Differential Raman scattering cross sections

Sec. 2.4, Eq. 2.4-6 shows that the differential Raman scattering cross section of a vibration of degeneracy gt with the frequency i>A of molecules in a liquid, excited by radiation with the frequency Pq equals ... 

The differential Raman scattering cross sections and depolarization ratios in the Fermi resonance region of carbon disulphide CS2 were measured and interpreted in terms of three bond polarizability parameters and the cubic force constant k 22 (Montero et al., 1984). 

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. 

The mean value of the absolute differential Raman scattering cross section of the Q-branch of nitrogen was established to be (Schrotter and Klockner 1979)... 

Most scattering cross sections of other Raman bands were measured against the nitrogen 2-branch as standard. Therefore the relative normalized differential Raman scattering cross section ... 

D. Y. Wu, M. Hayashi, S.H. Lin, and Z.Q. Tian, Theoretical Differential Raman Scattering Cross-Sections ofTotally-Symmetric Vibrational Modes of Free Pyridine and Pyridine-Metal Cluster Complexes, Spectrochimica Acta Part A... 

Normalized differential Raman scattering cross-sections for Q-branches of vibrational bands, relative to N2 (Schrotterand Kldckner, 1979). 

Experimentally determined relative normalized differential Raman scattering cross sections for selected gases were tabulated [263]. Their averages were compiled and updated in reviews [276,277] and more recently in Table 4.3-7 of Ref. 43. The data from which the averages were calculated agree with one another to within 20 %, with few exceptions. 

A. Absolute Differential Raman Scattering Cross Section of Nitrogen.212... 

B. Differential Raman Scattering Cross Sections of Gaseous Samples..213... 

The quantity (da/df2)j is called absolute differential Raman scattering cross section. It is often termed absolute Raman intensity as well. From q. (8.45) it is clear that (da/dn)i depends on several factors such as Vq and V and the absolute temperature T. In order to operate with comparable quantities that are independent fi-om the experimental conditions, the so-called "standard intensity" or "scattering coefficient" Sj is commonly used [73,253,260-263]... 

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. 

Direct determination of absolute Raman differential cross sections is quite difficult and tedious work often leading to incorrect results. It is easier to measure cross sections relative to some standard. The absolute differential Raman scattering cross sections of the sample can then be straightforwardly obtained. 

The absolute differential scattering cross section of the standard needs to be determined as precisely as possible. A number of measurements has been performed ovm-the past forty years [260,278-287]. The introduction of lasers in Raman spectroscopy and of computer processing of spectral data has improved highly the accuracy of Raman intensity measurements. As a result, the absolute differential Raman scattering cross section of nitrogen reported frrom different laboratories deviates within a few percent only [260,284,285,287]. 

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]... 

The absolute differential Raman scattering cross section of the line of the sample can be obtained from the relative value by using the absolute scattering cross section of nitrogen as given in Eq. (8.73). 

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)... 

The paramount difficulties in the experimental determination of accurate absolute infrared intensities and differential Raman scattering cross sections seem, however, to persist in the theoretical evaluation of these quantities as well. As we will see, predicted Raman intensities appear to be more consistent with experiment as compared to infrared intensities. 

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