ABSTRACT
This chapter discusses effective Hamiltonians of the type described by Van Vleck, where all contributions that are off-diagonal in vibrational or electronic quantum numbers in a particular basis set have been absorbed into the parameters of the effective Hamiltonian. The treatment of the rotational energy levels of linear triatomic molecules proceeds using the methods discussed by Hougen for diatomic molecules. The differences arise primarily because triatomic molecules possess a bending vibration that destroys the linear symmetry. In a linear triatomic molecule, there are four vibrational degrees of freedom, two of which are associated with the degenerate bending vibration, and two rotational degrees of freedom. Linear molecules possess a vanishing moment of inertia about the linear axis, and a nonvanishing moment of inertia perpendicular to the linear axis, which is the same for all such axes through the centre of mass.
