The interaction potential confining the stretching and translational motions of a molecular hydrogen physisorbed on the graphene surface has been calculated by means of the DFT/CC approach. Using a simple adiabatic separation of the stretching and translational motions, a set of effective stretching potentials is generated by performing a "finite box" integrating over the translational degrees of freedom. The resulting potentials, forming energetically narrow bands, are used to evaluate the corresponding average stretching energies, which are in turn compared to their experimental counterparts. The mass-dependent "translational" corrections of the purely stretching potential significantly improve the theory versus experiment agreement, thus evidencing their importance in the physisorption processes. Although not fully quantitative, the DFT/CC stretching potentials seem to exhibit physically correct shapes, as their morphing by only a few parameters allows for a quantitative fitting of the observed vibrational energies in terms of the effective (mass-dependent) interaction potentials.