How does LCDFT compare to SAC-CI for the treatment of valence and Rydberg excited states of organic compounds?

The computation of excitation energies for electronically excited states poses a challenge in quantum chemistry. In the present work, the performance of two related methodologies in this context, symmetry-adapted cluster-configuration interaction (SAC-CI) and time-dependent long-range corrected density functional theory (TDLCDFT), is compared in detail for the calculation of valence and Rydberg excitation energies against an experimental benchmark set comprising some organic compounds from different categories. Practically, the single- and double-linked excitation operators are considered in the SAC-CI wave functions. The considered LC density functionals include the combination forms of exchange and correlation functionals (BLYP, PBE, TPSS), pure functionals (tHCTH and B97-D), exchange-only functionals (HFS, HFB, and XAlpha), hybrid functionals (CAM-B3LYP, LC-ωPBE, ωB97, ωB97X), and dispersion-corrected hybrid functional ωB97X-D. Our results reveal that the SAC-CI gives the best performance for Rydberg excited states. However, the values of mean absolute deviation show that the applicability of some LC functionals is comparable to SAC-CI. For valence excited states, the functionals ωB97X-D, ωB97X, and LC-ωPBE outperform the other tested methods. Overall, the ωB97X-D functional is found to offer the best performance, and its validity compared with SAC-CI has also been verified by computing low-lying excited states of a few molecules as representative examples. Lastly, it is shown that not only is there a reasonable agreement between TDLCDFT and SAC-CI methods for the calculation of excitation energies but also the LC density functionals have quantitatively better overall performance for some excited states than the SAC-CI approach.