Facts and artifacts about aromatic stability estimation

The stability of a set of 105 five-membered π-electron systems (involving aromatic, non-aromatic and anti-aromatic species) was evaluated using six isodesmic reactions of which two belong to the subclass of homodesmotic reactions, which are based on cyclic and acyclic reference systems. We demonstrate that the ‘Resonance Energies’ derived from isodesmotic schemes have obvious flaws and do not correct or cancel other contributions to the energy, such as the changes of hybridization, homoconjugation of heterosubstituted cyclopentadienes, conjugative interactions of CC or CX (X=N or P) with a π or pseudo π orbital at Y (Y=O, S, NH, PH), strain, etc. as effectively as possible. Likewise, ‘aromatic stabilization energies (ASE)’ derived from homodesmotic schemes based on the acyclic reference compounds do not give satisfactory results. We strongly recommend that only cyclic reference compounds should be used for ASE and other aromaticity evaluations. The analysis is based on ab initio optimized geometries at B3LYP/6-311+G^∗∗.     

Adsorption of organic substances on broken clay surfaces: a quantum chemical study

Hydrogen-bonded interactions between local defect structures on broken clay surfaces modeled as molecular clusters and the organic molecules acetic acid, acetate, and N-methylacetamide (NMA) have been investigated. Density functional theory and polarized basis sets have been used for the computation of optimized interaction complexes and formation energies. The activity of the defect structures has been characterized as physical or chemical in terms of the strength of the hydrogen bonds formed. Chemical defects lead to significantly enhanced interactions with stronger hydrogen bonds and larger elongation of OH bonds in comparison to the physical defects. The type of interaction with the defect structure significantly influences the planarity of the model peptide bond in NMA. Both cases, enhancement of the planarity by increase of the CN double bond character and strong deviations from planarity, are observed.     

Molybdenum(VI)-complexes with chiral N,O-ligands derived from carbohydrates: synthesis, structure and catalytic properties in asymmetric olefin epoxidation

Novel chiral 2′-pyridinyl alcohols derived from isopropylidene-protected carbohydrates are reported. They show different characteristics at the hydroxy group, but are all suitable ligands for chiral molybdenum(VI) complexes of the type MoO₂L₂ (L = chiral 2′-pyridinyl alcoholate). MoO₂(acac)₂ served as starting material in the complex syntheses. The structure of one ligand and one dioxo complex were exemplary established by X-ray crystallography. For catalytic runs in the enantioselective epoxidation catalysis trans-methylstyrene was used as model substrate, tert-butylhydroperoxide and cumolhydroperoxide, resp., as the oxidant.     

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Applications of capillary electrophoresis in element speciation analysis of plant and food extracts

The performance of a new separation technique for metal-speciation — capillary electrophoresis (CE) — is presented. Polyhydroxy compounds such as polyphenols and organic tanning agents can be determined in the g/L range. Certain complexes of these compounds with iron (III) ions may also be directly or indirectly verified. The work has shown that it is possible to determine certain complexes existing in beverages (tea and coffee) by decomplexation with chelating agents (CDTA). The ligands released can be separated by CE and identified by their migration time and UV/VIS absorption spectra.     

The finite section method for Moore-Penrose inversion of Toeplitz operators

It is shown that for certain classes of infinite block Toeplitz matricesT(a)=[a _j-k ] ₀ the Moore-Penrose inverses of the finite sectionT _n (a)=[a _j-k ] ₀ ^n–1 converge to the Moore-Penrose inverse ofT(a). Furthermore the convergence for modified finite section methods and the finite section method for Wiener-Hopf integral and related operators are studied.     

Local Borel summability of Euclidean 311-1311-1311-1a simple proof via differential flow equations

It is shown how the differential flow equation (or, equivalently, the continous renormalization group) method can be employed to give an astonishingly easy proof of the local Borel summability of the renormalized perturbative Euclidean massive ₄ ⁴ .Supported by NSF grant # DMS-9100383     

Structural phase transitions in ‘hcp’ C70 single-crystals

The thermal expansion of vapor-grownC ₇₀ single crystals ahs been investigated using high-resolution capacitance dilatometry from 5–380 K. Measurements were made both parallel and perpendicular to the hexagonalc-axis. Three first-order phase transitions which we associate with the consecutive disordering of theC ₇₀ molecules are observed upon heating at 280 K (long-axis spinning), 300 K (long-axis precession) and 355 K (quasi-free rotation), respectively. The highest-temperature transition exhibits a very large (50 K) thermal hysteresis. Powder and single-crystal X-ray diffraction show that the crystals are predominantly hexagonal-close-packed (HCP) with an idealc/a1.63 above 360 K andc/a1.84 at 295 K.     

Hubbard-like models in high spatial dimensions

The present paper studies the properties of Hubbard-like models in high spatial dimensionsD. In a first par the limit of infinite dimension and its main features-i.e.i) the mapping onto a generalized atomic model with an additional auxiliary field andii) the validity of the local approximation for the self-energy-are worked out in a systematic (1/D)-expansion. Since the hopping matrix elements have to be properly scaled with the dimensionD, the (1/D)-expansion is also an expansion in the hopping amplitude. Thus for small hopping theD-limit may serve as a proper approximation for finite-dimensional systems. The second part of the paper adopts the hybridisation-perturbation theory of the single impurity Anderson model in order to construct a perturbation theory for the auxiliary field of the generalized atom which can also be interpreted as an expansion in the hopping amplitude. The non-crossing approximation (NCA) is used to study the antiferromagnetic phase transtion of theD-Hubbard model in the case of half filling: the critical temperature, the antiferromagnetic order parameter and the free energy of the lattice system are calculated. The NCA-results are in quite good agreement with recent results from the imaginary-time discretisation method.