Hybridization in some macrocyclic polyacetylenes

The hybridization in several cyclic polyacetylene compounds has been calculated by the maximum overlap method, assuming planar and non-planar geometries of the molecules. In the planar configuration the hybrids describing the molecular skeleton deviate from the corresponding bond directions. We have a few “bent” bonds, but in contrast to the situation in small rings, here the deviation angles are negative, i.e., the hybrids point toward the inside of the ring. Non-planar structures in which acetylene groups are kept in a plane and CCH₂ or CH₂ groups are displaced out of the plane show less deviation from the bond directions of bent bonds. Furthermore, the deviation angles decrease with an increase in the out-of-plane displacement of methylene groups. Finally, when the angle of bending of the molecules approaches 50°, the deviation vanishes, predicting a puckered conformation for the molecules. Correlation between CC stretching vibration frequencies and the corresponding CC bond overlap is discussed.     

Enaminone‐Based Synthesis of Dipodazine Derivatives

A series of racemic dipodazine analogues 9 were prepared in 22–80% yield from (3Z,6RS)‐3‐[(dimethylamino)methylidene]‐6‐methyl‐1‐(phenylmethyl)piperazine‐2,5‐dione ( 7 ) (Scheme 1), which was prepared in four steps from (RS)‐alanine methyl ester hydrochloride. The preparation of nonracemic 7 from (S)‐alanine methyl ester hydrochloride failed, since the introduction of the enamino functionality at position 3 of the precursor 6 was accompanied by almost complete racemization.     

Synthesis and Transformation of Methyl 2‐(6‐Hydroxy‐2‐phenylpyrimidin‐4‐yl)acetate: Simple Preparation of Pyrimidines with Heterocyclic Substituents

A simple and efficient synthesis of four new substituted pyrimidines, compounds 9a – d , from the title compound 3 is described. Conversion of 3 to methyl (E)‐3‐(dimethylamino)‐2‐(6‐methoxy‐2‐phenylpyrimidin‐4‐yl)prop‐2‐enoate ( 4 ), followed by condensation with various dinucleophiles according to the ‘enaminone methodology’, afforded the target compounds 9 in medium‐to‐good yields.     

Electrochemical and Structural Characterisation of Dip-Coated Fe/Ti Oxide Films Prepared by the Sol-Gel Route

Thin solid films of mixed Fe/Ti oxide composition (Fe/Ti molar ratios: 0.5∶1, 1∶1, 1.5∶1) have been made from Fe(NO₃)₃ alcoholic solution to which Ti(OiPr)₄ was added. Films have been deposited by the dip-coating technique and heat-treated at 300°C and 500°C. Powders of Fe/Ti oxide heat-treated at 300°C are amorphous, while powders annealed at 500°C for 40 hours transformed to mixed rutile, pseudobrookite and hematite phases. The structure of the XRD amorphous films was identified with the help of near-normal reflection absorption (6°) (IRRA) and near-grazing incidence angle (NGIA) spectroscopy. NGIA FT-IR spectra of films are characterised with a single phonon mode appearing in the spectral range 600–950 cm⁻¹ which shifts with increasing Ti concentration from 675 cm⁻¹ (Fe₂O₃) to 904 cm⁻¹ (TiO₂) thus exhibiting one-mode behavior. Electrochemical investigations made with the help of cyclic voltammetry (CV) and chronocoulometry (CPC) performed in 0.01M LiOH and in 1M LiClO₄/propylene carbonate electrolytes revealed that films are able to uptake reversibly Li⁺ ions with a charge capacity (Q) per film thickness (d) in the range 0.1–0.26 mC/cm²nm and 0.06 mC/cm²nm, respectively. The temperature at which the films were prepared alters the rate of Li⁺ insertion which is faster for less compact films obtained at 300°C. In situ UV-VIS spectroelectrochemical measurements revealed that Fe/Ti oxide films bleached in the UV spectral region (300 nm<λ<450 nm) and colored in the VIS spectral region (450 nm<λ<800 nm), thus exhibiting mixed anodic and cathodic electrochromism.     

Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, II

We construct the intertwining operator superalgebras and vertex tensor categories for the superconformal unitary minimal models and other related models.

     

Junction of three quantum wires: restoring time-reversal symmetry by interaction

We investigate the transport of correlated fermions through a junction of three one-dimensional quantum wires pierced by a magnetic flux. We determine the flow of the conductance as a function of a low-energy cutoff in the entire parameter space. For attractive interactions and generic flux the fixed point with maximal asymmetry of the conductance is the stable one, as conjectured recently. For repulsive interactions and arbitrary flux we find a line of stable fixed points with vanishing conductance as well as stable fixed points with symmetric conductance (4/9)(e(2)/h).     

Probing electron-electron interaction in quantum Hall systems with scanning tunneling spectroscopy

Using low-temperature scanning tunneling spectroscopy applied to the Cs-induced two-dimensional electron system (2DES) on p-type InSb(110), we probe electron-electron interaction effects in the quantum Hall regime. The 2DES is decoupled from bulk states and exhibits spreading resistance within the insulating quantum Hall phases. In quantitative agreement with calculations we find an exchange enhancement of the spin splitting. Moreover, we observe that both the spatially averaged as well as the local density of states feature a characteristic Coulomb gap at the Fermi level. These results show that electron-electron interaction can be probed down to a resolution below all relevant length scales.