Koplienko Trace Formula

Koplienko (Sib Math J 25(5): 735–743, 1984) gave a trace formula for perturbations of self-adjoint operators by operators of Hilbert–Schmidt class ${\mathcal{B}_2(\mathcal{H})}$ . Recently Gesztesy et?al. (Basics Z Mat Fiz Anal Geom 4(1):63–107, 2008) gave an alternative proof of the trace formula when the operators involved are bounded. In this article, we give a still another proof and extend the formula for unbounded case by reducing the problem to a finite dimensional one as in the proof of Krein trace formula by Voiculescu (On a Trace Formula of M. G. Krein. Operator Theory: Advances and Applications, vol. 24, pp. 329–332. Birkhauser, Basel, 1987), Sinha and Mohapatra (Proc Indian Acad Sci (Math Sci) 104(4):819–853, 1994).     

Phenalenyl-based organozinc catalysts for intramolecular hydroamination reactions: a combined catalytic, kinetic, and mechanistic investigation of the catalytic cycle

Herein, we report the synthesis and characterization of two organozinc complexes that contain symmetrical phenalenyl (PLY)-based N,N-ligands. The reactions of phenalenyl-based ligands with ZnMe(2) led to the formation of organozinc complexes [N(Me),N(Me)-PLY]ZnMe (1) and [N(iPr),N(iPr)-PLY]ZnMe (2) under the evolution of methane. Both complexes (1 and 2) were characterized by NMR spectroscopy and elemental analysis. The solid-state structures of complexes 1 and 2 were determined by single-crystal X-ray crystallography. Complexes 1 and 2 were used as catalysts for the intramolecular hydroamination of unactivated primary and secondary aminoalkenes. A combined approach of NMR spectroscopy and DFT calculations was utilized to obtain better insight into the mechanistic features of the zinc-catalyzed hydroamination reactions. The progress of the catalysis for primary and secondary aminoalkene substrates with catalyst 2 was investigated by detailed kinetic studies, including kinetic isotope effect measurements. These results suggested pseudo-first-order kinetics for both primary and secondary aminoalkene activation processes. Eyring and Arrhenius analyses for the cyclization of a model secondary aminoalkene substrate afforded ΔH(≠) =11.3?kcal?mol(-1) , ΔS(≠) =-35.75?cal?K(-1) mol(-1) , and E(a) =11.68?kcal?mol(-1) . Complex 2 exhibited much-higher catalytic activity than complex 1 under identical reaction conditions. The in situ NMR experiments supported the formation of a catalytically active zinc cation and the DFT calculations showed that more active catalyst 2 generated a more stable cation. The stability of the catalytically active zinc cation was further supported by an in situ recycling procedure, thereby confirming the retention of catalytic activity of compound 2 for successive catalytic cycles. The DFT calculations showed that the preferred pathway for the zinc-catalyzed hydroamination reactions is alkene activation rather than the alternative amine-activation pathway. A detailed investigation with DFT methods emphasized that the remarkably higher catalytic efficiency of catalyst 2 originated from its superior stability and the facile formation of its cation compared to that derived from catalyst 1.     

Efficient catalytic cyclizations of three and two imine assemblies: direct access to tetrahydroimidazo[1,5-c]imidazol-7-ones and imidazoles

A cascade cyclization involving union of three imines by an organocatalyst proline is established to afford new fused-tetrahydroimidazo[1,5-c]imidazol-7-ones with excellent regio- and stereoselectivity. Another dehydrogenative cyclization by union of two imines is developed using the Cu(OTf)(2)-Ag(2)O combo catalyst to furnish functionalized imidazoles.     

Mixed protonic-electronic conduction and dielectric response in layered vanadyl phosphate nanocomposites

The layered vanadyl phosphate, VOPO(4)2H(2)O, is employed to prepare nanosized conducting polypyrrole by redox intercalation method. Transport and dielectric properties of various compositions have been investigated by impedance technique over a temperature range of 300-120 K. Grain boundary conductivity is larger than the bulk conductivity. The conductivity reveals a discontinuity at about 212-235 K. The conductivity is predominantly ionic at high temperature and electronic at low temperature. The dielectric spectra reveal a peak in the frequency range up to 2 MHz for higher concentration of intercalated polypyrrole. The activation energy of conductivity relaxation is different from that of total conductivity derived from the impedance plot.     

Growth of carbon nanofibers on aligned zinc oxide nanorods and their field emission properties

Carbon nanofibers were grown by electrodeposition technique onto aligned zinc oxide (ZnO) nanorods deposited by hybrid wet chemical route on glass substrates. X-ray diffraction traces indicated very strong peak for reflections from (0 0 2) planes of ZnO. The Raman spectra were dominated by the presence of G band at about 1597 cm⁻¹ corresponding to the E_2g tangential stretching mode of an ordered graphitic structure with sp² hybridization and a D band at about 1350 cm⁻¹ originating from disordered carbon. Fourier transformed infrared studies indicated the presence of a distinct characteristic absorption peak at ∼511 cm⁻¹ for Zn-O stretching mode. Photoluminescence spectra indicated band edge luminescence of ZnO at ∼3.146 eV along with a low intensity peak at ∼0.877 eV arising out of carbon nanofibers. Field emission properties of these films and their dependence on the CNF coverage on ZnO nanorods are reported here. The average field enhancement factor as determined from the slope of the FN plot was found to vary between 1 × 10³ and 3 × 10³. Both the values of turn-on field and threshold field for CNF/ZnO were lower than pure ZnO nanorods.     

One-Pot,Three-Component Cycloaddition of Nonstabilized Azomethine Ylides to β-Nitrostyrene,a Highly Electron Deficient Dipolarophile

A facile route to tetra-substituted pyrrolidines has been accomplished by 1,3-dipolar cycloaddition reaction. Several pyrrolidine compounds have significant biological activity. A highly electron-deficient dipolarophile, β-nitrostyrene, was reacted with nonstabilized azomethine ylides derived from aryl aldehyde and L-phenylglycine in dry dimethyl formanide. The structures and stereochemistry of the cycloadducts were established by infrared, NMR spectroscopy, and single-crystal x-ray crystallographic analyses.     

Halogen-Free Room-Temperature Brønsted Acidic Ionic Liquid [Hmim]+ HSO4 − as a Recyclable Green “Dual Reagent” Catalysis for the Synthesis of Triarylmethanes (TRAMs)

Abstract

The halogen-free Brønsted acidic ionic liquid methylimidazolium hydrogen sulfate ([Hmim]⁺ HSO₄ ^?) acts as a very efficient catalyst for the one-pot, two-component Baeyer condensation of a variety of aromatic aldehydes with dimethyl or diethyl aniline at room temperature. This “green” reagent behaves as both catalyst and solvent; that is, it exhibits “dual-reagent catalysis.” The room-temperature acidic ionic liquid could be recycled several times with almost no loss in the yield of the reaction. This is the first report of the Baeyer synthesis with a halogen-free ionic liquid.     

Resonance Raman spectroscopic study for radial vibrational modes in ultra‐thin walled TiO2 nanotubes

The study reports the observation of radial vibrational modes in ultra‐thin walled anatase TiO₂ nanotube powders grown by rapid breakdown anodization technique using resonant Raman spectroscopic study. The as‐grown tubes in the anatase phase are around 2–5 nm in wall thickness, 15–18 nm in diameter and few microns in length. The E_{g(ν1,ν5,ν6)} phonon modes with molecular vibrations in the radial direction are predominant in the resonance Raman spectroscopy using 325 nm He–Cd excitation. Multi‐phonons including overtones and combinational modes of E_{g(ν1,ν5,ν6)} are abundantly observed. Fröhlich interaction owing to electron–phonon coupling in the resonance Raman spectroscopy of ultra‐thin wall nanotubes is responsible for the observation of radial vibrational modes. Finite size with large surface energy in these nanotubes energetically favor only one mode, B_1g(ν4) with unidirectional molecular vibrations in the parallel configuration out of the three Raman modes with molecular vibration normal to the radial modes. Enhanced specific heat with increasing temperatures in these nanotubes as compared to that reported for nanoparticles of similar diameter may possibly be related to the presence of the prominent radial mode along with other energetic phonon mode. The findings elucidate the understanding of total energy landscape for TiO₂ nanotubes. Copyright © 2015 John Wiley & Sons, Ltd.     

Sulfated Galactans of Champia indica and Champia parvula (Rhodymeniales,Rhodophyta) of Indian Waters

Sulfated galactans of the red seaweed species Champia indica and Champia parvula of Indian waters were extracted and purified by ion exchange chromatography. These were characterized by infrared and ¹³C NMR spectroscopy as well as by GC-MS analysis of alditol acetate derivatives produced by reductive hydrolysis/acetylation of sulfated and desulfated and their methylated samples. The sulfated galactans of these Champia species contained alternating β-(1→3)-linked galactopyranosyl units with sulfation at the 2-position and α-(1→4)-linked galactopyranosyl units having sulfation at both the 2- and 3-positions. Other minor substitutions included 6-O-methyl ether of the β-(1→3)-linked galactose residues only in Champia parvula.