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.     

Dimers of Nineteen‐Electron Sandwich Compounds: Crystal and Electronic Structures,and Comparison of Reducing Strengths

The dimers of some Group 8 metal cyclopentadienyl/arene complexes and Group 9 metallocenes can be handled in air, yet are strongly reducing, making them useful n‐dopants in organic electronics. In this work, the X‐ray molecular structures are shown to resemble those of Group 8 metal cyclopentadienyl/pentadienyl or Group 9 metal cyclopentadienyl/diene model compounds. Compared to those of the model compounds, the DFT HOMOs of the dimers are significantly destabilized by interactions between the metal and the central C?C σ‐bonding orbital, accounting for the facile oxidation of the dimers. The lengths of these C?C bonds (X‐ray or DFT) do not correlate with DFT dissociation energies, the latter depending strongly on the monomer stabilities. Ru and Ir monomers are more reducing than their Fe and Rh analogues, but the corresponding dimers also exhibit much higher dissociation energies, so the estimated monomer cation/neutral dimer potentials are, with the exception of that of [RhCp₂]₂, rather similar (?1.97 to ?2.15 V vs. FeCp₂^+/0 in THF). The consequences of the variations in bond strength and redox potentials for the reactivity of the dimers are discussed.     

syn and anti conformations in 2‐hydroxy‐5‐[(E)‐(4‐nitrophenyl)diazenyl]benzoic acid and two related salts

The crystal structures of 2‐hydroxy‐5‐[(E)‐(4‐nitrophenyl)diazenyl]benzoic acid, C₁₃H₉N₃O₅, (I), ammonium 2‐hydroxy‐5‐[(E)‐phenyldiazenyl]benzoate, NH₄⁺·C₁₃H₉N₂O₃⁻, (II), and sodium 2‐hydroxy‐5‐[(E)‐(4‐nitrophenyl)diazenyl]benzoate trihydrate, Na⁺·C₁₃H₈N₃O₅⁻·3H₂O, (III), have been determined using single‐crystal X‐ray diffraction. In (I) and (III), the phenyldiazenyl and carboxylic acid/carboxylate groups are in an anti orientation with respect to each other, which is in accord with the results of density functional theory (DFT) calculations, whereas in (II), the anion adopts a syn conformation. In (I), molecules form slanted stacks along the [100] direction. In (II), anions form bilayers parallel to (010), the inner part of the bilayers being formed by the benzene rings, with the –OH and –COO⁻ substituents on the bilayer surface. The NH₄⁺ cations in (II) are located between the bilayers and are engaged in numerous N—H...O hydrogen bonds. In (III), anions form layers parallel to (001). Both Na⁺ cations have a distorted octahedral environment, with four octahedra edge‐shared by bridging water O atoms, forming [Na₄(H₂O)₁₂]⁴⁺ units.     

Low-energy electron diffraction and induced damage in hydrated DNA

Elastic scattering of 5-30 eV electrons within the B-DNA 5'-CCGGCGCCGG-3' and A-DNA 5'-CGCGAATTCGCG-3' DNA sequences is calculated using the separable representation of a free-space electron propagator and a curved wave multiple scattering formalism. The disorder brought about by the surrounding water and helical base stacking leads to a featureless amplitude buildup of elastically scattered electrons on the sugar and phosphate groups for all energies between 5 and 30 eV. However, some constructive interference features arising from diffraction are revealed when examining the structural waters within the major groove. These appear at 5-10, 12-18, and 22-28 eV for the B-DNA target and at 7-11, 12-18, and 18-25 eV for the A-DNA target. Although the diffraction depends on the base-pair sequence, the energy dependent elastic scattering features are primarily associated with the structural water molecules localized within 8-10 A spheres surrounding the bases and/or the sugar-phosphate backbone. The electron density buildup occurs in energy regimes associated with dissociative electron attachment resonances, direct electronic excitation, and dissociative ionization. Since diffraction intensity can be localized on structural water, compound H2O:DNA states may contribute to energy dependent low-energy electron induced single and double strand breaks.