Packing of Large Two- and Three-Photon Activity Into Smallest Possible Unsymmetrical Fluorene Chromophores

The quantum chemical study of one-, two-, and three-photon absorption (1PA, 2PA, and 3PA) properties for a set of compact fluorene derivatives (FD) with combination of different donor and acceptor moieties on both sides of fluorene ring system is presented. The main goal of the study is to pack large two-photon (2P) and three-photon (3P) activity into smallest possible chromophore. Linear, quadratic, and cubic response time-dependent density functional theory was used to calculate 1PA, 2PA, and 3PA properties, respectively. We used CAMB3LYP/cc-pVDZ level of theory for all the property calculations. The 2P and 3P transition probabilities were recalculated using two-state model approach and found to be in good agreement with the response theory results for first excited state. To include the contributions from higher states, the three-state model was also employed to recalculate the 2P transition probabilities and found to be in excellent agreement with response theory. The 2P/3P tensor elements were also analyzed to find reasons behind large 2P/3P activities. All the orbitals involved in transition processes were studied in detail by both molecular orbital pictures (qualitatively) and overlap diagnostic Λ-values (quantitatively). The study reveals that the novel fluorene derivatives FD-12 and FD-13 have shown large 2PA cross-section values of 1100 G.M. and 1030 G.M.; and 3PA transition probabilities of 6.10 × 10¹⁰ a.u. and 4.85 × 10¹⁰ a.u., respectively, for transition <i>S</i>₀ → <i>S</i>₁. The largest 3PA transition probability of 4.04 × 10¹¹ a.u. was found with FD-12 for <i>S</i>₀ → <i>S</i>₂ excitation. The linear relationship between Λ-values and 2PA cross-section values was also studied