Degenerate and non-degenerate two-photon absorption of coumarin dyes

Two-photon absorption (2PA) spectroscopy is a robust bioimaging tool that depends on the determined cross-sections (sigma(2PA)). The absorption of both photons occurs simultaneously with equivalent (degenerate) or different (non-degenerate) photon energies, D-2PA and ND-2PA, respectively. The former has been investigated experimentally and computationally for many systems, while the latter remains relatively unexplored computationally and limited experimentally. In this study, response theory using time-dependent density functional theory (TD-DFT) and the 2-state model (2SM) have been utilized to investigate sigma(D-2PA) and sigma(ND-2PA) for the excitation to the lowest energy singlet state (S-1) of coumarin, coumarin 6, coumarin 120, coumarin 307, and coumarin 343. Solvents involved were methanol (MeOH), chloroform (ClForm), and dimethylsulfoxide (DMSO), where the latter leads to the largest sigma(2PA). Values of sigma(2PA) are largest for coumarin 6 and lowest for coumarin, which illustrates the effect of substituents. The 2SM clarifies how the largest cross-sections correspond to molecules with the largest transition dipole moments, mu(01). In general, sigma(D-2SM) computations agree with sigma(D-2PA). Moreover, sigma(ND-2SM) are in qualitative agreement with sigma(ND-2PA) with comparable enhancement relative to sigma(D-2PA). Overall, sigma(ND-2PA) are larger than sigma(D-2PA) where the increase is in the range of 22% to 49%, depending on the coumarin as well as the relative energies of the two photons. This work aids in future investigations into various fluorophores to understand their photophysical properties for ND-2PA.