The vibration-rotation problem in triatomic molecules allowing for a large-amplitude bending vibration

In this paper we derive an expression for the vibration-rotation Hamiltonian of a triatomic molecule. In the derivation we use a curvilinear bending coordinate and two rectilinear stretching coordinates in such a way that the Hamiltonian obtained is applicable for any triatomic molecule, linear or bent, and allows for large displacements of the bending coordinate (sometimes said to result from the molecule being “quasi-linear” but, in fact, of general occurrence). We derive a zeroth-order Hamiltonian to describe the energy levels associated with the bending vibration, and are able to fit the experimental results on HCN and DCN better than if we had used the standard formalism of rectilinear (and small) displacements. We also use the formalism to describe the dependence of the rotational constant B on the bending vibrational quantum number and apply the results to the microwave data on CsOH and CsOD.