The configuration interaction, perturbation theory, coupled cluster doubles, and random phase approximation methods are applied to a system of two quantum Drude oscillators interacting through dipole-dipole coupling. It is found that the random phase approximation gives the exact excitation energies and exact interaction energy of this system even when allowing only excitations into the first excited levels of the oscillators. In contrast, to obtain the exact results from configuration interaction or coupled cluster treatments of the model requires inclusion of excitations into all accessible excited configurations. (C) 2015 Elsevier B.V. All rights reserved.