The λ-equation is similar in structure to the amplitude equation (Eq. ( )), and therefore it can be solved in a similar fashion. Note that the λ-equation is solved with the level shift term E shift , being consistent with Eq. ( ). However, unlike the single-state case, it has to be solved even without the level shift E shift for energy calculations, because the MS energy (Eq. ( )) is no longer variationally minimized with respect to the excitation amplitude. Only when the coupling between different excitation classes are neglected, known as CASPT2-D, it can be done in a non-iterative manner. Once λ αβ pqrs,γ is determined, first-and second-order correlated density matrices 20 can be constructed and used in computing Y αβ pq and y αβ I,γ defined later.