W-MAP complexes

The rates of interconversion of the syn and anti isomers were found to be one to two orders of magnitude faster for W MAP complexes than for Mo MAP complexes. Little is known about the rates of interconversion of syn-and anti-protons for MAP species [2c], although the rates of syn/anti interconversions in bisalkoxide Mo imido alkylidene complexes have been found to vary over approximately six orders of magnitude [57]. It is not surprising that the sterically demanding NArj jg52 ligand would destabilize the syn isomer for steric reasons and lead to mixtures that contain both syn and anti species, as observed. 

Figure 2.19 Recent, W-MAP complexes for the olefin metathesis step.

Fig. 28 Z-Selective homocoupling of terminal alkenes catalyzed by W-MAP complexes...

Until recently, the vast majority of high-oxidation state Mo and W alkylidene complexes active for olefin metathesis were bisalkoxides, bisaryloxides, or biden-tate variations of aryloxides (biphenolates and binaphtholates). Calculations have suggested that catalysts that contain a stereogenic metal center, especially MAP complexes, are more efficient for electronic reasons [7]. 

Alternatively, monoaryloxide-pyrrolide (MAP) complexes of Mo and W have been developed. It was found that the methyUdene species of these complexes were quite stable toward bimolecular decomposition, yet very reactive [20]. As such, MAP catalysts are very efficient in reactions, including the ethenolysis of methyl oleate [21], enantioselective RCM [22], and Z-selective homocouplings and cross metatheses [23, 24]. MAP catalysts are further discussed in detail in Chapters 1, 6, and see Grubbs, Handbook of Metathesis, 2nd Edition, Volume 2, Chapter 7. 

The Schrock lab focused on the development of new catalysts to address the Z-selectivity for a simplified cross metathesis homocoupling of terminal alkenes (Fig. 28) [61,62]. While various Mo-MAP catalysts including the optimal ones for the previous systems failed to provide homocoupled internal olefins in high Z-selectivity, it was discovered that the less reactive W-based MAP complexes A and B supported by the sterically bulky HIPTO or the 3,3 -bismesityl-aryloxide... 

Conformal Mapping Every function of a complex variable w = f z) = u x, y) + iv(x, y) transforms the x, y plane into the u, v plane in some manner. A conformal transformation is one in which angles between curves are preserved in magnitude xnd sense. Every analytic function, except at those points where/ ( ) = 0, is a conformal transformation. See Fig. 3-48. 

Hofker, M.H., Walter, M.A., Cox, D.W. (1989). Complete physical map of the human heavy chain constant region gene complex. Proc. Natl. Acad. Sci. USA 86,5567-5571. 

G Mosser, C D rr, G Hauska and W Khibrandt (1994) A projection map of the cytochrome b6f complex from the spinach chloroplast membranes. International Congress on Electron Microscopy 1994, Les Editions de Physique 3 609-610... 

Practically, DMTA is limited to low frequencies (up to tens of hertz) and, consequently, provides information about relatively slow processes. Dielectric spectroscopy is a related approach in which an alternating electric field is applied to a sample and the complex permittivity is then obtained from phase and amplitude measurements of current and voltage again, it is possible to consider data in the frequency domain, the temperature domain, or even as frequency/temperature contour maps.2 ° 2 See Refs. 230 and 232 for a theoretical account of the underlying physics. The approach can provide information in the frequency range W -io" coupling the applied electric field... 

The mapping w = Log z is a single-valued and continuous function in its domain of definition, which is the set of all nonzero complex numbers its range is the strip -n < Im(w) < 0. Thus the function Log z is analytic. 

W. Fiedler, C. Borchers, M. Macht, S.O. Dei-ninger and M. Przybylski, (1998). Molecular characterization of a conformational epitope of hen egg white lysozyme by differential chemical modification of immune complexes and mass spectrometric peptide mapping. Bio-conj. Chem. 9, 236-241. 

Adam, G. C., Burbaum, J., Kozarich,J. W., Patricelli, M. P., Cravatt, B. F. (2004). Mapping enzyme active sites in complex proteomes. Journal of the American Chemical Society, 126, 1363—1368. 

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