Rigorous Franck–Condon absorption and emission spectra of conjugated oligomers from quantum chemistry

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Abstract
A harmonic Condon approach is used to calculate excitation and emission band shapes for the lowest dipole-allowed electronic transitions in conjugated oligomers: polyenes, oligorylenes, and para-phenylenevinylenes. Ground- and excited-state adiabatic energies, equilibrium structures, and vibrational modes are obtained within standard all-valence-electron molecular Hamiltonian incorporating extended configuration interaction. The interstate distortion is cast in normal coordinates and used to calculate transition probabilities from the zero-phonon initial state to the vibrational manifold of the final state. Spectral profiles are obtained as a superposition of Lorentzian line shapes. Theoretical band shapes reproduce prominent features in the absorption and fluorescence spectra of the oligomers in question. The strength of the bond-stretching vibronic progression increases with oligomeric length in polyenes, but decreases in para-phenylenevinylenes. In line with experiment, absorption and emission band shapes of para-phenylenevinylenes are obtained intrinsically nonsymmetric due to stiffening of the accepting vibrational modes in the excited state. The Stokes shifts of the apparent 0-0 features in the latter are reproduced and traced back to relaxations in slow, ring-torsional motions.