Shortcomings of Linear-Response TD-DFT for ESA Oscillator Strength Calculations

We present an evaluation of linear-response (LR) TD-DFT for the calculation of excited-state absorption (ESA) oscillator strengths. Specifically, we compare this approach with the computationally more expensive quadratic-response (QR) scheme, which we previously benchmarked, J. Chem. Theory Comput. 21 (2025) 4688, and analyze the deviations between the two approaches using various metrics. Three subsets of molecules and ESA transitions are considered: (i) subset A, a data set of 21 compact molecules comprising 53 ESA transitions, (ii) subset B consisting of 9 large molecules inspired by real-life fluorescent dyes, and (iii) subset C of selected molecules in their relaxed S₁ geometries. For subset A, we identify a clear relationship between the single-reference character of the excited states involved in the ESA process and the magnitude of the QR-LR deviations. Additionally, we observe a significant correlation between the contribution of the TD-DFT de-excitation vectors, the single-reference character of one of the two excited states, and the QR-LR discrepancies. For both subsets B and C, the correlations observed in subset A are less pronounced. Nevertheless, the largest outliers consistently involve at least one state with strong de-excitation components. Finally, we propose a simple linear correction for the unrelaxed LR oscillator strengths. Overall, LR-TD-DFT tends to almost systematically overestimate ESA oscillator strengths, especially when one of the two excited states involved exhibits large de-excitation contributions.