A new method for the exact calculation of vibrational–rotational energy levels of triatomic molecules

Abstract

A new method is presented for the calculation of the vibrational–rotational energy levels of a triatomic molecule. The method provides a means of solving Schödinger’s equation for the bound energy levels of a triatomic system as exactly as desired. The relative motion of the atoms is governed by a potential energy surface, which can be of arbitrary form, but must, naturally, be specified. The method utilizes the well developed techniques of molecular scattering theory and is formulated in a body‐fixed reference frame. The bound state energies appear in the theory as first order poles of a specially constructed T matrix element. Because the analytic behavior of these poles, as a function of the energy, is well defined, the exact bound state energies are easily found. The theory has been applied to the water molecule and results are presented for the lowest five vibrational–rotational energy levels corresponding to zero total angular momentum. These results agree well with previously published values.