We present benchmark interaction energy calculations of carbon dioxide physisorbed onto flat and curved polycyclic aromatic hydrocarbons as models of carbon nanotubes. The accuracy of the complete-basis-set second-order Møller–Plesset perturbation theory combined with a CCSD(T) coupled-cluster correction in a moderate basis set is first assessed for a series of CO2–(benzene, naphthalene, and pyrene) complexes to establish the basis set requirements. The same composite approach is then used to compute accurate interaction energies for 195 CO2–curved coronene geometries representing different intermolecular distances, orientations, and nanotube diameters. The CO2–curved coronene benchmark data set is then used to assess the performance of a wide variety of dispersion-including DFT functionals. Among them, only the nonlocal VV10 and double-hybrid B2PLYP-D3(BJ) functionals exhibit relative errors below 10%. Interestingly, all DFT variants deviate strongly from the benchmark at short-range because of overdamping. We show that these short-range deficiencies can be corrected by refitting the damping parameters of Grimme’s -D3 dispersion approach on the newly constructed data set and that the refitted parameters are also suitable for the complexes of CO2 with larger polycyclic aromatic hydrocarbons but not for the smaller CO2–benzene and CO2–naphthalene systems.