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.

In this communication, we show that coupled subsystem time-dependent density functional theory (subsystem TDDFT) [J. Neugebauer, J. Chem. Phys. 126, 134116 (2007)] in combination with projection-based embedding (PbE) is an exact subsystem theory in the sense that supermolecular TDDFT excitation energies can exactly be restored. A correct handling of the kernel contribution due to the enforced orthogonality is crucial in this context, which leads to different PbE kernel contributions in the A and B matrices of the general TDDFT eigenvalue problem. Although this formalism has been proposed before [D. V. Chulhai and L. Jensen, Phys. Chem. Chem. Phys. 18, 21032 (2016)], the symmetric eigenvalue problem used in that work implicitly introduces an approximation concerning this kernel contribution. We show that our treatment numerically exactly reproduces supermolecular results for the previously investigated helium dimer and for the fluoroethane molecule as a more challenging case with a partitioning of a covalent bond. We also demonstrate that the symmetric approximation can lead to significant deviations, including a wrong ordering of electronic transitions.

We analyze the ability of subsystem time-dependent density-functional theory (sTDDFT) to describe environmental response effects. To this end, we utilize the recently proposed "exact" version of sTDDFT relying on projection-based embedding (PbE), which so far was applied only for the special case of two subsystems. We con

We investigate the suitability of subsystem time-dependent density-functional theory (sTDDFT) for describing chiroptical properties with a focus on optical rotation parameters. Our starting point is a new implementation of the recently proposed projection-based, coupled frozen-density embedding (FDEc) framework. We adapt the generalized, non-Hermitian formulation of TDDFT and derive corresponding expressions for regular and damped response properties from subsystem TDDFT. We verify that our implementation of this “exact” formulation allows to reproduce supermolecular results of electronic circular dichroism (ECD) spectra, of optical rotatory dispersion, and of polarizabilities. We present a systematic test of the main approximations typically introduced in practical frozen-density embedding (FDE) calculations of response properties: (i) the use of approximate nonadditive kinetic-energy (NAKE) functionals, which can be avoided through projection techniques, (ii) the use of monomer (subsystem) basis sets rather than supersystem basis sets, and (iii) the neglect of intersubsystem response coupling within the so-called uncoupled FDE (or FDEu) approximation. While approximation (i) is known to generally lead to large errors for covalently bound subsystems, we present cases in which either the basis set or the coupling step are similarly or even (much) more important. In particular, we explicitly demonstrate by comparison to a fully coupled calculation that missing intersubsystem response couplings are responsible for the failure of FDE reported in a previous study [J. Chem. Theory Comput.20151153055315]. We show that good agreement with reference results can be obtained in this case even with standard NAKE approximations for the FDE potentials and efficient monomer basis sets, making calculations for larger systems well accessible.

Subsystem time-dependent density-functional theory (sTDDFT) making use of approximate non-additive kinetic energy (NAKE) functionals is known to be capable of describing excitation energy transfer (EET) processes in a variety of applications.Here we show that sTDDFT, especially when combined with projection-based embedding (PbE), can be employed for the entire range of photo-induced electronic couplings essential for modeling photophysical properties of complex chemical and biological systems, and therefore represents a complete toolbox for this class of problems. This means it is capable to capture the interaction/coupling associated with local-and charge-transfer (CT) excitons. However, this requires the choice of a reasonable diabatic basis. We therefore propose different diabatization strategies of the virtual orbital space in PbE-sTDDFT and show how CT excitations can be included in sTDDFT using NAKE functionals via a phenomenological approach.Finally, these electronic couplings are compared to couplings from a multistate fragment excitation difference (FED)-fragment charge difference (FCD) diabatization procedure. We show that both procedures, multistate FED-FCD and sTDDFT (with the right diabatization procedure chosen), lead to an overall good agreement for the electronic couplings, despite differences in their general diabatization strategy. We conclude that the entire range of photo-induced electronic couplings can be obtained using sTDDFT (with the right diabatization procedure chosen) in a black-box manner.