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

TL;DR

This paper analyzes the electronic structure of benzene and borazine using group theory and tight-binding models, exploring degeneracies, symmetry breaking, and applications to aromaticity and supersymmetry in hexagonal rings.

Contribution

It introduces an algebraic approach combining group theory and tight-binding models to describe electronic spectra and symmetry effects in benzene and borazine.

Findings

Degeneracy explained by $C_3$ symmetry and time-reversal symmetry.

Magnetic fields and defects induce degeneracy lifts.

Wave functions relate to aromaticity and electronic currents.

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.