Optical rotation direction-dependent

The presence of chirality introduces an additional component in the y direction. This component will rotate the polarization of die second-harmonic field with respect to the polarization of the incident radiation. The amount of optical rotation will depend on the relative magnitude of the chiral and achiral susceptibility components. Furthermore, Py changes sign between the enantiomers... 

Specific Rotation. Optical rotation is caused by individual molecules of the optically active compound. The amount of rotation depends upon how many molecules the light beam encounters in passing through the tube. When allowances are made for the length of the tube that contains the sample and the sample concentration, it is found that the amount of rotation, as well as its direction, is a characteristic of each individual optically active compound. 

Polarimetry. Polarimetry, or polarization, is defined as the measure of the optical rotation of the plane of polarized light as it passes through a solution. Specific rotation [ a] is expressed as [cr] = OcjIc where (X is the direct or observed rotation, /is the length in dm of the tube containing the solution, and c is the concentration in g/mL. Specific rotation depends on temperature and wavelength of measurement, and is a characteristic of each sugar it may be used for identification (7). 

A classical, and still most useful, physicochemical parameter for characterizing glycosaminoglycans is their specific optical rotation. For pure heparins from common sources, [a]80 = + 45 to + 53 ° (see Table II). The actual value depends on the relative proportions of monosaccharide constituents (that is, the L-idosyluronic acid residues make a less positive contribution than the n-glucosyluronic residues), and on the degree of sulfation of the preparation (that is, although sulfate groups may have little direct influence on the molecular rotation, they lower the value by acting as diluents ). 

When dissolved in more saline waters, xanthan gum produces a higher apparent viscosity than the same concentration of polyacrylamide (292). Prehydration of xanthan in fresh water followed by dilution in the saline injection water has been reported to provide higher viscosity than direct polymer dissolution in the same injection water. Optical rotation and intrinsic viscosity dependence on temperature indicate xanthan exists in a more ordered conformation in brine than in fresh water (293). 

Note that these definitions of optical rotation and circular dichroism for a particulate medium depend on the choice of the horizontal direction unless the medium is invariant with respect to arbitrary rotation about an axis parallel to the incident beam. 

Enantiomers are labeled (+) or (—), depending on the direction of rotation of the plane of polarization. For example, the isomer of [Co(en)3]3+ that rotates the plane of polarization to the right is labeled ( + )-[Co(en)3]3+, and the isomer that rotates the plane of polarization to the left is designated ( — )-[Co(en)3]3+. A 1 1 mixture of the ( + ) and ( —) isomers, called a racemic mixture, produces no net optical rotation because the rotations produced by the individual enantiomers exactly cancel. 

For oriented samples, the rotation of the plane-polarized light becomes a tensor - that is, the optical rotation becomes directionally dependent - and includes a contribution from the electric dipole-electric quadrupole polarizability tensor, which is traceless and thus vanishes for freely rotating molecules [30], The term arising from these quadrupolar interactions can be expressed as [30]... 

UC-OX, VC-OX, and WC-OX. The sum of all such contributions from asymmetric atoms constitutes the optical rotation of the molecule. Atoms not joined directly to asymmetric carbon atoms are assumed to have negligible, second-order effects. The contribution made to the optical rotation by one of the constituent structures, for example, UC-CX, is assumed to depend on the projected angle between the UC and CX bonds (see Fig. 3). In the carbohydrate series, this angle is readily determined from the con-... 

Schematic diagrams of die cell and apparatus for measuring die temperature dependence of die optical rotation of an aligned nematic liquid crystal cell. The birefringence cell is formed from microscope slides and die lines in the cell denote the rubbing direction for the glass plates and thus the direction for the nematic director n.

In equation 19 is one of the three rotation contributions in equation 5 which describes C2v-tetrahedral optical rotation at the wavelength of the sodium-D-line. The constant will be determined by the groups not directly attached to the particular asymmetric carbon atom. For instance, in I will depend on R, R and R, R. This means that Xij depends upon those ligands which appear in the v(R)-term of equation 5. For X it was found that equation 20 applies. ... 

Absolute structure, absolute configuration The structure of a crystal or molecule expressed in an absolute frame of reference. A chiral object or structure is nonsuperimposable on its mirror image. This absolute structure or configuration can often be correlated with other optical phenomena that depend on chirality, such as the direction of rotation of the plane of polarization of light by a solution of the crystal. 

R. Ahlrichs, M. Bar, M. Haser, H. Horn, C. Koknel, Electronic structure calculations on workstation computers The program system Turbomole, Chem. Phys. Lett. 162 (1989) 165 M. Haser, R. Ahlrichs, Improvements on the direct SCF method, J. Comput. Chem. 10 (1989) 104 O. Treutler, R. Ahlrichs, J. Chem. Phys. 102 (1995) 346 R. Bauernschmitt, R. Ahlrichs, Treatment of Electronic Excitations within the Adiabatic Approximation of Time Dependent Density Functional Theory, Chem. Phys. Lett. 256 (1996) 454 S. Grimme, F. Furche, R. Ahlrichs, An improved method for density functional calculations of the frequency-dependent optical rotation, Chem. Phys. Lett. 361 (2002) 321 F. Furche,... 

In this model, the symbols have the following meaning. ( )R(a3) ao(l)HD(a3) is the optical rotation produced by the vapour and depends on the number of absorption lengths ao and on the lineshape function D(o)) which takes the form of a Doppler-broadened dispersion curve for magnetic and electric field induced rotation ( )r will depend on the strength of the field and D(oa) on the direction and type of field (see table 2). The transmitted intensity 1 - Ij exp[-aoG(o))] where the lineshape function G(o)) for a single spectral component can usually be accurately described by a Doppler-broadened Lorentzian curve. Finally the terms B and C in equation (53) represent respectively the finite extinction ratio of the polarisers and a laser independent... 

The principle of a polarization-dependent optical isolator is shown in Fig. 1, which comprises a polarizer, an analyzer, and a Faraday rotator for providing a 45-degree polarization rotation. Direction of the analyzer is oriented 45 degrees relative to that of the polarizer. 

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