The Hartree-Fock and the Hartree-Fock-Clementi-Corongiu methods (Clementi, E.; Corongiu, G. Theochem. 2001, 543, 39) are selected to compute van der Waals potentials in the systems He-2, HeNe, HeAr, Ne-2, NeAr, Ar-2, benzene-He, benzene-Ne, and benzene-Ar and to determine the parameters needed for HF-CC computations of van der Waals interaction energies of naphthalene-He, naphthalene-Ne, and naphthalene-Ar; shallow double wells are predicted for the above naphthalene systems.