The physisorption energy of molecular hydrogen (H-2) on flat carbon nanoparticles (graphitic platelets) and polycyclic aromatic hydrocarbons (PAHs) is determined to be attractive between 3.5 and 7.2 kJ mol(-1), depending on the orientation of H-2 and on the particle size. Entropy, estimated from experimental data, reduces the interaction energy by 3.4 kJ mol(-1) at room temperature. Therefore, nanostructured graphitic platelets might be suitable for hydrogen storage. Computations have been carried out for PAHs from benzene to coronene using second order Moller-Plesset (MP2) theory at the basis set limit, and the results are extrapolated to graphene layers.