Chapter 20 - Molecular vibrations

Abstract

In this chapter, after a short introduction on the problem of separating translational and rotational molecular motions from the internal (vibrational) motions of the nuclei, and on the normal coordinate analysis in classical and quantum mechanics, we consider the interaction of the electronic with nuclear motions described by the so-called vibronic terms in the molecular Hamiltonian. Attention is focussed on the small correction terms beyond the Born–Oppenheimer approximation which are responsible for important structural effects in linear (Renner) and polyatomic (Jahn–Teller) molecules, to the non-crossing rule in diatomics and the conical intersections in polyatomics. We next discuss in some detail the Renner effect in the NH2 radical and the Jahn–Teller effect in the photoelectron spectroscopy of the CH4+ ion. Lastly, we study the valence force field approximation in the case of the linear HCN molecule, and the variational derivation of the Born–Oppenheimer approximation for non-degenerate and degenerate electronic ground states.