HOMO(the highest occupied molecular orbital) and LUMO(the lowest unoccupied molecular orbital) of four recalcitrant polycyclic aromatic hydrocarbons (PAHs) were calculated by MOPAC program(CaChe Co). The previous papers which reported experimental results about radical reaction of PAHs were reviewed. The reported radical reaction positions of four PAHs corresponded with predicted positions in which δE(HOMO-LUMO) was high. From these results, it appears that determining the δE(HOMO-LUMO) of a PAH is a promising method for predicting the radical reaction position.