A simplified multidimensional integral

We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.     

Sharpening of Hilbert’s lemniscate theorem

In this paper, we extend Hilbert’s lemniscate theorem to touching systems of curves. The result allows finding sharp constants in Bernstein type inequalities. Supported by OTKA TS44782. Supported by NSF grant DMS-0097484 and by OTKA T/034323, TS44782.     

Higher order Peierls distortion of one-dimensional carbon skeletons

In some one-dimensional chains with metallic band structures the energetically most advantageous distortion opens an energy gap non-linear in the distortion. The absence of a linear Peierls effect is due to the symmetry of the degenerate pair of orbitals at the Fermi level: they do not interact directly in the distorted system. The effect provides a natural bridging of the one-dimensional polyacetylene (linearly Peierls-distorted) to the two-dimensional graphite (not distorted) carbon skeletons. The simple explanation bears some generality.     

Conformations of antipyrines

Reliable conformational energetics is essential in interpreting and predicting structures of molecular crystals. We provide a combined density functional theory (DFT)-structural database study, demonstrating that this combination can be used as a foundation for this purpose. A subtle problem of nitrogen pyramidalization is used as the example in antipyrines, a group of bioactive molecules. Nitrogen pyramidalization on the two adjacent sp(3) nitrogens directly affects the orientation of the methyl and phenyl substituents, which tend toward opposite sides of the heteroaromatic ring, affecting crystal packing. Accordingly, the overwhelming majority of the structures of antipyrines in the Cambridge Structural Database (CSD) are either nearly planar or have substituents on the opposite sides of the ring. Recent powder X-ray structures by Lemmerer et al. identified propyphenazone, an antipyrine, to have two substituents on the same side in an apparently sterically crowded conformation. We show that the new structure, although counterintuitive, is not an outlier on the conformational map. A distribution of the conformations of all antipyrines listed in the CSD is in good agreement with the computed conformational map. We also examine the role of the hysteretic property of the phenyl torsion in propyphenazone and its indirect effects on its overall conformation.     

Rapid analysis of isomeric exogenous metabolites by differential mobility spectrometry-mass spectrometry

The direct separation of isomeric glucuronide metabolites from propranolol dosed tissue extracts by differential mobility spectrometry-mass spectrometry (DMS-MS) with the use of the polar gas-phase chemical modifier acetonitrile was demonstrated. The DMS gas-phase separation was able to resolve the isomeric metabolites with separation times on the order of milliseconds instead of minutes which is typically required when using pre-ionization chromatographic separation methods. Direct separation of isomeric metabolites from the complex tissue extract was confirmed by implementing a high-performance liquid chromatography (HPLC) separation prior to the DMS-MS analysis to pre-separate the species of interest. The ability to separate isomeric exogenous metabolites directly from a complex tissue extract is expected to facilitate the drug development process by increasing analytical throughput without the requirement for pre-ionization cleanup or separation strategies.     

Bonds or not bonds? Pancake bonding in 1,2,3,5-dithiadiazolyl and 1,2,3,5-diselenadiazolyl radical dimers and their derivatives

Unusually long bonds or short intermolecular contacts occur in the title compounds reminiscent of pancake bonding. Pancake bonding interactions seem analogous to π-stacking interactions, but they display much shorter contact distances than normally seen in van der Waals (vdW) dimers. The interpretation of these SN and SeN containing structures has been an outstanding challenge for some time. The antibonding (π*) singly occupied molecular orbital (SOMO) of the radical is the source of two-electron multicenter bonding (2e/mc). Preferred conformations thus can be traced back to SOMO-SOMO overlap. We used several computational methods to understand the nature of pancake bonding in the title compounds including four wave function methods (WFT) and a dozen density functional theories (DFT) including empirical dispersion corrections. We used experimental data and high level CCSD(T)/6-311++G(d,p) and MRPT2/6-311++G(d,p) calculations for comparison. The analysis provided the interpretation a wealth of experimental data including conformational preferences of these SN and SeN containing radical dimers leading to a better overall understanding of pancake bonding. Analysis of the various components of the inter-radical interactions showed that SOMO-SOMO bonding interaction and dispersion interaction contribute to the binding energy and neither of these interactions alone is sufficient to bind the dimer. The dimer is predicted to show weak diradical character.     

Tracking unstable steady states and periodic orbits of oscillatory and chaotic electrochemical systems using delayed feedback control

Experimental results are presented on successful application of delayed-feedback control algorithms for tracking unstable steady states and periodic orbits of electrochemical dissolution systems. Time-delay autosynchronization and delay optimization with a descent gradient method were applied for stationary states and periodic orbits, respectively. These tracking algorithms are utilized in constructing experimental bifurcation diagrams of the studied electrochemical systems in which Hopf, saddle-node, saddle-loop, and period-doubling bifurcations take place.     

George Inzelt: a tribute on the occasion of his 75th birthday

Journal of Solid State Electrochemistry -