Nature of the Free Electron Model. The Case of the Polyenes and Polyacetylenes

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Abstract
The wave functions and energy levels of the polyenes and polyacetylenes found on the basis of the simple sine curve potential model are compared with those given by more refined methods in which the π electrons are treated as electrons in a one-, two-, or three-dimensional core potential obtained from nuclear charge and shielding considerations. The results of the four treatments are in good agreement, and by considering the electron density distribution along the chain each treatment leads to the same conclusion, that each single bond and each double (or triple) bond in a long-chain polyene (or polyacetylene) must have, respectively, the same length as the single bond and double (or triple) bond in butadiene (or diacetylene). The values of the absorption maxima given by the four models are in good agreement with the experimental values.