The role of axis embedding on rigid rotor decomposition analysis of variational rovibrational wave functions

Approximate rotational characterization of variational rovibrational wave functions via the rigid rotor decomposition (RRD) protocol is developed for Hamiltonians based on arbitrary sets of internal coordinates and axis embeddings. An efficient and general procedure is given that allows employing the Eckart embedding with arbitrary polyatomic Hamiltonians through a fully numerical approach. RRD tables formed by projecting rotational-vibrational wave functions into products of rigid-rotor basis functions and previously determined vibrational eigenstates yield rigid-rotor labels for rovibrational eigenstates by selecting the largest overlap. Embedding-dependent RRD analyses are performed, up to high energies and rotational excitations, for the H(2) (16)O isotopologue of the water molecule. Irrespective of the embedding chosen, the RRD procedure proves effective in providing unambiguous rotational assignments at low energies and J values. Rotational labeling of rovibrational states of H(2) (16)O proves to be increasingly difficult beyond about 10,000 cm(-1), close to the barrier to linearity of the water molecule. For medium energies and excitations the Eckart embedding yields the largest RRD coefficients, thus providing the largest number of unambiguous rotational labels.