Assessment of Double-Hybrid Functionals for the Vertical Excitation Energies of Porphyrins

The vertical excitation energies of 13 porphyrins and metalloporphyrins were benchmarked using 28 double-hybrid (DH) density functionals within the full TD-DFT framework, in conjunction with the def2-TZVP basis set and CPCM solvation model. The assessed functionals comprise global double hybrids (GDHs), range-separated double hybrids (RSDHs), and their spin-component-/spin-opposite-scaled variants (SCS/SOS-GDHs and SCS/SOS-RSDHs). Performance was evaluated for the B, Q1, and Q3 bands by comparison with experimental absorption maxima. B2PLYP provides one of the most balanced overall agreements, with mean absolute errors of approximately 0.03, 0.06, and 0.07 eV for the B, Q1, and Q3 bands, respectively. B2GPPLYP, ωB88PP86, and ωPBEPP86 also yield MAEs below 0.1 eV for all three bands. In contrast, several SCS/SOS-RSDH functionals perform very well for the B band but show pronounced systematic underestimation for the Q bands, revealing substantial band dependence. Comparison with published multireference vertical excitation energies further shows that close agreement with experimental absorption maxima does not necessarily imply equally close agreement with theoretical vertical excitation energies, particularly for the Q states. Overall, the results highlight the importance of state-specific assessment when benchmarking DH functionals for porphyrinic excitations.