We have extended the continuum distorted wave eikonal initial state approximation for single ionization of atoms by ion impact to the molecular case where a model potential for the molecular target is introduced. The continuum wavefunctions of the ejected electrons are then calculated in the static-exchange potential field generated by the residual molecular ion. The Schwinger variational iterative method was used in the calculation of these continuum wavefunctions. We apply this model to the single ionization of the hydrogen molecule (H 2 ) by different bare projectiles. Doubly differential cross sections are calculated and compared with available experimental data for intermediate impact energies.