Non-Degenerate Two-Photon Absorption of Fluorescent Protein Chromophores

Two-photon absorption (2PA), where a pair of photons are absorbed simultaneously, is recognized as a potent bioimaging technique, which depends on the quantified 2PA probability, defined as cross-section (sigma(2PA)). The absorbed photons either have equivalent (omega(1) = omega(2)) or different frequencies (omega(1) not equal omega(2)), where the former is degenerate 2PA (D-2PA) and the latter is nondegenerate 2PA (ND-2PA). ND-2PA is of particular interest since it is a promising imaging technology with flexibility of photon frequencies and enhanced cross sections, however, it remains a relatively unexplored area compared to D-2PA. This work utilizes time-dependent density functional theory (TD-DFT) and second-order approximate coupled-cluster with the resolution-of-identity approximation (RI-CC2), for the excitation from S-0 to S-1, to investigate sigma(D-2PA) and sigma(ND-2PA) of FP chromophore models. Interestingly, comparing CAM-B3LYP with the RI-CC2 computations shows qualitative and, in fact, near quantitative agreement in the computed improvements of sigma(ND-2PA) for comparable (relative) frequency detunings, despite the known underestimations of 2PA cross sections, for TD-DFT results relative to RI-CC2 values. As expected from the 2-state model, the computed values of sigma(ND-2PA) are quantitatively larger than sigma(D-2PA), where chromophores with the largest values of sigma(D-2PA) show greater potential for sigma(ND-2PA) improvement. Anionic chromophores demonstrated improvements up to 14%, while substantial enhancements were observed in neutral chromophores with some achieving a 30% increase. This work investigates the ND-2PA photophysical characteristics of FP chromophores and identifies qualitative patterns in the computed properties of ND-2PA relative to D-2PA.