Depolarization of Raman lines

As stated in Secs. 1-7 and 1-8, it is possible, by using group theory, to classify the normal vibration into various symmetry species. Experimentally, measurements of the infrared dichroism and polarization properties of Raman lines of an orientated ciystal provide valuable information about the symmetry of normal vibrations (Sec. 1-23). Here we consider the polarization properties of Raman lines in liquids and solutions in which molecules or ions take completely random orientations.  

The intensity of the scattered light is proportional to the sum of squares of the individual a,fEj terms. Thus the ratio of the intensities in the y and z 

In a homogeneous liquid or gas, the molecules are randomly orientated, and we must consider the polarizability components averaged over all molecular orientations. The results are expressed in terms of two quantities a mean value) and y (anisotropy)  

These two quantities are invariant to any coordinate transformation. It can be shown that the average values of the squares of a,y are 

If the incident light is plane polarized (e.g. laser beam), with its electric vector in the z direction = 0), Eq. 19.8 becomes 

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Although polarization data are normally obtained for liquids and single crystals, it is possible to measure depolarization ratios of Raman lines from solids by suspending them in a material with similar index of refraction (27). 

The frequencies classified in suites IX and X belong to depolarized Raman lines and correspond to vibrations-rotation bands of the C type. They can be assigned to oscillations of A" symmetry. 

A review article has been published on depolarized Raman spectroscopy in molten salts, and it is discussed briefly here for the case of molten nitrates. Polarized (VV) and depolarized (HV) Raman scattering of the 1050 cm" line was used. The intensity of the isotropic part of the... 

In addition to the intensity and frequency of the Raman lines, the polarization character of the lines can be measured. In fact, what led Sir C. V. Raman to believe that he was observing a new phenomenon was the unique polarization properties of this new radiation. Usually, the observations are made perpendicular to the incident beam, which is plane-polarized, as at (a) in Fig. 15. The depolarization ratio p is defined as the intensity ratio of the two polarized components of the scattered light that are respectively parallel and perpendicular to the direction of the (polarized) incident beam when the polarization of the incident beam is perpendicular to the plane of propagation and observation (p = I /ll). 

Theoretically, 0=s p =s 3/4, depending on the nature and symmetry of the vibration. Nonsymmetric vibrations give depolarizations of 3/4. Symmetric vibrations give p ranging from 0 to 3/4. Accurate values of p are important for determining the assignment of a Raman line to a symmetric or an asymmetric vibration. 

Here, T is the observed line width (Av << F), 7d is the peak-to-valley intensity in the difference spectrum, and To is the peak height of the Raman line. Although this equation is for Lorentzian-shaped bands, the results are approximately the same for Gaussian-shaped bands (the constant 0.385 becomes 0.350). In the case of carbon disulfide-benzene mixtures, the smallest shift observed was -0.06 cm-1, and the associated error was 0.02 cm-1 (77). A convenient rotating system that can be used for (1) difference spectroscopy, (2) normal rotating sample techniques (solid and solution), and (3) automatic scanning of the depolarization ratios as a function of the wave number has been designed (45). 

The depolarization ratio of the Raman lines in the spectrum of a liquid compound, which is easy to measure, provides a means of distinguishing totally symmetrical vibrations from the rest. 

Vibrations of totally symmetric species (defined by the first row of the character tables) emit Raman lines which are polarized, the depolarization ratio pk can assume, according to Eqs. 2.4-11. .. 13 values of 0 < p < 6/7. All other Raman-active vibrations are emitting lines which are depolarized, they have a depolarization ratio of 6/7. The value 6/7 is appropriate for an arrangement, where the Raman radiation s investigated without an analyzer. If an analyzer is used 3/4 has to be taken instead. Cubic and icosahedral point groups are a special case the depolarization ratio for totally symmetric vibrations is 0. 

The XeFJ cation of C4 symmetry has the vibrational representation 3Raman active, but only 3oi + 3e are allowed in infrared absorption. Nine Raman lines attributable to fundamentals of XeF/ were observed, and assigned on the basis of their relative intensities, depolarization ratios, and by comparison with the spectra of related molecules (Table 4). The strong polarized lines at ca. 670 cm" and ca. 610... 

Strong polarized lines at 652 cm" and 585 cm" identify the [XeFsF J tetramer, and this is clearly the principal solute species in concentrated solution. The polarized Raman line at 621 cm" and the depolarized line at 508 cm" increase in intensity (relative to 652 cm" ) in more dilute solution their frequencies, relative intensities, and states of polarization correspond with the extra lines in hot liquid xenon hexafluoride, and, a little less closely, with the Raman spectrum of the vapour, (Table 8) which contains only XeFa molecules. We have little hesitation, therefore, in assigning these lines to a monomeric XeFj molecule. It is noteworthy that the... 

Our results add little to the question of the structure of ihe xenon hexafluoride molecule. The polarized Raman line al 621 cm could be assigned to the v, (a,) stretch of an octahedral molecule, and the depolarized line at 508 cm to V2 e,) the intensity pattern (v2 is comparable with i/ ) is very reminiscent of the Raman spectra of some isoelectronic molecules which are octahedral, viz. the hexahalogenotellurates(lV). Octahedral symmetry, however, cannot be reconciled with the complicated infrared spectrum of XeFs vapor, at least in the approximation of a simple harmonic force field. Pitzer and Bernstein have in any case provided persuasive evidence for XeFj monomer being substantially distorted in the Ti. bending mode from octahedral symmetry. This is in essential agreement with the bonding model proposed by Bartell and Gavin. ... 

B, Simic-Glavaski, D. A. Jackson, and J. G. Powles. Low frequency Raman lines in the depolarized wing of liquid toluene and benzene. Phys. Lett. A, 52 329-330 (1970). 

The symmetry property of a normal vibration can be determined by measuring the depolarization ratio. From an inspection of character tables (Appendix 1), it is obvious that d is nonzero only for totally symmetric vibrations. Then, Eq. 1.192 gives 0 < p < f, and the Raman lines are said to be polarized. For all nontotally symmetric vibrations, d is zero, and p = Then, the Raman lines are said to be depolarized. If the exciting line is plane polarized, these criteria must be changed according to... 

The symmetry properties of resonance Raman lines can be predicted on the basis of Eq. 19.15. For totally symmetric vibrations, a and =0. Then Eq. 19.15 gives 0 sp <. Nontotally symmetric vibrations (q=0) are classified into two types those which have symmetric scattering tensors, and those which have antisymmetric scattering tensors. If the tensor is symmetric, = 0 and y, 9 0. Then Eq. 19.15 gives Py, = (depolarized). If the tensor is... 

The electric-field vector of a Raman line may correspond to partial or total polarization of the electromagnetic radiation in that line, depending upon the degree of symmetry of the molecular motion(s) that spawn the line. Thus, the symmetry of a particular vibrational mode may be inferred from the polarization (or depolarization) of a Raman band. 

The polarization of the light in a Raman line is obtained experimentally by measuring a quantity called the depolarization ratio, p. It is defined by a ratio of the band areas observed when the light is passed through a polarizer turned first perpendicular, then parallel to the scattered light. The expression that results is... 

Actually, experimental evidence helped to resolve these conflicting assignments. Polarization measurements of the Raman lines observed in IF AsF solution in HF I have shown that the intense 711 cm line was polarized whereas the weak 732 cm line was depolarized. In octahedral species the totally symmetric vibration Pi is indeed polarized, whereas the P2 vibration is depolarized. This therefore provided clear support for the assignments that I l < t 2 Similar results were later also obtained in the study of BrFjAsFg in HF solution ), in vdiich the intense lower frequency 661 cm was polarized and the weaker buthighci frequency at 671 cm was depolarized, also indicating that < i 2-... 

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