Geometry Sensitive Schemes

The step-independence criterion sounds as if it demands that the scheme be stationary, but in fact it does not. It demands that the coefficients should not depend on the step-number, but they can still depend on the shape of the polygon. 

The two important avenues of exploration so far have been based on using either the distances between consecutive vertices (span-based criteria) or the angles at vertices (vertex-based criteria). 

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Finally we look at what can be achieved by changing the rules fundamentally, by considering non-stationary subdivision, in which the mask changes from step to step. In particular we consider geometry-sensitive schemes where the mask is itself determined locally and at every step from the geometry of the polygon. 

Recently, the annular geometry porous membrane DS coupled to a fluorometric detection system was shown to be applicable to the sensitive measurement of ambient ammonia (59). The detection scheme is based on... 

Reaction of Cytochrome cIinn with Bis(ferrozine)copper(II) Knowledge of the redox properties of cytochrome c was an encouragement to initiate a kinetics investigation of the reduction of an unusual copper(II) complex species by cyt c11. Ferrozine (5,6-bis(4-sulphonatophenyl)-3-(2-pyridyl)-1,2.4-triazine)286 (see Scheme 7.1), a ligand that had come to prominence as a sensitive spectrophotometric probe for the presence of aqua-Fe(II),19c,287 forms a bis complex with Cu(II) that is square pyramidal, with a water molecule in a fifth axial position, whereas the bis-ferrozine complex of Cu(I) is tetrahedral.286 These geometries are based primarily upon analysis of the UV/visible spectrum. Both complexes are anionic, as for the tris-oxalato complex of cobalt in reaction with cytochrome c (Section 7.3.3.4), the expectation is that the two partners will bind sufficiently strongly in the precursor complex to allow separation of the precursor formation constant from the electron transfer rate constant, from the empirical kinetic data. 

Hammond and Cole reported the first asymmetric photosensitized geometri-r cal isomerization with 1,2-diphenylcyclopropane (Scheme 2) [29]. The irradiation of racemic trans-1,2-diphenylcylcopropane 2 in the presence of the chiral sensitizer (R)-N-acetyl-1 -naphthylethylamine 4 led to the induction of optical activity in the irradiated solution, along with the simultaneous formation of the cis isomer 3. The enantiomeric excess of the trans-cyclopropane was about 1% in this reaction. Since then, several reports have appeared on this enantiodifferentiating photosensitization using several optically active aromatic ketones as shown in Scheme 2 [30-36]. The enantiomeric excesses obtained in all these reactions have been low. Another example of a photosensitized geometrical isomerization is the Z-E photoisomerization of cyclooctene 5, sensitized by optically active (poly)alkyl-benzene(poly)carboxylates (Scheme 3) [37-52]. Further examples and more detailed discussion are to be found in Chap. 4. 

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