In the work described in this thesis, the Feynman-Dyson perturbation theory, developed from quantum field theory, was employed in semiempirical calculations on trans - polyacetylene. A variety of soliton-like excited states of the molecule were studied by the PPP-UHF-RPA method. The results of this study provide useful information on the nature of these states, which are thought to account for the unique electrical conduction properties of trans - polyacetylene and similar conducting polymers. Feynman-Dyson perturbation theory was also used to extend Hartree-Fock theory by the inclusion of time-independent second-order self-energy insertions. The results of calculations on polyenes show that consideration of this approach is warranted, as the contribution of the second- order terms is significant. The computer program, written during the course of the research reported here, is discussed as well. / Ph. D.