The structural and energetic properties of polyfluorene and its derivatives were investigated, using quantum chemical calculations. Conformational analysis of bifluorene was performed by using ab initio (HF/6-31G* and MP2/6-31G*) and density functional theory (B3LYP/6-31G*) calculations. The results showed that the local energy minimum of bifluorene lies between the coplanar and perpendicular conformation, and the B3LYP/6-31G* calculations led to the overestimation of the stability of the planar pi systems. The HOMO-LUMO energy differences of fluorene oligomers and its derivatives — 9,9-dihexylfluorene (DHPF), 9,9-dioctylfluorene (PFO), and bis(2-ethylhexyl)fluorene (BEHPF) — were calculated at the B3LYP/6-31G* level. Energy gaps and effective conjugation lengths of the corresponding polymers were obtained by extrapolating HOMO-LUMO energy differences and the lowest excitation energies to infinite chain length. The lowest excitation energies and the maximum absorption wavelength of polyfluorene were also performed, employing the time-dependent density functional theory (TDDFT) and ZINDO methods. The extrapolations, based on TDDFT and ZINDO calculations, agree well with experimental results. These theoretical methods can be useful for the design of new polymeric structures with a reducing energy gap.

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In this work, HOMO-LUMO energy gap and the lowest excitation energy of poly [2,7-(9,9-dihexylfluorene)-co-alt-2,5-(decylthiophene) were performed by different methods. The obtained results indicate that TDDFT(B3LYP/6-31G*)//B3LYP/6-31G* calculations can be useful to provide reliable energetic and structural results of this polymer. The HOMO-LUMO predictions were not accurately obtained as compared to the experimental results. The inverse chain length approximation by using TDDFT(B3LYP/6-31G*)//B3LYP/6-31G* calculations provides energy gap of 2.50 eV, which is in an excellent agreement with the experimental data. However, it was found that the HOMO-LUMO energy gaps obtained from B3LYP calculations were still far from the experimental data.

Excited states of fluorene-ethylenedioxythiophene (FEDOT) and fluorene-S,S-dioxide-thiophene (FTSO2) monomers and dimers were studied by the symmetry-adapted cluster (SAC)-configuration interaction (CI) method. The absorption and emission peaks observed in the experimental spectra were theoretically assigned. The first three excited states of the optimized conformers, and the conformers of several torsional angles, were computed by SAC-CI/D95(d). Accurate absorption spectra were simulated by taking the thermal average for the conformers of torsional angles from 0 degrees to 90 degrees. The conformers of torsional angles 0 degrees, 15 degrees, and 30 degrees mainly contributed to the absorption spectra. The full width at half-maximum of the FEDOT absorption band is 0.60 eV (4839 cm(-1)), which agrees very well with the experimental value of 0.61 eV (4900 cm(-1)). The maximum absorption wavelength is located at 303 nm, which is close to those of the experimental band (327 nm). The calculated absorption spectrum of FTSO2 showed two bands in the range of 225-450 nm. This agrees very well with the available experimental spectrum of a polymer of FTSO2, where two bands are detected. The excited-state geometries were investigated by CIS/6-31G(d). These showed a quinoid-type structure which exhibited a shortening of the inter-ring distance (0.06 A for FEDOT and 0.04 A for FTSO2). The calculated emission energy of FEDOT is 3.43 eV, which agrees very well with the available experimental data (3.46 eV). The fwhm(E) is about 0.49 eV (3952 cm(-1)), while the experimental fwhm is 0.43 eV (3500 cm(-1)). For FTSO2, two bands were also found in the emission spectrum.

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