Nonadiabatic corrections to the wave function and energy

Nonadiabatic corrections in molecules composed of a few atoms are considered. It is demonstrated that a systematic perturbative expansion around the adiabatic solution is possible, with the expansion parameter being the electron-nucleus mass ratio to the power 3/4. Closed form formulae for the leading corrections to the wave function and to the energy are derived. Their applicability is demonstrated by a comparison of numerical results for the hydrogen molecule with the former nonadiabatic calculations and the experimental values. Good agreement with the recent experiment is achieved for the ground state dissociation energy of both H$_2$ and D$_2$.