Curvilinear coordinate formulation for vibration-rotation-large amplitude internal motion interactions
A theory for vibration-rotation-large amplitude internal motion interactions is developed using curvilinear coordinates for the vibrational degrees of freedom. An essential feature of the theory is our coordination of two transformations for the separation of vibration from rotation and vibration from the LAM, in zeroth order. Series expansion in the vibrational coordinates is used to obtain the full vibration-rotation-LAM Hamiltonian. A Van Vleck perturbation approach is used to obtain the effective rotation-LAM Hamiltonian for the molecule in the nth vibrational state. Reduction of the effective Hamiltonian has been made to (1) the zero angular momentum state of the molecule, (2) the zeroth order rotation-LAM Hamiltonian, and (3) the usual vibration-rotation Hamiltonian when the LAM takes on a small amplitude. The theory is applied to the water molecule treating the bending mode as the LAM. Fourier sine functions are used as the basis for the bending mode, harmonic oscillation functions for the two stretching modes, and Wang functions for the rotational motion. Using Hoy-Mills-Strey and Hoy-Bunker force constants and molecular geometry, the vibration-rotation- LAM energy levels for the water molecule have been calculated. The HMS constant yields better vibration-bending results and the HE constants better rotational results.