The rigid bender and semirigid bender models for the rotation-vibration Hamiltonian

Abstract

The rigid bender Hamiltonian used by Bunker and Stone ( J. Mol. Spectrosc., 41, 310 (1972)) is reviewed and applied to fit the recently obtained rotation-bending energy levels of the H 2O molecule. This rotation-bending Hamiltonian treats a triatomic molecule as bending with fixed bond lengths. A simple improvement is made by allowing the bond lengths to vary with the bond angle and the new Hamiltonian is called the semirigib bender Hamiltonian. This Hamiltonian allows for all the important stretch-bend interaction terms from the potential energy and rotation-bending interaction terms from the kinetic energy. As a result the variation of the rotational constants with bending vibrational state is treated better than by the rigid bender. The model is used to fit the rotation-bending energy levels of the H 2O molecule. While not as good as the nonrigid bender Hamiltonian of Hoy and Bunker ( J. Mol. Spectrosc., 52, 439 (1974)) the semirigid bender Hamiltonian is easier to apply to a larger molecule, and this is the reason for introducing it. At the end of the paper the rigid bender model is compared to a more approximate model in which the variation of the bending reduced mass with bending angle is ignored. The approximate model can introduce serious errors but since we know how the bending reduced mass varies with bond angle in the rigid bender model the approximation of the simpler model is unnecessary.