In Eq. ( ), the first term is the CASPT2 energy (α = β; Eq. ( )) or the coupling between states (α ̸ = β). The second term corresponds to the variational condition for the amplitude T γ pqrs (Eq. ( )), and the third term is the canonical condition for frozen MOs, which is required when the frozen core approximation is employed. The fourth term ensures the orthogonality between the independent and dependent orthogonal vectors in ICB (Eq. ( )), and the overlap matrix is defined by