Characterization of asymptotic distribution functions of ratio block sequences

In this paper we give necessary and sufficient conditions for the block sequence of the set X = {x ₁ < x ₂ < … < x _n < …} ⊂ ℕ to have an asymptotic distribution function in the form x ^λ.     

Imidazolium-tagged ferrocenyl diphosphanes in allylic substitution with heteroatom nucleophiles

Imidazolium-tagged ferrocenyl diphosphanes are useful ligands in palladium-catalyzed allylic substitutions with heteroatom nucleophiles. Substitution with phthalimide proceeds with high enantioselectivity (up to 92% ee) in various ionic liquids. Reaction with p-cresol as nucleophile affords allylation product in up to 62% ee, while using tolylsulfinate as a nucleophile gives a product with very little or no enantioselectivity. Under these reaction conditions, catalyst recyclability is challenging, and decrease in activity as well as enantioselectivity was observed.     

Analysis of NH3-TPD Profiles for CuSSZ-13 SCR Catalyst of Controlled Al Distribution – Complexity Resolved by First Principles Thermodynamics of NH3 Desorption,IR and EPR Insight into Cu Speciation**

NH₃ temperature-programmed desorption (NH₃-TPD) is frequently used for probing the nature of the active sites in CuSSZ-13 zeolite for selective catalytic reduction (SCR) of NO_x. Herein, we propose an interpretation of NH₃-TPD results, which takes into account the temperature-induced dynamics of NH₃ interaction with the active centers. It is based on a comprehensive DFT/GGA+D and first-principles thermodynamic (FPT) modeling of NH₃ adsorption on single Cu²⁺, Cu⁺, [CuOH]⁺ centers, dimeric [Cu-O-Cu]²⁺, [Cu-O₂²⁻-Cu]² species, segregated CuO nanocrystals and Brønsted acid sites (BAS). Theoretical TPD profiles are compared with the experimental data measured for samples of various Si/Al ratios and distribution of Al within the zeolite framework. Copper reduction, its relocation, followed by the intrazeolite olation/oxolation processes, which are concomitant with NH₃ desorption, were revealed by electron paramagnetic resonance (EPR) and IR. DFT/FPT results show that the peaks in the desorption profiles cannot be assigned univocally to the particular Cu and BAS centers, since the observed low-, medium- and high-temperature desorption bands have contributions coming from several species, which dynamically change their speciation and redox states during NH₃-TPD experiment. Thus, a rigorous interpretation of the NH₃-TPD profiles of CuSSZ-13 in terms of the strength and concentration of the active centers of a particular type is problematic. Nonetheless, useful connections for molecular interpretation of TPD profiles can be established between the individual component peaks and the corresponding ensembles of the adsorption centers.     

Probing electronic and regioisomeric control in an asymmetric Henry reaction catalyzed by camphor-imidazoline ligands

Starting from (R)-camphordiamine, 13 new camphor-annulated imidazoline ligands are synthesized in good yields as two regioisomeric series. Yields of up to 94% and good enantioselectivities up to 67% are achieved for the copper(II)-catalyzed Henry reaction giving the product stereoselectively according to the regioisomer used.     

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Reaction of 3-chloroquinoline-2,4-diones with ethanolamine and rearrangement of the reaction products

The reaction of tertiary α-chloroketones with ethanolamine has not been hitherto described in the literature. Herein, we describe the reaction of tertiary 3-chloroquinoline-2,4-diones with ethanolamine to give novel 3-(2-hydroxyethylamino)quinoline-2,4-diones. These compounds provide 3-(2-oxooxazolidin-3-yl)quinoline-2,4(1H,3H)-diones and new compounds with dimeric character after reaction with triphosgene. Molecular rearrangement proceeds during the reaction of 3-(2-hydroxyethylamino)quinoline-2,4-diones with isocyanic acid. Three types of reaction products arise: 2-(2-hydroxyethyl)imidazo[1,5-c]quinazoline-3,5-diones, 3-(2-hydroxyethyl)-3,3a-dihydro-2H-imidazo[4,5-]quinoline-4(5H)diones and primarily 5-hydroxy-1-(hydroxyethyl)-1′H-spiro[imidazolidine-5,3′-indole]-2,2′-diones. The reaction mechanism and product stereochemistry are discussed. The ¹H, ¹³C and ¹⁵N NMR spectra of the prepared compounds were measured, and all resonances were assigned from appropriate two-dimensional experiments.     

Detecting quantum states with a positive Wigner function beyond mixtures of Gaussian states

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.     

Solvatochromism as an efficient tool to study N,N‐dimethylamino‐ and cyano‐substituted π‐conjugated molecules with an intramolecular charge‐transfer absorption

A representative data set has been gained by the measurement of the electronic absorption spectra of 12 systematically selected push–pull systems with an intramolecular charge‐transfer (CT) absorption and the general structure D–π–A (D = donor, A = acceptor) featuring electron‐withdrawing CN groups, electron‐donating N(CH₃)₂ groups, and various π‐conjugated backbones in 32 solvents with different polarities. The longest‐wavelength absorption maxima λ_max and the corresponding wavenumbers $\tilde {v}_{{\rm max}} $ were evaluated from the UV/Vis spectra measured in 32 well‐selected solvents. The D–π–A push–pull systems were further characterized by quantum‐chemical quantities and simple structural parameters. Structure–solvatochromism relationships were evaluated by multidimensional statistic methods. Whereas solvent polarizability and solvent cavity size proved to be the most important factors affecting the position of λ_max, the solvent polarity was less important. The most important characteristics of organic CT compounds are the energy of the LUMO, the permanent dipole moment, the COSMO (COnductor‐like Screening MOdel) area, the COSMO volume, the number, and ratio of N,N‐dimethylamino and cyano groups, and eventually the number of triple bonds (π‐linkers). A relation between the first‐order polarizability α, the longest‐wavelength absorption maxima λ_max, and the structural features has also been found. The higher‐order polarizabilities β and γ are not related to the observed solvatochromism. Copyright © 2010 John Wiley & Sons, Ltd.