Gases Raman scattering cross sections

Relative and ab.solute Raman scattering cross sections have been measured by a number of groups and were summarized by Schrotter and Klockner (1979). The formula for the total differential Raman scattering cross section of a vibrational-rotational band has been given in Eq. 2.4-6 the internal field factor L is equal to 1 for ga.ses, see also Sec. 3.5.4. 

Eq. (8.45) shows that for an ordinary Raman experiment the absolute differential Raman scattering cross sections can be expressed in terms of derivatives of the molecular polarizability invariants a and y with respect to normal coordinates. These derivatives contain valuable information about the variation of molecular polarizability with vibrational motion. Gas-phase Raman scattering cross sections are most suited for intensity analysis since at low partial pressure of the sampling gas these quantities are not influenced by effects of intermolecular interactions, thus reflecting properties of individual molecules. 

The differential Raman scattering cross section of the line of a gas sample relative to that of the 2331 cm l line of nitrogen is given by [260]... 

As was shown in Chapter 8, the experimental gas phase differential Raman scattering cross sections are directly related to the molecular polarizability derivatives wifli respect to normal coordinates forming the supeitensor intensity analysis die dot/dQj derivatives are usually further transformed into different types of parameters. The eventual goal is to transfonn the experimental observables into molecular quantities reflecting electro-optical properties of simple molecular sub-units. Several formulations for parametric interpretation of Raman intensities have been put forward. In this chapter the basic principles and characteristics of the theories developed will be discussed. The mathematical formalism inherent of each theoretical approach will be illustrated with examples. 

On the basis of transferability properties for intensity parameters in the hydrocarbon series, Martin [309] has predicted depolarization ratios, scattering coefficients and absolute differential Raman scattering cross sections for propane in the gas-phase employing electro-optical parameters determined for ethane. A good correspondence between the predicted and experimental data has been achieved. A survey of calculated Raman spectra of other hydrocarbons is presented in the book of Gribov and Orville-Thomas [155]. Gussoni and co-workers [300,319] have predicted the Raman spectrum of polyethylene and perdeutero-polyethylene by transferring electro-optical parameters evaluated for methane and cyclohexane. 

Experimental and calculated spectral parameters for propyne in the gas phase (wavenumbers in cm, absolute differential Raman scattering cross sections (da/dn)j in I0 36 the depolarization ratios pj are dimensionless)... 

Calculated depolarization ratios and differential scattering cross sections (do/dn)i for propyne are presented in Table 9.10. The simulated Raman spectrum is compared with the experimental gas-phase spectral ciuve [317] in Fig. 9.4. The band half-widths are taken from the experiment. The lines of A] transitions have sharp features, while E-vibrations are characterized with much broader bands. Since no quantitative intensity data for this molecule exist, a qualitative assessment of the results obtained can be done only. Fig. 9.4 reveals that the overall shape of the Raman spectrum is reproduced correctly. The most intense Raman lines are calculated to be those positioned at 2941, 2142 and 930 cm with intensities decreasing in the same order in agreement with the experimental spectrum. These lines are highly polarized. The other vibrational transitions giving rise to low- or medium-intensity lines in the spectrum are predicted to have intensities of the same order. The most significant difference between calculated and... 

---