Classical rotational energy is defined as
and from this expression and the quantum mechanical expressions for the angular momenta, we may calculate the rotational energy levels for the four different molecule types as follows:
(!) Linear rotors. For linear rotors Ia = 0, Ib = Ic = I, and the energy levels may be found from simple quantum theory to be
where, since — J < K < J, the energy levels have a degeneracy of 2J + 1.
(ii) Spherical tops. For these molecules Ia = Ib = Ic = I, and the energy levels are found to be essentially the same as Equation (6.16), although in this case the degeneracy of the rotational energy levels is found to be partially lifted.
(iii) Symmetric rotors. For prolate symmetric rotors where Ia = Ia, Ib = Ic = Ib, classical rotational energy may be written as
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