Utilizing first-principles simulations, we study the electronic characteristics of a series of carbon nanocages exhibiting bipartite atomic configurations. These nanocages are constructed exclusively through the assembly of hexagonal and tetragonal rings. Our analysis demonstrates the emergence of frontier states within these nanocages, showcasing distinct symmetries as governed by well-established principles grounded in structural dimensions. Additionally, we observe the manifestation of spin-polarized arrangements at the edges of the finite-width versions of these zero-dimensional (0D) structures. Furthermore, we propose these nanocages as fundamental constituents for creating ordered one-dimensional (1D) and two-dimensional (2D) arrangements, aligning with recent experimental findings regarding fullerene-type nanostructures. Although various bonding configurations can link cage-like units, the resulting systems consistently exhibit semiconductor-like behavior for both 1D and 2D nanostructures. The details of interconnecting hierarchies influence the extent of localization of the frontier states within these crystalline systems, concurrently modulating the electronic band gap.

中文翻译：

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基于二分纳米笼单元的碳纳米结构的电子特性

利用第一原理模拟，我们研究了一系列表现出二分原子构型的碳纳米笼的电子特性。这些纳米笼专门通过六角形和四角形环的组装来构建。我们的分析证明了这些纳米笼内边界态的出现，展示了受基于结构维度的既定原理支配的独特对称性。此外，我们还观察到这些零维（0D）结构的有限宽度版本边缘处的自旋极化排列的表现。此外，我们建议这些纳米笼作为创建有序一维（1D）和二维（2D）排列的基本成分，与最近有关富勒烯型纳米结构的实验结果相一致。尽管各种键合配置可以连接笼状单元，但所得系统对于一维和二维纳米结构始终表现出类似半导体的行为。互连层次结构的细节影响这些晶体系统内前沿态的局部化程度，同时调制电子带隙。