The repartition of molecular hydrogen in space, and its depletion on solid particles in particular, is an important question of modern astrophysics. In this paper, we report a theoretical study of the physisorption of molecular hydrogen, H2, on a major component of the interstellar dust known as polycyclic aromatic hydrocarbons (PAHs). Two different density functional theory approaches were used: (i) the conventional Kohn−Sham theory and (ii) the subsystem-based approach (Kohn−Sham equations with constrained electron density, KSCED) developed in our group. The approximate exchange-correlation energy functional applied in all calculations and the nonadditive kinetic-energy functional needed in KSCED have a generalized gradient approximation form and were chosen on the basis of our previous studies. The results of both approaches show similar trends: weak dependence of the calculated interaction energies on the size of the PAH and negligible effect of the complexation of two PAH molecules on the adsorption of molecular hydrogen. The KSCED interaction energy calculated for the largest considered PAH (ovalene), amounting to 1.27 kcal/mol, is in excellent agreement with experimental estimates ranging from 1.1 to 1.2 kcal/mol, whereas the one derived from supermolecular Kohn−Sham calculations is underestimated by more than 50%. This result is in line with our previous studies, which showed that the generalized gradient approximation applied within the KSCED framework leads to interaction energies of weakly bound complexes that are superior to the corresponding results of supermolecular Kohn−Sham calculations.