Correlation of the Normal Modes

The decrease in the flnctnation for a higher-order mode is manifested in the declining intercept of the cnrves in the fignre. 

---

Correlation of the normal modes of benzene (6) with those of 1,2-didehydrobenzene (o-benzyne, 3). 

Detailed analyses of the vibrational spectra of raacromolecules, however, have provided a deeper understanding of structure and interactions in these systems (Krimm, 1960). An important advance in this direction for proteins came with the determination of the normal modes of vibration of the peptide group in A -methylacetamide (Miyazawa et al., 1958), and the characterization of several specific amide vibrations in polypeptide systems (Miyazawa, 1962, 1967). Extensive use has been made of spectra-structure correlations based on some of these amide modes, including attempts to determine secondary structure composition in proteins (see, for example, Pezolet et al., 1976 Lippert et al., 1976 Williams and Dunker, 1981 Williams, 1983). 

Theoretical calculation of the frequencies of the normal modes of vibration is possible and has been demonstrated for moderately complex molecules such as acetazolamide [34]. This facilitates assignment of the observed spectral bands beyond what may be possible by comparison with correlation tables and manual interpretation. The ability to predict the visual appearance of IR and Raman spectra is, however, more challenging since the inclusion of selection rules to ascertain which bands will be IR or Raman active and the calculation of their intensity must be considered. 

Substituting Eqs. (3.47) and (3.48) into Eq. (3.58), the time correlation function of the end-to-end vector, after some algebraic derivation, can be expressed in terms of the normal modes as ... 

The MP2 method usually gives satisfactory results (e.g., the frequencies of the normal modes). There are indications, however, that the deformations of the molecule connected with some vibrations strongly affecting the electron correlation (vibronic coupling) create too severe a test for the method the error may amount to 30 to 40% for frequencies of the order of hundreds of cm . as has been shown by D. Michalska. W. Zierkiewicz, D.C. Biehko, W. Wojciechowski, and T. Zeegers-Huyskens, J. Phys. Chan., AI05, 8734 (2001). 

The main purpose of a dynamical analysis of a molecule is to assign the vibrational transitions observed in infrared and Raman in terms of molecular motions. As mentioned above, chemical group frequency correlations have been the justification of most of the vibrational assignment. The description of the normal modes has posed some problems throughout the years. 

Figure 4.3 Correlation diagram between the local- and normal-mode limits as a function of the parameter E,. Note how the degeneracies typical of the local-mode limit are split and as % —> 1 become the almost harmonic spacings characteristic of the normalmode limit.

---