Group frequencies empirical determination

IV. Group frequencies are determined empirically by studying the spectra of many related molecules. 

The intensities of the infrared absorptions and of the inelastic scattered light (Raman) are determined by such electrical factors as dipole moments and polarizabilities. At the time of the pioneering studies on the infrared spectra of carbohydrates by the Birmingham school,7"11 calculations of the vibrational frequencies had been performed only for simple molecules of fewer than ten atoms.27,34,35 However, many tables of group frequencies, based on empirical or semi-empirical correlations between spectra and molecular structure, are available.32,34"37... 

While the structure and force field uniquely determine the vibrational frequencies of the molecule, the structure cannot in general be obtained directly from the spectrum. However, to a useful approximation, the atomic displacements in many of the vibrational modes of a large molecule are concentrated in the motions of atoms in small chemical groups, and these localized modes are to a good approximation transferable between molecules. Therefore, in the early studies of peptides and proteins (Sutherland, 1952), efforts were directed mainly to the identification of such characteristic frequencies and the determination of their relation to the structure of the molecule. This kind of analysis depended on empirical correlations of the spectra of chemically similar molecules. 

The S=Q stretching force constants. Although the main purpose of establishing the empirical relationships was to predict geometric parameters from frequencies and vice versa, force constants were also calculated to provide a consistent set for them in the whole series. Even if all vibrational frequencies are known for a molecule, approximations have to be introduced, as a rule, to determine a force field. Thus the valence force constants are, to a certain extent, dependent on the approximations used. For several of the molecules discussed here, not even a complete set of experimental frequencies is available. Accordingly, further simplifications were necessary. The SO group was looked upon as a separate entity, for which the well known expressions for a bent XY2 model were applied (Cyvin, I968). 

The characteristic frequencies of additive groups occur in IR spectra of polyatomic molecules under some conditions which are determined by the mechanics of molecular vibrations. Empirical spectrum-structure correlations were created on the basis of the characteristic frequencies of groups. The correlations allow the structural interpretation of IR spectrum to be performed, which comprises the detection of fragment sets and the subsequent building of probable molecular structures. 

One may wonder why we have not applied time—temperature superposition (TTS) to the dynamic frequency sweep data given in Figure 8.7, to determine the of SI-9/9, as numerous research groups (Adams et al. 1994 Balsara et al. 1998 Bates 1984 Bates et al. 1990 Floudas et al. 1994, 1996a, 1996b Lin et al. 1994 Modi et al. 1999 Rosedale and Bates 1990 Rosedale et al. 1995 Schulz et al. 1996 Wang et al. 2002 Winey et al. 1994) have done. As discussed in Chapter 6, application of TTS to flexible homopolymers has been practiced by two methods (1) by empirically... 

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