Left-circularly polarized radiation

Within a phase factor and amplitude, c 1 = e(2> is the vectorial part of the complex description of right and left circularly polarized radiation. The basis unit vectors c 1 c 1, and c 3 form the 0(3) cyclic permutation relations ... 

Circular dichroism (CD) spectroscopy is based on the difference of absorption of right and left circularly polarized radiation by chiral (dissymmetric) molecules. In peptide research CD spectra can give valuable information on the conformation of peptide molecules in solution. The differences in absorption (ellipticities, 9) are pronounced in the 200 to 220 nm region. The positive or negative Cotton effects allow empirical statements on the arrangement of peptide chains, through comparisons with the CD spectra of peptides that have helical, pleated sheet or random coil conformations, established by other means, e.g. by X-ray diffraction studies. Optical rotatory dispersion (ORD) spectroscopy, which is based on the different refraction of circularly polarized light by chiral compounds, is the older... 

The MCD experiment measures the difference in absorption between right and left circularly polarized radiation in a magnetic field. This technique is useful because, in favorable cases, the line shape can be... 

In VOA spectroscopy, differences between vibrational spectra for left-circularly polarized radiation and right-circularly polarized radiation are detected. By the early 2000s, spectrometers for measuring VOA had been developed and they became commercially... 

If circularly polarized radiation passes through an optically active medium and absorptions for right- and left-circularly polarized radiation are different, the resultant electric-field vector becomes... 

In this equation, Al(v,) and An(v,) indicate, respectively, absorbances for right- and left-circularly polarized radiation at wavenumber v,. To determine Al(v,) - Ar(v ), the value of 2 /i(5q)G(v,) should be known in advance of the VCD measurement by the method to be described later. 

Figure 2 Theoretical spin-resolved VB-XPS spectra of Coo.6Pto.4 for left (LCP) and right (RCP) circularly polarized radiation and photon energy hu 1253.6 eV.

Figure 15. Circular dichroism of the C=0 C li peak (BE = 292.7 eV) in fenchone at three different photon energies, indicated, (a) Photoelectron spectrum of the carbonyl peak of the (1S,4R) enantiomer, recorded with right (solid line) and left (broken line) circularly polarized radiation at the magic angle, 54.7° to the beam direction, (b) The circular dichroism signal for fenchone for (1R,4A)-fenchone (x) and the (lS,41 )-fenchone (+) plotted as the raw difference / p — /rep of the 54.7° spectra, for example, as in the row above, (c) The asymmetry factor, F, obtained by normalizing the raw difference. In the lower rows, error bars are included, but are often comparable to size of plotting symbol (l/ ,4S)-fenchone (x), (lS,4R)-fenchone (+). Data are taken from Ref. [38],...

The quantities /4 and Ajf are the decadic absorbances for left and right circularly polarized radiation, respectively. The ordinary IR absorption is given by the average of /4 and A, namely,... 

These later form a three-dimensional Stokes vector S [13-15] whose tip moves over the surface of a Poincare sphere as the radiation passes without attenuation along the optical axis. Figure 5.1 shows the connection between polarization and points on the Poincare sphere. Right circular polarization is represented by the north pole, left circular polarization by the south pole, linear polarizations by points in the equatorial plane, and elliptical polarization by the points between the poles and the equatorial plane. 

Figure B3.5.3 The relation of ellipticity to the differential absorption of circularly polarized radiation. The oscillating radiation sine wave, 01, is proceeding out of the plane of the paper towards the viewer. (A) Plane-polarized radiation is made up of left- and right-handed circularly polarized components, OL and OR, respectively. Absorption by a chromophore in a nonchiral environment results in an equal reduction in intensity of each component, whose resultant is a vector oscillating only in the vertical plane—i.e., plane-polarized radiation. (B) Interaction of the radiation with achiral chromophore leads to unequal absorption, so that combination of the emerging vectors, OL and OR, leads to a resultant that describes an elliptical path as it progresses out of the plane of the paper. The ratio of the major and minor axes of the ellipse is expressed by tan 0, thus defining ellipticity. The major axis of the ellipse makes an angle (q) with the original plane, which defines the optical rotation. This figure thus demonstrates the close relation between optical rotation and circular dichroism.

As described above, there are two forms of vibrational optical activity, one derived from infrared absorption and the other from Raman scattering. Both forms involve the differential response of a molecule to the modulation of polarization of the interacting radiation between right and left circularly polarized states. In the case of infrared absorption, VCD is defined as die differential absorbance for left minus that for right circularly polarized infrared radiation. This is expressed by the relation ... 

Cpl-induced asymmetric photochemistry is a way to conduct absolute asymmetric synthesis. The field is well developed. The method depends on the differential absorption of left and right circularly polarized radiation by the enantiomeric species of the reactants and thus on their g factor. The kinetic schemes are well developed, and for mechanistic questions as well as for the determination of molecular chiroptical constants cpl irradiation can be used with success. Unfortunately, the smallness of the enantiodifferentiating g factor prevents the method from being a match to the methods exploiting diastereomeric intermolecular interactions for thermal synthesis purposes. 

Nafie (1992) has given a review about the latest VOA instrumentation. Until 1988, the only measured form of ROA was incident circular polarisation (ICP) ROA, but as the process observed in Raman spectroscopy is a two-photon process, there are four possibilities for measuring Raman optical activity. ICP ROA is the unpolarized measurement of the Raman radiation emitted upon excitation with alternating right and left circularly polarized light. It is shown in Fig. 6.3-12, following the sketches of Nafie. As the first of the other possibilities scattered circular polarisation (SCP) ROA was measured. This... 

Because circular dichroism is a difference in absorption for left and right circularly polarized light, its theoretical description includes subtraction of the transition probabilities induced by left and right circularly polarized radiation. The interaction Hamiltonian that determines transition probability includes electric, , and magnetic, B, fields of electromagnetic circularly polarized radiation, and the electric, /i, and magnetic, m, dipole moments of the molecule. 

The quality of the right or left circular polarization depends on the relative amphtudes of the two phases and is readily adjusted by controlling the linear polarization of incident radiation (-45° with respect to the polarizer in the circnlar polarizer reflector) and the aforementioned phase shift in the reflective circular polarizer. 

Figure 7 Right circularly polarized (rcp) light. The electric dipole vector of the radiation describes a clockwise movement as it moves away from the observer. Left circularly polarized (Icp) light will describe an anticlockwise spiral.

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