It is important to note that, even though from a formal point of view an intruder state strictly implies an exact degeneracy, in practice, all perturbers Φ i associated to small energy denominators are considered intruder states. This is because the corresponding amplitudes will lead to artificially large contributions to the correlation energy. Rigorously speaking, it is possible that higher-order corrections compensate for that, though, for all practical purposes this is not relevant, because the perturbation expansion is generally considered up to second-order only (for a formal discussion on the matter, we suggest the excellent work by Olsen and Jørgensen 35 and references therein).