Non-adiabatic theory in terms of a single potential energy surface. The vibration-rotation levels of H2+ and D2+

The traditional formulation of a molecular wave function describing the motion of the electrons and the nuclei, in terms of the Born hierarchy, does not allow to account for the participation of the electrons in vibrational or rotational motions, except by recurring to a fully non-adiabatic treatment, abandoning completely the concept of a single potential energy surface for one electronic state of the molecule. An alternative approach has been presented recently, which is based on an exact separation in all possible dissociation limits, and which leads to a Hamiltonian for the nuclear motion with a geometry-dependent effective nuclear mass, that is different for vibration and rotation. This approach is now tested numerically. We account for the vibration-rotation spectrum of H2+ and D2+ in their electronic ground states in terms of a single potential energy curve, with spectroscopic accuracy, i.e. with errors of the order of a few hundredths of a cm−1. We byepass by far the accuracy that is achievable in terms of a geometry-independent effective mass.