Right-circularly polarized radiation

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,... 

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. 

Fig. 5.14 Typical normal emission Fe 3p photoemission spectra taken with ieft and right circularly polarized radiation hv = 150 eV) in dependence of the magnetization M and M . Upper panel epitaxial 10 ML thick iron overlayer on W(llO) lower panel iron islands on W(llO) after annealing the epitaxial film to about 1,000 K. From [52], used with permission...

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... 

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... 

The unit electric-field vectors in the x, y-plane of circularly polarized radiation traveling along the z axis are described as = cos a> t -z/c) and Uy = sin co t - z/c), where -I- sin and - sin correspond, respectively, to the left- and right-circularly polarized radiation. 

The clockwise or right-hand turning movement of the electric-field vector at a particular point on the z axis looking back from the traveling direction is shown in Figure 22.3b for right-circularly polarized radiation. 

As explained, the polarization plane of linearly polarized radiation can be tilted when it passes through a crystal that has any anisotropy or a medium in which molecules are oriented. In general, the rotation of the plane of polarization is a function of the thickness of the crystal or medium and the difference between the refractive indices along the two orthogonal axes perpendicular to the direction of incident radiation. CD spectroscopy detects differences in the absorption of a chiral molecule for left- and right-circularly polarized radiation. 

A block diagram of a VCD spectrometer is shown in Figure 22.5. The units to generate circularly polarized radiation (an optical filter, a linear polarizer, and a PEM) are inserted between a Fourier transform-infrared (FT-IR) spectrometer and the detector. Left- and right-circularly polarized radiation are generated with a fixed frequency by the PEM, and the signal synchronized with the PEM is detected. 

Vibrational circular dichroism (VCD) is defined as circular dichroism (CD) in vibrational transitions in molecules. These transitions typically occur in the infrared (IR) region of the spectrum and hence a VCD spectrometer is an infrared spectrometer that can measure the circular dichroism associated with infrared vibrational absorption bands. CD is defined as the difference in the absorption of a sample for left versus right circularly polarized radiation. This difference is zero unless the sample possesses molecular chirality, either through its constituent chiral molecules or through a chiral spatial arrangement of non-chiral molecules. 

Generally speaking, the phenomenon of optical activity can be explained considering that a chiral species interacts in a different manner with the two chiral— namely, circularly polarized—components of linearly polarized light. In particular, the optical rotation arises from the fact that left and right circularly polarized radiations propagate in the optically active medium with different velocities (circular birefringence). In other words, rii (X) in which ni (X) ad mr(A)... 

Vibrational circular dichroism (VCD) and Raman optical activity (ROA) are the two principal forms of vibrational optical activity (VOA). In a similar fashion to what has been discussed for other chiroptical methods, VOA is a spectroscopic measure of the differential response of a chiral molecule to left- versus right-circularly polarized radiation, however, during a vibrational transition. VCD and ROA have become powerful tools for the determination of AC of chiral molecules in the solution state after nearly 40 years of evolution, although the application of ROA still lags behind that of VCD." ... 

---