Raman scattering isotropic molecules

Raman scattering is envisaged as the process of reradiation of scattered light by dipoles induced (P) in the molecules by the incident light and modulated by the vibrations of the molecules (a.3). In normal Raman scattering by molecules in isotropic media, the dipoles are simply those that result from the action of the electric field component, E, of the incident light on the molecules,... 

M. Thibeau, A. Gharbi, Y. Le Duff, and V. Sergiescu. A comparative study of Rayleigh and Raman depolarized light scattering by a pure fluid of isotropic molecules. J. Phys. (Paris), 55 641-651 (1977). 

M. Thibeau. Rayleigh and Raman Depolarized Light Scattering by Isotropic Molecules. In B. Vodar and Ph. Marteau, (eds.). High Pressure Science and Technology, Pergamon, New York, 1980, pp. 724-726. 

T. Bancewicz and S. Kielich. Isotropic Raman scattering for non-totally symmetric vibrations of correlated molecules with intrinsic optical anisotropy. J. Chem. Phys., 75 107-109 (1981). 

V. Sergiescu. On the usefulness of the lattice-gas model in the theory of the DID Rayleigh and Raman depolarized scattering by a fluid of isotropic molecules. Physica C, 97 292-298 (1979),... 

V. Scattering in the Raman Vibrational Bands of Optically Isotropic Molecules... 

The influence of multipolar polarizabilities has been examined subsequently in several optically isotropic molecules such as CH4, CD4, neopentane, CF4, or SF6 [4,7-14,17,18]. In this review, our attention is focused on CF4 for which both Rayleigh [8,13] and Vi Raman [17,18] depolarized and isotropic bands have been studied and published by us. In the Rayleigh studies, we measured the /j (v) and / (v) intensities that are scattered by gaseous CF4 up to 340 cm-1, in... 

V. SCATTERING IN THE RAMAN VIBRATIONAL BANDS OF OPTICALLY ISOTROPIC MOLECULES... 

The theory of Raman scattering simplifies dramatically in the far-from-resonance (FFR) limit, where the exciting laser radiation is far from the lowest allowed excited electronic state of the molecule [15]. In this limit, the interaction of the light with the molecule is approximately the same for both the incident and the scattered radiation. There, the Raman tensor becomes symmetric and this symmetry reduces the number of Raman invariants from three to two, the isotropic and (symmetric) anisotropic invariants. The antisymmetric anisotropic invariant vanishes, by its antisymmetric definition in Eqs. (7) and (9), and we have... 

ROA and Raman intensity are proportional to the square of a tensor quantity, as expressed in Equation [1]. For Raman scattering only the square of the polarizability is needed, whereas ROA intensity arises from the product of the polarizability and an ROA tensor. The ROA tensor are approximately three orders of magnitude smaller than the polarizability, and hence an ROA spectrum is approximately three orders of magnitude smaller than its parent Raman spectrum. As noted above, the Greek subscripts of the tensor refer to the molecular axis system. However, for both Raman and ROA, linear combinations of products of tensors can be found that do not vary with the choice of the molecular coordinate frame. Such combinations are called invariants. All Raman intensities from samples of randomly oriented molecules can be expressed in terms of only three invariants, called the isotropic invariant, the symmetric... 

Polarization effects are another feature of Raman spectroscopy that improves the assignment of bands and enables the determination of molecular orientation. Analysis of the polarized and non-polarized bands of isotropic phases enables determination of the symmetry of the respective vibrations. For aligned molecules in crystals or at surfaces it is possible to measure the dependence of up to six independent Raman spectra on the polarization and direction of propagation of incident and scattered light relative to the molecular or crystal axes. 

In Raman spectroscopy the intensity of scattered radiation depends not only on the polarizability and concentration of the analyte molecules, but also on the optical properties of the sample and the adjustment of the instrument. Absolute Raman intensities are not, therefore, inherently a very accurate measure of concentration. These intensities are, of course, useful for quantification under well-defined experimental conditions and for well characterized samples otherwise relative intensities should be used instead. Raman bands of the major component, the solvent, or another component of known concentration can be used as internal standards. For isotropic phases, intensity ratios of Raman bands of the analyte and the reference compound depend linearly on the concentration ratio over a wide concentration range and are, therefore, very well-suited for quantification. Changes of temperature and the refractive index of the sample can, however, influence Raman intensities, and the band positions can be shifted by different solvation at higher concentrations or... 

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