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The effective rotation-bending Hamiltonian of a triatomic molecule, and its application to extreme centrifugal distortion in the water molecule

1974; Elsevier BV; Volume: 52; Issue: 3 Linguagem: Inglês

10.1016/0022-2852(74)90191-x

1096-083X

A.R. Hoy, P. R. Bunker,

Quantum, superfluid, helium dynamics

This paper is concerned with the determination of the shape of the potential energy surface of a triatomic molecule over a wide range of values for the bending coordinate, and numerical integration of the wave equation is used in order to relate the shape of the potential surface directly to the rotation-bending energies. The rotation-vibration Hamiltonian that is used was derived by Hougen, Bunker, and Johns [J. Mol. Spectrosc. 34, 136 (1970)] in a manner that allowed explicitly for the dependence of the inverse moment of inertia tensor elements on the bending angle. We now treat the stretching vibrational coordinates in this Hamiltonian by Van Vleck perturbation theory to obtain the effective rotation-bending Hamiltonian. We call this Hamiltonian the nonrigid bender Hamiltonian, in contrast to the simpler rigid-bender Hamiltonian used by Bunker and Stone [J. Mol. Spectrosc. 41, 310 (1972)]. The Hamiltonian is used to calculate the energies of the higher rotational energy levels (J ≅ 10) of the v2 = 0 and 1 states of H2O, D2O, and HDO from the equilibrium structure and force constants of the water molecule, and a slight refinement of the structure and force field has been possible. The fit is at the level where any further improvement will necessitate considering the breakdown of the Born-Oppenheimer approximation among other higher-order corrections. Many of the ideas developed here can be applied to the treatment of the rotation-vibration problem in any molecule having a large amplitude coordinate, or a coordinate on which a moment of inertia element strongly depends.