Highly excited vibrational eigenstates of nonlinear triatomic molecules. Application to H2O

Abstract

Highly accurate quantum-mechanical calculations are presented for highly excited vibrational states of H2O. The vibration Hamiltonian operator Ĥvib for a nonlinear triatomic molecule is given in Radau coordinates. A direct product basis is chosen, and the Hvib matrix is evaluated in the discrete variable representation (DVR) for the symmetrized Radau coordinates. Vibrational eigenstates are computed from the DVR Hvib via the successive diagonalization/truncation technique. A comparison of the computed eigenvalues with those observed demonstrate the accuracy of our model. Highly excited vibrational states, up to 30 000 cm−1 above the zero-point energy, are reported for the potential energy surface (PES) given by Jensen [J. Mol. Phys., 133, 438 (1989)]. Using natural orbital expansions, the eigenfunctions of vibrational states are analyzed to understand the origins of the dynamical mixing of the vibrational modes. The local/normal mode transitions, Fermi resonances, Darling–Dennison interactions, and the mode separabilities are investigated. Statistical studies on the energy level spacings are presented for two different types of PES.