leading to an infinitely large amplitude and a divergent perturbation series. This is caused by a degeneracy between Ψ (0) and a perturber Φ i in the zeroth-order approximation. The first obvious solution to this situation would be to include the intruder state Φ i in the reference wave function. However, this is not always possible or desired in CASPT2, as it involves changing the active space of the underlying CASSCF optimization and potentially leads to the appearance of new intruder states, the need of additional electronic states in the state-averaging procedure or to exceedingly expensive calculations. The other option is to change the partitioning of the Hamiltonian. If the degeneracy between the intruder state Φ i and Ψ (0) is the result of the approximate description provided by the zeroth-order Hamiltonian, while the true energies of these states are different, one could modify the structure of Ĥ(0) to lift this accidental degeneracy. In fact, the potential existence of an ISP is intimately coupled to the form of the zeroth-order Hamiltonian. For instance, an internally contracted approach based on Dyall's Hamiltonian 32 is known to be practically free from intruder states, as in the case of NEVPT2. Thus, it seems a natural choice to focus the efforts for solving the ISP in CASPT2 on modifying Ĥ(0) , analogously to the strategy followed by Roos and Andersson 23 and Forsberg and Malmqvist 24 several years ago, with the introduction of the real and imaginary level shift techniques, respectively.