Benchmarking dressed TDDFT: a critical appraisal of double-excitation energies and oscillator strengths

The popularity of time-dependent density functional theory (TDDFT) inarguably stems from its attractive trade-off between computational affordability, chemical accuracy, and fundamental rigour. However, within the adiabatic approximation that is almost always used in practice, TDDFT has been plagued by its inability to capture excited states of double-excitation character. Recent efforts have addressed this problem by extending the original formulation of dressed TDDFT (DTDDFT) [1], so that it reproduces not just the excitation energies but also the oscillator strengths of such states [2]. The frequency-dependent exchange-correlation (xc) kernel in this improved DTDDFT was recently shown, for example, to correctly capture the elusive low-lying 2 ¹A_g / 1 ¹B_u curve-crossing in butadiene [3]. Here, we provide the first extensive test of DTDDFT to predict the excited states of a wide range of molecules, possessing predominantly and partial double-excitation character, as characterised in the recent updated work of Kossoski et. al. [4]. We consider multiple flavours of DTDDFT, each defined by the ingredients and approximations used to construct the xc kernel. Basis set and xc functional dependence are also investigated.

[1] N. T. Maitra, F. Zhang, R. J. Cave and K. Burke, JCP 120, 5932-5937 (2004)

[2] D. B. Dar and N. T. Maitra, JCP 159, 211104 (2023)

[3] D. B. Dar and N. T. Maitra, JPCL 16, 703-709 (2025)

[4] F. Kossoski, M. Boggio-Pasqua, P.-F. Loos and D. Jacquemin, JCTC 20, 5655-5678 (2024)