Displacement vectors of localized vibrational modes around a charged soliton in Trans-polyacetylene

The localized vibrational modes of finite polyacetylene with a charged soliton are calculated taking full degrees of freedom into consideration. The displacement vectors of each localized vibrational mode are obtained and shown in this report. The vectors are discussed in connection with mode mixing. The localized modes are successfully classified into branch modes of four modes: translational, amplitude oscillation, third localized and staggered. Displacement patterns of localized modes indicate that the coupling between the two types of C-C stretching branch modes is weak, but there is a strong coupling between one of the C-C stretching modes and the C-H bending mode. Calculated frequencies and infrared intensities are found to be in good agreement with the infrared spectrum. Furthermore, it has been found that a force constant matrix obtained from a short cluster model is not suitable for calculation in the case of a long polyacetylene chain.