A note on the Fourier coefficients of half-integral weight modular forms

In this note, we show that the algebraicity of the Fourier coefficients of half-integral weight modular forms can be determined by checking the algebraicity of the first few of them. We also give a necessary and sufficient condition for a half-integral weight modular form to be in Kohnen’s +-subspace by considering only finitely many terms.     

Convergent synthesis of panclicin-D via intramolecular SN2 displacement approach

A convergent enantioselective synthesis of panclicin-D has been reported from simple octanal using syn aldol reaction via intramolecular S_N2 displacement reaction for the first time towards the construction of anti-β-lactones in panclicin-D. The key steps involved are C-allylation, asymmetric aldolization under Crimmins condition, intramolecular S_N2 displacement, and Mitsunobu esterification reaction.     

Graphite epoxide

Oxidation of graphite may be carried out by reaction with meta-chloroperoxybenzoic acid to yield graphite epoxide. Scanning tunneling microscopy (STM) showed that the functionalization occurs at the edges rather than on the basal plane of the graphite. Quantification of the epoxide content is possible through the deepoxidation reaction using MeReO3/PPh3.     

Synthesis,crystal structures and fluorescence properties of two new di- and polynuclear Cd(II) complexes with N2O donor set of a tridentate Schiff base ligand

Two new Cd(II) complexes, having one binuclear structure [Cd₂(L)₂(Cl)₂] (1) and another azido bridged one-dimensional zig-zag polynuclear network [Cd₃(μ_1,1-N₃)₄(L)₂{H₂N(CH₂)₂N(C₂H₅)₂} · H₂O]_n (2) have been synthesized from a tridentate N₂O donor Schiff base ligand LH, [LH = (OCH₃)(OH)C₆H₃CHN(CH₂)₂N(C₂H₅)₂], which is the condensation product of 2-hydroxy-4-methoxybenzaldehyde and 2-diethylaminoethylamine. Both the complexes 1 and 2 have been characterized by elemental analyses, IR & ¹H NMR spectroscopy, TGA and fluorescence studies. Finally their structures have been established by single crystal X-ray diffraction method. Structural study reveals that in the complex 1, two Cd(II) centers are held together by two μ₂-phenolato oxygen atoms and the terminal chlorine atom occupies the apical site of the square pyramidal environment of each metal center. In case of complex 2, the trinuclear asymmetric unit contains octahedral Cd(II) centers which are further held together by doubly end-on azido bridging to form a zig-zag polynuclear structure. It also displays intraligand ¹(π–π^∗) fluorescence and can potentially serve as photoactive material.     

Synthesis and properties of umbelliferone-nitroxide radical hybrid compounds as fluorescence and spin-label probes

Two hybrid compounds 6 and 7, linked via an ester-bond between the 7-hydroxyl residue of an umbelliferone 1 and a carboxylic acid residue of two nitroxide radicals 3 and 4, and one hybrid compound 8, linked via an ester-bond between a 3-carboxylic acid residue of umbelliferone 2 and a hydroxyl residue of nitroxide radical 5, were synthesized in good yields, and their fluorescence and ESR spectra before and after the addition of l-ascorbic acid sodium salt in PBS (pH 7.0) were measured. The ESR intensities of 6 and 7 were proportionally reduced after the addition of ascorbic acid sodium salt, and their fluorescence intensities were increased maximally by eight- and nine-fold, respectively. However, the fluorescence intensity of 8 was essentially unchanged.     

Two Zn(II) and one Mn(II) complexes using two different hydrazone ligands: spectroscopic studies and structural aspects

Three new coordination complexes of Zn(II) and Mn(II) have been synthesised using two different tridentate N,N,O donor hydrazone ligands, Hpbh and Hacpbh respectively. The complexes [Zn(pbh)₂] (1) and [Zn(acpbh)₂] (2) have been synthesized by the treatment of ZnSO₄ · 7H₂O with Hpbh and Hacpbh hydrazone ligands, respectively. The Mn(II) complex [Mn(acpbh)₂] (3) was obtained on reacting Mn(NO₃)₂ · 4H₂O with the ligand Hacpbh. The ligands Hpbh and Hacpbh were prepared by condensing pyridine-2-carboxaldehyde and 2-acetylpyridine with benzhydrazide respectively. Inspite of varying the carbonyl functionality attached to the pyridine moiety present in the hydrazone ligands in both the Schiff bases, we obtained three mononuclear complexes 1, 2, and 3 which were clearly characterized from single crystal X-ray diffraction studies. Spectroscopic investigations like IR and UV/Vis have been carried out for 1, 2, and 3. Fluorescence studies have been performed for 1 and 2. For 3 cyclic voltammetry, room temperature magnetic study and EPR measurements have been recorded.     

Understanding local electrophilicity/nucleophilicity activation through a single reactivity difference index

A local reactivity difference index R(k) is shown to be able to predict the local electrophilic and/or nucleophilic activation within an organic molecule. Together with the electrophilic and/or nucleophilic behavior of the center k given by the sign, the magnitude of the R(k) index accounts for the extent of the electronic activation, a behavior that allows for the use of the R(k) index as a measure of the molecular reactivity especially in polar processes.     

Ligating properties of a potentially tetradentate Schiff base [(CH3)2NCH2CH2N=CHC6H3(OH)(OMe)] with zinc(II), cadmium(II), cobalt(II), cobalt(III) and manganese(III) ions: synthesis and structural studies

A series of Zn(II), Cd(II), Co(II), Co(III) and Mn(III) complexes with the Schiff base [(CH3)2NCH2CH2N=CHC6H3(OH)(OMe)], LH, derived from 2-dimethylaminoethylamine and o-vanillin, has been synthesised and structures of all the products have been established by X-ray crystallography. In the cases of zinc and cadmium, dimeric complexes [Zn(LH)2(NCS)] [Zn2(L)(mu(1,1)-CH3COO)(NCS)3] (1), [Cd2(L)2(Cl)2] (2) and [Cd2(L)2(NCS)2] (3), and for cobalt and manganese, monomeric complexes [Co(LH)2(NCS)]2 [Co(NCS)4] (4), [Co(LH)2(NCS)]ClO4 (5), [Co(L)(N3)(o-vanillinate)] x 0.5 MeOH (6) and [Mn(LH)2(MeOH)2](ClO4)3 (7), are formed with various terminal ligands. All the complexes have been characterised by elemental analysis and IR spectra. UV-Vis and NMR spectroscopy, magnetic, and electrochemical studies, were also carried out where feasible. The Schiff base functions as a bi-, tri- or tetra-dentate chelating agent and coordinates via the protonated or deprotonated phenolic oxygen, amine and imine nitrogens, and only in case of 1 with the methoxy oxygen atoms, to the metal ion leading to the formation of mono- or bi-metallic complexes.     

Surface area measurement of functionalized single-walled carbon nanotubes

Single-walled carbon nanotubes have been functionalized and the specific surface areas of the functionalized nanotubes measured. Contrary to expectations, functionalization leads to a decrease in specific surface area compared to that of the unfunctionalized nanotubes. Treatment with a concentrated 1:1 nitric/sulfuric acid mixture followed by high-temperature baking at 1000 degrees C was found to increase the specific surface area of the nanotubes. For the unfunctionalized SWNTs, this treatment increases the specific surface area (SSA) by 20%. In the case of SWNTs functionalized by n-butyl groups the increase in the SSA was nearly 2-fold with the value increasing from 410 (drying at 110 degrees C) to 770 m2/gm (acid and bake treatment followed by drying at 110 degrees C). For the ozonized SWNTs, the SSA increases more than 3-fold from 381 (drying at 110 degrees C) to 1068 m2/gm (acid and bake treatment followed by drying at 110 degrees C). SEM images indicate that the nanotubes rebundle in the solid state with an average bundle size of 10-30 nm. AFM studies show that the ozonized tubes have been cut to short bundles after ozonolysis. Hydrogen uptake studies carried out on the baked ozonized tubes led to a 3 wt % hydrogen uptake at 77 K and 30 bar.