| Abstract
| - The bond curvature (K), derived from the Directional-Curvature Theory, is developed as a simple and efficient criterion for structures and chemical anisotropy of sidewall [2+1] cycloadditions on single-walled boron nitride nanotubes (SWBNNTs). The origin of the relationship between the chemical anisotropy of SWBNNTs and the bond curvature is explained based on the viewpoint of hybrid orbital theory. The first-principle calculations for the additions on various types of the SWBNNTs show that not those single-parameter criteria, but the K, in which the two parameters R and θ are involved, can solely determine the structure types of the cycloadditions on the B−N bonds and predict the chemical anisotropy of the SWBNNTs. The larger the K is, the more easily the B−N bond is broken, and the binding energies of the opened structures change linearly with K. For the cycloaddition on SWBNNTs with moderate diameter, the boundary of K for determining whether the B−N bond is broken or not is about 1.45 nm−1.
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