Transformations in Optics

Vanasse, G. A., and Strong, J. D. (1958). Application of Fourier transforms in Optics Interferometric spectroscopy. In Classical Concepts of Optics (J. D. Strong, ed.), Appendix F. Freeman, San Francisco. 

Mertz, L. Transformation in Optics, John Wiley and Sons, New York 1965... 

Southern and Porter (29) and Kwei et ah (30, 31) have reported the production of transparent polyethylene from normally translucent polyethylene by a variety of deformation processes. The deformation process results in crystalline entities with dimensions less than the wavelength of light in size, thereby not causing light scattering and consequently the resultant transparency. Similar changes in crystalline morphological dimensions may be responsible for the transformation in optical proper-... 

Moreover, fermentation of various a-substituted cycloalkanone enol esters results in optically active six-, eight-, ten-, and twelve-membered ring ketones with 70—96% ee (84). Isolated enzymes catalyze similar transformations, bacillus coagulans and Candida glindracea]i 2Lse OF (Meito Sangyo) hydrolyze a number of cycHc and acycHc enol esters, giving ketones in 40—80% yield and 14—85% ee (85,86). 

Reaction of optically active a-sulphinyl acetate 298a with prochiral carbonyl compounds proceeds with a high asymmetric induction - , the degree of which depends on the nature of substituents at the carbonyl group (equation 252 Table 22) . The jS-hydroxy sulphoxides 422 formed may be transformed to optically active p-hydroxycarboxylic esters 423 (equation 253) and optically active long-chain lactones 424 99 (equation 254). Corey and coworkers have used this method to introduce a chiral centre at C-3 in their synthesis of maytansin °°, and Papageorgiou and Benezra for the synthesis of chiral a-hydroxyalkyl acrylates 425 ° (equation 255). 

A.G. Marshall and F.R. Verdun, Fourier Transforms in NMR, Optical and Mass Spectrometry A User s Handbook, Elsevier Science, Amsterdam (1990). 

Acid-catalyzed hydrolysis of the latter followed by Jones oxidation furnished racemic peshawarine (43) (Scheme 12). Simanek et al. (59) transformed the same amino acetal 47, obtained in optically active form from the Emde degradation of rhoeadine methiodide (48), to ( )-43, also by hydrolysis and oxidation. However, the optical activity was lost during hydrolysis (Scheme 12). 

When pyridinium salt 187 was transformed to an indolo[2,3-a]quinolizidine compound in a similar way and the unsaturated lactone 188 was hydrogenated over platina catalyst, a mixture of vallesiachotamine-type compounds (189 di-astereomers) epimeric at C-20 was formed (134). These compounds have also been prepared in optically active form from vallesiachotamine (9), thus producing the first chemical correlation between synthetic and natural vallesiachotamine derivatives (134). 

There are two possible approaches for the preparation of optically active products by chemical transformation of optically inactive starting materials kinetic resolution and asymmetric synthesis [44,87], For both types of reactions there is one principle in order to make an optically active compound we need another optically active compound. A kinetic resolution depends on the fact that two enantiomers of a racemate react at different rates with a chiral reagent or catalyst. Accordingly, an asymmetric synthesis involves the creation of an asymmetric center that occurs by chiral discrimination of equivalent groups in an achiral starting material. This can be done either by enan-tioselective (which involves the reaction of a prochiral molecule with a chiral substance) or diastereoselective (which involves the preferential formation of a single diastereomer by the creation of a new asymmetric center in a chiral molecule) synthesis. 

Starting from a racemate, it is possible to prepare mixtures of enantionmers with a preponderance of one form in them. We have described this in asymmetric transformations, consequently we have first and second order asymmetric transformations. In a first order there is a shift of the equilibrium to the side of formation of one of the enantiomers in solution while in a second order there is a complete conversion of the racemate into one of the optically active forms. 

Another type of diradical intermediate species (27) in Cope rearrangement is formed during thermolysis of optically active frans-4,9-dimethyl-1,2,6,7-cyclodecatetraene 2425 which was studied in order to distinguish between concerted and stepwise mechanisms of Cope rearrangement. The transformation of optically active trans-24 via a concerted mechanism would lead to optically active tetraenes 25 and 26, while the participation... 

Let us briefly mention some formal aspects of the above-introduced formalism, which have been discussed in detail by Blaizot and Marshalek [218]. First, it is noted that the both the Schwinger and the Holstein-Primakoff representations are not unitary transformations in the usual sense. Nevertheless, a transformation may be defined in terms of a formal mapping operator acting in the fermionic-bosonic product Hilbert space. Furthermore, the interrelation of the Schwinger representation and the Holstein-Primakoff representation has been investigated in the context of quantization of time-dependent self-consistent fields. It has been shown that the representations are related to each other by a nonunitary transformation. This lack of unitarity is a consequence of the nonexistence of a unitary polar decomposition of the creation and annihilation operators a and at [221] and the resulting difficulties in the definition of a proper phase operator in quantum optics [222]. 

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