Rotating Molecules

Abstract

In Chap. 2, we have learned that molecules vibrate around their equilibrium geometrical structures. In the three-dimensional space, molecules not only vibrate but also rotate. This rotational motion is, in fact, also quantized. That is, the rotational energy of a freely rotating molecule in the gas phase takes only discrete values. This is greatly different from the rotational motion of a solid body in classical mechanics. An important aspect of the rotational motion is that it allows us to determine the geometrical structure of molecules. Knowing the energy difference between the discrete energy levels directly leads to the determination of the geometrical structure of a molecule. In this chapter, we will express the rotational energy of a molecule in classical mechanics and learn a procedure for treating it in quantum mechanics. In the course of learning this procedure, we will deepen our understanding of the quantum theory of angular momentum. We will further discuss the method for determining the geometrical structures of molecules based on data obtained from a rotational spectrum through a number of examples.