Singular Sturm—Liouville problems with nonnegative and indefinite weights

This article is concerned with the oscillatory properties of the eigenfunctions of a class of singular Sturm—Liouville problems—(p y)+q y=w y on (a, b), where the weight functionw vanishes on a subinterval of positive measure, or where the weight functionw changes sign on (a, b).This work was supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38.     

The synthesis and reactivity of the heptanuclear dianion [Os7(CO)20]2− including the synthesis and structural characterizations of the compounds [Os7(CO)20(AuPEt)3 2] and [Os8(CO)20(η6-C6H6]

Reduction of the heptaosmium cluster [Os₇(CO)₂₁] With [Et₄N][NH₄) gives the cluster dianion [Os₇(CO)₂₀]^2–,1, in high yield. The reaction of the dianion with [AuPR ₃Cl] (R=Et or Ph) in the presence of TlPF₆ forms [Os₇((CO)₂₀(AuPR ₃)₂] [R=Et (2a);R = Ph(2b)] in 80% yield, while the corresponding reaction with (Os(C₆H₆)(CH₃CN)₃]²⁺ gives [Os₈(CO)₂₀ ( ⁶-C₆H₆)] (3) in reasonable yield (ca. 30%). The dianion,1, and the clusters2 and3 have been fully characterized by bout spectroscopic and crystallographic methods. The crystal structure of the [Ph₄P]⁺ salt of1 shows that the metals in the anion adopt a capped octahedral geometry, with all twenty carbonyl ligands in terminal sites. The metal core geometry in2a is best described as a tricapped octahedron, and is based on the structure of the dianion1 with two adjacent octahedral faces capped by the Au atoms of the two AuPEt₃ groups. In a similar fashion, the geometry of3 is related to that of1 with the addition of an Os(C₆H₆) unit capped to a triangular face, to give a bicapped octahedral framework.     

Heterometallic MIIRuIII2 compounds constructed from trans-[Ru(Salen)(CN)2]- and trans-[Ru(Acac)2(CN)2]-. Synthesis, structures, magnetic properties, and density functional theoretical study

The synthesis, structures, and magnetic properties of four cyano-bridged M(II)Ru(III)2 compounds prepared from the paramagnetic Ru(III) building blocks, trans-[Ru(salen)(CN)2]- 1 [H2salen = N,N'-ethylenebis(salicylideneimine)] and trans-[Ru(acac)2(CN)2]- (Hacac = acetylacetone), are described. Compound 2, {Mn(CH3OH)4[Ru(salen)(CN)2]2}.6CH3OH.2H2O, is a trinuclear complex that exhibits antiferromagnetic coupling between Mn(II) and Ru(III) centers. Compound 3, {Mn(H2O)2[Ru(salen)(CN)2]2.H2O}n, has a 2-D sheetlike structure that exhibits antiferromagnetic coupling between Mn and Ru, leading to ferrimagnetic-like behavior. Compound 4, {Ni(cyclam)[Ru(acac)2(CN)2]2}.2CH3OH.2H2O (cyclam = 1,4,8,11-tetraazacyclotetradecane), is a trinuclear complex that exhibits ferromagnetic coupling. Compound 5, {Co[Ru(acac)2(CN)2]2}n, has a 3-D diamond-like interpenetrating network that exhibits ferromagnetic ordering below 4.6 K. The density functional theory (DFT) method was used to calculate the molecular magnetic orbitals and the magnetic exchange interaction between Ru(III) and M(II) (Mn(II), Ni(II)) ions.     

Synthesis and antiviral evaluation of some novel [1,2,4]triazolo[4,3-β][1,2,4]triazole nucleoside analogs

Ribosylation of 3-amino-5H-[1,2,4]triazolo[4,3-b][1,2,4]triazole ( 1 ) with l-O-acetyl-2,3,5-tri-O-benzoyl-D-ribofuranose and stannic chloride resulted in the following protected nucleoside analogs: 3-amino-1-(2,3,5-tri-O-benzoyl-β-D-ribofuranosyl)[1,2,4]triazolo[4,3-β][1,2,4]triazole ( 4 ), 3-amino-1-(2,3,5-tri-O-benzoyl-α-D-ribofuranosyl)[1,2,4]triazolo[4,3-β][1,2,4]triazole ( 5 ), 3-amino-1-(2,3,5-tri-O-benzoyl-β-D-ribofuranosyl)[1,2,4]triazolo[4,3-β][1,2,4]triazole ( 5 ), and 3-(2,3,5-tri-O-benzoyl-β-D-ribofuranosyl) amino-5H-[1,2,4]triazolo[4,3-b]-[1,2,4]triazole ( 7 ). Compounds 4–6 were deprotected to 3-amino-1-β-D-ribofuranosyl[1,2,4]triazolo[4,3-b][1,2,4]-triazole ( 3 ), 3-amino-1-α-D-ribofuranosyl[1,2,4]triazolo[4,5-b][1,2,4]triazole ( 8 ), and 3-imino-2H-2-β-D-ribo-furanosyl[1,2,4]triazolo[4,3-b][1,2,4]triazole ( 9 ), while 7 could not be deprotected without decomposition. Compounds 1, 4, 6, 7 , and 9 were screened and found to have no antiviral activity.     

Iridium(III) and rhodium(III) cyclometalated complexes containing sulfur and selenium donor ligands

Treatment of [M(Buppy)₂Cl]₂ (M=Ir (1), Rh (2); BuppyH=2-(4^′-tert-butylphenyl)pyridine) with Na(Et₂NCS₂), K[S₂P(OMe)₂], and K[N(Ph₂PS)₂]₂ afforded monomeric [Ir(Buppy)₂(S^∧S)] (S^∧S=Et₂NCS₂ (3), S₂P(OMe)₂ (4), N(PPh₂S)₂ (5)) and [Rh(Buppy)₂(S^∧S)] (S^∧S=Et₂NCS₂ (6), S₂P(OMe)₂ (7), N(PPh₂S)₂ (8)), respectively. Reaction of 1 with Na[N(PPh₂Se)₂] gave [Ir(Buppy)₂{N(PPh₂Se)₂}] (9). The crystal structures of 3, 4, 7, and 8 have been determined. Treatment of 1 or 2 with AgOTf (OTf=triflate) followed by reaction with KSCN gave dinuclear [{M(Buppy)₂}₂(μ-SCN)₂] (M=Ir (10), Rh (11)), in which the SCN⁻ ligands bind to the two metal centers in a μ-S,N fashion. Interaction of 1 and 2 with [Et₄N]₂[WQ₄] gave trinuclear heterometallic complexes [{Ir(Buppy)₂}₂(μ-WQ₄)] (Q=S (12), Se (13)) and [{Rh(Buppy)₂}₂{(μ-WQ)₄}] (Q=S (14), Se (15)), respectively. Hydrolysis of 12 led to formation of [{Ir(Buppy)₂}₂{W(O)(μ-S)₂(μ₃-S)}] (16) that has been characterized by X-ray diffraction.     

Regioselective Synthesis of Polycyclic and Heptagon-embedded Aromatic Compounds through a Versatile π-Extension of Aryl Halides

A versatile π-extension reaction was developed based on the three-component cross-coupling of aryl halides, 2-haloarylcarboxylic acids, and norbornadiene. The transformation is driven by the direction and subsequent decarboxylation of the carboxyl group, while norbornadiene serves as an ortho-C−H activator and ethylene synthon via a retro-Diels–Alder reaction. Comprehensive DFT calculations were performed to account for the catalytic intermediates.     

Palladium‐Catalyzed Cross‐Dehydrogenative Functionalization of C(sp2)H Bonds

The catalytic cross‐dehydrogenative coupling (CDC) reaction has received intense attention in recent years. The attractive feature of this coupling process is the formation of a C? C bond from two C? H moieties under oxidative conditions. In this Focus Review, recent advances in the palladium‐catalyzed CDC reactions of C(sp²)? H bond are summarized, with a focus on the period from 2011 to early 2013.