Reference CC3 Excitation\nEnergies for Organic Chromophores:\nBenchmarking TD-DFT, BSE/<i>GW</i>, and Wave Function Methods

To expand the QUEST database of highly accurate vertical\ntransition\nenergies, we consider a series of large organic chromogens ubiquitous\nin dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide.\nWe compute, at the CC3 level of theory, the singlet and triplet vertical\ntransition energies associated with the low-lying excited states.\nThis leads to a collection of more than 120 new highly accurate excitation\nenergies. For several singlet transitions, we have been able to determine\nCCSDT transition energies with a compact basis set, finding minimal\ndeviations from the CC3 values for most states. Subsequently, we employ\nthese reference values to benchmark a series of lower-order wave function\napproaches, including the popular ADC(2) and CC2 schemes, as well\nas time-dependent density-functional theory (TD-DFT), both with and\nwithout applying the Tamm–Dancoff approximation (TDA). At the\nTD-DFT level, we evaluate a large panel of global, range-separated,\nlocal, and double hybrid functionals. Additionally, we assess the\nperformance of the Bethe–Salpeter equation (BSE) formalism\nrelying on both <i>G</i><sub>0</sub><i>W</i><sub>0</sub> and ev<i>GW</i> quasiparticle energies evaluated\nfrom various starting points. It turns out that CC2 and ADC(2.5) are\nthe most accurate models among those with respective O(N5) and O(N6) scalings with system size. In contrast,\nCCSD does not outperform CC2. The best performing exchange–correlation\nfunctionals include BMK, M06–2X, M06-SX, CAM-B3LYP, ωB97X-D,\nand LH20t, with average deviations of approximately 0.20 eV or slightly\nbelow. Errors on vertical excitation energies can be further reduced\nby considering double hybrids. Both SOS-ωB88PP86 and SOS-ωPBEPP86\nexhibit particularly attractive performances with overall quality\non par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less\nefficient. BSE/ev<i>GW</i> calculations based on Kohn–Sham\nstarting points have been found to be particularly effective for singlet\ntransitions, but much less for their triplet counterparts.