Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Investigation of molecular polarizabilities and derivatives in halomethanes

The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.

Metal complexes of cyclen and cyclam derivatives useful for medical applications: a discussion based on thermodynamic stability constants and structural data

A series of the most common chelators used in magnetic resonance imaging ( MRI) and in radiopharmaceuticals for medical diagnosis and tumour therapy, H(4)dota, H(4)teta, H(8)dotp and H(8)tetp, is examined from a chemical point of view. Differences between 12- and 14-membered tetraazamacrocyclic derivatives with methylcarboxylate and methylphosphonate pendant arms and their chelates with divalent first-series transition metal and trivalent lanthanide ions are discussed on the basis of their thermodynamic stability constants, X- ray structures and theoretical studies.

Cyclam derivatives containing three acetate pendant arms: synthesis, acid-base, metal complexation and structural studies

The ligands 1,4,8,11-tetraazacyclotetradecane-1,4,8-triacetic-11-methylphosphonic acid (H(5)te3a1p) and 1,4,8,11-tetraazacyclotetradecane-1,4,8-triacetic acid (H(3)te3a) were synthesized, the former one for the first time. The syntheses of these ligands were achieved from reactions on 1,4,8,11-tetraazacyclotetradecane-1,4,8-tris( carbamoylmethyl) hydroiodide (te3am center dot HI), and compounds (Hte3am)(+), 1, and (H(7)te3a1p)(2+), 4, were characterized by X-ray diffraction. Structures of two other compounds resulting from side-reactions, (H(2)te2lac)(2+), 2, and (H(4)te2a2p(OEt2))(2+), 3, were also determined by X-ray diffraction. Potentiometric titrations of H(5)te3a1p and H(3)te3a were performed at 298.2 K and ionic strength 0.10 mol dm(-3) in NMe4NO3 to determine their protonation constants. H-1 and P-31 NMR titrations of H(5)te3a1p were carried out in order to determine the very high first protonation constant of this ligand and to elucidate the sequence of protonation. Potentiometric studies of the two ligands with Ca2+, Mn2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Pb2+ metal ions performed in the same experimental conditions showed that the complexes of H5te3a1p present very high thermodynamic stability while complexes of H(3)te3a, particularly Co2+ and Zn2+, are even more stable. P-31 NMR spectra of the cadmium(II) complex of H(5)te3a1p showed that the phosphonate moiety was coordinated to the metal ion. The UV-vis-NIR spectroscopic data and magnetic moment values of Co2+ and Ni2+ complexes of H(5)te3a1p and H(3)te3a together with the EPR of the corresponding Cu2+ complexes indicated that all these complexes adopt distorted octahedral coordination geometries in solution. This was confirmed by the single crystal structure of [Cu-2(Hte3a)(H2O)(3)Cl]Cl-0.5(ClO4)(0.5) center dot 2H(2)O that showed two distorted octahedral copper centres bridged by a N-acetate pendant arm with a Cu center dot center dot center dot Cu distance of 4.890(1) angstrom. The first one is encapsulated into the macrocyclic cavity surrounded by four nitrogen and two oxygen donors from the macrocycle, whereas the second one is on the periphery of the macrocycle and is coordinated to two oxygen atoms of one acetate pendant arm in chelating fashion, one chloride and three water molecules.

Fulvalene titanium and zirconium complexes: synthesis and NMR study of phosphanido-, alkyl-, and alkynyl-derivatives. X-ray crystal structures of [{Ti(η5−C5H5)(μ−PPH2)}2{μ−(η5−C5H4−η5−C5H4)}] and [{Zr(η5−C5H5)(μ−C≡CSiMe3)}2{μ−(η5−C5H4−η5−C5H4)}]

Reaction of with one or two equivalents of LiPPh2 afforded the new phosphanidometal(III) complexes . Reaction of 2 with LiC≡CSiMe3 led to the diamagnetic zirconium(III) alkynyl derivative [{Zr(C5H5)(μ−C≡CSiMe3)}2(μ−η5−C5H4−η5−C5H4], 7. Alkylation of 6 with LiCH2CMe2Ph gave [{Zr(η5−C5H5)(CH2CMe2Ph)2}2{μ−(η5−C5H4)}], 8. A detailed NMR study of complexes 3 and 4 allowed the observation of the spectral behaviour of the eight different fulvalene protons through their coupling to the 31P nucleus. The fluxional behaviour of complex 7 was studied by dynamic DNMR, and kinetic parameters for the σ-π-conversion of the alkynyl ligand were determined. The molecular structures of complexes 3 and 7 were determined by X-ray diffraction methods.

Metal cluster expansion by addition of low valent group 14 reagents: III. Reaction of bis[bis(trimethylsilyl)methyl]tin with M3(CO)12 or its derivatives (M = Fe, Ru, or Os): the crystal and molecular structures of M3(μ-SnR2)2(CO)10(R = CH(SiMe3)2; M = Ru or Os)

The stannylene [SnR2] (R = CH(SiMe3)2) reacts in different ways with the three dodecacarbonyls of the iron triad: [Fe3(CO)12] gives [Fe2(CO)8(μ-SnR2)], [Ru3(CO)12] gives the planar pentametallic cluster [Ru3(CO)10(μ-SnR2)2], for which a full structural analysis is reported, while [Os3(CO)12] fails to react. Different products are also obtained from three nitrile derivatives: [Fe3-(CO)11(MeCN)] gives [Fe2(CO)6(μ-SnR2)2], which has a structure significantly different from that of known Fe2Sn2 clusters, [Ru3(CO)10(MeCN)2] gives the pentametallic cluster described above, while [Os3(CO)10(MeCN)2] gives the isostructural osmium analogue, which shows the unusual feature of a CO group bridging two osmium atoms.

Reaction of 2-methyl-1,4-naphthoquinone and its 3-substituted derivatives with active methylene group anions and with diazo compounds

The reaction of 2-chloro-3-methyl-1,4-naphthoquinone (3) with the anion of ethyl cyanoacetate led to a mixture of two epimeric fused-ring cyclopropane compounds, characterised as exo- and endo-1-cyano-1 -ethoxycarbonyl-1a-methyl-1a,7a-dihydro-1H-cyclopropa[b]naphthalene-2,7-dione (8) and (9). Various hydrolysis products of these were prepared and an X-ray crystallographic analysis was carried out on one of them, 1-carbamoyl-1 -carboxy-1a-methyl-1a,7a-dihydro-1H-cyclopropa[b]-naphthalene-2,7-dione (17). The reaction of 2-methyl-1,4-naphthoquinone (1) with ethyl diazoacetate gave a fused pyrazoline derivative, 3-ethoxycarbonyl-4-hydroxy-9a-methyl-1,9a-dihydro-benz[f]indazol-9-one (22), while reaction of 2-methyl-3-nitro-1,4-naphthoquinone (5) with diazomethane led to a fused Δ2-isoxazoline N-oxide, 3a-methyl-3,3a-dihydroisoxazolo[3,4-b]naphthalene-4,9-dione 1-oxide (26).

New furoquinoline alkaloid and flavanone glycoside derivatives from the leaves of Oricia suaveolens and Oricia renieri (Rutaceae)

Fractionation of the methanol extract of the leaves of Oricia renieri and Oricia suaveolens (Rutaceae) led to the isolation of 13 compounds including the hitherto unknown furoquinoline alkaloid named 6,7-methylenedioxy-5-hydroxy-8-methoxydictamnine (1) and a flavanone glycoside named 5-hydroxy-40-methoxy-7-O-[a-Lrhamnopyranosyl(1000→500)-b-D-apiofuranosyl]-flavanoside (2), together with 11 known compounds (3–13). The structures of the compounds were determined by comprehensive analyses of their 1D and 2D NMR, mass spectral data and comparison. All compounds isolated were examined for their activity against human carcinoma cell lines. The alkaloids 1, 5, 12, 13 and the phenolic 2, 8, 11 tested compounds exhibited non-selective moderate cytotoxic activity with IC50 8.7–15.9mM whereas compounds 3, 4, 6, 7, 9 and 10 showed low activity.

On the relationships between molecular conformations and intermolecular contacts toward crystal self-assembly of mono-, di-, tri-, and tetra-oxygenated xanthone derivatives

Oxygenated xanthones have been extensively investigated over the years, but there are few reports concerning their crystal structure. Our chemical investigations of Brazilian plants resulted in the isolation of four natural products named 1-hydroxyxanthone (I), 1-hydroxy-7-methoxyxanthone (II), 1,5-dihydroxy-3-methoxyxanthone (III), and 1,7-dihydroxy-3,8-dimethoxyxanthone (IV). The structures of these compounds were established on the basis of single crystal X-ray diffraction. The xanthone nucleus conformation is essentially planar with the substituents adopting the orientations less sterically hindered. In addition, classical intermolecular hydrogen bonds (O-H center dot center dot center dot O) present in III and IV give rise to infinite ribbons. However, the xanthone I does not present any intermolecular hydrogen bonds, meanwhile the xanthone II presents only a non-classical one (C-H center dot center dot center dot O). The crystal packing of all xanthone structures is also stabilized by pi-pi interactions. The fingerprint plots, derived from the Hirshfeld surfaces, exhibited significant features of each crystal structures.

Synthesis of new fluorous modular chiral ligand derivatives from amino alcohols and application in enantioselective carbon-carbon bond-forming alkylation reactions

N-Trifluoracyl beta-chalcogeno amides and N-perfluoracyl beta-thio amide ligands were prepared by a simple and efficient reaction sequence. These new ligands were evaluated in palladium-catalyzed alkylation of rac-(E)-1,3-diphenyl-2-propenyl acetate in the presence of dimethyl malonate and an enantioselectivity of up to 99% was obtained. After catalysis, the fluorous ligand can be easily recovered by liquid-liquid extraction and reused without loss in the activity. (C) 2010 Elsevier Ltd. All rights reserved.

In vitro Trypanocidal Activity of Phenolic Derivatives from Peperomia obtusifolia

The trypanocidal activity of crude extracts and fractions from the leaves and stems of Peperomia obtusifolia (Piperaceae) was evaluated in vitro against the epimastigote forms of Trypanosoma cruzi. Bioactivity-guided fractionation of the most active extracts afforded seven known compounds, including three chromanes, two furofuran lignans and two flavone C-diglycosides. The most active compounds were the chromanes peperobtusin A and 3,4-dihydro-5-hydroxy-2,7-dimethyl-8-(2 ``-methyl-2 ``-butenyl)-2-(4`-methyl-1`,3`-pentadienyl)-2H-1-benzopyran-6-carboxylic acid, with IC(50) values of 3.1 mu M (almost three times more active than the positive control benznidazole, IC(50) 10.4 mu M) and 27.0 mu M, respectively. Cytotoxicity assays using peritoneal murine macrophages indicated that the chromanes were not toxic at the level of the IC(50) for trypanocidal activity. This is the first report on the trypanocidal activity besides unspecific cytotoxicity of chromanes from Peperomia species. Additionally it represents the first time isolation of 3,4-dihydro5-hydroxy-2,7-dimethyl-8-(2 ``-methyl-2 ``-butenyl)-2-(4`-methyl-1`,3`-pentadienyl)-2H-1-benzopyran-6-carboxylic acid from P. obtusifolia.

Natural chromens and chromene derivatives as potential anti-trypanosomal agents

The aim of the study was to investigate the anti-trypanocidal activities of natural chromene and chromene derivatives. Five chromenes were isolated from Piper gaudichaudianum and P. aduncum, and a further seven derivatives were prepared using standard reduction, methylation and acetylation procedures. These compounds were assayed in vitro against epimastigote forms of Trypanosoma cruzi, the causative agent of Chagas disease. The results showed that the most of the compounds, especially those possessing electron-donating groups as substituents on the aromatic ring, showed potent trypanocidal activity. The most active compound, [(2S)-methyl-2-methyl-8-(3 ``-methylbut-2 ``-enyl)-2-(4`-methylpent-3`-enyl)-2H-chromene-6-carboxylate], was almost four times more potent than benznidazole (the positive control) and showed an IC50 of 2.82 mu M. The results reveal that chromenes exhibit significant anti-trypanocidal activities and indicate that this class of natural product should be considered further in the development of new and more potent drugs for use in the treatment of Chagas disease.

Excited-state dynamics of polyfluorene derivatives in solution

The excited-state dynamics of two polyfluorene copolymers, one fully conjugated containing phenylene vinylene units alternated with 9,9`-dihexylfluorenyl groups and the other segmented by -(CH2)(8)- spacer, were studied in dilute solution of different solvents using a picosecond single-photon timing technique. The excited-state dynamics of the segmented copolymer follows the Forster resonant energy-transfer model which describes intrachain energy-transfer kinetics among random oriented chromophores. Energy transfer is confirmed by analysis of fluorescence anisotropy relaxation with the measurement of a short decay component of about 60 ps. The fluorescence decay surface of the fully conjugated copolymer is biexponential with decay times of about 470 and 900 ps, ascribed to deactivation of chain moieties containing trans and cis isomers already in a photostationary condition. Thus, energy transfer is very fast due to the conjugated nature and rigid-rod-like structure of this copolymer chain.

Pyrodysinoic Acid Derivatives from the Marine Sponge Dysidea robusta

Three new nitrogen-containing terpenes related to pyrodysinoic acid (1) have been isolated from the sponge Dysidea robusta collected in Brazil. Isopyrodysinoic acid (2), 13-hydroxyisopyrodysinoic acid (3), and pyrodysinoic acid B (4) were obtained from the crude extract of D. robusta and identified by analysis of spectroscopic data. Pyrodysinoic acid B (4) is the first furodysin or furodysinin sesquiterpene derivative with a trans junction between the two six-membered rings of the 1,2,3,4,4a,7,8,8a-octahydro-1,1,6-trimethylnaphthalene moiety.

Synthesis, Spectroscopic Studies and X-ray Crystal Structures of New Pyrazoline and Pyrazole Derivatives

The synthesis and characterization of some pyrazoline compounds of 1,3-diketones with hydrazine derivatives, namely, 1-(S-benzyldithiocarbazate)-3-methyl-5-phenyl-5-hydroxypyrazoline (1); 1-(2-thiophenecarboxylic)-3-methyl-5-phenyl-5-hydroxypyrazoline (2); 1-(2-thiophenecarboxylic)-3,5-dimethyl-5-hydroxypyrazoline (3); 1-(S-benzyldithiocarbazato)-3-methyl-5-phenylpyrazole (4); 1-(2-thiophenecarboxylic)-3-methyl-5-phenylpyrazole (5) and 1-(S-benzyldithiocarbazate)-3,5-dimethylpyrazole (6) are reported. Studies by IR, ((1)H, (13)C)-NMR spectroscopies and single crystal X-ray diffraction revealed that compounds (1)(,) (2) and (3) are formed as pyrazoline, whereas (4) and (5) are formed as pyrazole derivatives only under acidic conditions. Compound (1) crystallizes in orthorhombic P2(1)2(1)2(1), a = 6.38960(10) angstrom, b = 12.9176(3) angstrom, c = 21.2552(5) angstrom, (2) crystallizes in monoclinic, P2(1)/n, a = 11.3617(2) angstrom, b = 8.4988(2) angstrom, c = 92.8900(10)angstrom and beta = 92.8900(5)degrees, (3) crystallizes in monoclinic, C2/c, a = 15.9500(5) angstrom, b = 9.3766(3) angstrom, c = 16.6910(5)angstrom and beta = 113.825(2)degrees, (4) crystallizes in monoclinic, P2(1)/c, a = 15.228(4) angstrom, b = 5.5714(13) angstrom, c = 19.956(5)angstrom and beta = 91.575(7)degrees and (6) crystallizes in orthorhombic, P2(1)2(1)2(1), a = 5.3920(2) angstrom, b = 11.2074(5) angstrom, c = 21.885(1)angstrom . The (3) derivative represents the first pyrazoline compound prepared from 2,4-pentanedione and characterized crystallographically.