Molecular hydrogen adsorption in a nanoporous metal organic framework structure (MOF-74) was studied via van der Waals density-functional calculations. The primary and secondary binding sites for H$_2$ were confirmed. The low-lying rotational and translational energy levels were calculated, based on the orientation and position dependent potential energy surface at the two binding sites. A consistent picture is obtained between the calculated rotational-translational transitions for different H$_2$ loadings and those measured by inelastic neutron scattering exciting the singlet to triplet (para to ortho) transition in H$_2$. The H$_2$ binding energy after zero point energy correction due to the rotational and translational motions is predicted to be $\sim$100 meV in good agreement with the experimental value of $\sim$90 meV.