High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

Rhodium(I) carbonyl complexes with α-diimine ligands containing amino or hydroxy substituents

-Diimines, RN:C(R)C(R):NR(LL) derived from glyoxal, GLL (R=H) abbreviated as GAA (R= R=4-dimethylaminophenyl) or GHA (R= R=4-hydroxyphenyl), and derived from biacetyl, BLL (R=Me) abbreviated as BDH (R=R= NH₂), BOH (R=NH₂, R=OH) react with carbonylrhodium(I) compounds to give different products depending on the imino substituents in the ligand and/or the solvent employed. The reaction of -diimines bearing amino groups, such as GAA or BDH with [RhCl(CO)₂]₂ in acetone yields binuclear [RhCl(CO)₂]₂(-LL) while in CH₂Cl₂ ionic [Rh- (CO)₂(LL)]⁺[RhCl₂(CO)₂]^– species are obtained. In acetone [RhCl(CO)₂]₂(-GAA) exists as an equilibrium mixture between two different neutral binuclear species; [Rh(CO)₂(BDH)]⁺ exists as a mixture of two species containing chelate or monodentate bonded diimine respectively. GAA or BDH react in situ with [RhCl(CO)(C₂H₄)]₂ in benzene to yield tetracoordinated monocarbonylated [RhCl(CO)(LL)] compounds. -Diimines (LL) bearing hydroxy groups, such as GHA or BOH react with [RhCl(CO)₂]₂ or [RhCl(CO)(C₂H₄)]₂ to give pentacoordinated dicarbonylated [RhCl(CO)₂(LL)] compounds.     

High-order nonlinear initial-value problems countably determined

We give a numerical approximation of the solution of a high-order nonlinear initial-value problem by making use of certain properties of an adequate Schauder basis.     

Novel hydridoirida-beta-diketones containing small molecules, CO, or ethylene: their behavior in coordinating solvents such as dimethylsulfoxide or acetonitrile

New hydridoirida-beta-diketones [IrH[(PPh2(o-C6H4CO))2H](CO)]ClO4 2 and [IrH[(PPh2(o-C6H4CO))2H](olefin)]BF4 (olefin = C2H4, 5; 1-hexene, 10) have been prepared. These complexes may afford new diacylhydridoiridium(III) derivatives. In chloroform solution, complex 2 is in equilibrium with the deprotonated diacylhydride trans-[IrH(PPh2(o-C6H4CO))2(CO)] complex 3. In DMSO, deprotonation of 2 occurs to yield the kinetically favored product 3, which isomerizes to the thermodynamically favored complex cis-[IrH(PPh2(o-C6H4CO))2(CO)] 4. Reprotonation of 4 with HBF4 in chlorinated solvents gives the cation in 2. In coordinating solvents such as dimethyl sulfoxide or acetonitrile, complex 5 undergoes displacement of ethylene to afford [IrH{(PPh2(o-C6H4CO))2H](L)]BF4 (L = DMSO, 7; CH3CN, 9). Complexes 5 and 7 undergo deprotonation by NEt3 to give the corresponding diacylhydrides. The ethylene complex gives only trans-[IrH(PPh2(o-C6H4CO))2(C2H4)] 6, while the dimethyl sulfoxide derivative affords a mixture of trans- and cis-[IrH(PPh2(o-C6H4CO))2(DMSO)] 8. Complex 10 shows inhibited alkene rotation around the Ir-olefin axis. All of the complexes were fully characterized spectroscopically. Single-crystal X-ray diffraction analysis was performed on complexes 3, 4, and 9. The 13C NMR and X-ray data point to a carbenoid character in the carbon atoms bonded to iridium in the irida--diketone fragment, so that it can be considered as an acyl(hydroxycarbene) moiety.     

Formation of 18e− and 16e− Acyl(η3‐cyclooctenyl)rhodium(III) Complexes in the Reaction of Cationic (Cycloocta‐1,5‐diene)rhodium(I) Compounds with 2‐(Diphenylphosphino)benzaldehyde

The reaction of cationic diolefinic rhodium(I) complexes with 2‐(diphenylphosphino)benzaldehyde (pCHO) was studied. [Rh(cod)₂]ClO₄ (cod=cycloocta‐1,5‐diene) reacted with pCHO to undergo the oxidative addition of one pCHO with (1,2,3‐η)cyclooct‐2‐en‐1‐yl (η³‐C₈H₁₃) formation, and the coordination of a second pCHO molecule as (phosphino‐κP)aldehyde‐κO(σ‐coordination) chelate to give the 18e⁻ acyl(allyl)rhodium(III) species [Rh(η³‐C₈H₁₃)(pCO)(pCHO)]ClO₄ (see 1 ). Complex 1 reacted with [Rh(cod)(PR₃)₂]ClO₄ (R=aryl) derivatives 3 – 6 to give stable pentacoordinated 16e⁻ acyl[(1,2,3‐η)‐cyclooct‐2‐en‐1‐yl]rhodium(III) species [Rh(η³‐C₈H₁₃)(pCO)(PR₃)]ClO₄ 7 – 10 . The (1,2,3‐η)‐cyclooct‐2‐en‐1‐yl complexes contain cis‐positioned P‐atoms and were fully characterized by NMR, and the molecular structure of 1 was determined by X‐ray crystal diffraction. The rhodium(III) complex 1 catalyzed the hydroformylation of hex‐1‐ene and produced 98% of aldehydes (n/iso=2.6).     

Rhodium(I) complexes with bidentate nitrogen heterocycles and their reactions with tin(II) chloride and carbon monoxide

Summary Cleavage of [{Rh(diolefin)Cl}₂] by bidentate heterocyclic chelating ligands (LL) has been studied, and diolefin neutral, ionic or ion-pair type compounds are formed depending on the ligands and/or the Rh: (LL) ratio employed. When the reactions are performed in media saturated with CO and with Rh: (LL)=21, only carbonylated ion-pair complexes are formed. The diolefin compounds react with tin(II) chloride yielding species containing trichlorostannato-groups. Subsequent reaction with CO leads to displacement of the diolefin and formation of the corresponding dicarbonyl species.     

Reactions of hydridoirida-β-diketones with amines or with 2-aminopyridines: formation of hydridoirida-β-ketoimines, PCN terdentate ligands, and acyl decarbonylation

The hydridoirida-β-diketone [IrHCl{(PPh(2)(o-C(6)H(4)CO))(2)H}] (1) reacts with benzylamine (C(6)H(5)CH(2)NH(2)) to give the hydridoirida-β-ketoimine [IrHCl{(PPh(2)(o-C(6)H(4)CO))(PPh(2)(o-C(6)H(4)CNCH(2)C(6)H(5)))H}] (2), stabilized by an intramolecular hydrogen bond. 2 reacts with water to undergo hydrolysis and amine coordination giving hydridodiacylamino [IrH(PPh(2)(o-C(6)H(4)CO))(2)(C(6)H(5)CH(2)NH(2))] (3). Cyclohexylamine or dimethylamine lead to hydridodiacylamino [IrH(PPh(2)(o-C(6)H(4)CO))(2)L] (4-5). In chlorinated solvents hydridodiacylamino complexes undergo exchange of hydride by chloride to afford [IrCl(PPh(2)(o-C(6)H(4)CO))(2)L] (6-9). The reaction of 1 with hydrazine (H(2)NNH(2)) gives hydridoirida-β-ketoimine [IrHCl{(PPh(2)(o-C(6)H(4)CO))(PPh(2)(o-C(6)H(4)CNNH(2)))H}] (10), fluxional in solution with values for ΔH(?) of 2.5 ± 0.3 kcal mol(-1) and for ΔS(?) of -32.9 ± 3 eu. A hydrolysis/imination sequence can be responsible for fluxionality. 2-Aminopyridines (RHNC(5)H(3)R'N) react with 1 to afford cis-[IrCl(PPh(2)(o-C(6)H(4)CO))(PPh(2)(o-C(6)H(4)CHNRC(5)H(3)R'N))] (R = R' = H (11), R = CH(3), R' = H (12), R = H, R' = CH(3) (13)) containing new terdentate PCN ligands in a facial disposition and cis phosphorus atoms as kinetic products. The formation of 11-13 requires imination of the hydroxycarbene moiety of 1, coordination of the nitrogen atom of pyridine to iridium, and iridium to carbon hydrogen transfer. In refluxing methanol, complexes 11-13 isomerize to afford the thermodynamic products 14-16 with trans phosphorus atoms. Chloride abstraction from complexes [IrCl(PPh(2)(o-C(6)H(4)CO))(PPh(2)(o-C(6)H(4)CHNRC(5)H(4)N))] (R = H or CH(3)) leads to decarbonylation of the acylphosphine chelating group to afford cationic complexes [Ir(CO)(PPh(2)(o-C(6)H(4)))(PPh(2)(o-C(6)H(4)CHNRC(5)H(4)N))]A, 17 (R = H, A = ClO(4)) and 18 (R = CH(3), A = BF(4)) as a cis/trans = 4:1 mixture of isomers. Single crystal X-ray diffraction analysis was performed on 6, 9, 13, and 14.     

Synthesis and catalytic activity of some cationic complexes of rhodium(I) with norbornadiene and group Vb ligands

Summary The syntheses of [Rh(NBD)L₂ ]ClO₄ complexes (L=nitrogen donor ligand), obtained from [Rh(NBD)₂]ClO₄, and their reactions with triphenylphosphine and carbon monoxide are described.The catalytic activity of some of these and related complexes is considered.