THE BENDER, THE RIGID-BENDER, AND THE NON-RIGID BENDER MODELS FOR A ROTATING-VIBRATING TRIATOMIC OR TETRA-ATOMIC MOLECULE

Abstract

The molecules $H_{2}O$ and HNCO are examples of molecules that suffer extreme centrifugal distortion of the rigid-rotor model when the rotational quantum numbers have values of about 10. This necessitates inclusion of terms such as $P_{z}^{10}$ and $P_{z}^{12}$ in the rotational Hamiltonian in order to fit the $data.^{1,2}$ This is unsatisfactory in that (a) Data reduction is not greatly achieved, (b) It is impossible to extrapolate the energy expression to predict higher energy levels, and (c) The rotational constants obtained (A, B, C, $D_{J}$, etc.) are not uniquely determined. This extreme centrifugal distortion results from the flexibility of the $H-O-H$ and $H-N-C$ bending coordinates which, therefore, change by a large amount as a result of the centrifugal forces of molecular rotation. The rigid-rotor is not a good zeroth-order model to use for calculating the rotational energy leveles in such a case. We have developed the rigid-bender $model^{3,4}$ which provides a much better zeroth-order model for fitting the rotational energy levels of such molecules. The application of this model, and of the more refined non-rigid bender model, to such centrifugal distortion problems will be discussed. The application of the models to the interpretation of the unusual anharmonicity effects in the $\hat{A}$ state of HCN and the ground state of HCNO will also be discussed. One interesting result is that although the equilibrium of HCNO is bent the zero-point structure is linear.