Perturbative approaches to highly excited molecular vibrations of H2O, D2O, and HDO

Molecular vibrations of water are studied using Van Vleck perturbation theory. In these calculations, the OH stretches are expressed in terms of the Morse coordinate, yi =[1−exp(−αri)]/α, and its conjugate momentum, while the bend is treated in a traditional manner. Nearly degenerate perturbative calculations are presented for bond and normal-mode representations. The eigenvalues agree well with those obtained variationally. The coefficients of the perturbatively derived, effective Hamiltonians are compared to those of spectroscopic Hamiltonians with similar structural forms. The former are derived from the potential of Halonen and Carrington [J. Chem. Phys. 88, 4171 (1988)], whereas the latter are treated as spectral fitting parameters. The fit parameters are accurately reproduced.