The posterior correction breaks an inherent property of CASPT2: CASPT2-IPEA has an additional source of non-invariance. Specifically, the perturbation energy of CASPT2-IPEA is not invariant with respect to rotations among active MOs, whereas that of the original CASPT2 (including all MS-CASPT2 variants) is. The same non-invariance can be found in other MRPTs. However, CASPT2 employs an internal contraction scheme, whereas the other MRPTs do not, so the non-invariance in CASPT2 poses a unique problem. As long as we are concerned with the perturbation energy, this non-invariance can only be detected by careful examination. This is because CASPT2 usually employs quasi-canonical orbitals in the perturbation part, and the Fock matrix in the active orbital block is thus diagonal; the perturbation energy is therefore uniquely determined for the given molecular and electronic structure unless there are no degeneracies in the active orbital. However, the non-invariance has to be carefully addressed when developing analytic derivatives, because part of the derivation can be simplified with the invariance property (i.e., the non-canonical approach). Therefore, we cannot obtain analytic derivatives of CASPT2-IPEA just by evaluating the derivative contribution of the additional term (the third term of Eq. ( ), for instance). Note that the non-invariance discussed here is totally different from that with respect to rotations among reference states, where the original MS-CASPT2 is not suitable for finding MECIs. The choice of internal contraction scheme (single-state singlereference (SS-SR) or multistate MR) is also irrelevant. In OpenMolcas, only the SS-SR internal contraction scheme is implemented, so the implemented XMS-CASPT2 is not fully invariant, although the original theory is.