text: For symmetric rotors a quantum number J is associated with the total angular momentum of the molecule. For a given value of J, there is a 2J+1- fold degeneracy with the quantum number, M taking the values +J ...0 ... -J. The third quantum number, K is associated with rotation about the principal rotation axis of the molecule. In the absence of an external electrical field, the rotational energy of a symmetric top is a function of only J and K and, in the rigid rotor approximation, the energy of each rotational state is given by
  where  and  for a prolate symmetric top molecule or  for an oblate molecule.
  This gives the transition wavenumbers as
  which is the same as in the case of a linear molecule. With a first order correction for centrifugal distortion the transition wavenumbers become
  The term in D has the effect of removing degeneracy present in the rigid rotor approximation, with different K values.