A three-dimensional semiclassical quantization of H2O

Abstract

The semiclassical mechanics of the vibrations of H₂O is examined. The analysis makes use of the work of Sibert, Reinhardt, and Hynes [J. Chem. Phys. 7 7, 3595 (1982)] in which the two‐dimensional stretching dynamics of ‘‘local mode’’ molecules was examined. There an approximate but accurate Hamiltonian was derived via the techniques of nonlinear mechanics. Quantization of this Hamiltonian, which has the form of a hindered rotor, gives vibrational energies in excellent agreement with direct quantum calculations of the H₂O model Hamiltonian. In the present treatment we significantly advance the techniques developed in the earlier work to incorporate the bending degree of freedom and to generalize the treatment to be able to examine more realistic potential energy surfaces. Our results, which extend to energies as high as 22 000 cm⁻¹, are in good agreement with the corresponding quantum mechanical calculation of Child and Lawton [Chem. Phys. Lett. 8 7, 217 (1982)] and demonstrate that a twofold hindered rotor Hamiltonian provides a good description of the three‐dimensional vibrational eigenvalues.