Vibrational analysis of polyacetylene and copoly(acetylene+acetylene-d ₂): In-plane vibrations of trans-polyene chains

Normal coordinate calculations have been performed for the in-plane vibrations of several trans-polyene chains from butadiene to polyacetylene in order to obtain a set of force constants commonly applicable to short and long polyenes. The force field finally obtained consists of short range forces, which are primarily determined by the frequency data on short polyenes, and long range interactions which are important in explaining the data on polyacetylene. The long range interactions between the C=C stretching coordinates as far as the fifth neighbor have significant effects on the dynamical properties of the infinite chain. Frequencies of some Raman active vibrations are greatly lowered by the long range terms to become comparable with the experimental frequencies of polyacetylene. These vibrations shift to higher frequencies steeply as the phase difference between adjacent HC=CH units increases from zero. Such steep dispersion as well as the other features of calculated dispersion curves are fully consistent with the expectation based on the Raman spectra of copoly(acetylene + acetylene-d₂). Further support for the dispersion curves is given by a general agreement between the experimental Raman spectra and theoretical spectra calculated for model copolymer chains using an approximate equation of resonance Raman intensity.