Infinite-order non-Born-Oppenheimer perturbation theory for systems with intersecting potentials

A full perturbation expansion on the Born-Oppenheimer (BO) approximation was presented for the crossing of electronic potential energy surfaces. An analytical expression for the eigenstates and energies of two intersecting electronic states was derived as a function of α. The electronic states were coupled by a single nuclear coordinate. The complete resummation of the Brillouin-Wigner perturbation series in the Born-Oppenheimer basis was done to rederive the expression for the energy eigenstates. To show the possiblility to base a full perturbation expansion on the BO expansion even where theelectronic potential energy surfaces cross was the main aim of the study. Divergences of nonadiabatic coupling was found to cancel strictly order by order.