Second-order Moller-Plesset (MP2) calculations (using the approximate resolution of the identity, RI-MP2) in the TZVPP basis are performed to study the interaction of molecular hydrogen with the aromatic systems C6H5 X (X = H, F, OH, NH2, CH3, and CN), C10H8 (naphthalene and azulene), C14H10 (anthracene), C24H12 (coronene), p-C6H4(COOH)(2) (terephthalic acid), and p-C6H4(COOLi)(2) (dilithium terephthalate). Various adsorption positions are studied for C6H5F. The most favorable configuration places H-2 above the aromatic plane with its axis pointing toward the middle of the ring. The electronic (van der Waals) interaction energy for the differently substituted benzenes correlates with the ability of the substituents to enrich the aromatic system electronically. The largest interaction energy (among the singly substituted benzenes) is found for aniline (4.5 kJ mol(-1)). Enlarging the aromatic system increases the interaction energy; the value for coronene amounts to 5.4 kJ mol(-1). Extending the basis set and including terms linear in the interelectronic distances increases the interaction energy by about 1 U mol(-1) relative to that of the TZVPP basis, whereas the inclusion of higher excitations by coupled-cluster calculations (including all single and double excitations with a perturbative estimate of triples, CCSD(T)) decreases the interaction energy by about the same amount.