Revisiting the performance of time-dependent density functional theory for electronic excitations: Assessment of 43 popular and recently developed functionals from rungs one to four

TL;DR

This study evaluates over 40 density functionals for electronic excitation energies using a large benchmark set, finding that certain functionals outperform more complex methods and confirming the relevance of Jacob's ladder in TDDFT.

Contribution

The paper provides a comprehensive assessment of 43 functionals for TDDFT excitation energies, offering practical recommendations and confirming the validity of Jacob's ladder.

Findings

ωB97X-D and BMK perform best with RMSE of 0.28 eV

Hybrid meta-GGAs are not necessarily better than hybrid GGAs

Basis set effects and nonlocal correlation influence accuracy

Abstract

In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between performance and accuracy. The functionals $\omega$B97X-D and BMK are found to offer the best performance overall with a Root-Mean Square Error (RMSE) of 0.28 eV, better than the computationally more demanding CIS(D) wavefunction method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for TDDFT excitation energies, though hybrid meta-GGAs are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.