  Attachment of chemical substituents (such as polar moieties) constitutes an
efficient and convenient way to modify physical and chemical properties of
conjugated polymers and oligomers. Associated modifications in the molecular
electronic states can be comprehensively described by examining scattering of
excitons in the polymer's backbone at the scattering center representing the
chemical substituent. Here, we implement effective tight-binding models as a
tool to examine the analytical properties of the exciton scattering matrices in
semi-infinite polymer chains with substitutions. We demonstrate that chemical
interactions between the substitution and attached polymer are adequately
described by the analytical properties of the scattering matrices. In
particular, resonant and bound electronic excitations are expressed via the
positions of zeros and poles of the scattering amplitude, analytically
continued to complex values of exciton quasi-momenta. We exemplify the
formulated concepts by analyzing excited states in conjugated phenylacetylenes
substituted by perylene.
