Detailed ab initio molecular orbital calculations on the interactions of molecular hydrogen, H2, with various poly-aromatic hydrocarbons (PAHs) as a model system for graphene were carried out to accurately describe the physisorption phenomenon. The binding energies corrected for the basis set superposition error, ΔEbind(BSSE), were obtained using the optimized geometries at the MP2 level with a large basis set and were compared with the single point binding energies, denoted as ΔEbind(BSSE-s), using large basis sets on the geometries optimized at the small basis sets, such as SVP and TZVP. The calculations showed that the ΔEbind(BSSE-s) values were similar to those at the MP2 level with the large basis sets. The binding strength increased gradually with increasing size of the PAHs. The ΔEbind(BSSE-s) for an infinite graphene sheet was estimated to be -1.70 kcal mol(-1) using the non-linear curve fitting method. The present work could be expected to provide more useful and reliable information on H2 physisorption.