Vibrational angular momentum in the theory of vibration-rotation spectra

Abstract

The theory of the vibrational angular momentum term\(\hat \pi _\alpha ^2 \) in the effective molecular rotational Hamilton operator is briefly reviewed. Novel vibrational matrix elements of\(\hat \pi _\alpha ^2 \), off-diagonal in the basis of the coupled linear oscillator basis functions, are derived for asymmetric top molecules. These matrix elements contain two or three distinct vibrational quantum numbers, respectively. A group-theoretical scheme; the use of repeated Jahn’s rules, is given for testing the existence of the proposed matrix elements. Finally suggestions are made for the application of the latter.