Results of density-functional calculations on cis-and trans-1,4-polybutadiene are presented. The resulting band structures are compared with those of polyethylene and trans-polyacetylene. Charge-density plots of the highest occupied rt band show that the results are in accordance with the intuitive concept of localized pi bonds. Tight-binding fits of the band structure show that polybutadiene can be regarded as a copolymer between polyethylene and polyacetylene. A detailed study of the single-particle energies of polybutadiene, polyethylene, polyacetylene, and ethylene allows finally a determination of some of the parameters for an extended Hubbard model that can describe the rr electrons of extended hydrocarbons. It is shown that the nearest-neighbor Hubbard parameters are small, indicating that further interactions are effectively screened.