Lewis Base Behavior of Bridging Nitrido Ligands of Titanium Polynuclear Complexes

The Lewis base behavior of μ₃‐nitrido ligands of the polynuclear titanium complexes [{Ti(η⁵‐C₅Me₅)(μ‐NH)}₃(μ₃‐N)] ( 1 ) and [{Ti(η⁵‐C₅Me₅)}₄(μ₃‐N)₄] ( 2 ) to MX Lewis acids has been observed for the first time. Complex 1 entraps one equivalent of copper(I ) halide or copper(I ) trifluoromethanesulfonate through the basal NH imido groups to give cube‐type adducts [XCu{(μ₃‐NH)₃Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}] (X=Cl ( 3 ), Br ( 4 ), I ( 5 ), OSO₂CF₃ ( 6 )). However, the treatment of 1 with an excess (≥2 equiv) of copper reagents afforded complexes [XCu{(μ₃‐NH)₃Ti₃(η⁵‐C₅Me₅)₃(μ₄‐N)(CuX)}] (X=Cl ( 7 ), Br ( 8 ), I ( 9 ), OSO₂CF₃ ( 10 )) by incorporation of an additional CuX fragment at the μ₃‐N nitrido apical group. Similarly, the tetranuclear cube‐type nitrido derivative 2 is capable of incorporating one, two, or up to three CuX units at the μ₃‐N ligands to give complexes [{Ti(η⁵‐C₅Me₅)}₄(μ₃‐N)_4?n{(μ₄‐N)CuX}_n] (X=Br ( 11 ), n=1; X=Cl ( 12 ), n=2; X=OSO₂CF₃ ( 13 ), n=3). Compound 2 also reacts with silver(I ) trifluoromethanesulfonate (≥1 equiv) to give the adduct [{Ti(η⁵‐C₅Me₅)}₄(μ₃‐N)₃{(μ₄‐N)AgOSO₂CF₃}] ( 14 ). X‐ray crystal structure determinations have been performed for complexes 8 – 13 . Density functional theory calculations have been carried out to understand the nature and strength of the interactions of [{Ti(η⁵‐C₅H₅)(μ‐NH)}₃(μ₃‐N)] ( 1′ ) and [{Ti(η⁵‐C₅H₅)}₄(μ₃‐N)₄] ( 2′ ) model complexes with copper and silver MX fragments. Although coordination through the three basal NH imido groups is thermodynamically preferred in the case of 1′ , in both complexes the μ₃‐nitrido groups act as two‐electron donor Lewis bases to the appropriate Lewis acids.     

Weakly compact operators on non-complete normed spaces

We prove that weakly compact operators on a non-reflexive normed space cannot be bijective. We also show that, in the above result, bijectivity cannot be relaxed to surjectivity. Finally, we study the behaviour of surjective weakly compact operators on a non-reflexive normed space, when they are perturbed by small scalar multiples of the identity, and derive from this study the recent result of Spurný [A note on compact operators on normed linear spaces, Expo. Math. 25 (2007) 261–263] that compact operators on an infinite-dimensional normed space cannot be surjective.     

Molecular Nitrides with Titanium and Group 13–15 Elements

Several heterometallic nitrido complexes were prepared by reaction of the imido–nitrido titanium complex [{Ti(η⁵‐C₅Me₅)(μ‐NH)}₃(μ₃‐N)] ( 1 ) with amido derivatives of Group 13–15 elements. Treatment of 1 with bis(trimethylsilyl)amido [M{N(SiMe₃)₂}₃] derivatives of aluminum, gallium, or indium in toluene at 150–190 °C affords the single‐cube amidoaluminum complex [{(Me₃Si)₂N}Al{(μ₃‐N)₂(μ₃‐NH)Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}] ( 2 ) or the corner‐shared double‐cube compounds [M(μ₃‐N)₃(μ₃‐NH)₃{Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}₂] [M=Ga ( 3 ), In ( 4 )]. Complexes 3 and 4 were also obtained by treatment of 1 with the trialkyl derivatives [M(CH₂SiMe₃)₃] (M=Ga, In) at high temperatures. The analogous reaction of 1 with [{Ga(NMe₂)₃}₂] at 110 °C leads to [{Ga(μ₃‐N)₂(μ₃‐NH)Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}₂] ( 5 ), in which two [GaTi₃N₄] cube‐type moieties are linked through a gallium–gallium bond. Complex 1 reacts with one equivalent of germanium, tin, or lead bis(trimethylsilyl)amido derivatives [M{N(SiMe₃)₂}₂] in toluene at room temperature to give cube‐type complexes [M{(μ₃‐N)₂(μ₃‐NH)Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}] [M=Ge ( 6 ), Sn ( 7 ), Pb ( 8 )]. Monitoring the reaction of 1 with [Sn{N(SiMe₃)₂}₂] and [Sn(C₅H₅)₂] by NMR spectroscopy allows the identification of intermediates [RSn{(μ₃‐N)(μ₃‐NH)₂Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}] [R=N(SiMe₃)₂ ( 9 ), C₅H₅ ( 10 )] in the formation of 7 . Addition of one equivalent of the metalloligand 1 to a solution of lead derivative 8 or the treatment of 1 with a half equivalent of [Pb{N(SiMe₃)₂}₂] afford the corner‐shared double‐cube compound [Pb(μ₃‐N)₂(μ₃‐NH)₄{Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}₂] ( 11 ). Analogous antimony and bismuth derivatives [M(μ₃‐N)₃(μ₃‐NH)₃{Ti₃(η⁵‐C₅Me₅)₃(μ₃‐N)}₂] [M=Sb ( 12 ), Bi ( 13 )] were obtained through the reaction of 1 with the tris(dimethylamido) reagents [M(NMe₂)₃]. Treatment of 1 with [AlCl₂{N(SiMe₃)₂}(OEt₂)] affords the precipitation of the singular aluminum–titanium square‐pyramidal aggregate [{{(Me₃Si)₂N}Cl₃Al₂}(μ₃‐N)(μ₃‐NH)₂{Ti₃(η⁵‐C₅Me₅)₃(μ‐Cl)(μ₃‐N)}] ( 14 ). The X‐ray crystal structures of 5 , 11 , 13 , 14 , and [AlCl{N(SiMe₃)₂}₂] were determined.     

Effect of random longitudinal vibrations on the Poiseuille flow of a complex liquid

In this work, the rectilinear Poiseuille flow of a complex liquid flowing in a vibrating pipe is analyzed. The pipe wall performs oscillations of small amplitude that can be adequately represented by a weakly stochastic process, for which a quasi-static perturbation solution scheme is suggested. The flow is analyzed using the Bautista–Manero–Puig constitutive equation, consisting on the upper-convected Maxwell equation coupled to a kinetic equation to account for the breakdown and reformation of the fluid structure. A drastic enhancement of the volumetric flow is predicted in the region where the fluid experiences pronounced shear-thinning. Finally, flow enhancement is predicted using experimental data reported elsewhere for wormlike micellar solutions of cetyl trimethyl ammonium tosilate.     

(Non)commutative Isotropization in Bianchi I with Barotropic Perfect Fluid and Λ Cosmological

Using the WKB-like and Hamilton procedures classical solutions to commutative and noncommutative cosmology are found. This is carried out in the Bianchi type I cosmological model coupled to barotropic perfect fluid and cosmological constant. Noncommutativity is achieved by modifying the symplectic structure considering that minisuperspace variables do not commute, using a deformation between all the minisuperspace variables. It is shown that the anisotropic parameter β _±nc for some value in the Λ cosmological term and noncommutative θ parameter, present a dynamical isotropization until a critical cosmic time t _c . After this time the effects of minisuperspace noncommutativity in the isotropization seem to disappear.     

Titanium alkali metal nitrido complexes

Treatment of [(Ti(eta5-C5Me5)(mu-NH))3(mu3-N)] with alkali metal bis(trimethylsilyl)amido reagents in toluene afforded the complexes [M(mu3-N)(mu3-NH)2[Ti3(mu5-C5Me5)3(mu3-N)]]2 (M = Li (2), Na, (3), K (4)). The molecular structures of 2 and 3 have been determined by X-ray crystallographic studies and show two azaheterometallocubane cores [MTi3N4] linked by metal-nitrogen bonds. Reaction of the lithium derivative 2 with chlorotrimethylsilane or trimethyltin chloride in toluene gave the incomplete cube nitrido complexes [Ti3(eta5-C5Me5)3(mu-NH)2(mu-NMMe3)(mu3-N)] (M = Si (5), Sn (6)). A similar reaction with indium(I) or thallium(I) chlorides yielded cube-type derivatives [M(mu3-N)(mu3-NH)2[Ti(eta5-C5Me5)3(mu3-N)] (M=In (7), Tl (8)).     

Screening method for pesticides in air by gas chromatography/tandem mass spectrometry

A multiresidue method for determining more than 70 pesticides in air has been validated using a single injection with gas chromatography/tandem mass spectrometry (GC/MS/MS). The method validation considered both stages of sampling and analysis. The sampling method, based on active sampling using sorption in sorbent cartidges, was validated by generating standard atmospheres. Performance parameters of the method were evaluated, with a reduction in the limits of quantification by injecting a higher volume of sample extract, and increase of selectivity by the use of MS/MS detection mode. The method was based on solid-phase extraction, which permits a degree of automation. The best adsorbents were found to be Chromosorb 106 and Tenax TA. The retention capacity of these sampling sorbents allows up to 1440 L of air to be sampled without any breakthrough for most of the compounds. Data were generated for assessing the potential exposure of bystanders. The application of the method to the analysis of the air in urban locations near agricultural areas showed that pesticides were present in most of the samples.     

Rhodium/iridium-titanium azaheterometallocubanes

Treatment of [[Ti(eta5-C5Me5)(mu-NH)]3(mu3-N)] (1) with the diolefin complexes [[MCl(cod)]2] (M = Rh, Ir; cod = 1,5-cyclooctadiene) in toluene afforded the ionic complexes [M-(cod)(mu3-NH)3Ti3(eta5-C5Me5)3(mu3-N)]Cl [M = Rh (2), Ir (3)]. Reaction of complexes 2 and 3 with [Ag(BPh4)] in dichloromethane leads to anion metathesis and formation of the analogous ionic derivatives [M(cod)(mu3-NH)3Ti3-(eta5-C5Me5)3(mu3-N)][BPh4] [M = Rh (4), Ir (5)]. An X-ray crystal structure determination for 5 reveals a cube-type core [IrTi3N4] for the cationic fragment, in which 1 coordinates in a tripodal fashion to the iridium atom. Reaction of the diolefin complexes [[MCl(cod))2] (M = Rh, Ir) and [[RhCl(C2H4)2]2] with the lithium derivative [[Li(mu3-NH)2(mu3-N)-Ti3(eta5-C5Me5)3(mu3-N)]2] x C7H8 (6 C7H8) in toluene gave the neutral cube-type complexes [M(cod)(mu-NH)2(mu3-N)Ti3-(eta5-C5Me5)3(mu3-N)] [M = Rh (7), Ir (8)] and [Rh(C2H4)2(mu3-NH)2(mu3-N)Ti3(eta5-C5Me5)3(mu3-N)] (9), respectively. Density functional theory calculations have been carried out on the ionic and neutral azaheterometallocubane complexes to understand their electronic structures.     

Hydrocarbon species mu3-CCH2-, mu3-CCH3 and mu-CHCH3 supported on Ti3O3

Treatment of the mu3-ethylidyne complex [{TiCp*(mu-O)}3(mu3-CMe)](1), (Cp*=eta5-C5Me5) with alkali metal amides leads to the oxoheterometallocubane derivatives [M(mu3-O)3{(TiCp*)3(mu3-CCH2)}] [M = Li (2), Na (3), K (4), Rb (5), Cs (6)] containing the naked carbanion mu3-CCH2-; the addition of triphenylmethanol and tert-butanol to the compounds 2-6 gives rise to the oxoderivatives [{TiCp*(mu-O)}3(mu-CHMe)(OCR3)][R = Me (7), Ph (8)] which show a mu-ethylidene bridge on the surface model Ti3O3.