However, if we can develop a theory akin to the organic Kekulé model 29 for boron materials to explain their stabilities and properties without extensive quantum calculations is still an open question. The 3c-2e bond in boron system was considered as a result of bond resonance, and the concept of aromaticity has been borrowed from carbon materials to explain the exceptional stability of boron polyhedral molecules 23, 24, 25 and planar boron clusters 1, 26, 27, 28. Historically a three-center two-electron (3c-2e) bond model 19 derived from the octet rule has been adopted to explain the unusual geometry and the high stability of electron-deficient boron materials 20, 21, 22. Therefore, theories of bonding that can predict the properties and stabilities of a large class of materials without quantum calculations, are always highly desirable for materials development. Even though today’s quantum calculations can give more accurate results, the lack of a clear chemical picture or intuitive understanding of the computational results made them hard to be used in materials design and synthesis. In the development of organic chemistry, the theory of aromaticity, which allows us to understand the bonding of the organic materials intuitively without performing extensive quantum calculations, plays a central role in materials design and synthesis. Although extensive computational studies have been dedicated to exploring the electronic structures of these boron materials 15, 16, 17, 18, theoretical understanding of the bonding configurations of these materials is still lacking. Based on extensive quantum calculations, Tang and coauthors proposed that the high stability of boron triangular sheets with holes, compared to the triangular boron lattice, can be attributed to a π-to-σ self-doping mechanism 15. A key feature of these boron isomers is the preference for hexagonal holes within their triangular lattices 6, 11, 13, 14. ![]() Recently, new boron materials including planar boron clusters 1, 2, 3, 4, boron cages 5, 6, boron nanotubes 7, 8, and monolayer boron sheets (borophene) 9, 10, 11, 12, have attracted significant attention.
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