4 - Symmetry of Wavefunctions in Vibration-Rotation Spectroscopy

Abstract

Vibrational and rotational basis functions are built up by iterated applications of appropriate ladder operators to a lowest energy state function. The transformations under the symmetry operations and time reversal of these generating operators, and then of the generated functions, are investigated. A first classification is made according to the transformation properties under the orientation operation number one called R (the highest order rotation axis or rotation-reflection axis). Basis functions of higher symmetry are defined as linear combinations of appropriate pairs, which transform in the simplest way under the second orientation operator R′ (a binary symmetry axis normal to R, or a reflection plane containing R). It is found that appropriate phase conventions for the adopted basis functions simplify the results. The investigation is then extended to vibration-rotation functions. Application is made to molecules of different rotational properties (symmetric, spherical, and asymmetric rotors, and to linear molecules).