Asymmetric synthesis of (R,S)- and (R,R)-4-hydroxy-5-(α-substituted)-hydroxymethyl[2.2]paracyclophane and derivatives by stereoselective addition to (R)-4-hydroxy-5-formyl[2.2]paracyclophane and derivatives

Highly diastereoselective nucleophilic addition reactions of organometallic reagents to formyl[2.2]paracyclophane derivatives which were ortho-substituted by hydroxy-, alkoxy- and trimethylsilyloxy-groups are reported. The absolute configuration of the newly formed secondary alcohols is assigned on the basis of the X-ray diffraction study as well as chemical correlation. The magnitude of the asymmetric induction and even the sense of chirality of the forming asymmetric carbon atoms of the alcohols depended on the nature of the ortho-substituents.     

Cyclosporins of Symmetry P21 – a Series of Clathrates

A series of isomorphous clathrates(cyclosporin A: solvent = 1 : 1) is reported. Thestructure of the tetrahydrofuran (1) anddibutylether (2) clathrates have been determinedby X-ray single crystal diffraction. The cyclosporinmolecules in both structures are associated via vander Waals interactions forming cavities occupied bysolvent molecules. The structure refinement based onroom-temperature data sets show significant disorderof the side chains of the cyclosporin A molecule withno adequate model of the solvent molecule in bothstructures. In contrast, the position of dibutyletherwas successfully localised using a low-temperaturedata set for 2.     

A Hypergraph Version of a Graph Packing Theorem by Bollobás and Eldridge

Two n‐vertex hypergraphs G and H pack, if there is a bijection such that for every edge , the set is not an edge in H. Extending a theorem by Bollobás and Eldridge on graph packing to hypergraphs, we show that if and n‐vertex hypergraphs G and H with with no edges of size 0, 1, and n do not pack, then either

1. one of G and H contains a spanning graph‐star, and each vertex of the other is contained in a graph edge, or
2. one of G and H has edges of size not containing a given vertex, and for every vertex x of the other hypergraph some edge of size does not contain x.

     

Pseudocompact Algebras and Highest Weight Categories

We develop a new approach to highest weight categories $\cal{C}$ with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasi-hereditary pseudocompact algebras. For $\cal{C}$ admitting a Chevalley duality, we define and investigate tilting modules and Ringel duals of the corresponding pseudocompact algebras. Finally, we illustrate all these concepts on an explicit example of the general linear supergroup GL(1|1).     

Performance of the spin-flip and multireference methods for bond breaking in hydrocarbons: a benchmark study

Benchmark results for spin-flip (SF) coupled-cluster and multireference (MR) methods for bond-breaking in hydrocarbons are presented. The nonparallelity errors (NPEs), which are defined as an absolute value of the difference between the maximum and minimum values of the errors in the potential energy along bond-breaking curves, are analyzed for (i) the entire range of nuclear distortions from equilibrium to the dissociation limit and (ii) in the intermediate range (2.5-4.5 A), which is the most relevant for kinetics modeling. For methane, the spin-flip and MR results are compared against full configuration interaction (FCI). For the entire potential energy curves, the NPEs for the SF model with single and double substitutions (SF-CCSD) are slightly less than 3 kcal/mol. Inclusion of triple excitations reduces the NPEs to 0.32 kcal/mol. The corresponding NPEs for the MR-CI are less than 1 kcal/mol, while those of multireference perturbation theory are slightly larger (1.2 kcal/mol). The NPEs in the intermediate range are smaller for all of the methods. The largest errors of 0.35 kcal/mol are observed, surprisingly, for a spin-flip approach that includes triple excitations, while MR-CI, CASPT2, and SF-CCSD curves are very close to each other and are within 0.1-0.2 kcal/mol of FCI. For a larger basis set, the difference between MR-CI and CASPT2 is about 0.2 kcal/mol, while SF-CCSD is within 0.4 kcal/mol of MR-CI. For the C-C bond breaking in ethane, the results of the SF-CCSD are within 1 kcal/mol of MR-CI for the entire curve and within 0.4 kcal/mol in the intermediate region. The corresponding NPEs for CASPT2 are 1.8 and 0.4 kcal/mol, respectively. Including the effect of triples by energy-additivity schemes is found to be insignificant for the intermediate region. For the entire range of nuclear separations, sufficiently large basis sets are required to avoid artifacts at small internuclear separations.     

pH-controlled photoinduced electron transfer in the [(Mo6Cl8)L6]-calix[4]resorcine-dimethylviologen system

A pH-controlled photoinduced electron transfer in the supramolecular system [(Mo(6)Cl(8))L(6)]-calix[4]resorcine-dimethylviologen is reported.     

Ore’s conjecture for k=4 and Grötzsch’s Theorem

A graph G is k-critical if it has chromatic number k, but every proper subgraph of G is (k?1)-colorable. Let f _k (n) denote the minimum number of edges in an n-vertex k-critical graph. In a very recent paper, we gave a lower bound, f _k (n)≥(k, n), that is sharp for every n≡1 (mod k?1). It is also sharp for k=4 and every n≥6. In this note, we present a simple proof of the bound for k=4. It implies the case k=4 of two conjectures: Gallai in 1963 conjectured that if n≡1 (mod k?1) then \(f_k (n)\tfrac{{(k + 1)(k - 2)n - k(k - 3)}} {{2(k - 1)}}\) , and Ore in 1967 conjectured that for every k≥4 and \(n \geqslant k + 2,f_k (n + k - 1) = f(n) + \tfrac{{k - 1}} {2}(k - \tfrac{2} {{k - 1}})\) . We also show that our result implies a simple short proof of Grötzsch’s Theorem that every triangle-free planar graph is 3-colorable.     

Cavity-Free Lasing and 2D Plasma Oscillations in Optically Excited InGaN Heterostructures

We demonstrate lasing emission of optically excited InGaN LD structures without intentional resonant cavity formation. We observe the equal mode-spacing character of this effect in the back-scattering geometry after exceeding the threshold excitation intensity. The homogeneity of the effect and stable mode spacing exclude participation of defects or wafer edges in lasing. We propose a lasing mechanism based on optically excited 2D electron–hole plasma oscillations, which act as a dynamical grating and resonantly couple the lasing modes separated by the plasma frequency, similar to the case of DFB lasers. The observed anomalous mode spacing is determined by the eigenfrequency of the plasma oscillations.     

Debundling of multiwalled carbon nanotubes in N,N-dimethylacetamide by polymers

Structure and properties of the dispersions of multiwalled carbon nanotubes (MWCNTs) in N,N-dimethylacetamide (DMAc) with different dispersing polymers: polyvinylpyrrolidone (PVP), poly(ethyleneoxide), triblock copolymers poly(ethyleneoxide)-b-poly(propyleneoxide)-b-poly(ethyleneoxide) (Pluronic F127 and Pluronic F108), ethylenediamine tetrakis(ethoxylate-b-propoxylate) tetrol, and ethylenediamine tetrakis(propoxylate-b-ethoxylate) tetrol (Tetronic) of different molecular weights were studied. All studied polymers were shown to be able to disperse MWCNT in DMAc, and MWCNT dispersions appear free of aggregates by visual inspection even after 3 months of keeping at room temperature. Dispersions were characterized by UV–VIS absorption spectroscopy and dynamic light scattering measurements. PVP was found to be the best dispersing polymer for MWCNT in DMAc. It was shown that the yield of the dispersed MWCNT and the average particle size of the MWCNT in DMAc depend on the chemical nature, molecular weight of the dispersing polymer, and solvent quality. The difference in dispersive capacity of the studied polymers is attributed to different dispersion mechanisms for PVP (“polymer wrapping” model) and for other studied dispersing polymers (“loose adsorption” model), which have different efficiencies in DMAc. It was revealed that an increase of dispersing polymer (PVP) concentration at the range of 4.7–37.6 g l^?1 results in an average particle size enlargement and MWCNT final concentration reduction.