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 extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, 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 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, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the 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 noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

A flexible self-consistent field method, called target state optimization (TSO), is presented for exploring electronic excited configurations and localized diabatic states. The key idea is to partition molecular orbitals into different subspaces according to the excitation or localization pattern for a target state. Because of the orbital-subspace constraint, orbitals belonging to different subspaces do not mix. Furthermore, the determinant wave function for such excited or diabatic configurations can be variationally optimized as a ground state procedure, unlike conventional ΔSCF methods, without the possibility of collapsing back to the ground state or other lower-energy configurations. The TSO method can be applied both in Hartree-Fock theory and in Kohn-Sham density functional theory (DFT). The density projection procedure and the working equations for implementing the TSO method are described along with several illustrative applications. For valence excited states of organic compounds, it was found that the computed excitation energies from TSO-DFT and time-dependent density functional theory (TD-DFT) are of similar quality with average errors of 0.5 and 0.4 eV, respectively. For core excitation, doubly excited states and charge-transfer states, the performance of TSO-DFT is clearly superior to that from conventional TD-DFT calculations. It is shown that variationally optimized charge-localized diabatic states can be defined using TSO-DFT in energy decomposition analysis to gain both qualitative and quantitative insights on intermolecular interactions. Alternatively, the variational diabatic states may be used in molecular dynamics simulation of charge transfer processes. The TSO method can also be used to define basis states in multistate density functional theory for excited states through nonorthogonal state interaction calculations. The software implementing TSO-DFT can be accessed from the authors.