For the CCSD state, R = r 0 = 1 and L = 1+ Λ, where Λ = Λ1 + Λ2 is the CCSD Lambda operator. For EOM-EE-CCSD target states, l 0 = 0. The amplitudes of R and L in Eqs. ( ) and ( ) for target states are computed by diagonalizing Ĥ in the space of the reference, singly excited, and doubly excited determinants using standard techniques such as the generalized Davidson procedure. Whereas such strategies are effective for computing low-lying excited states, their straightforward application to obtain high-lying core-excited states is in general impractical. Further, the presence of the valence continuum and the diagonal preconditioner being inappropriate for the doublesdoubles block of the Hamiltonian results in erratic behavior of such strategies for computing core-level states. For computing core-excited states, the core-excited block of Ĥ, defined by omitting the reference and purely valenceexcited determinants from the configuration space, is diagonalized instead of Ĥ. In Ref. 13 and this study, we call this block the CVS-0 model Hamiltonian Ĥcore . Whereas only the coupling of the core-excitation configurations with the purely valence doubly excited configurations are problematic from the convergence viewpoint, the removal of the purely valence singly excited determinants makes the spectrum of the CVS-0 Hamiltonian to be that of purely core-excited states. This feature is attractive for directly computing the lowest coreexcited states without a significant loss of dynamical correlation. We denote the EOM-EE-CCSD operators that diagonalize Ĥcore as Rcore and Lcore .