Lattice-vibration localization in doped polythiophene

Vibration modes around bipolarons in polythiophene are investigated numerically by considering a chain of finite length with different boundary conditions within the framework of tight-binding model. When the periodic boundary condition is applied, we find seven localized modes, among which three are of even parity and four of odd parity. One of the even modes is due solely to the influence of sulfur heteroatom in the heterocycle and is believed to be responsible for the mode around 700 cm^-1 observed in the Raman spectrum of polythiophene. The dependence of intensities of these localized modes on the chain length is also investigated. When the ends of the chain are left open, it is shown that new surface modes are created from the highest optical branch. These modes may be identified as the high-frequency modes observed in infrared active vibration and resonant Raman scattering absorption experiments.