Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates (TBE) extracted to the full configuration interaction accuracy on the database developed by Loos, P.F., at al. in 2018 (Loos2018). Two optimization techniques, namely block-localized excitation (BLE) and target state optimization (TSO), are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy (SMD) constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, better than CIS(D_∞), CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat less than STEOM-CCSD (RMSE of 0.14 eV) and CCSD (RMSE of 0.11 eV) wave function methods. Interestingly, MSDFT-NOSI performs noticeably better than TDDFT at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with the ground state and the lowest triplet energies from KS-DFT calculations, it was found that the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a non-interacting reference may be adopted in MSDFT calculations in which state interaction is key.