  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$_2$.
