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, <i>J. Chem. Theory Comput.</i> <b>21</b> (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 <i>S</i>₁ 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.