Electron−Phonon Coupling in Phenyleneethynylene Oligomers:  A Nonlinear One-Dimensional Configuration-Coordinate Model

In many conjugated polymers, coupling of the torsional motions to the electronic excitation plays a major role in the spectroscopy and photophysics. In a recent paper [ J. Phys. Chem. B 2006, 110, 18844], we developed a multidimensional exciton model of electron−torsion coupling that accounts for a number of unusual features in the spectroscopy of poly(phenyleneethynylene). This paper reduces that multidimensional exciton model to a one-dimensional configuration-coordinate (CC) model to facilitate interpretation of the spectroscopy and to allow extension to more complex systems. Because the CC model is derived from a more exact multidimensional model, the approximations inherent in the CC model can be examined quantitatively. The CC model accurately accounts for the line shapes in absorption and emission and the evolution of those shapes with oligomer length. Both fully anharmonic torsional potentials and nonlinear coupling are needed to predict these properties. In addition, the entropic contributions in the CC model give rise to strong effects that are not evident in the potential energy of a single torsion. When the number of torsions is small, the shape of the entropic portion of the potential is far from the harmonic shape it acquires in the limit of large dimensionality. Strongly non-Gaussian line shapes result. The CC model accurately predicts the nonlinearity of the transition energy versus 1/ N without including broken conjugation. Such plots may therefore not be an unambiguous method for measuring the effective conjugation length in polymers.