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Occurrence of electron transfer was studied for different combinations of polycyclic aromatic hydrocarbons (PAHs) and DNA bases as electron donors or acceptors and free radicals only as electron acceptors. Geometries of all the molecules and radicals were optimized in aqueous medium employing the polarizable continuum model. Single electron transfer (SET) and sequential proton loss electron transfer mechanisms were investigated employing Gibbs free energies of the appropriate neutral, anionic and cationic species. Barrier energies involved in these phenomena were calculated using the Marcus theory. The SET barrier energies were found to be linearly correlated with $\mathrm{\Delta }E=$ (Electron affinities of acceptors – Ionization potentials of donors). SET barrier energies from the DNA bases to the PAHs follow the order Cy $>$ Th $\approx$ Ad $>$ Gu, whereas SET barrier energies from the PAHs to the DNA bases follow the order Gu $>$ Ad $>$ Th $\approx$ Cy. Thus, guanine, among the DNA bases, is the best electron donor to the PAHs and worst electron acceptor from the same.