Rotatory reflections

A twofold rotation around the molecular axis of cA-7,2-dichloroethylene is not a covering operation, because the rotation exchanges hydrogens and chlorines. However, the compound operation of the twofold rotation followed by a reflection in a plane perpendicular to the molecular axis - a C2 followed by a ah — is a covering operation. The combination of an n—fold rotation and a reflection in a perpendicular plane is called a rotatory-reflection or improper rotation, symboUzed Sn-... 

Not all rotatory-reflections are unfamihar operations. An S is just a C followed by a (T/i - this is equivalent to the mirror reflection alone. S2 is equal to the inversion, because the rotation reverses the signs of the coordinates measured along axes (of the coordinate system) perpendicular to the axis (of rotation), and the reflection reverses the sign of the third coordinate. 

Improper Rotations A rotation by 360/n about an axis followed by a reflection in a plane perpendicular to the axis is called rotation-reflection symmetry operation. A combined operation of this kind is called a rotation-reflection or an improper rotation and is denoted by the symbol Sn standing for the combination of a rotation through an angle 2%/n about some axis and reflection in a plane perpendicular to the axis. C4 operation followed by reflection through the plane of molecule gives S4 axis. If we use the symbol oh to denote the reflection in the plane perpendicular to rotatory-reflection axis we can write... 

If a sample is excited with polarized light and emission is measured through a second set of polarizers parallel and perpendicular to the first polarizer, the ratio of the two emission signals reflects the rotatory freedom of the chromophore. In practice, binding of a second molecule to the labeled one can be detected if the size of the chromophore complex increases considerably. The advantage of this method is that no changes in quantum yield are necessary for the observation of the binding reaction. 

The reflection of only one component, RCP or LCP, in incident linearly polarized light can be observed as a very strong rotatory power. 

Many substances can rotate the plane of polarization of a ray of plane polarized light. These substances are said to be optically active. The first detailed analysis of this phenomenon was made by Biot, who found not only the rotation of the plane of polarization by various materials (rotatory polarization) but also the variation of the rotation with wavelength (rotatory dispersion). This work was followed up by Pasteur, Biot s student, who separated an optically inactive crystalline material (sodium ammonium tartrate) into two species which were of different crystalline form and were separately optically active. These two species rotated the plane of polarized light equally but in opposite directions and Pasteur recognized that the only difference between them was that the crystal form of one was the mirror image of the other. We know to-day, in molecular terms, that the one necessary and sufficient condition for a substance to exhibit optical activity is that its molecular structure be such that it cannot be superimposed on its image obtained by reflection in a mirror. When this condition is satisfied the molecule exists in two forms, showing equal but opposite optical properties and the two forms are called enantiomers. 

In the Schoenfiies system the improper axis is an axis of rotation-reflection (see page 52). In the Internationa) system the axis of rotatory inversion ( ) is ore of n-fold rotation followed by inversion (see Fig. 3.29). 

Cathou et al. (459) found that the Cotton effect near 270 nm in the ORD spectrum of RNase disappeared on interaction with either 2 -CMP or 3 -CMP. The X-ray studies (120) (see Fig. 23) clearly show that no tyrosine residues are in close contact with the substrate. Thus the change in rotatory behavior must reflect either (1) a shift in protein structure on association of the nucleotide or (2) the induction of a Cotton effect of the opposite sign in the bound nucleotide. In the independent spectral and chemical studies of Irie and Sawada (480), the reduced nucleotide 5,6-dihydrouridine-2 (3 )-phosphate, known to interact with the enzyme, showed no difference spectrum. With nucleotides containing... 

Organic materials with large optical rotations include cholesteric liquid crystals, molecules and polymers with chiral jt-conjugated systems, especially [n]helicenes [21, 31, 139]. The most important factor contributing to their large optical rotations is anomalous optical rotatory dispersion (ORD), which is associated with the presence of absorption (or reflection) with large rotational strength (Fig. 15.30). 

Fock 18, 19 hamiltonian 16 kinetic energy 16 Laplacian 85 logical 86 mathematical 84 matrix element of 16 momentum 16 nabla 85 symmetry 27, 38 optical rotation 33 optical rotatory power 33 orbital energy 18 order of reaction 55 order of reflection 36 order parameters 36 oscillator strength 33 osmole 51... 

As early as in 1951 de Vries showed that a twisted stack of birefringent layers is an adequate model for a cholesteric structure in order to reproduce a principally correct spectral dependence of the optical rotation also around the selective reflection band as it was recorded in a different way for Fig. 4.6-8. Even if the layer thickness is formally reduced to zero the optical rotation and its spectral dependence is preserved. Several other approaches were reported to describe particular effects of the cholesteric structure such as the selective reflectance or the rotatory anomaly (e.g. Chandrasekhar and Prasad, 1971 Chandrasekhar and Ranganath, 1974 SchSnhofer et al., 1983 Eidner et al., 1989). 

The rotatory power of the cholesteric mesophase at a wave length larger or smaller than that of the reflected... 

The rotatory behavior of poIy-/3-benzyl-L-aspartate presents an exception to the rule that L-residues favor helices of the same sense, for it has a bo of about - -600 (Blout and Karlson, 1958), as well as a far ultraviolet dispersion and changes in [to ]x on forming the random coil that are obviously opposite in sign to those of poly-7-benzyl-L-glutamate (Karlson et al., 1960). In addition, its enantiomorph, poly-/3-benzyl-D-aspartate behaves as a normal L-polypeptide (Blout and Karlson, 1958). The systematic investigations of Bradbury et al. (1959, 1960a, b) and Karlson et al. (1960) leave little doubt that helical poly-/8-benzyl-L-aspartate has a sense opposite to that of the standard polymers and that its rotatory parameters reflect this... 

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