Asymmetric Top

Example: H2O, OClO

The diagram below shows the eigenvalues of energy for the oblate and prolate case of an asymmetric top. In the prolate case, the energies decrease with increasing K, whereas in the oblate case, energies increase with increasing K. For values of IB between IA and IC, the diagram provides the energy of the asymmetric top. We describe here the asymmetric top by using a pair of projection quantum numbers Ka and Kc of the symmetric extreme cases. The rotational state is completely defined by the three quantum numbers JKaKc.
The energies of an asymmetric top with a total angular momentum J = 3 according to Dennison & Hecht (in "Molecular Spectra in Quantum Theory II, Eds. Bates, Academic Press, 1962). The principal moments of inertia are arbitrarily set to IA = 1 and IC = 2. The diagram indicates the position of the energy levels for an IB that varies between the oblate and the prolate extreme case.


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