For the acetone molecule it is possible to compare the TDKS spectrum directly to LR-TDDFT results without post-processing, but this becomes more difficult for larger molecules, especially in high-quality basis sets. This is demonstrated in Fig. for the methionine molecule at the SRC1-r1/def2-TZVP level. In this case, the TDKS spectrum predicts an intense peak at 532 eV, in quantitative agreement with the O(1s) → LUMO transition from a LR-TDDFT/CVS calculation, but several low-intensity "pre-edge" features appear below this. These features are missing from the LR-TDDFT spectrum, indicating that they do not originate from O(1s) orbitals. Instead, they correspond to excitations from N(1s) orbitals into the highest-energy virtual MOs. (The latter are orthogonalized discretized continuum states rather than valence virtual orbitals. ) The nature of these quasiunbound excitations becomes clear if one computes all o × v states afforded by the LR-TDDFT eigenvalue problem in Eq. ( ), which is feasible for very small molecules in small basis sets. Examining this complete set of transitions, one finds a semi-continuous sequence of states that connects each of the x-ray K-edges (carbon, nitro-gen, oxygen, . . .), as shown in Fig. . These are core → continuum excitations, which are called are called "intruder states" in Ref. 65. They ought to have exceeding small lifetimes but are bound in the TDKS calculation by the finite basis set. In the small basis sets where one can afford to compute all o × v states (as in Fig. ), these transitions to the continuum mostly have very small oscillator strengths, but results below demonstrate that they can acquire significant intensity in higher-quality basis sets.