Corrections to the Born-Oppenheimer approximation by means of perturbation theory

We develop an efficient method for the calculation of corrections to the Born-Oppenheimer approximation by means of perturbation theory. The perturbation terms through sixth order in the small parameter κ=(m/M)1/4, where m and M are, respectively, electronic and nuclear masses, allow the construction of an effective vibrational Hamiltonian that takes into account adiabatic and nonadiabatic effects. The latter is negative and linearly dependent on the vibrational quantum numbers. We illustrate the application of the main equations and verify the general results by means of an exactly solvable model of two coupled harmonic oscillators