ABSTRACT. This paper is concerned with the global smooth isometric immersion in M 3 of complete simply connected negative curved surfaces. A sufficient condition involving the rate of decay of the curvature at infinity is imposed.
Unsolvated, trinuclear, homometallic, rare-earth-metal multimethyl methylidene complexes [{(NCN)Ln(μ(2)-CH(3))}(3)(μ(3)-CH(3))(μ(3)-CH(2))] (NCN = L = [PhC{NC(6)H(4)(iPr-2,6)(2)}(2)](-); Ln = Sc (2a), Lu (2b)) have been synthesized by treatment of [(L)Ln{CH(2)C(6)H(4)N(CH(3))(2)-o}(2)] (Ln = Sc (1a), Lu (1b)) with two equivalents of AlMe(3) in toluene at ambient temperature in good yields. Treatment of 1 with three equivalents of AlMe(3) gives the heterometallic trinuclear complexes [(L)Ln(AlMe(4))(2)] (Ln = Sc (3a), Lu (3b)) in good yields. Interestingly, 2 can also be generated by recrystallization of 3 in THF/toluene, thereby indicating that the THF molecule can also induce C-H bond activation of 2. Reaction of 2 with one equivalent of ketones affords the trinuclear homometallic oxo-trimethyl complexes [{(L)Ln(μ(2) -CH(3))}(3) (μ(3)-CH(3))(μ(3)-O)] (Ln = Sc(4a), Lu(4b)) in high yields. Complex 4b reacts with one equivalent of cyclohexanone to give the methyl abstraction product [{(L)Lu(μ(2) -CH(3) )}(3) (μ(3) -OC(6)H(9))(μ(3)-O)] (5b), whereas reaction of 4b with acetophenone forms the insertion product [{(L)Lu(μ(2)-CH(3))}(3){μ(3)-OCPh(CH(3))(2)}(μ(3)-O)] (6b). Complex 4a is inert to ketone under the same conditions. All these new complexes have been characterized by elemental analysis, NMR spectroscopy, and confirmed by X-ray diffraction determination.
Two new trinuclear μ3 -bridged rare-earth metal phosphinidene complexes, [{L(Ln)(μ-Me)}3 (μ3 -Me)(μ3 -PPh)] (L=[PhC(NC6 H4 iPr2 -2,6)2 ](-) , Ln=Y (2 a), Lu (2 b)), were synthesized through methane elimination of the corresponding carbene precursors with phenylphosphine. Heating a toluene solution of 2 at 120 °C leads to an unprecedented ortho CH bond activation of the PhP ligand to form the bridged phosphinidene/phenyl complexes. Reactions of 2 with ketones, thione, or isothiocyanate show clear phospha-Wittig chemistry, giving the corresponding organic phosphinidenation products and oxide (sulfide) complexes. Reaction of 2 with CS2 leads to the formation of novel trinuclear rare-earth metal thione dianion clusters, for which a possible pathway was determined by DFT calculation.
Mononuclear amidinate yttrium complex C4H9C(NR)2Y(o‐CH2C6H4NMe2)2 (R=2,6‐iPr2C6H3) and a series of binuclear rare‐earth metal complexes bearing a bridged amidinate ligand [(RN)2C(CH2)4C(NR)2][RE{CH2C6H4(o‐NMe2)}2]2 (R=2,6‐iPr2C6H3, RE=Y, Lu, Sc) were synthesized and fully characterized. The catalytic behavior of these complexes for (co)polymerization of conjugated dienes such as isoprene and myrcene in the presence of co‐catalyst [Ph3C][B(C6F5)4] was investigated. These catalytic systems show impressively high activity and 3,4‐regioselectivity in living (co)polymerization. The binuclear bridged amidinate yttrium catalytic system not only exhibits the highest activity among the reported catalytic systems for 3,4‐polymerization of isoprene but also allows the steady polymerization in a living manner from −20 to 80 °C. Compared with the dramatic drop of 3,4‐selectivity for the mononuclear analogue, the binuclear catalytic system still shows moderate 3,4‐selectivity at 80 °C. Moreover, a facile one‐pot synthetic strategy for a polymer blend containing 3,4‐ and 1,4‐polyisoprene (PIP) was established through the in situ modification of the active amidinate yttrium species by addition of an excess amount of AlMe3.
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