Expected profit functional form

While there have been a considerable number of structural models for these multinuclear zinc enzymes (49), there have only been a few functional models until now. Czamik et al. have reported phosphate hydrolysis with bis(Coni-cyclen) complexes 39 (50) and 40 (51). The flexible binuclear cobalt(III) complex 39 (1 mM) hydrolyzed bis(4-nitro-phenyl)phosphate (BNP-) (0.05 mM) at pH 7 and 25°C with a rate 3.2 times faster than the parent Coni-cyclen (2 mM). The more rigid complex 40 was designed to accommodate inorganic phosphate in the in-temuclear pocket and to prevent formation of an intramolecular ju.-oxo dinuclear complex. The dinuclear cobalt(III) complex 40 (1 mM) indeed hydrolyzed 4-nitrophenyl phosphate (NP2-) (0.025 mM) 10 times faster than Coni-cyclen (2 mM) at pH 7 and 25°C (see Scheme 10). The final product was postulated to be 41 on the basis of 31P NMR analysis. In 40, one cobalt(III) ion probably provides a nucleophilic water molecule, while the second cobalt(III) binds the phosphoryl group in the form of a four-membered ring (see 42). The reaction of the phosphomonoester NP2- can therefore profit from the special placement of the two metal ions. As expected from the weaker interaction of BNP- with cobalt(in), 40 did not show enhanced reactivity toward BNP-. However, in the absence of more quantitative data, a detailed reaction mechanism cannot be drawn. 

Company objectives. The notion of an optimal strategy is obviously sensitive to the choice of objective function. Like most economic models, the multi-channel literature has tended to assume that all firms seek to maximize some form of (expected) gross profit. While this may be the ultimate aim for most companies, certain legitimate channel strategies are not tied directly to this, at least not in the short run. 

Abstract The selective catalytic activation/functionalization of sp C-H bonds is expected to improve synthesis methods by better step number and atom economy. This chapter describes the recent achievements of ruthenium(II) catalysed transformations of sp C-H bonds for cross-coupled C-C bond formation. First arylation and heteroarylation with aromatic halides of a variety of (hetero)arenes, that are directed at ortho position by heterocycle or imine groups, are presented. The role of carboxylate partners is shown for Ru(II) catalysts that are able to operate profitably in water and to selectively produce diarylated or monoarylated products. The alkylation of (hetero)arenes with primary and secondary alkylhalides, and by hydroarylation of alkene C=C bonds is presented. The recent access to functional alkenes via oxidative dehydrogenative functionalization of C-H bonds with alkenes first, and then with alkynes, is shown to be catalysed by a Ru(ll) species associated with a silver salt in the presence of an oxidant such as Cu(OAc)2. Finally the catalytic oxidative annulations with alkynes to rapidly form a variety of heterocycles are described by initial activation of C-H followed by that of N-H or O-H bonds and by formation of a second C-C bond on reaction with C=0, C=N, and sp C-H bonds. Most catalytic cycles leading from C-H to C-C bond are discussed. 

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