Raman and Infrared Band Shapes

In Chapters 7 and 12 it was shown how depolarized Rayleigh scattering can be used to probe molecular rotations in fluids. Measurements of the band shapes of infrared vibra- 

A normal mode / is inactive or active in the Raman spectrum depending on whether (dal/dQi) and (dfijdQi) are zero. The symmetry of the normal mode may in most cases be used to determine which modes are active and which are isotropic (only (dal/dQi) different from zero). 

In Raman scattering it is usually assumed that the vibration and rotation of a molecule are mutually independent so that the Ivh spectrum in Eqs. (15.3.2) factors into a product of independent terms, one depending solely on rotation and the other on vibration. This assumption has not yet been justified by experiment. When this assumption is made it may be seen (cf. Appendix 7. B) that for vibrations of cylindrically symmetric molecules that preserve the molecular symmetry, Ivh is proportional to 7 2(11 (0)-u ( )) where u is a unit vector along the molecular symmetry axis. 

The theory for infrared absorption (Fulton, 1971) proceeds by showing that the 

In infrared absorption experiments, one measures the absorption coefficient k(co) as a function of a . Since the complex refractive index is N — n + Ik, it may be shown that e = 2me (Landau and Lifshitz, 1960). Thus in order to relate k, the measured quantity, to e and then to the dipolar correlation function [Eq. (15.3.5)], one must knowhow the refractive index n (co) changes through the band. 

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