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The electronic structure and band symmetries of the ferroelectric phase of poly (vinylidene fluoride) (PVDF) are studied by using the first-principles density-functional method. Our calculated results agree well with the angle-resolved photoemission experiments. We find that the PVDF crystal has an energy gap of about 6 eV at the Γ-point. Large dispersion of the valence band is found only along the chain direction, which is consistent with the quasi-one-dimensional nature of PVDF. In particular, the band symmetries of the valence states deduced theoretically are in good agreement with experiment. Finally, further investigations on the electronic structure of poly(trifluoroethylene) (PTrFE) reveal that the replacement of -( CH2- CF2)- by -( CHF- CF2)- does not change major features of the band structure.