Similarities between single reference perturbation theory based on a CASSCF wavefunction and multireference perturbation theory based on a reference space spanned by a CAS

The first-order wave-operator Ω(1)α for state specific perturbative methods, based an a single-reference state CASSCF (or CASSCI) wavefunction |α〉, is shown to be similar to the first-order wave-operator Ω(1) for multireference perturbation theory (MRPT) when the zeroth-order states {|p〉} that span the reference space are forced degenerate with energy Eα0, where Eα0 is the zeroth-order energy of the CASSCF (or CASCI) state of interest |α〉. Therefore, state-specific methods, like CASPT2, are similar to (forced) degenerate MRPT based on a reference space spanned by a complete active space (CAS).