Die vibronische Kopplung in Koordinationsverbindungen am Beispiel von Hexahalogenokomplexen

Ohne Zusammenfassung

---

The vibronic coupling in coordination compounds. hexahalogeno complexes as example

     

Intensity distribution in the vibronic side bands of the Γ7(2 T 2g ) → Γ8(4 A 2g ) origin of ReX 6 2- doped K2PtCl6-type crystals

Intensities of vibronic transitions are calculated using an electronic vibrational coupling scheme of symmetrized and localized interactions. The model consists of an active central ion subject to a valence force field originating from nearest-neighbor displacements. The intensities of vibronic fundamentals are obtained from a generalized Lorentzian line shape function which is applied to the ₇(² T _2g ) ₈(⁴ A _2g ) transition of ReCl ₆ ^2- and ReBr ₆ ^2- in various cubic host crystals A₂MX₆ (A = Rb, Cs; M = Te, Sn, Pb; X = Cl, Br). Relative intensities of the odd vibronic side bands are calculated without knowing actual values for ligand field and spin-orbit coupling parameters, and considering only octahedral vibrational frequencies. The sidebands acquire intensity by a coupling which is cubic in the electron coordinates and linear in the nuclear normal coordinates. With some necessary approximations the present model is able to reproduce the experimental intensity distribution satisfactorily.Dedicated to Professor Dr. H. Hartmann on the occasion of his 65th birthday     

Clusters as crystal fragments of silicon bulk

Silicon clusters of 13 to 43 atoms were studied with the semi-empirical method SINDO1. Crystalline structures of face-centered cubic (fcc), hexagonal close packed (hcp) and diamond type and noncrystalline structures of icosahedral type were compared. Noncrystalline structures are most stable for clusters up to 13 atoms. Clusters with 19 and more atoms of the fcc structure are preferable to the less dense diamond structure. With more than 35 Si atoms, the diamond structure is favored over the hcp structure. The binding energy of fcc and hcp structures decreases and that of the diamond structure increases with increasing cluster size. A similar trend is observed for the HOMO-LUMO energy gap which is taken as a measure of the band gap.     

Observability for systems with more outputs than inputs and asymptotic observers

Both authors are partly supported by: NSERC GRANT OGP 0036498     

Some questions related to modeling in cellular biology

Several years ago, we decided to switch our main focus of interest toward the field of modeling cellular biology. Several reasons motivated this move: first cellular and molecular biology offer a fantastic new source of physical and mathematical problems. Second, to understand the function of cellular microdomains, modeling and computer simulations are necessary tools to organize and structure experimental observations. We review here some questions we have started to address.     

Partial Star Products: A Local Covering Approach for the Recognition of Approximate Cartesian Product Graphs

This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local approach that covers a graph by small subgraphs, so-called partial star products, and then utilizes this information to derive the global factors and an embedding of the graph under investigation into Cartesian product graphs.