Degree-regular triangulations of torus and Klein bottle

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.     

Theoretical study of unimolecular rearrangements of vinylidenes to acetylenes

The rearrangement of vinylidene to acetylene has been studied in detail by the density functional method, using Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Parr. The rearrangement of the anion, as well as that of fluoro‐substituted systems, has also been investigated, in order to determine the effect of fluorine substitution on the activation barrier to the 1,2‐hydrogen shift, as well as the relative migratory aptitudes of hydrogen and fluorine. Natural bond orbital analysis is invoked to gain insight into the mechanisms of the rearrangements. Basis size effects are also discussed, particularly in relation to anionic systems. The need to include diffuse functions in geometry optimizations of anionic systems is reinforced by the present calculations. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Mirror image nanostructures

Chiral molecules that self-assemble to form chiral supramolecular structures exhibit interesting structural features reminiscent of tertiary and quaternary structures of proteins and have applications in catalysis and nonlinear optics. Often, these structures are hierarchical, with their chiral structure difficult to interpret on the molecular scale. In this communication, we observe chiral assembling molecules that form well-defined helices with a pitch of 28 nm. We observe the behavior in both R- and S-enantiomers of the molecule, forming mirror image nanostructures. The molecular chirality is determined by the dimethyloctyl alkyl coil of the molecule and is located more than 4 nm from the hydrogen-bonding segment. The nanostructures observed are not hierarchical, which could be a result of the significant separation between the stereocenter and hydrogen-bonding dendron. The subtle structural modification at the periphery of the molecule biases the supramolecular assembly, which is driven primarily by strong hydrogen-bonding and pi-pi stacking interactions.     

Palladium(II) complexes of aliphatic amines and their oxidation by chloramine‐T in perchloric acid medium

The formation of palladium(II) complexes with aliphatic amines and their oxidation by chloramine‐T in perchloric acid medium has been studied. The spectrophotometric studies showed the formation of 1:1 and 1:2 complexes between palladium(II) and amine in absence of HClO₄. An increase in [HClO₄] in reaction mixture suppresses the complex formation and in presence of [HClO₄] ～10^?3 mol dm^?3 only a 1:1 complex between palladium(II) and amine has been observed. The effect of Cl^? on the complex formation has also been studied. Palladium(II)‐catalyzed oxidation of these amines by chloramine‐T showed a first‐order dependence of rate with respect to each—oxidant, substrate, catalyst, and H⁺. The mechanism consistent with kinetic data for the oxidation process has been proposed in absence as well as in presence of initial [Cl^?]. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 603–612, 2002     

NMR spectroscopic study of the inclusion complex of desloratadine with β-cyclodextrin in solution

Desloratadine (DES) is an antihistamine used in the treatment of allergies and chronic urticaria. ¹H NMR spectroscopic study of varying ratios of DES and β-Cyclodextrin (β-CD) in D₂O suggests the formation of a 1:1 inclusion complex formed by the penetration of Cl-substituted aromatic ring into the β-CD cavity. The stoichiometry and binding constant of the complex were determined by Scott’s method.     

Enantioselective separation on a naturally chiral surface

Kinked-stepped, high Miller index surfaces of metal crystals are chiral and, therefore, exhibit enantiospecific properties. Previous temperature-programmed desorption (TPD) spectra have shown that the desorption energies of R-3-methylcyclohexanone (R-3-MCHO) on the chiral Cu(643)(R) and Cu(643)(S) surfaces are enantiospecific (J. Am. Chem. Soc. 2002, 124, 2384). Here, a comparison of the TPD spectra from Cu(111), Cu(221), Cu(533), Cu(653)(R&S), and Cu(643)(R&S) surfaces reveals that the enantiospecific desorption occurs from the chiral kink sites on the Cu(643) surfaces. Titration of the chiral kink sites with I atoms confirms this assignment of desorption features in the TPD spectra. Finally, the enantiospecific difference in the desorption energies of R- and S-3-MCHO has been used as the basis for demonstration of an enantioselective, kinetic separation of racemic 3-MCHO into its purified components during adsorption and desorption on the Cu(643)(R&S) surfaces.     

Complexation of Fluvastatin Sodium with β-Cyclodextrin: NMR Spectroscopic Study in Solution

¹H NMR spectroscopic study of fluvastatin sodium (FLU), β-Cyclodextrin (β-CD) and their mixtures confirmed the formation of FLU/β-CD inclusion complex in solution. The stoichiometry of the complex was determined to be 1:1 and the overall binding constant (K _s) was calculated to be 340 M⁻¹. Two dimensional COSY, ROESY and DEPTO experiments were performed for the unambiguous assignment of aromatic proton resonances and it was found that two isomeric forms of FLU are present in solution. It was confirmed with the help of ROESY spectral data that only F-substituted aromatic ring penetrates the β-CD cavity and there is chiral differentiation by the β-CD as one of the isomer binds more strongly, which is indicated by the intensity of correlation peaks. The mode of penetration of the guest into the β-CD cavity was also established and structure of the complex has been proposed.     

Enantioselective synthesis of (R)-phenylephrine hydrochloride

An efficient method for the synthesis of enantiomerically pure (R)-phenylephrine hydrochloride 1 is described using a Sharpless asymmetric dihydroxylation as the key step.     

Oxidation of lysine by ferricyanide in presence of osmium(VIII)

Osmium(VIII) catalysed oxidation of lysine by ferricyanide in excess ferrocyanide shows a complex kinetics. The order in lysine falls, from 1 to 0 while that in ferricyanide increases from 0 to 2 with large increase in lysine concentration. The rates were directly proportional to [Os(VIII)] and {Const.+[Fe(CN) ₆ ⁴ ]}. A suitable mechanism is proposed and discussed.

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Oxidation von lysin mittels ferricyanid in der gegenwart von osmium(VIII)

Zusammenfassung Die von Os(VIII) katalysierte Oxidation von Lysin mit Ferricyanid in überschüssigem Ferrocyanid zeigt eine komplexe Kinetik. Bei starker Steigerung der Lysinkonzentration fällt die Ordnung bezüglich Lysin von 1 auf 0, während bezüglich Ferricyanid eine Erhöhung, von 0 auf 2 festzustellen ist. Die Geschwindigkeitskonstanten waren direkt proportional zu [Os(VII)] und {Const.+[Fe(CN) ₆ ⁴ ]}. Es wird ein möglicher Mechanismus vorgeschlagen und diskutiert.

     

Role of palladium in the redox electrochemistry of ferrocene monocarboxylic acid encapsulated within ORMOSIL networks

We report herein the effect of palladium on the redox electrochemistry of ferrocene monocarboxylic acid encapsulated within an organically modified sol-gel glass network (ORMOSIL). It has been found that amount of palladium and its geometrical distribution significantly alter the redox electrochemistry of FcMCA. The geometrical distribution of palladium has been controlled by two methods: (i) palladium is allowed to link within nanostructured network of the ORMOSIL which was subsequently availed from the reactivity of palladium chloride and trimethoxysilane; (ii) palladium powder is encapsulated together FcMCA thus allowing the presence of palladium within the nanoporous domain. The content of palladium is varied by controlling the reaction dynamics of palladium chloride and trimethoxysilane interaction. For this we initially allowed to trigger hydrolysis, condensation and poly-condensation of trimethoxysilane and dimethyldiethoxysilane in acidic medium and subsequently partially dried ORMOSIL film was allowed to interact with palladium chloride. Even with partially dried ORMOSIL derived from trimethoxysilane and dimethyldiethoxysilane undergoes rapid interaction with palladium chloride and the transparent color of ORMOSIL changed to a black colour due to the formation of palladium silicon linkage. The palladium-silicon linkage has been identified by NMR, UV-VIS and transmission electron spectroscopy. The electrochemistry of FcMCA encapsulated within such an ORMOSIL matrix has been studied. Excellent redox electrochemistry of ferrocene monocarboxylic acid having peak potential separation tending to 0 for a multilayered electrode was investigated. The palladium content has been found to affect the redox electrochemistry of ferrocene as well as electrocatalytic efficiency of new ORMOSIL material. The electroanalysis of NADH is reported. The modified electrode is very sensitive to NADH with lowest detection limit of < 1 microM.