Intermolecular interaction potentials for benzene, propane, perfluoromethane, furan, thiophene, selenophene, pyridine, phosphorine dimers and benzene-methane, benzene-chlorobenzene, benzene-bromobenzene complexes were calculated using the BLYP, B97 (B98), BP86, BPBE, PBE, PW91, B3LYP, B3PW91, BMK, PBE1PBE, APF, ωB97 (ωB97X), CAM-B3LYP, LC-ωPBE, B2PLYP, mPW2PLYP, TPSS, M06L, M05, M052X, M06, M062X and M06HF functionals with Grimme's dispersion correction methods of D2, D3 and D3BJ versions. The calculated potentials were compared with the CCSD(T) level potentials to evaluate the accuracy of the dispersion corrected DFT methods for calculating the intermolecular interaction energies of hydrocarbon molecules and molecules including heteroatoms (N, P, O, S, Se, F, Cl and Br). The performance of the calculations depends strongly on the choice of the functional and the dispersion correction method. None of the combinations of the functionals and the dispersion correction methods can reproduce well the CCSD(T) level interaction potentials of all the complexes. The improvement of the functionals from GGA to hybrid GGA, meta GGA or meta hybrid GGA is not essential for improving the performance. The significant functional dependence suggests that the scaling factors, which were determined for each functional by fitting, are the cause of the dependence. The performance of the calculations of hydrocarbon molecules is much better than that of the molecules including heteroatoms. A smaller number of molecules including heteroatoms were used for the reference data of the fitting compared with hydrocarbon molecules, which might be one of the causes of the worse performance of the calculations of molecules including heteroatoms.