Influence of Vibrations on Molecular Structure Determinations. I. General Formulation of Vibration—Rotation Interactions

Abstract

The structure of a polyatomic molecule derived from observed spectroscopic moments of inertia differs appreciably from both the equilibrium structure and the zero‐point average structure. A perturbation expansion of the moments of inertia is derived here in a form which allows the vibrational displacements to be referred to any fixed configuration of the atoms as origin. A method for evaluating the expansion coefficients is given which proceeds ``atom by atom.'' Linear WXYZ, branched WXYZ, and symmetric WXY₃ molecules are treated in detail. Empirical data show that the anharmonicity of the vibrations gives rise to the most important of the corrections required to obtain the equilibrium structure. Except for a few molecules, the anharmonicity is not accurately known. It is shown, however, that to a practical approximation the anharmonic contributions are completely absorbed in displacing the average configuration from the equilibrium one. Therefore the moments of inertia for the zero‐point average configuration of a molecule can be derived from the observed effective moments by applying corrections which depend only upon the harmonic part of the vibrational potential.