From Benzene to Graphene: Exploring the Electronic Structure of Single-Layer and Bilayer Graphene Using Polycyclic Aromatic Hydrocarbons

Abstract

In this work, two exercises are described that are designed to teach students about the evolution and behavior of the electronic bands of graphene and bilayer graphene. These exercises involve performing extended Huckel molecular orbital theory calculations on polyacenes and polycyclic aromatic hydrocarbons. In the first exercise, students investigate how the molecular orbitals of polyacenes converge into bands as polyacene size increases. Further, students learn that long-range interactions cause frontier-orbital crossing as the size of the polyacene increases. In the second exercise, the concepts of band structures, band crossing, and k-space are explored using the results of frontier orbital calculations on π-stacked dimers of polycyclic aromatic hydrocarbons, which represent molecular analogues of layered 2D materials. The results of these calculations show how the geometry and layer–layer offset of the dimer system can affect its electronic structure, and the results can be extrapolated to provide a framework for understanding why subtle changes in the relative orientations of the layers in bilayer graphene can produce qualitative changes in the electronic properties. These calculations are easily implemented with Python or with widely available algebraic manipulation software such as Maple or Mathematica. These exercises are accessible to students who have experience with extended Huckel molecular orbital theory and are suitable for inclusion in the physical chemistry curriculum at the upper-level undergraduate or introductory graduate level.