  We calculate the electronic and optical excitations of polythiophene using
the GW approximation for the electronic self-energy, and include excitonic
effects by solving the electron-hole Bethe-Salpeter equation. Two different
situations are studied: excitations on isolated chains and excitations on
chains in crystalline polythiophene. The dielectric tensor for the crystalline
situation is obtained by modeling the polymer chains as polarizable line
objects, with a long-wavelength polarizability tensor obtained from the
ab-initio polarizability function of the isolated chain. With this model
dielectric tensor we construct a screened interaction for the crystalline case,
including both intra- and interchain screening. In the crystalline situation
both the quasi-particle band gap and the exciton binding energies are
drastically reduced in comparison with the isolated chain. However, the optical
gap is hardly affected. We expect this result to be relevant for conjugated
polymers in general.
