A variational localized representation calculation of the vibrational levels of the water molecule up to 27 000 cm^-1

We have calculated variationally highly excited vibrational (J = 0) levels of the water molecule up to ∼ 27 000 cm^-1 (relative to the minimum of the potential surface), for a global Sorbie-Murrell-type potential surface. The calculation has been performed in Radau coordinates, using the recently developed DVR-DGB variational approach [Z. Bačić and J. C. Light, J. Chem. Phys. 85, 4594 (1986); 86, 3065 (1987)]. 110 symmetric and 77 antisymmetric vibrational levels have been determined accurately, requiring diagonalization of relatively small Hamiltonian matrices of dimension ∼600. Many of the calculated levels correspond to large amplitude bending vibrations. Nearest neighbor level spacing statistics for the calculated levels above 18 000-20 000 cm^-1 conform closely to a Wigner distribution, suggesting classically chaotic behavior in this energy range. Convergence rates of these variational calculations for H₂O are comparable to those seen earlier for LiCN/LiNC and HCN/HNC. The DVR-based vibrationally adiabatic approach introduced by Light and Bačić [J. Chem. Phys. 87, 4008 (1987)] has also been tested here. Perturbative inclusion of the nonadiabatic corrections has allowed reliable identification of vibrational (J = 0) levels of H ₂O up to 18 000-20 000 cm^-1. With this model potential energy surface, reasonable agreement (∼1%) is obtained with experimentally known vibrational states to ∼20 000 cm^-1.