On the electronic structure of benzene and borazine: An algebraic description

Abstract

The spectrum of a hexagonal ring is analysed using concepts of group theory and a tight-binding model with first, second and third neighbours. The two doublets in the spectrum are explained with the $C_3$ symmetry group together with time-reversal symmetry. Degeneracy lifts are induced by means of various mechanisms. Conjugation symmetry breaking is introduced via magnetic fields, while $C_3$ breaking is studied with the introduction of defects, similar to the inclusion of fluorine atoms. Concrete applications to benzene and borazine are shown to illustrate the generality of our description. Wave functions are described in connection with partial or full aromaticity. Electronic density currents are found for all cases. A detailed study of a supersymmetry in a $6$-ring is presented and its consequences on electronic spectra are discussed.

arXiv comment24 pages, 12 figures

References in corpus (6)

• The electronic properties of graphene
• First experimental realization of the Dirac oscillator
• Tight-binding couplings in microwave artificial graphene
• Dirac Point and Edge States in a Microwave Realization of Tight-Binding Graphene-like Structures
• Disordered graphene and boron nitride in a microwave tight-binding analog
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Cited by in corpus (4)

• Boundary Condition Analysis of First and Second Order Topological Insulators
• Effects of zigzag edge states on the thermoelectric properties of finite graphene nanoribbons
• Molecular orbitals of an elastic artificial benzene
• Hidden duality and accidental degeneracy in cycloacene and Möbius cycloacene