Density functional theory study on the Raman spectra of negative polarons and negative bipolarons in Na-doped poly(p-phenylene)

Density functional theory with the 6-31G* basis set and the BYLP nonlocal exchange-correlation functional has been used for the normal coordinate calculations of the neutral, radical anion, and dianion species of p-terphenyl to p-sexiphenyl. The bands attributed to negative polarons and negative bipolarons in the reported Raman spectra of Na-doped poly(p-phenylene) have been successfully assigned on the basis of the present calculations. The calculated atomic displacements have indicated that the Raman bands not corresponding to the zone-center modes of neutral poly(p-phenylene) are due to negative polarons and negative bipolarons. The Raman bands characteristic of negative polarons and negative bipolarons have been identified. The frequency of the inter-ring CC stretch is sensitive to the structural changes in going from benzenoid to quinoid structure in negative polarons and negative bipolarons.