AN INVESTIGATION OF THE ALGEBRAIC STRUCTURE OF VIBRATIONAL-ROTATIONAL INTERACTION TERMS OF HIGH ORDER IN POLYATOMIC MOLECULES.

Abstract

This research was supported by the Air Force Cambridge Research Laboratories, Office of Aerospace Research.Author Institution: Physics Department, Providence College, ProvidenceIn recent years, the theory of vibrational-rotational (v-r) interactions in polyatomic molecules has reached a formidable degree of complexity, in particular, in its applications to the derivation of terms of sixth power in the angular momentum. In an attempt to simplify these derivations, and to extend some of them to terms of eighth to twelfth power in the angular momentum, we have developed an algebraic procedure which follows closely the conventional treatment of v-r interactions in diatomic molecules. The minimum of an energy function consisting of the rotational kinetic energy of a non-rigid asymmetric rotor and of the potential energy of a more-dimensional anharmonic oscillator is chosen as the origin of a new coordinate system. A ``Minimization Theorem'' simplifies substantially the algebraic procedures. The derivation of general results is straightforward but the structure of the terms of high order thus obtained is rather involved. Only a systematic analysis of these structures, and the development of methods suitable for the evaluation of these terms makes the application of our results to particular molecular models feasible