A multiplier theorem for the sublaplacian on the Heisenberg group

A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory of g-functions.

Crystallographic identification of a ‘stepped-cubane’ structure for the Cu4O4 core in [Cu4L2(bipy)4(µ3-OH)2][ClO4]4(HL = 5-hydroxy-6-methylpyridine-,4-dimethanol, bipy = 2,2′-bipyridine)

The structure of [Cu4L2(bipy)4(µ3-OH)2][ClO4]4 containing a Vitamin B6 ligand, pyridoxine (5-hydroxy-6-methylpyridine-3,4-dimethanol, HL), and 2,2′-bipyridine (bipy) has been determined by single-crystal X-ray analysis. This is the first report on a copper(II) complex having a ‘stepped-cubane’ structure. The compound crystallizes in the triclinic space group P[1 with combining macron](Z= 1) with a= 11.015(3), b= 11.902(1), c= 13.142(2)Å, α= 105.07(1), β= 102.22(1) and γ= 99.12(1)°; R= 0.054). The co-ordination geometry around each copper is trigonally distorted square pyramidal. Two of the basal sites are occupied by bipyridyl nitrogens in a bidentate fashion. The remaining basal positions for Cu(1) are filled by a phenolic oxygen and a 4-hydroxymethyl oxygen of the L moiety, whereas for Cu(2) they are occupied by two µ3-OH oxygens. The axial sites are occupied by a µ3-OH oxygen and the 4-hydroxymethyl oxygen of the same pyridoxine for Cu(1) and Cu(2), respectively. Both the bridging nature of the 4-hydroxymethyl oxygen of the L moiety and the unsymmetrical bridging nature of the µ3-OH groups with axial–equatorial bridging are novel features. The structure is discussed in relation to stepped-cubane structures reported in the literature. A comparative study is also made with µ3-hydroxo-bridged copper(II) complexes. Both the plasticity effect of CuII and the stacking interactions between the various rings appear to be important in stabilizing this unusual structure.

Organometallic derivatives of diphosphazanes. 2. Seven-coordinated Group 6 metal tricarbonyl complexes of diphosphazane ligands. X-ray crystal structure of [WI2(CO)3{P(OPh)2}2NPh]

The reactions of the complexes [MI2(CO)3-(NCMe)2] (M = Mo, W) with the diphosphazane ligands RN{P(OPh)2}2 (R = Me, Ph) in CH2Cl2 at room temperature afford new seven-coordinated complexes of the type [MI2(CO)3{P(OPh)2}2NR]. The molybdenum complexes are sensitive to air oxidation even in the solid state, whereas the tungsten complexes are more stable in the solid state and in solution. The structure of the tungsten complex [WI2(CO)3{P(OPh)2}2NPh] has been determined by single-crystal X-ray diffraction. It crystallizes in the orthorhombic system with the space group Pna 2(1), a = 19.372 (2) angstrom, b = 11.511 (1) angstrom, c = 15.581 (1) angstrom, and Z = 4. Full-matrix least-squares refinement with 3548 reflections (I > 2.5-sigma-(I)) led to final R and R(w) values of 0.036 and 0.034, respectively. The complex adopts a slightly distorted pentagonal-bypyramidal geometry rarely observed for such a type of complexes; two phosphorus atoms of the diphosphazane ligand, two iodine atoms, and a carbonyl group occupy the equatorial plane, and the other two carbonyl groups, the apical positions.

On Paley-Wiener Theorems for the Heisenberg Group

In this paper we prove two Paley-Wiener-type theorems for the Heisenberg group. One is for the group Fourier transform which is the analogue of the classical Paley-Wiener theorem. The other one is for the spectral projections associated to the sub-Laplacian

Stereochemistry of 2'-5' linked nucleic acids: crystal and molecular structure of ammonium adenylyl-2',5'-adenosine tetrahydrate: a core fragment of 2'-5' oligo A's produced by interferon induced adenylate synthetase

The preponderance of 3'-5' phosphodiester links in nucleic acids is well known. Albeit less prevalent, the 2'-5' links are specifically utilised in the formation of 'lariat' in group II introns and in the msDNA-RNA junction in myxobacterium. As a sequel to our earlier study on cytidylyl-2',5'-adenosine we have now obtained the crystal structure of adenylyl-2',5'-adenosine (A2'p5'A) at atomic resolution. This dinucleoside monophosphate crystallizes in the orthorhombic space group P2(1)2(1)2(1) with a = 7.956(3) A, b = 12.212(3) A and c = 36.654(3) A. CuK alpha intensity data were collected on a diffractometer. The structure was sloved by direct methods and refined by full matrix least squares methods to R = 10.8%. The 2' terminal adenine is in the commonly observed anti (chi 2 = 161 degrees) conformation and the 5' terminal base has a syn (chi 1 = 55 degrees) conformation more often seen in purine nucleotides. A noteworthy feature of A2'p5'A is the intranucleotide hydrogen bond between N3 and O5' atoms of the 5' adenine base. The two furanose rings in A2'p5'A show different conformations - C2' endo, C3' endo puckering for the 5' and 2' ends respectively. In this structure too there is a stacking of the purine base on the ribose O4' just as in other 2'-5' dinucleoside structures, a feature characteristically seen in the left handed Z DNA. In having syn, anti conformation about the glycosyl bonds, C2' endo, C3' endo mixed sugar puckering and N3-O5' intramolecular hydrogen bond A2'p5'A resembles its 3'-5' analogue and several other 2'-5' dinucleoside monophosphate structures solved so far. Striking similarities between the 2'-5' dinucleoside monophosphate structures suggest that the conformation of the 5'-end nucleoside dictates the conformation of the 2' end nucleoside. Also, the 2'-5' dimers do not favour formation of miniature classical double helical structures like the 3'-5' dimers. It is conceivable, 2-5(A) could be using the stereochemical features of A2'p5'A which accounts for its higher activity.

Synthesis, characterization, and thermal degradation studies on group VIA derived weak-link polymers

Polymers containing group VIA derived weak links, viz. poly(styrene disulfide) (PSD), poly- (styrene tetrasulfide) (PST), and poly(styrene diselenide) (PSDSE), have been synthesized. The polymers PSD and PST were characterized by NMR, IR, UV, TGA, and fast atom bombardment m w spectrometric (FABMS) techniques. The presence of different configurational sequences in PSD and PST were identified by *3C NMR spectroscopy. PSDSE, being insoluble in common organic solvents, was characterized using solid-state lac NMR (CP-MAS) spectroscopy. Thermal degradation of polymers under direct pyrolysis-mass spectrometric (DP-MS) conditions revealed that all the polymers undergo degradation through the weaklink scission. A comparative study of the pyrolysis products of these polymers with that of poly(styrene peroxide) (PSP) revealed a smooth transformation down the group with no monomer (styrene or oxygen) formation in PSP to only styrene and selenium metal in PSDSE. This trend of group VIA is explained from the energetics of the C-X bond (X = 0, S, and Se) which also seems to be important in addition to the weak X-X bond cleavage. In PSP and PSD, the behavior is also explained from the energetics of the alkoxy and thiyl radicals. The unique exothermic degradation in PSP compared to endothermic degradation in PSD and PSDSE is explained from the nature of the producta of degradation.

Synthesis, spectral characterisation and single-crystal structure of a bicyclic tetraphosphapentazane tetraoxide, N5P4ET5O4(OC6H3Me2-2,6)2

Reaction of the bicyclic phosphazane N5P4Et5Cl2 with 2,6-dimethylphenol and subsequent oxidation of the product by aqueous hydrogen peroxide yields N5P4Et5O4(OC6H3Me2-2,6)2 in 85% yield. Its structure has been established by NMR spectroscopy and single-crystal X-ray diffraction. The compound crystallises in the monoclinic space group C2/c with a= 21.245(5), b= 10.879(2), c= 16.450(6)Å, ?= 123.94(2)°, Z= 4, R= 0.066. The structural features are compared with those of bicyclic ?5-phosphazenes of type N5P4R3(NR1R2)5(NHR3)(R1,R3= Me or Et, R2= H or Me). The observed conformation of the N3P3 rings in the present compound is mainly dictated by the maximisation of the stabilising influence of �negative hyperconjugative interactions� between the nitrogen lone pairs and the adjacent P�X ?* orbitals.

Quantum Properties in Transport Through Nanoscopic Rings:Charge-Spin Separation and Interference Effects

Many of the most intriguing quantum effects are observed or could be measured in transport experiments through nanoscopic systems such as quantum dots, wires and rings formed by large molecules or arrays of quantum dots. In particular, the separation of charge and spin degrees of freedom and interference effects have important consequences in the conductivity through these systems. Charge-spin separation was predicted theoretically in one-dimensional strongly inter-acting systems (Luttinger liquids) and, although observed indirectly in several materials formed by chains of correlated electrons, it still lacks direct observation. We present results on transport properties through Aharonov-Bohmrings (pierced by a magnetic flux) with one or more channels represented by paradigmatic strongly-correlated models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation. Interference effects could also be controlled in certain molecules and interesting properties could be observed. We analyze transport properties of conjugated molecules, benzene in particular, and find that the conductance depends on the lead configuration. In molecules with translational symmetry, the conductance can be controlled by breaking or restoring this symmetry, e.g. by the application of a local external potential. These results open the possibility of observing these peculiar physical properties in anisotropic ladder systems and in real nanoscopic and molecular devices.

Metathesis of carbon dioxide and phenyl isocyanate catalysed by group(IV) metal alkoxides: An experimental and computational study

The insertion reactions of zirconium(IV) n-butoxide and titanium(IV) n-butoxide with a heterocumulene like carbodiimide, carbon dioxide or phenyl isocyanate are compared. Both give an intermediate which carries out metathesis at elevated temperatures by inserting a second heterocumulene in a head-to-head fashion. The intermediate metallacycle extrudes a new heterocumulene, different from the two that have inserted leading to metathesis. As the reaction is reversible, catalytic metathesis is feasible. In stoichiometric reactions heterocumulene insertion, metathesis and metathesis cum insertion products are observed. However, catalytic amounts of the metal alkoxide primarily led to metathesis products. It is shown that zirconium alkoxides promote catalytic metathesis (isocyanates, carbon dioxide) more efficiently than the corresponding titanium alkoxide. The difference in the metathetic activity of these alkoxides has been explained by a computational study using model complexes Ti(OMe)(4) (1bTi) and Zr(OMe)(4) (1bZr). The computation was carried out at the B3LYP/LANL2DZ level of theory.

Crystal structure of a daturalactone - a withanolide

The crystal structure of a daturalactone derivative has been determined by X-ray structural analysis. The compound crystallizes in orthorhomic space group P2(1)2(1)2(1) with cell parameters a = 15.141(1) angstrom, b = 18.425(1) angstrom, c = 19.251(2) angstrom. The structure was solved by direct methods and refined to R = 0.082. The asymmetric unit contains two non-equivalent molecules. Extensive hydrogen bonding is present. The conformations of the rings are A: a distorted half-chair, B: a perfect half-chair, C: a chair, D: an envelope-half chair and E: a twist boat. Ring junctions A/B, B/C, C/D are all trans fused. Methyl carbons C(18), C(19), C(27) and the lactone moiety is beta-oriented whereas the methyl carbons C(21) and C(28) are alpha-oriented.