AB INITIO CALCULATIONS OF RAMAN INTENSITIES

It has been, therefore, of great inqrartance to derive complete polarizability tensors and compute Raman intensities by ab Mtio MO calculations. The remarkable efforts of scientists from several leading research groiqts have resulted in successfiil realization of diese goals [166-168,175,177,178,181,336-341]. Current program systems for ab initio calculations provide these quantities as a standard output resulting from appbcation of analytic derivative methods [153,170-172]. 

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A rather limited number of theoretical studies on saturated dithietane systems have been reported during the last 10 years. Most of them are devoted to theoretical calculations of geometries of the 1,3-systems. One can also find ab initio calculations of their interconversions and the normal mode frequencies and theoretical predictions of spectroscopic parameters such as infrared (IR) and Raman intensities. 

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). 

Ab initio calculations of vibrational wavenumbers for D20 gave detailed results on IR and Raman intensities.612 High-resolution Raman spectra of vapour-phase H20, HOD and D20 gave a very detailed interpretation of line intensities for v2 bands.613... 

Fig. 28.30 Comparison among y values obtained with different methods for polyene systems of increasing chain length (see Ref. 244). (A) / from calculated (ab initio 6-31G) Raman intensities (x) y from ab initio (6-31G) calculations ( ) / from experimental Raman cross sections ( ) y from THG measurements.

Hartree-Fock theory is a rigorous ab initio theory of electronic structure and has a vast array of successes to its credit. Equilibrium structures of most molecules are calculated almost to experimental accuracy, and reasonably accurate properties (e.g., dipole moments and IR and Raman intensities) can be calculated from HF wave functions. Rela-... 

Raman vibrational frequencies and intensities of octane, dodecane and hexadecane corrformers were calculated using quantum mechanical ab initio methods. The results agreed with various trends observed in the experimental spectra of alkanes, as well as several observations from the experimental Raman spectra of PEs. The data obtained indicated that ab initio calculated Raman data on alkanes provided valuable information regarding the interpretation of polymer Raman spectra, in particular information concerning issues where interpretation based on experimental verification was not possible. 23 refs. 

Raman-active transition in the spectra of polyenes. Comparison of ab initio calculated Raman intensities for n-alkanes and rrnns-polyenes gives parallel information [91,92]. Note that when the number of carbon atoms in the chains increases, the Raman intensities of saturated and conjugated chains differ remarkably in their behav-... 

Blom, C. E., Altona, C. (1977b). Application of self-consistent-field ab initio calculations to organic molecules V. Ethene General valence force field scaled on harmonic and anharmonic data, infrared and Raman intensities. Molecular Physics, 34, 111. 

Calculated spectral characteristics for propyne obtained by transferring bond polarizability parameters are compared with those evaluated by RHF/6-3 lG(d,p) ab initio MO calculations [311] in Table 9.10 and Fig. 9.4. It is seen that the predicted spectrum obtained in applying the bond polarizability model is in better agreement with experiment than the ab initio estimated spectrum. More advanced quantum mechanical computations are, evidently, needed to satisfactorily calculate the Raman intensities of propyne. The computations employing transferable sets of polarizability derivatives are simple and give good results. 

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