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, ωB97X, and MN15 are used, and their results are compared to RI-CC2. This comparison involves assessing key photophysical properties, including 2PA cross-sections (σ2PA) 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. 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.