Two-Photon Absorption of Quadrupolar Dyes: Performance of Density Functional Approximations

We benchmark a representative set of exchange–correlation functionals for the 2PA strengths of centrosymmetric quadrupolar dyes using CC2 as reference. Owing to the C i symmetry, the dominant 2PA channel of these compounds proceeds through a symmetry-allowed A g → A u → A g pathway, significantly differing from the process in dipolar dyes. We analyze the response using a three-state framework. Many functionals reproduce the qualitative CC2 structure–property trends, indicating that TD-DFT can capture the main chemical effects. However, substantial deviations remain in absolute magnitudes and in the ordering of closely related systems. These errors primarily originate from the transition-dipole-moment contribution, especially the upper S 1 → S 2 transition, while energetic detuning plays a secondary role. Low-exact-exchange global hybrids, such as B3LYP and PBE0, tend to overestimate the 2PA strengths, whereas range-separated hybrids typically underestimate them. A reasonably balanced performance is obtained with higher-exact-exchange hybrids, particularly MN15, BMK, M06–2X, and BH&HLYP. Overall, MN15 yields the lowest global error for this benchmark set, while CAM-B3LYP remains effective for preserving relative trends despite its systematic underestimation of absolute responses.