The Assymetric Top

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.

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.