Spectral properties of zeroth-order pseudodifferential operators

Let Q be a self-adjoint, classical, zeroth order pseudodifferential operator on a compact manifold X with a fixed smooth measure dx. We use microlocal techniques to study the spectrum and spectral family, {E_S}_{S∈$\text{R}$} as a bounded operator on L²(X, dx).Using theorems of Weyl (Rend. Circ. Mat. Palermo, 27 (1909), 373–392) and Kato (“Perturbation Theory for Linear Operators,” Springer-Verlag, 1976) on spectra of perturbed operators we observe that the essential spectrum and the absolutely continuous spectrum of Q are determined by a finite number of terms in the symbol expansion. In particular Spec_ESSQ = range(q(x, ξ)) where q is the principal symbol of Q. Turning the attention to the spectral family {E_S}_{S∈$\text{R}$}, it is shown that if $\text{dE}\text{ds}$ is considered as a distribution on $\text{R}$×X×X it is in fact a Lagrangian distribution near the set $\text{{σ=0}?}\text{T}{}^1\text{(}\text{R}\text{×X×X)}\text{0}$ where (s, x, y, σ, ξ,η) are coordinates on T¹($\text{R}$×X×X) induced by the coordinates (s, x, y) on $\text{R}$×X×X. This leads to an easy proof that$\text{?(Q)}$ is a pseudodifferential operator if ?∈C^∞($\text{R}$) and to some results on the microlocal character of E_s. Finally, a look at the wavefront set of $\text{dE}\text{ds}$ leads to a conjecture about the existence of absolutely continuous spectrum in terms of a condition on q(x, ξ).     

A Six-Coordinate Tris(3,5-dimethyl-1-pyrazolyl)methane-Thallium(I) Complex with a Stereochemically Inactive Lone Pair: Syntheses and Solid State Structures of {[HC(3,5-Me(2)pz)(3)](2)Tl}PF(6) and {[HC(3,5-Me(2)pz)(3)]Tl}PF(6) (pz = Pyrazolyl)

The addition of the tris(pyrazolyl)methane ligand HC(3,5-Me(2)pz)(3) (pz = pyrazolyl ring) to a THF solution of TlPF(6) results in the immediate precipitation of {[HC(3,5-Me(2)pz)(3)](2)Tl}PF(6). The structure has been determined crystallographically. The arrangement of the nitrogen donor atoms about the thallium is best described as a trigonally distorted octahedron. The thallium atom sits on a crystallographic center of inversion; thus the planes formed by the three nitrogen donor atoms of each ligand are parallel. The Tl-N bond distances range from 2.891(5) to 2.929(5) ? (average = 2.92) ?. The lone pair on thallium is clearly stereochemically inactive and does not appear to influence the structure. The pyrazolyl rings are planar, but are tilted with respect to the thallium atom so as to open up the N.N intraligand bite distances. The thallium(I) complex with a ligand to metal ratio of 1/1, {[HC(3,5-Me(2)pz)(3)]Tl}PF(6), is prepared in acetone by the reaction of equimolar amounts of HC(3,5-Me(2)pz)(3) and TlPF(6). The structure of the cation is a trigonal pyramid, with Tl-N bond distances that range from 2.64(1) to 2.70(1) ? (average = 2.67) ?. Pyrazolyl ring tilting is also observed in this complex, but the degree of tilting is smaller. Crystal data for {[HC(3,5-Me(2)pz)(3)](2)Tl}PF(6): monoclinic, P2(1)/c, a = 9.210(6) ?, b = 13.36(1) ?, c = 16.067(8) ?, beta = 92.48(5) degrees, V = 1975(2) ?(3), Z = 2, R = 0.029. For {[HC(3,5-Me(2)pz)(3)]Tl}PF(6): monoclinic, P2(1)/n, a = 10.685(2) ?, b = 16.200(5) ?, c = 13.028(3) ?, beta = 94.02(2) degrees, V = 2249.6(8) ?(3), Z = 4, R = 0.042.     

The synthesis of platinum and palladium cluster compounds with isocyanide or functionalised phosphine ligands. Crystal structures of [Pt5(CO)(μ-CO)5{Ph2PCH2C(O) Ph}4 and [Pt5(μ-CNC6H3Me2-2, 6)3(CNC6H3Me2-2, 6)5 {Ph2PCH2C(O) Ph}2]

The reaction of the ketophosphine ligand Ph₂PCH₂C(O)Ph (P～O) with [PtCl₂(NCMe)₂] and carbon monoxide in THF in the presence of an excess of zinc afforded the 70 electron pentanuclear cluster [Pt₅(CO)(μ-CO)₅(P～O)₄] (1). Reaction of the palladium(0) complex [Pd₂(dba)₃] CHCl₃ (dba = dibenzylideneacetone) with Ph₂PCH₂C(O)R [R = Ph or C₅H₄Fe(C₅H₅)] under SO₂ led to the pentapalladium cluster compounds [Pd₅(μ₃-SO₂)₂ (μ-SO₂)₂ {Ph₂PCH₂C(O)R}₅] (2a,R = Ph;2b,R = C₅H₄Fe(C₅H₅)), Cluster (1) reacts with 2,6-xylyl isocyanide, CNC₆H₃Me₂-2,6 to give a red cluster of formula [Pt₅(μ-CNC₆H₃Me₂-2, 6)₃ (CNC₆H₃Me₂-2, 6)₅ (P～O)₂] (3) and a green complex (4). The corresponding complexes (6) and (7) were also obtained by using PPh₃ instead of P～O. Clusters (2a) and (2b) react with [NEt₃Bz] Cl to give[NEt₃Bz][Pd₃(μ-SO₂)₂ (μ-Cl){Ph₂PCH₂C(O)R}₃](8a,R = Ph;8b,R = C₅H₄Fe(C₅H₅)). The molecular structures of (1) and (3) were determined by single-crystal X-ray diffraction analyses.     

Synthesis and structures of cadmium(II) complexes of a series of multinucleating N/S donor ligands

The coordination chemistry of a series of bis-bidentate ligands with cadmium(II) ions has been investigated. The ligands, containing two N,S-donor chelating (pyrazolyl/thioether) fragments, have afforded complexes of a variety of structural types (dinuclear M₂L₂ ‘mesocate’ complexes, a one-dimensional chain coordination polymer and a simple mononuclear complex) according to whether the bis-bidentate ligands act as bridges spanning two metal ions, or a tetradentate chelate to a single metal ion. The p-phenylene and m-biphenyl spaced ligands L¹ and L³ form dinuclear M₂L₂ complexes where the ligands are arranged in a ‘side-by-side’ fashion. In contrast the m-phenylene spaced ligand L² forms a one-dimensional coordination polymer where the ligands adopt a highly folded conformation. The 1,8-naphthalene spaced ligand L⁴ adopts a tetradendate chelating mode and affords a simple mononuclear complex.     

Addition of Pt(PBu(t)(3)) groups to Ru(5)(CO)(12)(eta(6)-C(6)H(6))(mu(5)-C). Synthesis, structures, and dynamical activity

The reaction of Ru(5)(CO)(12)(eta(6)-C(6)H(6))(mu(5)-C), 7, with Pt(PBu(t)(3))(2) yielded two products Ru(5)(CO)(12)(eta(6)-C(6)H(6))(mu(6)-C)[Pt(PBu(t)(3))], 8, and Ru(5)(CO)(12)(eta(6)-C(6)H(6))(mu(6)-C)[Pt(PBu(t)(3))](2), 9. Compound 8 contains a Ru(5)Pt metal core in an open octahedral structure. In solution, 8 exists as a mixture of two isomers that interconvert rapidly on the NMR time scale at 20 degrees C, DeltaH() = 7.1(1) kcal mol(-1), DeltaS() = -5.1(6) cal mol(-)(1) K(-)(1), and DeltaG(298)(#) = 8.6(3) kcal mol(-1). Compound 9 is structurally similar to 8, but has an additional Pt(PBu(t)(3)) group bridging an Ru-Ru edge of the cluster. The two Pt(PBu(t)(3)) groups in 9 rapidly exchange on the NMR time scale at 70 degrees C, DeltaH(#) = 9.2(3) kcal mol(-)(1), DeltaS(#) = -5(1) cal mol(-)(1) K(-)(1), and DeltaG(298)(#) = 10.7(7) kcal mol(-1). Compound 8 reacts with hydrogen to give the dihydrido complex Ru(5)(CO)(11)(eta(6)-C(6)H(6))(mu(6)-C)[Pt(PBu(t)(3))](mu-H)(2), 10, in 59% yield. This compound consists of a closed Ru(5)Pt octahedron with two hydride ligands bridging two of the four Pt-Ru bonds.     

Development of an Improved Liquid Chromatographic Method for the Analysis of Doxycycline

Summary An improved LC method is described for the separation of doxycycline and its impurities. The separation of 2-acetyl-2-decarboxamidodoxycycline from the main peak doxycycline is much better than that obtained with official pharmacopoeia methods. The method is robust and shows good selectivity, repeatability, linearity and sensitivity. Eight commercial samples were examined using the method developed. The method uses an XTerra RP-18, 5 m (25 cm × 4.6 mm I. D.) column kept at a temperature of 35 °C. UV detection is performed at 280 nm. The mobile phase consists of acetonitrile – 0.2 M tetrabutylammonium hydrogen sulphate pH 7.0 – 0.3 M ethylenediaminetetraacetate pH 7.0 – water (130:350:350:170, v/v/v/v).     

Speciation analysis of mercury by solid-phase microextraction and multicapillary gas chromatography hyphenated to inductively coupled plasma-time-of-flight-mass spectrometry

This paper reports the development of an analytical approach for speciation analysis of mercury at ultra-trace levels on the basis of solid-phase microextraction and multicapillary gas chromatography hyphenated to inductively coupled plasma-time-of-flight mass spectrometry. Headspace solid-phase microextraction with a carboxen/polydimethylsyloxane fiber is used for extraction/preconcentration of mercury species after derivatization with sodium tetraethylborate and subsequent volatilization. Isothermal separation of methylmercury (MeHg), inorganic mercury (Hg2+) and propylmercury (PrHg) used as internal standard is achieved within a chromatographic run below 45 s without the introduction of spectral skew. Method detection limits (3 x standard deviation criteria) calculated for 10 successive injections of the analytical reagent blank are 0.027 pg g(-1) (as metal) for MeHg and 0.27 pg g(-1) for Hg2+. The repeatability (R.S.D., %) is 3.3% for MeHg and 3.8% for Hg2+ for 10 successive injections of a standard mixture of 10pg. The method accuracy for MeHg and total mercury is validated through the analysis of marine and estuarine sediment reference materials. A comparison of the sediment data with those obtained by a purge-and-trap injection (PTI) method is also addressed. The analytical procedure is illustrated with some results for the ultra-trace level analysis of ice from Antarctica for which the accuracy is assessed by spike recovery experiments.