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.
Frozen-density-embedding (FDE) linear response time-dependent density functional theory (TDDFT) is generalized to the case of spin-unrestricted reference orbitals. FDE-TDDFT in the uncoupled approximation is applied to calculate vertical excitation energies of diatomic radicals interacting with closed-shell atoms (helium) or molecules like water. Unrestricted FDE-TDDFT can reproduce the vertical valence excitation energies obtained from conventional supermolecular TDDFT with good accuracy, provided that a good embedding potential is available. To investigate the influence of approximate embedding potentials, we also combine the unrestricted FDE-TDDFT formalism with projection-operator and potential reconstruction techniques, thus enabling calculations with accurate ("exact") embedding potentials.
Paper published as part of the special topic on Spin Chemistry
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