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Local States in Polyenes and Annulenes: Single Substitutions

The paper proposes a new derivation of the conditions for appearance of local states in polyene chains and annulene rings as well as expressions for the local state energies in the Hiickel approximation. Perturbations of the Coulomb and resonance integrals in systems without bond alternation as well as in systems exhibiting bond alternation, have been considered. The method employs a direct analysis of the Huckel determinant of the perturbed system, which is simpler than the existing Green-function method. As a further advantage, it accounts also for the size of the investigated systems.