Vibrating Molecules

Abstract

When we visualize the geometrical structure of molecules, we think of it as a static image consisting of bond lengths and angles. In reality, however, chemically bound atoms are constantly changing their positions with each other. This dynamical motion is called molecular vibration. A point of note is that this vibration is qualitatively different from what has been described as vibration in classical mechanics. As introduced in Chap. 1, the energy of molecular vibration can only take discrete values. Explaining this experimental observation requires the introduction of quantum mechanics. In this chapter, we will learn how to treat molecular vibration using quantum mechanics. We also seek to understand the meaning of eigenenergy and eigenfunction in quantum mechanics by looking at the case of molecules. Finally, we will discover that the number of normal modes based on which the vibrational form of polyatomic molecules can be described is equal to the number of degrees of freedom, by taking triatomic molecules as a concrete example.