The complexes of a DNA base bound to graphitic systems are studied. Considering naphthalene as the simplest graphitic system, DNA base–naphthalene complexes are scrutinized at high levels of ab initio theory including coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] at the complete basis set (CBS) limit. The stacked configurations are the most stable, where the CCSD(T)/CBS binding energies of guanine, adenine, thymine, and cytosine are 9.31, 8.48, 8.53, 7.30 kcal/mol, respectively. The energy components are investigated using symmetry-adapted perturbation theory based on density functional theory including the dispersion energy. We compared the CCSD(T)/CBS results with several density functional methods applicable to periodic systems. Considering accuracy and availability, the optB86b nonlocal functional and the Tkatchenko–Scheffler functional are used to study the binding energies of nucleobases on graphene. The predicted values are 18–24 kcal/mol, though many-body effects on screening and energy need to be further considered.