Abstract:

The Hückel molecular orbital method is an approximate model to describe the interactions of π-electrons in a conjugate system. In structural chemistry textbooks, the recursive formulas for the eigendeterminants and eigenenergy levels of conjugated π-electrons systems have been directly provided, without derivation. Based on mathematical induction, this work shows how these recursive formulas are derived for linear and monocyclic conjugated polyenes, and clarifies the characteristics and regularity of the eigenenergy levels. This information is suitable for students who lack mathematical knowledge with regard to topics such as the group theory and graph theory.

Key words: Conjugated polyenes, Eigendeterminants, Recurrence formula, Eigenenergy levels