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 as an illustration 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.

中文翻译：

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关于苯和硼嗪的电子结构：代数描述

使用群论的概念和具有第一，第二和第三邻居的紧密绑定模型来分析六角环的光谱。光谱中的两个双峰用C 3对称群和时间反转对称性解释。简并提升是通过各种机制引起的。共轭对称断裂是通过磁场引入的，而C 3断裂是通过引入缺陷来研究的，类似于引入氟原子。苯和硼嗪的具体应用如下所示。波函数是结合部分或全部芳香性来描述的。在所有情况下都可以找到电子密度电流。提出了对6环中超对称性的详细研究，并讨论了其对电子光谱的影响。