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

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate prediction of vertical excitation energies is crucial for understanding molecular properties and electronic transitions.
• Existing methods like time-dependent density functional theory (TD-DFT) and wave function theory (WFT) have limitations in accuracy and computational cost.
• Multistate density functional theory (MSDFT) offers a promising alternative for describing excited states.

Purpose of the Study:

• To assess the performance of MSDFT with nonorthogonal state interaction (MSDFT-NOSI) for calculating vertical excitation energies.
• To compare MSDFT-NOSI against theoretical best estimates and established computational methods.
• To investigate the impact of different optimization techniques and transition density functional (TDF) estimations on MSDFT-NOSI accuracy.

Main Methods:

• The study evaluated 100 vertical excitation energies using MSDFT-NOSI on the Loos2018 database.
• Two optimization techniques (block-localized excitation and target state optimization) and two TDF estimation methods were examined.
• Performance was benchmarked against full configuration interaction (FCI) accuracy, TD-DFT, and various WFT methods (CIS(D∞), LR-CC2, ADC(3), STEOM-CCSD, LR-CCSD).

Main Results:

• MSDFT-NOSI with the M06-2X functional and spin-multiplet degeneracy constraint achieved a root-mean-square error (RMSE) of 0.22 eV, significantly better than TD-DFT (0.43 eV).
• MSDFT-NOSI showed comparable or better accuracy than several WFT methods, with errors smaller than CIS(D∞), LR-CC2, and ADC(3) (0.28 eV), but larger than STEOM-CCSD (0.14 eV) and LR-CCSD (0.11 eV).
• The performance of MSDFT-NOSI was consistent across valence, Rydberg, singlet, triplet, and double-excitation states, and using PBE0 functional resulted in a systematic deviation.

Conclusions:

• MSDFT-NOSI provides a robust and accurate method for calculating vertical excitation energies, outperforming traditional TD-DFT.
• Density functional approximations developed for ground-state Kohn-Sham DFT can be effectively applied to MSDFT calculations where state interaction is important.
• This benchmark validates MSDFT-NOSI as a valuable tool for electronic structure studies of excited states.