Set up the secular determinants for cyclobutadiene, benzene, and cyclooctatetraene and diagonalize them by using mathematical software. Use your results to show that the π molecular orbitals of monocyclic polyenes with an even number of carbon atoms follow a pattern in which:

• The π molecular orbitals of lowest and highest energy are non-degenerate.

• The remaining π molecular orbitals exist as degenerate pairs.