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.