Visualization of the Jahn-Teller distortion using as platform the extended Hückel Theory

Abstract

Teaching the Jahn-Teller theorem offers several challenges. For many students, the first encounter comes in coordination chemistry, which can be difficult due to the already complicated nature of transition-metal complexes. A deep understanding of the Jahn-Teller theorem requires that one is well acquainted with quantum mechanics and group theory. Jahn-Teller effects arise from incomplete shells of degenerate orbitals. It is the first-order Jahn-Teller effect. As a result, geometric distortions produced are quite small and normally lead to dynamic effects only. The Jahn-Teller effect is encountered both in organic compounds and in transition-metal complexes. In this work, a simplification of the extended Hückel molecular orbital theory is applied to demonstrate the spontaneous distortion of 1,3,5,7-cyclooctatetraene and the cyclobutadiene molecule as a consequence of the Jahn-Teller effect. The exercise is easily implemented with widely available algebraic manipulation software such as Mathematica. This exercise is suitable in the physical chemistry curriculum at the upper-level undergraduate. In contrast we will see that the JT effect is not observed in benzene.