An interesting consequence of the non-invariance is the dependence on the orthonormalization procedure: perturbation energies are different with different orthonormalization procedures when linear dependency exists, even if the number of independent vectors are the same and the diagonal approximation for the Fock operator (CASPT2-D) 7 is employed. The difference is noticeable even when only exact linear dependency exists; in other words, the first-order interacting space spans the same space. By contrast, the dependence is negligibly small without IPEA shift. A numerical example is summarized in Tables and (Supplementary Material). In this study, Löwdin's canonical orthonormalization is employed. Other orthonormalizations may be used as long as certain conditions hold true (Eqs. ( )-( )). Another consequence is the further violation of the size-extensivity; this is briefly discussed in Section IV A with some numerical results. Note that the CASPT2-IPEA energy is invariant with respect to rotations among orthogonal ICCs, as the IPEA shift does not modify the procedure for solving CASPT2 equations.