Rotational and vibration-rotation spectra of polyatomic molecules

6 ROTATIONAL AND VIBRATION-ROTATION SPECTRA OF POLYATOMIC MOLECULES 

From the rotational or vibration-rotation spectra of a diatomic molecule such as HCl, we can calculate the internuclear distance directly from the measurement of the spacing of the lines. This simplicity is absent in polyatomic molecules except in certain special cases. We consider only a few simple examples to illustrate the difficulties. 

Since the molecule is symmetrical, the two bond distances are equal thus only one distance appears in the moment of inertia. We can calculate this internuclear distance directly from the line spacings in the vibration-rotation band just as we did for HCl. 

The four vibrational modes for carbon dioxide are shown in Fig. 25.3. The first vibration is the totally symmetric stretching vibration, = 1388.3 cm This vibration does not produce a band in the infrared since it does not produce an oscillation in the dipole moment of the molecule. The second and third vibrations in Fig. 25.3 differ only in that the bending occurs in mutually perpendicular planes. Thus the vibration is doubly degenerate the frequency is the same for both modes V2 = 667.3 cm The fourth mode is the asymmetric stretching vibration and has a third distinct frequency  

If we ignore anharmonicity, the vibrational energy of the CO2 molecule can be written as a sum of terms  

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Until now we have only considered the rotation and vibration-rotation spectra of polyatomic molecules. The information to be gained from electronic hands is here much more limited than in the case of diatomic molecules. As mentioned already in section 31, the reason for this is a twofold one on the experimental side the diffuse character of the electronic spectra in most cases, due to causes which we shall discuss in the next chapter on the theoretical side the greater difficulty of finding suitable means to classify the electronic states. 

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