Accurate interaction energies of nonpolar (argon) and polar (water) adsorbates with graphene-based carbon allotropes were calculated by means of a combined density functional theory (DFT) ab initio computational scheme. The calculated interaction energy of argon with graphite (-9.7 kJ mol(-1)) is in excellent agreement with the available experimental data. The calculated interaction energy of water with graphene and graphite is -12.8 and -14.6 kJ mol(-1), respectively. The accuracy of combined DFT ab initio methods is discussed in detail based on a comparison with the highly precise interaction energies of argon and water with coronene obtained at the coupled-cluster CCSD (T) level extrapolated to the complete basis set (CBS) limit. A new strategy for a reliable estimate of the CBS limit is proposed for systems where numerical instabilities occur owing to basis-set near-linear dependence. The most accurate estimate of the argon and water interaction with coronene (-8.1 and -14.0 kJ mol(-1), respectively) is compared with the results of other methods used for the accurate description of weak intermolecular interactions.