Considerations on the Rotation—Vibration of Triatomic Molecules

Abstract

In order to incorporate the variations of the moments of inertia and the reduced masses for vibration generated by large‐amplitude vibrations into a treatment of the vibration—rotation interaction of polyatomic molecules, we investigate the use of the instantaneous moments of inertia to define the rotating reference frame. This technique does not suffer from the disadvantage of tying the treatment to any equilibrium configuration and treats all vibrating molecules as asymmetric tops. The case of large‐amplitude bending in triatomic molecules is used to illustrate the general features of such a method. An adiabatic approximation is used to separate the stretching from the bending vibrations, exhibiting the important aspects of the coupling of these modes. The properties of angular momenta are utilized, and the resulting equations for the bending vibration are a set of coupled differential equations which are analogous to the algebraic equations encountered in the treatment of the rotational motion of asymmetric‐top molecules. As a simple test of the validity of the Hamiltonian, the l‐type doubling parameter is calculated for a number of molecules in good agreement with experiment.