Example: H2O, OClO
The energy eigenvalues of oblate and prolate extreme cases of the assymetric
top are shown on the below figure schematically. The energy values decrease for
prolate case with the increasing K value whereas they increase for the oblate
case. If one changes IB between
IA and IC then one can obtain the energy of antisymmetric
top. The assymetric top thus can be described by quantum numbers projections
Ka, Kc of the symmetric threshold case. Three quantum
numbers JKaKc fully determine the rotational state.
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The energies of antisymmetric top with total kinetic moment J = 3 according to Dennison & Hecht (in "Molecular Spectra in Quantum Theory II, Eds. Bates, Academic Press, 1962). The main moment of inertia has arbitrary value and IA = 1 and IC = 2. The figure shows energy level positions if one varies B between boundary prolate and oblate cases. |