Ab initio calculations of the interaction potential between Cu (or Cu+) and Ar (or Kr) have been carried out. A range of theoretical methods, including Hartree-Fock (HF), Moeller-Plesset perturbation methods to second order (MP2), and single and double excitation coupled cluster methods, with the perturbational effect of triple excitations (CCSD(T)), were employed with relativistic pseudopotential basis sets. The effects of bond functions and diffuse polarization (f, g, h) functions were tested on the calculation of the weak intermolecular interactions. Potential energy curves were obtained for all four complexes by MP2 and CCSD(T) methods. For CuKr, even with the largest basis set used, a binding energy that is only 37% of the measured value was obtained. Possible reasons for the disagreement are discussed.