Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction

Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole moments are computed using the same geometries (MP2/6-31G(*)) and basis set (TZVP) as in our previous ab initio benchmark study on electronically excited states. The results from TD-DFT (with the functionals BP86, B3LYP, and BHLYP) and from DFT/MRCI are compared against the previous high-level ab initio results, and, in particular, against the proposed best estimates for 104 singlet and 63 triplet vertical excitation energies. The statistical evaluation for the latter reference data gives the lowest mean absolute deviations for DFT/MRCI (0.22 eV for singlets and 0.24 eV for triplets) followed by TD-DFT/B3LYP (0.27 and 0.44 eV, respectively), whereas TD-DFT/BP86 and TD-DFT/BHLYP are significantly less accurate. The energies of singlet states with double excitation character are generally overestimated by TD-DFT, whereas triplet state energies are systematically underestimated by the currently investigated DFT-based methods.