ABSTRACT
A diatomic molecule, such as CO, N2, or O2, consists of two nuclei and a handful of electrons. The simplest example is the hydrogen molecule, H2, consisting of two protons and two electrons. Electrostatic interactions involving the charged nuclei and the electrons lead to an effective attraction between the two nuclei, which is the very reason the molecule is formed. This attraction can often be described using the following picture: Imagine fixing the distance R between the two nuclei. Now consider the molecule’s electrons interacting with each other while also subjected to the electric field created by the nuclei. The behavior of those electrons is described by quantum mechanics. Specifically, quantum mechanics predicts in this case that, for each value of R, the molecule can take on discrete energy levels E0(R), E1(R), etc. If the temperature of the system is not too high then the higher energy levels are often thermally inaccessible.1 We thus concentrate on the lowest energy level E0(R). By adding this energy to the energy of internuclear electrostatic interaction, we obtain a function V (R), which can be thought of as an effective potential felt by the nuclei. The typical V (R) looks like the curve shown in Figure 4.1. In the limit R → ∞ the two atoms do not interact with one another so that V (R) approaches a constant value. R being too small results in a repulsive interaction such that V (R) becomes very high. The existence of a minimum of V (R) at an intermediate value R = R0 signifies a chemical bond. That is, mutual approach of two atoms lowers their total potential energy. Conversely, separating the two atoms requires expending energy.
