Vibrational analysis of a trans-polyacetylene chain

By an ab initio calculation based on the local density approximation of den sity-functional theory, the force constants up to the fifth nearest-neighbo r carbon-hydrogen unit are determined to obtain the in-plane and out-of-pla ne phonon spectrum of tra ns-polyacetylene. The calculated phonon frequenci es at the Gamma point coincide well with that of the observed infrared and Raman spectra of trans-polyacetylene. It is shown that the coupling between vibrations along different directions in the plane is crucial to obtain co rrectly the dispersion curves of acoustic phonons.