The hydrogen storage capacities of the recently synthesized tetraindenocoranulene C44H18 and pentaindenocorannulene C50H20 have been investigated and compared with those of corannulene and C-60. The results for the physisorption of a single H-2 on the concave side indicate that the adsorption energies (E-ads) for tetraindenocorannulene and pentaindenocorannulene are very similar, 2.9 and 3.0 kcal/mol, respectively. The later values are slightly larger than that estimated for corannulene, 2.4 kcal/mol, and about half of the encapsulation energy of H-2 in C-60, 5.4 kcal/mol. The differences in adsorption energies can be explained considering the dipole moments of the molecules. For C50H20 and C44H18 they are very similar, 4.0 and 3.7 Debye. However, it is much smaller in corannulene, 2.0 Debye, which explains the lower E-ads observed for the later polyarene. The E-ads presents a different behavior on the electron-poor convex side; they are nearly identical for all of the molecules considered. The interaction energies on the convex side, determined for corannulene, tetraindenocorannulene, pentaindenocorannulene, and C-60, are 1.2, 1.1, 1.1, and 1.2 kcal/mol, respectively. The hydrogen storage capabilities are discussed in terms of the results obtained for the sandwich complexes between pentaindenocorannulene with benzene or corannulene. As a by product, we estimated the complexation energies for the benzene-pentaindenocorannulene and corannulene-pentaindenocorannulene pairs as 6.0 and 8.3 kcal/mol, respectively. Finally, we replaced some carbon atoms in corannulene and pentaindenocorannulene with nitrogen atoms. The adsorption energies were increased; C16N4H10 has nearly the same adsorption energy as the much larger pentaindenocorannulene. In the case of pentaindenocorannulene, the introduction of six nitrogen atoms (12% of carbon atoms replaced) increases the adsorption energy, about 0.2 kcal/mol. The present results showed that the introduction of a small number of nitrogen atoms can increase the adsorption energy in carbon structures without increasing the weight of the material too much, but the increment seems to be strongly dependent on the position of the nitrogen atoms.