Knowledge Bank

A theory for vibration-rotation-large amplitude internal motion interactions is developed using curvilinear coordinates for the vibrational degrees of freedom. An essential feature to the theory is our coordination of two transformations for the separation of vibration from rotation and vibration from the LAM in seroth order. Series expansion in the vibrational coordinates is used to obtain the full vibration-rotation-LAM Hamiltonian. A Van Vleck perturbation scheme is used to obtain the effective rotation-LAM Hamiltonian, $HREFF$, for the molecule in the nth vibrational state. The theory has been applied to calculating the energy levels of the water molecule, treating the bending mode as a LAM. The vibration-rotation-LAM energy levels have been calculated using the Hoy-Mills-Strey and Hoy-Bunker force constants and molecular geometry. For the vibration-LAM energy levels in the zero angular momentum state 1) our results using the HB force constants are better than the results of Bunker and co-workers using the HBJ theory: and 2) our results using the HMS force constants are better than the results from the HMS vibration-rotation theory. For the rotational energy levels, the HB force constants give better results than the HMS force constants with our calculation. Further, for the $J=10$ levels, our results are 70% better than those of Bunker and co-workers using the HBJ theory and the HB force constants.