Particles-on-a-sphere method for computing the rotational-vibrational spectrum of H 2O

Abstract

An adiabatic separation of fast stretching from slow bending and rotational motion has been made for the water molecule. Two programs are presented; one solves the Schrödinger equation over the radial coordinates to obtain the stretching eigenvalues and eigenfunctions, as well as an effective bending potential and moment of inertia. The second program uses the results of the first as part of the Hamiltonian to solve the Schrödinger equation over the angular variables in order to obtain the rotational-bending levels. The radial program can construct the effective bending potential in either of two ways. The first is to solve the radial equation at only the equilibrium bending angle, and use the resulting wavefunctions to average over the radial coordinates at selected bending angles. The second method is to solve the radial equation at several values of the bending angle, and use the eigenvalues as points on the effective bending potential. The angular program presented here is suitable for using the results from the first method, and may be used with the results of the second method provided that only one value for the moment of inertial is used as input.