Knowledge Bank

The effective rotational Hamiltonian of molecules with two periodic large-amplitude motions were derived in terms of effective tunneling parameters similarly to the procedure described for one-dimensional problems. The various forms of this Hamiltonian depend on the molecular symmetry group and the site symmetry of the localized functions. These results suggest an analogy between molecular symmetry groups and the space groups of crystals. A generalized method is described to derive an effective rotational Hamiltonian from the molecular symmetry group, the site symmetry group, and the generators required to generate the former group from the latter. It is compared to the more specific method developed by Coudert and Hougen for $(H2O)2\mathrm{<mrow\; data-mjx-texclass="ORD">2,3</mrow>}$ and $(NH3)2,\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$.