![]() b In carbon materials, the resonance of alternating 2c-2e π bonds leads to a resonant bond. ![]() ![]() ![]() To note that here in this paper, we consider all the boron atoms in the flat triangular lattice-based boron materials are sp 2 hybridized, leading to the flatness of borophene, which has been acknowledged in literatures of various 2D boron sheets, boron fullerenes, and etc 6, 8, 17.Ī In a triangular boron network (pink), the resonance of alternating 3c-2e σ bonds in neighboring triangles leads to a diamond-shape resonant 3c-2e bond. An analogue of the 3c-2e σ bond resonance in the triangular boron lattice is the bonding configurations of sp 2 hybridized hydrocarbon materials, where two alternating two-center two-electron (2c-2e) π bonds resonate to form a more stable resonant bond (Fig. Like the resonance of π bonds in benzene molecules we expect the resonance and delocalization of these 3c-2e bonds in the triangular lattice to greatly reduce the energy of the system (Fig. Each 3c-2e bond in each configuration is localized and only half of the two-dimensional (2D) space (triangles) can be filled by 3c-2e bonds. There are two possible bonding configurations for the triangular network, one in which 3c-2e σ bonds are formed by the overlapping of three sp 2 orbitals in the upper triangles (blue) and the other the lower triangles (green). 1a, where each sp 2 hybridized B atom has three 3c-2e σ bonds with its six neighboring B atoms. Besides the advance of the basic knowledge of boron chemistry and the understanding of the experimental puzzles, it provides an efficient tool for the design and synthesis of various boron-based materials.Ī sigma resonance theory for flat triangular boron materialsĪ flat triangular boron network is presented in Fig. With this theory, the bonding configurations and properties of various boron materials can be easily derived and understood. Here, based on the resonance of 3c-2e and 2c-2e bonds in triangular lattice-based flat boron materials, we present such a theory. 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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