Dispersion interactions and van der Waals C-6 coefficients are studied in small model systems involving copper, silver, and gold atoms. We investigate a novel method where the intermolecular dispersion interactions are characterized by interatomic C-6 coefficients that can be used to formulate the dispersion energy as a separate contribution to the total interaction energy at long distances. We obtain the C-6 coefficients from a least-squares fit to the interaction energy surface. Other significant effects to the long-range interaction energy such as multipole-multipole and induction energy are explicitly taken into account. The electronic structure calculations are performed at the coupled cluster level including single, double, and perturbative triple excitations (CCSD(T) level) with triple-zeta basis sets.