B 2 N 3 . C 5 structure was subsequently used as a template to design boron sesquinitride, B 2 N 3 , in both tetragonal and hexagonal forms. Table shows the corresponding atomic substitutions of carbon at the three different positions of Table by boron and nitrogen. The geometry converged atomic positions were found to be close to the matrix C 5 allotropes. It can be observed that the cell volumes of tet-B 2 N 3 and h-B 2 N 3 are almost the same as well as the total energies with however a slightly lower value for the former. The crystal structures are shown in Figs. and in ball-and-stick and tetrahedral representations. B 3 N 3 . Subsequently, the equiatomic boron nitride, B 3 N 3 , was designed in both crystal systems by inserting an extra boron at 0, 0, 0 for tet-B 3 N 3 and at ⅓, ⅔, 0 for h-B 3 N 3 as shown in Table (the 2 nd and 4 th data columns). The resulting structures after full geometry relaxation are shown in Figs. and. They exhibit a preserved pristine boron sesquinitride structures expanded with additional boron, thus achieving equiatomic stoichiometry. The total energies favor tet-B 3 N3, which also has a larger volume, indicating a lower density.