almost vanishes (less than 0.001 eV or even negative). Only the energy of the $8h$ site of the N-containing form is higher by 0.008 eV. The present calculations imply that the $4c$ site is the major interstitial for pure $\alpha$-T boron, whereas for C/N-containing $\alpha$-T boron comparable amounts of $8i$-site atoms are present and the occupation of the $8h$ site is the smallest.

This different order of $\Delta E_{f}$ for $4c$ and $8i$ sites between pure and C/N-containing $\alpha$-T boron is consistent with the experiment in Table \[tbl:alpha-tetra\]. If the recently discovered $\alpha$-T forms are regarded as pure: $8h$ and $8i$ sites are observed in impurity-containing forms and $4c$ sites are observed in the pure form. In our calculations, the bond lengths of C or N at the $2b$-site to their neighbors are short, [*i.e.*]{}, 1.57 and 1.59 Å, respectively. The corresponding value for pure B$_{50}+ 2$B$_{4c}$ is 1.70 Å. In general, in icosahedron-based boron crystals, [*inter*]{}icosahedral bonds are the shortest ones but the value is at most 1.69 Å. The experimental value of 1.63 Å for traditional $\alpha$-T boron (see Fig. \[fig:POS\]) is too short for B-B bonds, so that the measured value may be evidence for C or 