Two-dimensional localized vibrational modes of polythiophene around a bipolaron

In consideration of the influence of a planar polythiophene configuration, we study the localized vibrational modes around a bipolaron by using a two-dimensional Su-Schrieffer-Heeger model. With the periodic boundary condition, we find fourteen localized modes. Among them, four infrared active localized modes and four Raman active ones could be used to interpret the four observed intense infrared absorption lines at 1020, 1120, 1200, and 1323 cm(-1), and the four resonant-Raman-scattering absorption peaks at 700, 1047, 1175, and 1270 cm(-1), respectively. With the free-end boundary condition, five modes from the highest optical branch become localized near the surface. Four of them may be identified as the high-frequency modes in infrared active vibration and resonant Raman-scattering absorption experiments.