In the ongoing search for promising compounds for hydrogen storage, novel porous metal-organic frameworks (MOF) have been discovered recently[1]. Well defined binding sites were deduced from inelastic neutron scattering (INS) spectroscopy of the rotational transitions of the adsorbed molecular hydrogen. In light of this discovery we performed ab initio density functional theory (DFT) calculations of the adsorption of molecular hydrogen on this class of microporous MOF to compare different adsorption sites. As a first step, we study the case of H2 adsorbed on benzene. The DFT code used, Abinit, is based on plane-waves and pseudopotentials. Different approximations for the exchange-correlation potentials were accessed for a set of relevant properties (binding energy, energetically favored configuration, distance between the adsorbents and adsorbates). In particular, theoretical rotational spectra of the adsorbed H2 were obtained that could be compared to the experimental INS spectra.