A. Size-extensivity of single-state CASPT2-IPEA Here, we briefly discuss the size-extensivity of CASPT2-IPEA. CASPT2 is not a sizeextensive method even without IPEA shift. The theoretical basis for this has been already term in Eq. ( )) without the two constraint conditions mentioned above. "Analytic1" and "Analytic2" refer to the gradients with the first (Section II C 3) and second (Section II C 4) constraint conditions, respectively. "Analytic" includes all contributions, so we expect the computed gradients are fully analytic.