In the L-edge case, the CVS active space consists of Ti(2p) orbitals only, along with the full virtual space. LR-TDDFT/CVS calculations based on this active space are in quantitative agreement with the corresponding features in the TDKS calculation as demonstrated in Fig 8b . Note that even when dipole filtering is applied, the TDKS simulation is based on a time-evolving density matrix that includes all of the occupied MOs at every time step. As such, the quantitative agreement with LR-TDDFT/ CVS calculations that we document here demonstrates that there is essentially no error in the CVS approximation for this example. This observation is significant, because whereas the CVS approximation has been carefully benchmarked for K-edge spectra, less is known about its accuracy for L-and M-edge spectra. In the latter cases, the nominal initial-state orbitals in the second and third shell may not be energetically well separated from other orbitals, leading to larger errors when the CVS approximation is applied. In principle, interior eigenvalue solvers can be used to address the veracity of the CVS approximation in such cases, but this has so far been done only in a very limited way. Although we do not see any evidence for a breakdown of the CVS approximation for the L-edge of TiO 2 molecule, the question is worth examining in larger systems. TDKS simulations provide a means to obtain spectra that do not invoke any active-space approximation.