Theoretical analysis of solvent effects on nitrogen NMR chemical shifts in oxazoles and oxadiazoles

Using quantum chemistry methods we have evaluated the solvent effects on the ¹⁴N NMR chemical shifts in five oxa- and oxadiazoles dissolved in twelve solvents. These solvents differ in their polarity with the dielectric constants varying from 2 to 80. Moreover, three of them have a hydrogen-bond donor character. All possible hydrogen-bonding in the water solution with the oxygen and nitrogen (hydrogen-acceptor) centers in oxazoles (2) and oxadiazoles (3) have been considered in our studies. It has been shown that both the pure solvent and hydrogen-bonding effects are significant and result in ¹⁴N magnetic shielding increase. In water solutions the pure solvent effect is larger than the hydrogen-bonding effect. In addition, the solvent effect has been analyzed in terms of its direct and indirect contributions. It should be emphasized that our theoretical results for ¹⁴N chemical shifts in oxa- and oxadiazoles remain in a very good agreement with the accurate experimental data.     

Error bounds for non-selfadjoint PDE eigenvalue problems

We introduce a posteriori bounds for the eigenfunctions (eigenvalues) of non-selfadjoint diagonalizable PDE-eigenvalue problems which incorporates an inexact solution of the corresponding generalized matrix eigenvalue problem. The estimates combine the standard perturbation results with the saturation assumption for the eigenfunctions. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Maximum principles and nonexistence results for radial solutions to equations involving p‐Laplacian

We obtain the variant of maximum principle for radial solutions of, possibly singular, p‐harmonic equations of the form as well as for solutions of the related ODE. We show that for the considered class of equations local maxima of |w| form a monotone sequence in |x| and constant sign solutions are monotone. The results are applied to nonexistence and nonlinear eigenvalue problems. We generalize our previous work for the case h≡0. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive solution of elliptic PDE-eigenvalue problems.

In this paper we introduce a new adaptive algorithm (AFEMLA) for elliptic PDE-eigenvalue problems. In contrast to other approaches the algebraic eigenvalue problem does not have to be solved to full accuracy. We incorporate the iterative solution of the resulting finite dimensional algebraic eigenvalue problems in the adaptation process in order to balance the cost with the costs for the iterative eigenvalue method. We present error estimates that incorporate the discretization errors, approximation errors in the eigenvalue solver and roundoff errors. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular and supramolecular helicity induction in trityl group-containing compounds: The case of chiral 3,3,3-triphenylpropionic acid derivatives

The process of dynamic chirality transmission from permanent chirality element to stereodynamic triphenylmethyl group placed in the distance of 4 bonds, has been studied for series of optically active 3,3,3-triphenylpropionic acid derivatives. Structural analysis, carried out with the use of complementary methods and supported by theoretical calculations, enabled us to determine the mechanism of chirality transmission. The observed chirality transfer phenomenon, demonstrated unequivocally as raising of non-zero Cotton effects in the region of UV absorption of trityl group, is a cascade process driven by weak intramolecular interactions. Despite the much larger inductor-effector distance, the sensitivity in chirogenesis is comparable to other stereodynamic probes reported so far. In the crystalline phase, the combination of trityl group with amino acid moiety results in the formation of helical superstructures, where individual molecules are held together by hydrogen bonding cascades. The proper combination of functionalities in the molecule skeleton allows, to some extent, the control over the association process and authorizes determination of the trityl group as the supramolecular synthon.     

Heterolepic β-Ketoiminate Zinc Phenoxide Complexes as Efficient Catalysts for the Ring Opening Polymerization of Lactide

Zinc phenoxide complexes L¹ZnOAr 1 – 4 (L¹=Me₂NC₂H₄NC(Me)CHC(Me)O) and L²ZnOAr 5 – 8 (L²=Me₂NC₃H₆NC(Me)CHC(Me)O) with donor-functionalized β-ketoiminate ligands (L^1/2) and OAr substituents (Ar=Ph 1 , 5 ; 2,6-Me₂-C₆H₃ 2 , 6 ; 3,5-Me₂-C₆H₃ 3 , 7 ; 4-Bu-C₆H₄ 4 , 8 ) with tuneable electronic and steric properties were synthesized and characterized. 1 – 8 adopt binuclear structures in the solid state except for 5 , while they are monomeric in CDCl₃ solution. 1 – 8 are active catalysts for the ring opening polymerization (ROP) of lactide (LA) in CH₂Cl₂ at ambient temperature and the catalytic activity is controlled by the electronic and steric properties of the OAr substituent, yielding polymers with high average molecular weight (M_n) and moderately controlled molecular weight distribution (MWDs). 1 and 5 showed a living polymerization character and kinetic studies on the ROP of L–LA with 1 and 5 proved first order dependencies on the monomer concentration. Homonuclear decoupled ¹H-NMR analyses of polylactic acid (PLA) formed with rac-LA proved isotactic enrichment of the PLA microstructure.     

The Influence of Two‐Dimensional Organization on Peptide Conformation

Molecular crowding plays a significant role in regulating molecular conformation in cellular environments. It is also likely to be important wherever high molecular densities are required, for example in surface‐phase studies, in which molecular densities generally far exceed those observed in solution. Using on‐surface circular dichroism (CD) spectroscopy, we have investigated the structure of a synthetic peptide assembled into a highly packed monolayer. The immobilized peptide undergoes a structural transition between α‐helical and random coil conformation upon changes in pH and ionic concentration, but critically the threshold for conformational change is altered dramatically by molecular crowding within the peptide monolayer. This study highlights the often overlooked role molecular crowding plays in regulating molecular structure and function in surface‐phase studies of biological molecules.     

Performance evaluation of a rapid-scanning quadrupole mass spectrometer in the comprehensive two-dimensional gas chromatography analysis of pesticides in water

The performance of a novel rapid-scanning (20,000 amu/s) quadrupole mass spectrometer (qMS) has been evaluated in the comprehensive 2-D gas chromatography (GC×GC) analysis of pesticides contained in water. Analyte extraction was performed by using direct solid-phase microextraction (SPME). The MS system was operated using a rather wide m/z 50-450 mass range and a 33 Hz spectral production rate, a frequency which was found sufficient for reliable quantification. The qMS performance was evaluated considering: (i) number of data points per peak, (ii) mass spectral quality, (iii) extent of peak skewing, and (iv) consistency of retention times. Seven-point calibration curves (external calibration) were constructed for 28 pesticides over the limit of quantification range of 100 μg/L (1, 5, 10, 25, 50, and 100 μg/L). The solid-phase microextraction-GC×GC-qMS method was validated by calculating limits of detection and quantification, intraday peak area precision, accuracy, and intraday retention-time precision. A series of tap water samples were subjected to analysis, fortunately giving negative results.