Nature of the Free Electron Model. The Simple Case of the Symmetric Polymethines

In the case of the polymethines $${\mathrm{H}}_2\mathrm{C}=\mathrm{CH}(\mathrm{CH}=\mathrm{CH}{)}_{\text{j−1}}\mathrm{CH}{\displaystyle {lim}^{\oplus }}{}_2$$ and $${\mathrm{H}}_2\mathrm{C}=\mathrm{CH}(\mathrm{CH}=\mathrm{CH}{)}_{\text{j−1}}\mathrm{C}{\displaystyle {lim}^{\ominus }}{\mathrm{H}}_2$$ the wave functions and energy levels of the π electrons given by the one‐dimensional free electron model are compared with those given by more elaborate methods in which the π electrons are treated as electrons in a one‐ or two‐dimensional core potential obtained from nuclear charge and shielding considerations. The results of the three treatments are in good agreement, and thus the reliability of the simple free electron model is justified.