Accurate singlet and triplet excitation energies using the Localized Hartree-Fock Kohn-Sham potential

► We assess the Localized Hartree-Fock with exchange-only kernel (LHFX) approach, which is free from the Self-Interaction-Error (SIE) and from empirical parameters, for a large database of singlet and triplet excitation energies. ► We find that the LHFX method outperforms the state-of-the-art hybrid TD-DFT approaches. ► The LHFX method provides the same accuracy for all different classes of excitations.