Inter-subsystem charge-transfer excitations in exact subsystem time-dependent density-functional theory

We investigate the ability of projection-based embedding (PbE)/subsystem density-functional theory to describe intersubsystem charge-transfer (CT) excitations. To this end, we derive the corresponding subsystem time-dependent density-functional theory (sTDDFT) working equations including the response kernel contributions for three different popular projection operators currently in use in connection with PbE. We demonstrate that supermolecular electronic excitation spectra can be fully restored with this "exact" sTDDFT. Both intra- and intersubsystem CT excitations can be described correctly, provided that suitable long-range corrected functionals and basis sets of sufficient flexibility are used. In particular, we show that outgoing CT excitations can be described in individual subsystem calculations without intersubsystem response coupling. We introduce efficient techniques to restrict the virtual-orbital space to obtain reasonable CT excitation energies with heavily reduced computational cost. Finally, we demonstrate the ability to extract electronic couplings between CT and local excitations with this new formulation of exact sTDDFT.