Statistical Thermodynamics

3 Energy and Interactions

For a given chemical system, applying the statistical mechanics starts with writing a function called the partition function. The writing requires that we know the energy of each molecule in the system. We learn in this chapter how to describe and specify the energy of each molecule.

In the absence of an applied external field and in the absence of interaction between molecules, the energy of a molecule consists of the energy due to the movement of the molecule as a whole and the energy for the movement of atoms within the molecule. We first use classical mechanics to describe the movements and the kinetic energy. Toward the end of the chapter, we learn quantum‐mechanical methods to describe the kinetic energy. “Classical” means that the movement of a molecule follows Newton's equation of motion. It does not only describe the center‐of‐mass translation but also the rotation and the vibration.

In Sections 3.1 and 3.2, we first consider kinetic energy of atoms and ions and kinetic energy of diatomic molecules, respectively, that do not interact with each other. In Section 3.3, we look at the energy of polyatomic molecules. Then, in Section 3.4, we learn different types of interaction between molecules. In these four sections, we rely on classical mechanics. After examining briefly an extensive nature of the interaction in Section 3.5, we turn to quantum mechanics to describe all the components of the energy in Section 3.6.

3.1 Kinetic Energy and Potential ...