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 (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 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.