Vibronic Effects in the 11Bu(11B2) Excited Singlet States of Oligothiophenes. Fluorescence Study of the 11Ag(11A1) ← 11Bu(11B2) Transition in Terms of DFT, TDDFT, and CASSCF Methods

A combined DFT/TDDFT approach has been applied for calculating the Huang−Rhys (HR) parameters along the totally symmetric normal coordinates for the 11Ag(11A1) ←11Bu (11B2) electronic transition in a series of oligothiophenes containing from 2 to 6 thiophene rings. The calculations required optimized molecular geometries for both the ground state and the excited molecular state. The excited state geometry optimization was carried out by means of the time-dependent density functional theory (TDDFT) based methodology implemented in the Turbomole 5.9 package of programs. The results for the three smallest oligothiophenes were verified by generating the theoretical vibronic structures and comparing them with the high-resolution fluorescence spectra measured for matrix-isolated molecules. For bithiophene a comparison was also made of the theoretical results obtained for different basis sets and the most popular exchange-correlation functionals. The best results were then confronted with the HR parameters based on the molecular geometries calculated at the CASSCF level of theory. The results obtained within the DFT/TDDFT approach are in very good agreement with the available experimental data for bithiophene, terthiophene, and quaterthiophene molecules.