Conjugated Compounds. II. Simple Potential Energy Functions, Absorption Spectra, and Ionization in Linear Polyenes

The π-electrons of a linear conjugated system are considered in terms of two simple models for the potential energy, (A) a rectangular well and (B) a " cosine-squared " well. In each case it is possible to account quantitatively for the positions of long wavelength absorption bands, their intensities, and the ionization energies in ethylene, butadiene, hexatriene, and octatetraene with the use of two parameters, the breadth and depth of the well. By comparing the models with actual periodic potential energies calculated along the long axes of polyene molecules, it is shown that an effective nuclear charge of carbon of Z?≈1 is appropriate for the models under consideration. The assumptions involved in the application of simple one-dimensional potential energy functions to linear conjugated systems are considered in detail.