Set up the secular determinants for the homologous series consisting of ethene, butadiene, hexatriene, and octatetraene and diagonalize them by using mathematical software. Use your results to show that the π molecular orbitals of linear polyenes obey the following rules:

•   The π molecular orbital with lowest energy is delocalized over all carbon atoms in the chain.

•   The number of nodal planes between C2p orbitals increases with the energy of the π molecular orbital.