Localized vibrational modes around bipolarons in polythiophene

Localized modes of lattice vibration in polythiophene are investigated numerically by considering a chain of finite length. With the periodic boundary condition, we find three even-parity and four odd-parity modes. One of the even modes due to the sulfur heteroatom in the heterocycle is believed to be responsible for what is observed around 700 cm-1 in the Raman spectrum of polythiophene. With the free-end boundary condition, several modes from the highest optical branch become localized near the surface. These modes may be identified as the high-frequency modes observed in infrared-active vibration and resonant-Raman-scattering absorption experiments.