Excitation energies of embedded open-shell systems: Unrestricted frozen-density-embedding time-dependent density-functional theory.

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.