Concerning the problems related to approximate NAKE functionals, the two solution strategies of either using reconstructed embedding potentials or switching to a projectionbased embedding formalism as an alternative have both been transferred to the subsystem TDDFT context as well. As already mentioned in Section 4.3, the work in Ref. 107 employed reconstructed embedding potentials, which considerably improved the accuracy of excitation energies for local excitations, even though no corrections to the NAKE-NAXC kernel had been considered. One particular problem in connection with approximate NAKPs is the possible electron leaking (or electron spill-out) if diffuse monomer or even supermolecular basis sets are employed. In connection with excited states, especially the structure of unoccupied orbitals can suffer dramatically from that problem . In a pragmatic approach avoiding the need for reconstructing potentials, Treß et al. used all-electron pseudopotentials for atoms in the environment in addition to the standard approximate embedding potentials to mimic the effect of repulsive potential contributions . A related approach had been proposed by Hättig and co-workers within the QM/MM-context before . For their test set comprising 11 systems, including solvated molecules, host-guest systems, and complexes of (small) organic molecules, the mean absolute deviation for excitation energies could be considerably reduced in this way.