Unrestricted Hartree-Fock calculations for a one-dimensional infinite periodic system have been employed to characterize a cross-talk system between trans-1,4-polybutadiene and a small molecule, O-2. The total energy, the energy band structure, and the longitudinal linear polarizability have been investigated. The presence of O-2 has been found to influence in a quantitatively as well as a qualitative way the energy band structure of polybutadiene.