Vibrations of polyatomics

The eigenvalue problem was introduced in Section 7.3, where its importance in quantum mechanics was stressed. It arises also in many classical applications involving coupled oscillators. The matrix treatment of the vibrations of polyatomic molecules provides the quantitative basis for the interpretation of their infrared and Raman spectra. This problem will be addressed tridre specifically in Chapter 9. 

The formulation of the preceding section is very general. We are interested, however, in rotations and vibrations of polyatomic molecules. We therefore discuss now specific applications of the algebraic method beginning with the simple case of one-dimensional coupled oscillators, presented in Section 3.3 in the Schrodinger picture. In the algebraic theory, as mentioned, one associates to each coordinate, x, and related momentum, px = — iti d/dx, an algebra. For... 

Amat, G., Nielsen, H. H., and Tarrago, G. (1971), Rotational-Vibration of Polyatomic Molecules, M. Dekker, New York. 

Simanouti (Shimanouchi) T (1949) The normal vibrations of polyatomic vibrations as treated by Urey-Bradley field. J Chem Phys 17 245-248... 

Raman spectroscopy (Section 4.10) aids the study of the vibrations of polyatomic molecules. For a vibration to be Raman active, it must give a change in the molecular polarizability. For many molecules with some symmetry, one or more of the normal modes correspond to no change in... 

The more complex rotations and vibrations of polyatomic molecules are subject to the same principles, and distribution laws of the same kind apply, as will be shown in the following section. 

The modes of vibration of polyatomic anions60 are primarily determined by the number of atoms present and the symmetry of the free ions (Table 1), and the IR frequencies of these high-symmetry free ions are well characterized (Figure 6a). 

Simanouti, T. The normal vibrations of polyatomic molecules as calculated by Urcy-Bradley field. II. Vibrations of polythene, ethane, and their deuterium compounds. J. chem. Phys. 17, 734—737 (1949). 

---