By revealing and invoking a novel concrete (topological and electronic) shell structure, inherent in hexagonal polycyclic aromatic hydrocarbons (PAHs), it is illustrated that the celebrated but largely empirical Hückel and Clar rules for aromaticity and stability can be derived, interrelated, and connected to shell closures, with well-identified stability and aromaticity maxima versus the number of π-electrons, analogous to the ionization energy curves in the periodical table of the elements, versus atomic number. This is because such shell structure is described in terms of topological/geometrical indices, n, l, m_l, s, m_s, analogous to the corresponding atomic quantum numbers, demanding (2l + 1) × (2s + 1) occupied π-electrons for given l. The frontier orbitals are composed of core and valence (annulene) orbitals in such a way that the benzene “core orbitals” (l = 0) are expanded and combined, “propagating” successively from benzene to the larger layers, like gigantic superbenzenes, distinguished in those with an aromatic central benzene core, odd n, and satisfying the traditional Hückel/Clar rules, and those with a nonaromatic central ring following the opposite trends. All “superbenzenes” are fully aromatic, satisfying the generalized Hückel’s law suggested here. These results can be projected and/or expanded to other PAHs of all sizes up to infinite graphene, elucidating, among other things, graphene’s sensitivity to edge morphology and size.

中文翻译：

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经典插图：Clar的六重奏和Hückel的（4 n + 2）π电子规则

通过揭示并调用六角形多环芳烃（PAH）中固有的新型混凝土（拓扑和电子）壳结构，可以说明，可以得出，相互关联和联系的，广为人知的Hückel和Clar芳香性和稳定性法则。壳封闭，具有公认的稳定性和芳香性最大值与π电子数的关系，类似于元素周期表中的电离能曲线与原子数的关系。这是因为这种壳结构是根据拓扑/几何指数n，l，m _l，s，m _{s来描述的}类似于相应的原子量子数，对于给定的l，要求（2 l +1）×（2 s +1）占据π电子。前沿轨道由核和价环（环戊烯）组成，苯这样的“核轨道”（l = 0）被扩展和合并，从苯开始“传播”到更大的层，例如巨型超苯。在具有芳族中心苯核的化合物中，奇数n，并且满足传统的Hückel/ Clar规则，以及具有非芳香族中心环的规则遵循相反的趋势。所有“超苯”都是完全芳香的，满足此处建议的广义Hückel定律。这些结果可以被投影和/或扩展到所有尺寸直至无穷石墨烯的其他PAH，尤其是阐明了石墨烯对边缘形态和尺寸的敏感性。