Validation of local hybrid functionals for TDDFT calculations of electronic excitation energies

The first systematic evaluation of local hybrid functionals for the calculation of electronic excitation energies within linear-response time-dependent density functional theory (TDDFT) is reported. Using our recent efficient semi-numerical TDDFT implementation [T. M. Maier et al., J. Chem. Theory Comput. 11, 4226 (2015)], four simple, thermochemically optimized one-parameter local hybrid functionals based on local spin-density exchange are evaluated against a database of singlet and triplet valence excitations of organic molecules, and against a mixed database including also Rydberg, intramolecular charge-transfer (CT) and core excitations. The four local hybrids exhibit comparable performance to standard global or range-separated hybrid functionals for common singlet valence excitations, but several local hybrids outperform all other functionals tested for the triplet excitations of the first test set, as well as for relative energies of excited states. Evaluation for the combined second test set shows that local hybrids can also provide excellent Rydberg and core excitations, in the latter case rivaling specialized functionals optimized specifically for such excitations. This good performance of local hybrids for different excitation types could be traced to relatively large exact-exchange (EXX) admixtures in a spatial region intermediate between valence and asymptotics, as well as close to the nucleus, and lower EXX admixtures in the valence region. In contrast, the tested local hybrids cannot compete with the best range-separated hybrids for intra- and intermolecular CT excitation energies. Possible directions for improvement in the latter category are discussed. As the used efficient TDDFT implementation requires essentially the same computational effort for global and local hybrids, applications of local hybrid functionals to excited-state problems appear promising in a wide range of fields. Influences of current-density dependence of local kinetic-energy dependent local hybrids, differences between spin-resolved and "common" local mixing functions in local hybrids, and the effects of the Tamm-Dancoff approximation on the excitation energies are also discussed.