The breakdown of the Born-Oppenheimer approximation: the effective vibration-rotation hamiltonian for a diatomic molecule

Abstract

An effective vibration-rotation hamiltonian for the ground electronic state of a diatomic molecule is derived. The contact transformation used to account for the effect of the excited electronic states is complicated by the parametric dependence of the zeroth-order electronic energies on the internuclear distance. The effective vibration-rotation hamiltonian contains an effective internuclear potential and two effective reduced masses, one for the vibrational and one for the rotational kinetic energies. Although the method is applied to ¹Σ diatomic molecules it can readily be extended to other states and polyatomic molecules.