NON-BORN-OPPENHEIMER CORRECTIONS IN AN EXACTLY SOLVABLE MODEL OF THE HYDROGEN-ION MOLECULE

We have obtained some exact solutions for a solvable model for the hyd rogen molecular ion where the Coulomb interaction between the electron and the nuclei is replaced by a harmonic potential. We have also obta ined the solutions to this model within the ordinary Born-Oppenheimer (BO) approximation for the electronic and nuclear degrees of freedom. The model shows some of the qualitative features of the real system an d allows for a detailed study of non-adiabatic effects on the electron ic structure through the calculation of the first-order corrections to the BO approximation, resulting from the nuclear kinetic energy and t he vibronic coupling. The results are of interest in the context of no n-adiabatic treatment of molecules and for the description of molecule s in external magnetic fields.