Mittelwertbildung und Reihentransformation

Ohne Zusammenfassung     

Über Symmetrisierung konvexer Gebilde

Ohne Zusammenfassung     

Untersuchungen über Perylen und seine Derivate

Ohne ZusammenfassungDie Mikroanalysen wurden im Institut für pharmazeutische Chemie von Herrn Dr.Fritz Stimler durchgeführt.     

Über eine Klasse konvergenzerhaltender Integraltransformationen und den Äquivalenzsatz derC- undH-Verfahren

Ohne Zusammenfassung     

Photoredox reactions of Cr(III) mixed-ligand complexes

Irradiation of chromium(III) complexes with oxalate and pyridinedicarboxylate ligands (pda = 2,3-, 2,4-, or 2,5-dicarboxylate) leads to diverse behaviors, dictated by light energy, presence of oxygen and the ligand nature. Irradiation within the MC bands is unaffected by O₂ and results in ligand substitution. The LMCT excitation is effective only when oxalate is coordinated to Cr(III); then electron transfer from oxalate to central ion generates an intermediate, consisted of a Cr(II)species and the C₂O₄^? radicals. The species undergo fast redox reactions dependent on the presence of O₂ and the pda ligand.(1) In anoxic medium the fast outersphere electron transfer from Cr(II) to solvent, generates hydrated electrons and re-oxidizes the chromium centre to Cr^III. Then geminate recombination regenerates substrate, whereas competitive release of the C₂O₄^? radical leads to substitution of one oxalate ligand by two water molecules (aquation induced by the LMCT excitation). In the presence of the pda ligand the outersphere electron transfer is accompanied by the innersphere CT, generating Cr(III) coordinated to two radical ligands: C₂O₄^? and pda^3?; the intermediate releases also e_aq^?, but this reaction is slower than that of the homoleptic oxalate complex. Hydrated electrons are scavenged also by the released radicals. All these processes are completed within microseconds and in consequence, the Cr(III) complexes irradiated in deoxygenated solutions are insensitive to subsequent oxygenation.(2) When UV-irradiation is carried out in oxygenated medium reaction of Cr(II) species with molecular oxygen competes with the outer- or inner electron transfer observed in anoxic medium. Both these pathways result in generation of chromate(VI). Quantum yield of the Cr(VI) production is sensitive to the presence and structure of pda ligand, decreasing within the series 2,3-pda > 2,4-pda > 2,5-pda.     

Orbital relaxation and the third-order induction energy in symmetry-adapted perturbation theory

Theoretical investigations of the induction interaction between closed-shell molecules which fully account for the orbital relaxation effects are presented. Explicit expressions for the third-order induction energy in terms of molecular integrals and orbital energies are given and implemented within the sapt2008 program for symmetry-adapted perturbation theory (SAPT) calculations. Numerical investigations for the He–He, He–LiH, Ar–Ar, H₂–CO, H₂O–H₂O, and H₂O–NH₃ model dimers show that the orbital relaxation increases the third-order induction interaction by 15 to 50% at near-equilibrium geometries, with the largest effect observed for complexes involving highly polar monomers. At large intermonomer separations, the relaxed third-order induction energy perfectly recovers the difference $\delta E^{\rm HF}_{\rm int}$ between the Hartree–Fock interaction energy and the sum of the uncorrelated SAPT contributions through second order in the intermolecular interaction operator. At the near-equilibrium geometries, the sum of the relaxed third-order induction and exchange-induction energies reproduces, however, only a small fraction (6 to 15%) of $\delta E^{\rm HF}_{\rm int}$ for the nonpolar systems and about 40 to 60% for the polar ones. A comparison of the complete SAPT calculations with the coupled-cluster treatment with single, double, and noniterative triple excitations [CCSD(T)] suggests that the pure SAPT approach with all the available third-order corrections is more accurate for nonpolar systems while for the polar ones the hybrid approach including $\delta E^{\rm HF}_{\rm int}$ gives better results.     

Hydrogen bonds and local symmetry in the crystal structure of gibbsite

First‐principles quantum mechanical calculations of NMR chemical shifts and quadrupolar parameters have been carried out to assign the ²⁷Al MAS NMR resonances in gibbsite. The ²⁷Al NMR spectrum shows two signals for octahedral aluminum revealing two aluminum sites coordinated by six hydroxyl groups each, although the crystallographic positions of the two Al sites show little difference. The presence of two distinguished ²⁷Al NMR resonances characterized by rather similar chemical shifts but quadrupolar coupling constants differing by roughly a factor of two is explained by different character of the hydrogen bonds, in which the hydroxyls forming the corresponding octahedron around each aluminum site, are involved. The Al‐I site characterized by a C_Q = 4.6 MHz is surrounded by OH? groups participating in four intralayer and two interlayer hydrogen bonds, while the Al‐II site with the smaller quadrupolar constant (2.2 MHz) is coordinated by hydroxides, of which two point toward the intralayer cavities and four OH‐bonds are aligned toward the interlayer gallery. In high‐resolution solid‐state ¹H CRAMPS (combination of rotation and multiple‐pulse spectroscopy) four signals with an intensity ratio of 1:2:2:1 are resolved which allow to distinguish six nonequivalent hydrogen sites reported in the gibbsite crystal structure and to ascribe them to two types of structural OH groups associated with intralayer and interlayer hydrogen bonds. This study can be applied to characterize the gibbsite‐like layer—intergallery interactions associated with hydrogen bonding in the more complex systems, such as synthetic aluminum layered double hydroxides. Copyright © 2010 John Wiley & Sons, Ltd.     

Zur Theorie der Limitierungsverfahren

Ohne Zusammenfassung