Intramolecular potential function of polyatomic molecules by vibration-rotation interactions

Abstract

INTRODUCTION Vibration—rotation interactions appear in various fields of molecular spectroscopy and their investigation is of considerable interest. The theory of the vibration—rotation energy of molecules was first formulated by Wilson and Howard'; it has since been brought to perfection by H. H. Nielsen and his co-workers2. Amat and others3 have extended Nielsen's second-order theory to the fourth-order and have elucidated many interesting phenomena which have come to light through the recent development of spectroscopic techniques. High-resolution infrared spectroscopy should be a fertile field for the application of the theory; indeed, the theory has already led to outstanding findings on the molecular structure and potential functions. The study of asymmetric-top molecules by the infrared4 is painstaking, because the spectra are very complicated. In this connection the work by Mills5, Werner6, and Dows7 should be mentioned. They have shed fresh light on this field. On the other hand, microwave spectroscopy can treat even asymmetric-top molecules rather easily, because the microwave spectrum involves only simple rotational transitions. In this situation it must be evident that the cooperation of infrared and microwave spectroscopists promises substantial progress in both fields: the introduction of knowledge about asymmetric-top molecules into the study of the infrared spectrum will give us a basis for the analysis of the complicated pattern of the infrared spectra, while at the same time the introduction of the knowledge of vibrating molecules into the study of microwave spectra will open up a vast new field to the microwave spectroscopists, who have thus far been primarily concerned with the vibrationally-ground states. In each case, the guiding principle is the theory of vibration—rotation interactions, and the results to be obtained concern the properties of vibrating molecules. Before entering into detail on individual examples, it would be worthwhile to summarize the main sources of the vibration—rotation interactions. The first one is the change in the moments of inertia; the moments of inertia are not constant when atoms vibrate about their equilibrium positions. If we expand the instantaneous moments of inertia in terms of the normal coordinates: = J(e) + a3(')Q +>[A83'(') — 8sC)3'3()]QjQ' (1)