where E k is the energy of the k th eigenstate of the fc-CVS-EOM-CCSD Hamiltonian. The approximate valence resolvent can, for example, originate from lower-level methods (e.g., valence fc-CVS-EOM-CCS, valence fc-CVS-EOM-CC2, etc.) for which the valence response is restricted to the valence singly excited determinant space and the doubly excited determinants are either omitted or included in a perturbative fashion in the response equations. An alternative approach involves approximating the Ĥval block of the fc-CVS-EOM-CCSD Hamiltonian by its valence singles-singles block, omitting the problematic coupling of the valence singly and doubly excited determinants and the preconditioning of valence doubles-doubles block in the X-ray regime. When the CVS-0 approach is augmented by this latter approximate valence resolvent F uS,k (ω), the approach is referred to as the CVS-uS ("uS" stands for "uncoupled valence singles") approach. In effect, such approaches only approximate the intermediate states in the SOS expressions of twophoton moments, while still using the high-level correlated energies and wave functions of the initial and final states. Further, since the intermediate states in the SOS expressions dominated by doubly excited valence determinants do not couple significantly with the ground state via the one-electron dipole moment operator, the impact of the omission (or perturbative inclusion) of valence doubly excited determinants is primarily through the dilution of dynamical correlation in the energies and wave functions of the intermediate states involved in the valence resolvent.