Doubly degenerate vibrational levels of spherical top molecules Definition of basis functions as irreducible tensors of O(3)

Although the vibrational wavefunctions for a doubly degenerate level of a spherical top molecule do not form the basis for an irreducible representation of the rotation group, we show that it is possible to define vibration-rotation basis functions as irreducible tensors of this group. We consider successively two important cases: the fundamental ν ₂( E) and the sublevel ℓ = 2 of the first overtone of a triply degenerate fundamental. From this we show that the method can be easily generalized.