Polyenes
Polyenes are an important class of molecules. Polyenes consist of an extended
p-system. Typically, polyenes have alternating double bonds and do not enjoy the resonance stabilization of aromatic hydrocarbons. They are found in carotenoids and retinals, important biological pigments. Polyenes are also important because many dyes have linear conjugated p-systems.We compare the free electron (FE) model of polyenes and the Huckel method. These will be applied to ethylene and butadiene with some generalization made about longer polyenes. The free electron model (FE) model is based on the particle in a box problem. The energy levels are even and odd just as the molecular orbitals in polyenes alternate between even (A) and odd (B) symmetry. The Huckel approach is outlined in "Chemical Applications of Group Theory" by Cotton (Wiley-Interscience).
The Huckel approximation assumes that all overlaps Sij = 0. In addition it assumed that all interaction energies Hij = 0 unless i = j
±1. That is to say, interaction energies are zero unless the atoms are adjacent to one another. We define the following:a
= Hii, the energy of an electron in a pp orbital before interaction with other orbitals.b
= Hij, the energy of interaction between orbtials on adjacent carbons.By setting all of the
a equal to zero we can determine the energy of the electrons relative to the energy of the electrons in an isolated carbon pp orbital. Once we have constructed the matrix of interaction energies we can diagonalize it to obtain the energies of the molecular orbitals.