Two-Photon Absorption by Fluorene Derivatives: Systematic Molecular Design

In this article, we employ a systematic approach to the computational quantum chemical study of the two-photon absorption (2PA) properties of 161 representative molecules containing a symmetrically substituted fluorene unit. The molecules studied contain meta- or para-substituted phenyl groups, five- and six-membered heterocycles, and benzo derivatives of five-membered heterocycles. The computational procedure employed to calculate the 2PA parameters was previously described [Chem. Mater. 2008, 20, 4142] and is based on semiempirical electronic structure methods: the RM1 model to optimize the molecular geometry and the INDO/S method to calculate the spectroscopic properties of the molecules. We further advance a new, simplified expression employed to calculate an approximate three-level contribution of the imaginary part of the negative component of the second hyperpolarizability. We then show that, in order to rationalize the 2PA cross sections for the substituted fluorenes, the three-level approximation has to be adapted to include a fourth state. That done, we advance that the parameter most responsible for the large observed variation in the calculated values of the 2PA cross sections for the substituted fluorenes is the effective transition dipole moment between the 1PA-active state and the two 2PA-active states. Based on our results, we discuss three structural effects that can contribute to the value of the 2PA cross section and show how they can be tuned. We conclude by propositioning novel putative molecules with potentially large values of 2PA cross sections, such as 2,2'-(9,9-dialkyl-9H-fluorene-2,7-diyl)dibenzo[d]oxazole.