ABSTRACT
The rotational energy levels of molecules are active in microwave and far-infrared (IR) spectroscopy and in light scattering experiments. The absorption or emission of light due to rotational motion is allowed only for polar molecules, although nonpolar ones can absorb weakly through induced moments. Light scattering due to rotations is permitted whenever the polarizability is anisotropic. In this chapter, we discuss two types of pure rotational spectra, microwave/far-IR and rotational Raman scattering. With these techniques, it is possible to resolve quantized rotational energy levels for freely rotating (gas phase) molecules. Rotational spectroscopy is often applied to the determination of structure and dipole moments of small molecules, the latter through the use of the Stark effect. Being more closely spaced than vibrational and electronic energy levels, rotational quantum levels can contribute to fine structure in vibrational and electronic spectroscopy of gases. In addition to rotational motion of the entire molecule, some molecules undergo internal rotation about single bonds, which ranges from being quite hindered to relatively free. Molecules in liquids do not rotate freely, as a rule, and their reorientational motion is more difficult to treat quantum mechanically and does not lead to discrete spectral lines. An exception to this rule is discussed in Section 8.4, where the rotational Raman spectrum of H2 dissolved in water is analyzed. Still, there are spectroscopic manifestations of reorientational motion in liquids, which will be considered in the discussion of depolarized Rayleigh scattering. (See also Chapter 5.)
The quantum mechanical solution to the rigid rotor problem is an example of a model for which the Schrödinger equation is exactly solvable. In this section, we review the treatment for a diatomic molecule and extend it to the case of polyatomic molecules having different degrees of symmetry. There are two important caveats to the treatment of this section. The first is that it applies to rigid molecules, while real molecules undergo vibrational motion, even at absolute zero. What is derived for rigid rotors is a good approximation provided the amplitude of vibrational motion is small. The second point to keep in mind when comparing theory to reality is that a free rotor experiences no angular dependent forces (torques), so what is predicted by theory does not apply for liquids, solids, or even dense gases where intermolecular interactions come into play.
