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Control vector parametrization is one of the most frequently used techniques for determining numerically the optimal control profile for batch process optimization. In this article, we suggest the Karhunen−Loéve eigenfunctions as trial functions for obtaining a better representation of the exact optimal control profile while keeping the number of coefficients to be determined as small as possible. The procedure for finding the K−L trial functions is demonstrated on a batch electrochemical process for glyoxylic acid synthesis, and closed-loop optimization by control vector parametrization with K−L trial functions is studied by simulation. The results show that only two trial functions are needed for a satisfactory representation of the open-loop profiles, and as a consequence of the reduced solution space, the on-line computation need is greatly relieved, and the optimization algorithm converges more rapidly and more stably.

Two ytterbocene derivatives containing aromatic nitrogen ligands, (C5H5)2YbCbz(THF) (1) and (C5H5)2YbPzMe2(THF) (4), were synthesized, and their reactivities toward N,N‘-diisopropylcarbodiimide, phenyl isothiocyanate, and phenyl isocyanate were studied. Abstraction of cyclopentadienyl from (C5H5)3Yb with 1 equiv of carbazole (HCbz) in THF at room temperature gives 1. Reaction of 1 with N,N‘-diisopropylcarbodiimide (ⁱPrN&dbd;C&dbd;NⁱPr) results in monoinsertion of ⁱPrN&dbd;C&dbd;NⁱPr into the Yb−N(Carbazolate) bond, yielding the ytterbocene guanidinate (C5H5)2Yb[ⁱPrN&bondDotb;C(Cbz)&bondDotb;NⁱPr] (2), while treatment of 1 with 1 equiv of phenyl isothiocyanate (PhNCS) gives the unexpected monocyclopentadienylytterbium complex (C5H5)Yb[S&bondDotb;C(Cbz)&bondDotb;NPh]2(THF) (3) and (C5H5)3Yb(THF), which may be rationalized by the ligand rearrangement of the monoinsertion product (C5H5)2Yb[S&bondDotb;C(Cbz)&bondDotb;NPh]. (C5H5)3Yb reacts with 3,5-dimethylpyrazole (HPzMe2) in a 1:1 ratio at ambient temperature to form complex 4. Reaction of 4 with PhNCO gives the insertion product (C5H5)2Yb[OC(&dbd;NPh)PzMe2](THF) (5). In contrast to 1, however, complex 4 does not react with ⁱPrNCNⁱPr under the same conditions. All these complexes were characterized by elemental analysis and spectroscopic properties. The structures of complexes 2−5 were also determined by X-ray single-crystal diffraction analyses. These reactions present the first example of 1,3-heterocumulene insertions into the Ln−N(aromatic ring) bond and provide a new strategy for introducing a substituent at the nitrogen atom of organic heterocycle compounds.

The synthesis, structures, and reactivity of new lanthanocene complexes incorporating amidinate ligand [^tBuN&bondDotb;C(ⁿBu)&bondDotb;N^tBu] are described. Treatment of Cp2LnⁿBu (Ln = Er (1), Y (2), Gd (3)) with N,N‘-di-tert-butylcarbodiimide results in monoinsertion of carbodiimide into the Ln−C σ-bond to yield the title compounds Cp2Ln[^tBuN&bondDotb;C(ⁿBu)&bondDotb;N^tBu] (Ln = Er (4), Y (5), Gd (6)). Complexes 4−6 were characterized by elemental analysis and IR and mass spectroscopies. The structures of complexes 4 and 5 were determined through X-ray single-crystal diffraction analysis. It is shown that compound 5 is a fine catalyst for cyclotrimerization of phenyl isocyanate.

Cp‘2LnR(THF) (Cp‘ = C5H4CH3) reacted with phenyl isocyanate to form the PhNCO insertion products [Cp‘2Ln(OC(R)NPh)]2 [R = n-butyl, Ln = Sm (1), Dy (2), Er (3); R = α-naphthyl, Ln = Dy (4)]. It was found that an excess of PhNCO did not affect the nature of the final complexes, a single insertion only being observed and excess PhNCO forming a cyclotrimer (5). The reaction of Cp‘HoCl2(THF)3 with BuⁿLi and subsequently with 2 equiv of PhNCO in THF gave Ho[OC(Buⁿ)NPh)]3 (6) and [Cp‘2Ho(OC(Buⁿ)NPh)]2 (7), which can be rationalized by the rearrangement reaction of the di-insertion product Cp‘Ho[OC(Buⁿ)NPh]2(THF)x. The structures of 1, 4·THF, 5·THF and 7 were determined by X-ray diffraction, revealing an unusual bonding mode of the amido groups arising from the insertion of PhNCO into the Ln−C σ-bonds and that the O&bondDotb;C&bondDotb;N fragment of the OC(R)NPh ligand acts as both a bridging and side-on chelating group.

Amidation of a variety of hydrocarbons with PhI&dbd;NTs catalyzed by ruthenium and manganese meso-tetrakis(pentafluorophenyl)porphyrins 1 and 2 afforded N-substituted amides in up to 92% yields with good to excellent substrate conversions. By employing catalyst 2, exceptionally high turnovers (up to 2600) were achieved, and the amidations can be effected by directly using PhI(OAc)2/NH2R as amidating reagents; in the case of R = COCF3 a direct amination was realized in up to 90% yield.