The effect of carbon surface curvature and ring structure on the gas-carbon interaction potential is not well understood. Potentials derived from gas-graphite adsorption measurements are commonly used in molecular simulations with curved carbon surfaces, e.g., nanotubes, fullerenes, and other nanoporous carbons. Presented here are quantum mechanical (QM) calculations of the interactions of nitrogen and oxygen with three carbon surfaces of different curvatures (graphite, C-60 fullerene, and C-168 schwarzite). Generally, QM calculations at the CCSD(T) level are required to obtain accurate interaction energies for these systems; here a recently developed, computationally efficient Hybrid Method for Interaction Energies (HM-IE) of comparable accuracy was used. Atom-site intermolecular potentials fit to the quantum mechanical results produce accurate predictions of the experimentally measured second virial coefficient of adsorption for nitrogen on graphite. The QM-based gas-carbon potentials for C-60 and C-168 were found to be different than for graphite, and result in increased adsorption energies for nitrogen on these surfaces. We conclude that molecular simulations based on the assumption that the gas-carbon interaction potentials are invariant to carbon surface curvature and ring structure may result in incorrect property predictions.