A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Finite element modal solutions of planar photonic crystal fibers with rectangular air-holes

Modal solutions of planar photonic crystal waveguides with rectangular air-holes are presented by using a rigorous full-vectorial finite element-based approach. The effective indices, mode field profiles, spot-sizes, power confinements, modal hybridness, beat lengths and group velocity dispersions are shown for the fundamental and higher order modes of the quasi-TE and TM polarizations.     

Dithiolate complexes of manganese and rhenium: X-ray structure and properties of an unusual mixed valence cluster Mn3(CO)6(mu-eta2-SCH2CH2CH2S)3

Treatment of Mn(2)(CO)(10) with 3,4-toluenedithiol and 1,2-ethanedithiol in the presence of Me(3)NO.2H(2)O in CH(2)Cl(2) at room temperature afforded the dinuclear complexes Mn(2)(CO)(6)(mu-eta(4)-SC(6)H(3)(CH(3))S-SC(6)H(3)(CH(3))S) (1), and Mn(2)(CO)(6)(mu-eta(4)-SCH(2)CH(2)S-SCH(2)CH(2)S) (2), respectively. Similar reactions of Re(2)(CO)(10) with 3,4-toluenedithiol, 1,2-benzenedithiol, and 1,2-ethanedithiol yielded the dirhenium complexes Re(2)(CO)(6)(mu-eta(4)-SC(6)H(3)(CH(3))S-SC(6)H(3)(CH(3))S) (3), Re(2)(CO)(6)(mu-eta(4)-SC(6)H(4)S-SC(6)H(4)S) (4), and Re(2)(CO)(6)(SCH(2)CH(2)S-SCH(2)CH(2)S) (5), respectively. In contrast, treatment of Mn(2)(CO)(10) with 1,3-propanedithiol afforded the trimanganese compound Mn(3)(CO)(6)(mu-eta(2)-SCH(2)CH(2)CH(2)S)(3) (6), whereas Re(2)(CO)(10) gave only intractable materials. The molecular structures of 1, 3, and 6 have been determined by single-crystal X-ray diffraction studies. The dimanganese and dirhenium carbonyl compounds 1-5contain a binucleating disulfide ligand, formed by interligand disulfide bond formation between two dithiolate ligands identical in structure to that of the previously reported dimanganese complex Mn(2)(CO)(6)(mu-eta(4)-SC(6)H(4)S-SC(6)H(4)S). Complex 6, on the other hand, forms a unique example of a mixed-valence trimangenese carbonyl compound containing three bridging 1,3-propanedithiolate ligands. The solution properties of 6 have been investigated by UV-vis and EPR spectroscopies as well as electrochemical techniques.     

Thermal Analysis of Hexachloroplumbate and Chlorides Containing Complex Divalent Lead 2,2'-bipyridine Cations

Lead(II) 2,2'-bipyridine hexachloroplumba tetetrahydrate was synthesized and investigated by DTA, TG and DTG. IR spectroscopy and other methods enabled the identification of some of the decomposition products. Comparative studies on the corresponding chlorides: [Pb(bipy)]Cl₂ and [Pb(bipy)₃]Cl₂, which can be considered as precursors of the hexachloroplumbate, were also undertaken. X-ray measurements enabled the tentative determination of the crystal structure of [Pb(bipy)]Cl₂. Hexachloroplumbate decomposes with the liberation of chlorine, water and organic ligands, and the process is accompanied by the simultaneous transition of Pb(IV)→Pb(II). Chlorides release only ligands upon heating. Residues comprised always PbCl₂. This revised version was published online in August 2006 with corrections to the Cover Date.     

Synthesis, structures and reactivity of triosmium clusters containing terminal pyrazines, bridging hydroxy and methoxycarbonyl ligands

Four triosmium carbonyl clusters bearing terminal pyrazines, bridging hydroxy and methoxycarbonyl ligands of general formula [Os₃(CO)₉(μ-OH)(μ-OMeCO)L] (1, L = pyrazine; 2, L = 2-methylpyrazine; 3, L = 2,3-dimethylpyrazine; 4, L = 2,3,5-trimethylpyrazine) were synthesized by the reactions of [Os₃(CO)₁₂] with the corresponding pyrazine derivatives and water in the presence of a methanolic solution of Me₃NO in moderate yields. Compounds [Os₃(CO)₉(μ-OH)(μ-OMeCO)L] react with a series of two electron donor ligands, L′ at ambient temperature to give [Os₃(CO)₉(μ-OH)(μ-OMeCO)L′] (5, L′ = PPh₃; 6, L′ = P(OMe)₃; 7, L′ = ^tBuNC; 8, L′ = C₅H₅N) in good yields by the displacement of the pyrazine ligands. This implies that the pyrazine ligands in 1–4 are relatively labile. Compounds 2, 3, 4, and 8 were characterized by single crystal X-ray diffraction analyses. All the four compounds possess two metal–metal bonds and a non-bonded separation of two osmium atoms defined by Os(1)Os(3), which are simultaneously bridged by OH and MeOCO ligands and a heterocyclic ligand is terminally coordinated to one of the two non-bonded osmium atoms.     

Triosmium clusters derived from the reactions of thioureas with dodecacarbonyltriosmium: Crystal structures of [Os3(CO)11{η 1-SC(NMe2)2}], [Os3(CO)9(μ-OH)(μ-OMeOCO){η 1-SC(NMe2)2}] and [(μ-H)Os3(CO)9{μ 3-NHC(S)NH2}]

The reaction of [Os₃(CO)₁₂] with tetramethylthiourea in the presence of a methanolic solution of Me₃NO·2H₂O at 60° yields the compounds [Os₃(CO)₁₁{η ¹-SC(NMe₂)₂}] (1) in 56% yield and [Os₃(CO)₉(μ-OH)(μ-MeOCO){η ¹-SC(NMe₂)₂}] (2) in 10% yield in which the tetramethylthiourea ligand is coordinatedvia the sulfur atom at an equatorial position. Compound2 is a 50 e^? cluster with two metal-metal bonds and the hydroxy and methoxycarbonyl ligands bridging the open metal-metal edge. In contrast, the analogous reaction of [Os₃(CO)₁₂] with thiourea gives the compounts [(μ-H)Os₃(CO)₁₀{μ-NHC(S)NH₂}] (3) in 8% yield and [(μ-H)Os₃(CO)₉{₃-NHC(S)NH₂}] (4) in 30% yield. In3, the thioureato ligand bridges two osmium atomsvia the sulfur atom, whereas in4 in addition to the sulfur bridge, one of the nitrogen atoms of thioureato moiety bonds to the remaining osmium atom. The decacarbonyl compounds 3 can also be obtained in 50% yield from the reaction of [Os₃(CO)₁₀(MeCN)₂] with thiourea at ambient temperature. Compound3 converts to4 (65%) photochemically. Compound1 reacts with PPh₃ and acetonitrile at ambient temperature to give the simple substitution products [Os₃(CO)₁₁(PPh₃)] and [Os₃(CO)₁₁(MeCN)], respectively, while with pyridine, the oxidative addition product [(μ-H)Os₃(CO)₁₀(μ-NC₅H₄] is formed at 80°C. All the new compounds are characterized by IR,¹-H-NMR and elemental analysis together with the X-ray crystal structures of1,2 and4. Compound1 crystallizes in the triclinic space group P $P\bar 1$ with unit cell parametersa = 8.626(3) Å,b = 11.639(3) Å,c = 12.568(3_ Å,α = 84.67(2)°,β = 75.36(2)°,γ = 79.49(3)°,V = 1199(1) ų, andZ = 2. Least-squares refinement of 4585 reflections gave a final agreement factor ofR = 0.0766 (R _w = 0.0823). Compound2 crystallizes in the monoclinic space group P2_1/n with unit cell parametersa = 9.149(5) Å,b = 17.483(5) Å,c = 15.094(4) Å,β = 91.75(2)°,V = 2413(2) ų, andZ = 4. Least-squares refinement of 3632 reflections gave a final agreement factor ofR = 0.0603 (R _w = 0.0802). Compound4 crystallizes in the monoclinic space group C2/c with unit cell parametersa = 13.915(7) Å,b = 14.718(6) Å,c = 17.109(6) Å,β = 100.44(3)°,V = 3446(5) ų, andZ = 8. Least-squares refinement of 2910 reflections gave a final agreement factor ofR = 0.0763 (R _w = 0.0863).     

An efficient palladium-catalyzed Negishi cross-coupling reaction with arylvinyl iodides: facile regioselective synthesis of E-stilbenes and their analogues

A general synthetic route for the Pd-catalyzed cross-coupling of an arylzinc reagent with arylvinyl iodides (Negishi cross-coupling) has been developed. The system permits efficient and selective preparation of E-stilbenes and their analogues. It also functions effectively at low levels of catalyst loading without the need for an additional ligand and tolerates a wide range of functional groups including heteroaromatic substrates. A systematic study of various parameters was performed and correlated with catalyst-substrate activity.     

Module-based assembly of copper(II) chloranilate compounds: syntheses, crystal structures, and magnetic properties of [[Cu(2)(CA)(terpy)(2)][Cu(CA)(2)]](n)() and [[Cu(2)(CA)(terpy)(2)(dmso)(2)][Cu(CA)(2)(dmso)(2)](EtOH)](n)(H(2)CA = chloranilic acid, terpy = 2,2':6',2' '-terpyridine, dmso = dimethyl sulfoxide)

Two new copper(II) compounds of chloranilate and 2,2':6',2' '-terpyridine have been synthesized, and the structures have been solved by the single-crystal X-ray diffraction method. The crystal structure of [[Cu(2)(CA)(terpy)(2)][Cu(CA)(2)]](n)(1), where H(2)CA = chloranilic acid and terpy = 2,2':6',2' '-terpyridine, consists of two modules, the dimer unit [Cu(2)(CA)(terpy)(2)](2+) and the anionic mononuclear unit [Cu(CA)(2)](2)(-), forming an alternated chain. The chain is stabilized by semicoordinating and additional but efficient secondary bonding interactions. The crystal structure of [[Cu(2)(CA)(terpy)(2)(dmso)(2)][Cu(CA)(2)(dmso)(2)](EtOH)](n)(2), where dmso = dimethyl sulfoxide, consists of solvent molecules and two discrete modules, the dimer unit [Cu(2)(CA)(terpy)(2)(dmso)(2)](2+) and the anionic mononuclear unit [Cu(CA)(2)(dmso)(2)](2)(-). The dimer units form a layer by secondary bonding interactions, and the monomer units and ethanol molecules are introduced between the layers. The magnetic properties of 1 and 2 have been investigated in the temperature range 2.0-300 K. A weak ferromagnetic interaction was observed in 1, J(a) = 2.36 cm(-)(1) and zJ(b) = -0.68 cm(-)(1) while no exchange coupling was observed in 2.