Symmetry of Wavefunctions in Vibration-Rotation Spectroscopy

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).