Here, intermediate normalization is assumed (this is the case of CASPT2), thus assigning a unit coefficient to the reference wave function. In the trivial case where w ref = 1, all amplitudes must be zero and thus the first-order correction does not contribute at all to Ψ . On the other hand, increasingly small values of w ref imply larger contributions to the total wave function from Ψ ; this is the typical situation. The limiting case w ref = 0 is formally possible only in the presence of a true intruder state, where the amplitude of the offending state Φ i diverges, T i → ∞. In practice, accidental exact degeneracies almost never occur and small energy denominators are instead the typical cause of troubles, leading to large amplitudes that outweigh the reference wave function. This situation is associated to small values of w ref , which we shall recognize as a signature of the intruder state problem.