Raman electro-optical parameters

The calculation of the electro-optical parameters describing Raman intensities is not yet very advanced, because of the paucity of data. Nevertheless, some success was achieved in calculations of the intensity of infrared absorption. The results on trans and gauche bond-rotation in ethylene glycol146 could be taken as a model for carbohydrates. Indeed, similar electro-optical parameters (/aCH, /aOH, /aCC, and /aCO) were calculated. This leads to the expectation that calculations of the intensity of the vibrational spectra of carbohydrates may be accomplished in the near future. In addition, the delicate problem of accounting for molecular interactions in calculating infrared intensities could be approached as it was for v(CCC) and i CO) vibrations in acetone.149 This will allow interpretation of weak, as well as strong, i.r. bands, in order to determine the structural properties of molecules. 

The necessary derivations with respect to the small displacements can be performed either numerically, or, more recently, also analytically. These analytical methods have developed very rapidly in the past few years, allowing complete ab initio calculation of the spectra (frequencies and intensities) of medium sized molecules, such as furan, pyrrole, and thiophene (Simandiras et al., 1988) however, with this approach the method has reached its present limit. Similar calculations are obviously possible at the semi-empirical level and can be applied to larger systems. Different comparative studies have shown that the precise calculation of infrared and Raman intensities makes it necessary to consider a large number of excited states (Voisin et al., 1992). The complete quantum chemical calculation of a spectrum will therefore remain an exercise which can only be perfomied for relatively small molecule. For larger systems, the classical electro-optical parameters or polar tensors which are calibrated by quantum chemical methods applied to small molecules, will remain an attractive alternative. For intensity calculations the local density method is also increasing their capabilities and yield accurate results with comparatively reduced computer performance (Dobbs and Dixon, 1994). 

M. Gussoni, in Advances in Infrared and Raman Spectroscopy, R. J. Clark and R. Hester, Eds., Heyden, London, 1979, pp. 61-126. Infrared and Raman Intensities from Electro-Optical Parameters. 

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. 

Cartesian reference fiame, geometrical data, definition of internal and symmetry coordinates and a matrix for sulfiir dioxide were already given in Section 9.I1.B. The application of valence-optical theory of Raman intensities results in the set of electro-optical parameters given by Eq. (9.43). If these quantities are substituted inside the brace of Eqs. (9.33) and (9.34), the elements of ([a]) array are obtained... 

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. 

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