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

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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.