Left-polarized radiation

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,... 

Plane-polarized radiation comprises two circularly polarized vectors of equal intensity, one right-handed and the other left-handed (Fig. B3.5.3A), which are separately measured in the CD spectrometer by means of a photoelastic modulator. A chromophore situated... 

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.

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 ... 

The first manifestation of VCD in the optical train of a spectrometer is the modulation of the intensity of the infrared beam in synchronization with the modulation of the polarization as the beam passes through the circular dichroic sample. The phase of the synchronization is opposite for negative and positive VCD bands. More specifically, in reference to the definition of VCD in Eq. (1), there will be a synchronization between larger transmission (smaller absorbance) and right CP radiation for positive VCD bands, and between larger transmission and left CP radiation for negative VCD bands. 

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. 

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. 

Figure 16-28. Ooct-OPV5 in its nematic phase at 190°C. Left polarized-light optical micrograph (scale bar 50 pm Zeiss photomicroscope). Right X-ray diffraction scan (d-2d scanning in transmission mode, CuKa radiation, 2=1.5418 A).

Figure 5.17 Left valence-band photoemission spectra from a seven-monolayer-thick HCP (0001) Co film on W taken with linearly polarized radiation for opposite magnetization directions. Right corresponding asymmetry values for binding energies between —2 eV and Ep-Experiment (Bansmann et al. 2000).

Fig. 5.7 Left spin resolved photoemission spectra for thin iron films on W(llO) taken with unpolarized light (hv = 21.22 eV). Right spin integrated spectra taken with circularly polarized radiation (hv = 21.2 eV) for emission angles between 0° < 6 < 15°. The thin lines in the MCDAD spectra mark the position of the valence band maxima in normal emission. Reprinted from [26], Copyright (1998), with permission from Elsevier...

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... 

Fig. 14. Infrared images of spherulites using perpendicular left, top) and parallel right, top) polarized radiation obtained from PEG (My=35 K), quenched from 100"C to room temperature. The images were obtained by plotting the 1343 cm CH2 wag vibrational mode of the PEG chain. The image at the bottom is a dichroic ratio image obtained by pixel-by-pixel division of the upper two. (reproduced from Snively CM, Koenig JL (1999) Spectroscopy)...

For right-circularly polarized radiation the electric field vector rotates clockwise when looking into the oncoming wave, i.e. at the source of the radiation. Circular polarization of photons corresponds to the two possible projections of the photon s spin on the direction of propagation, S, called helicity. Right-circularly polarized photons have = — 1 and thus Sz = —h, while left-circularly polarized photons have nis = 1. Plane-polarized radiation can then be expressed as a superposition of left-and right-circulary polarized waves with the same refractive index, rir uj) = =... 

In Section 7.1 we discussed that plane or linear polarized radiation can be expressed as the superposition of left-circularly polarized and right-circularly polarized waves with the same refractive index. If the refractive indices for left- and right-circularly polarized radiation, however, differ by... 

In order to derive a quantum mechanical expression for the mixed dynamic electric dipole magnetic dipole polarizability tensor we have to evaluate the time-dependent expectation value of the electric dipole operator ( o(t) Aa l o(f)) in the presence of the time-dependent magnetic induction of left- or right-circularly polarized radiation... 

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