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The coefficients sufficient to construct all the invariant (with respect to elements of the symmetry group Oh) cubic harmonics and the invariant cubic rotator (known also as the Wigner) functions are given up to l=30. Description of various problems in which symmetry plays an important role can be much simplified if one uses functions which are either invariant under action of elements of the symmetry group or which transform in a convenient way under such actions. Interaction of molecules of axial symmetry can be described by the 91 spherical harmonics, Y lm where the angles define the orientation of the symmetry axis of a molecule [1], If the molecules are not axially symmetric, the spherical rotator functions, (Ω), are necessary, in general; Ω defines the orientation of the molecule and, usually, is expressed by the Euler angles Spherical harmonics in a primed system, obtained from an unprimed system by a rotation , can be expressed by the spherical harmonics in the unprimed system:

Combinations of the spherical harmonics and the spherical rotator functions invariant with respect to the symmetry group O h