Analysis of the excited-state absorption spectral bandshape of oligofluorenes

We present ultrafast transient absorption spectra of two oligofluorene derivatives in dilute solution. These spectra display clear vibronic structure, which we analyze rigorously using a time-dependent formalism of absorption to extract the principal excited-state vibrational normal-mode frequencies that couple to the electronic transition, the configurational displacement of the higher-lying excited state, and the reorganization energies. We can model the excited-state absorption spectrum using two totally symmetric vibrational modes with frequencies 450 (dimer) or 400 cm$^{-1}$ (trimer), and 1666 cm$^{-1}$. The reorganization energy of the ground-state absorption is rather insensitive to the oligomer length at 230 meV. However, that of the excited-state absorption evolves from 58 to 166 meV between the oligofluorene dimer and trimer. Based on previous theoretical work [Shukla et al., Phys. Rev. B \textbf{67}, 245203 (2003)], we assign the absorption spectra to a transition from the $1B_u$ excited state to a higher-lying $mA_g$ state, and find that the energy of the excited-state transition with respect to the ground-state transition energy is in excellent agreement with the theoretical predictions for both oligomers studied here. These results and analysis permit profound understanding of the nature of excited-state absorption in $\pi$-conjugated polymers, which are the subject of general interest as organic semiconductors in the solid state.