Evaluating the Tamm-Dancoff Approximation for Two-Photon Absorption Properties

Two-photon absorption (2PA) is a powerful tool in nonlinear optics, enabling advanced applications like high-resolution microscopy and photodynamic therapy. In this study, we explore the 2PA properties of 20 chromophores using time-dependent density-functional theory (TD-DFT), TD-DFT with the Tamm-Dancoff approximation (TDA), and the resolution-of-identity approximation in conjunction with the second-order approximate coupled-cluster (RI-CC2). TDA's performance in predicting 2PA properties remains insufficiently characterized compared to (full) TD-DFT, where the functionals CAM-B3LYP, MN15, and ωB97X are used, and their results are compared to RI-CC2. This comparison involves assessing key photophysical properties, including 2PA cross sections (σ^2PA) and dipole moments (μ₀₀, μ₁₁, μ₀₁, and Δμ). Among the tested functionals, MN15 demonstrated the lowest mean absolute errors (MAEs) for the computed photophysical properties for both TDA and TD-DFT. Our findings indicate that TDA captures qualitative trends and provides slightly more accurate quantitative predictions with generally lower MAEs than TD-DFT. These findings suggest that the use of TDA has significant potential as a cost-effective alternative to (full) TD-DFT for predicting 2PA properties.