A molecule is composed of positively charged nuclei surrounded by electrons. The stability of a molecule is due to a balance among the mutual repulsions of nuclear pairs, attractions of nuclear–electron pairs, and repulsions of electron pairs as modified by the interactions of their spins. Both the nuclei and the electrons are in constant motion relative to the center of mass of the molecule. However, the nuclear masses are much greater than the electronic mass and, as a result, the nuclei move much more slowly than the electrons. Thus, the basic molecular structure is a stable framework of nuclei undergoing rotational and vibrational motions surrounded by a cloud of electrons described by the electronic probability density.

In this chapter we present in detail the separation of the nuclear and electronic motions, the nuclear motion within a molecule, and the coupling between nuclear and electronic motion.

Nuclear structure and motion

We consider a molecule with Ω nuclei, each with atomic number Zα and mass Mα(α = 1, 2, …, Ω), and N electrons, each of mass me. We denote by Q the set of all nuclear coordinates and by r the set of all electronic coordinates. The positions of the nuclei and electrons are specified relative to an external set of coordinate axes which are fixed in space.