CeO₂(111) surfaces with oxygen vacancies (O_v) at the surface and in the bulk. We show that, on a stoichiometric CeO₂(111) surface, H₂ dissociates and forms surface hydroxyls (OH). On the pre-reduced CeO_2−x samples, both films and powders, hydroxyls and hydrides (Ce−H) are formed on the surface as well as in the bulk, accompanied by the Ce³⁺ ↔ Ce⁴⁺ redox reaction. As the O_v concentration increases, hydroxyl is destabilized and hydride becomes more stable. Surface hydroxyl is more stable than bulk hydroxyl, whereas bulk hydride is more stable than surface hydride. The surface hydride formation is the kinetically favorable process at relatively low temperatures, and the resulting surface hydride may diffuse into the bulk region and be stabilized therein. At higher temperatures, surface hydroxyls can react to produce water and create additional oxygen vacancies, increasing its concentration, which controls the H₂/CeO₂ interaction. The results demonstrate a large diversity of reaction pathways, which have to be taken into account for better understanding of reactivity of ceria-based catalysts in a hydrogen-rich atmosphere.     

Growth and Atomic-Scale Characterization of Ultrathin Silica and Germania Films: The Crucial Role of the Metal Support

The present review reports on the preparation and atomic-scale characterization of the thinnest possible films of the glass-forming materials silica and germania. To this end state-of-the-art surface science techniques, in particular scanning probe microscopy, and density functional theory calculations have been employed. The investigated films range from monolayer to bilayer coverage where both, the crystalline and the amorphous films, contain characteristic XO₄ (X=Si,Ge) building blocks. A side-by-side comparison of silica and germania monolayer, zigzag phase and bilayer films supported on Mo(112), Ru(0001), Pt(111), and Au(111) leads to a more general comprehension of the network structure of glass former materials. This allows us to understand the crucial role of the metal support for the pathway from crystalline to amorphous ultrathin film growth.