DFTB+ simulation of B$_{\mathrm{x}}$N$_{\mathrm{y}}$ species formation for boron nitride nanotubes synthesis

Using DFTB+ MD simulations we analyze B$_{\mathrm{x}}$N$_{\mathrm{y}}$ species formation in a cooling mixture of boron atoms and nitrogen dimer. These species could be precursors of boron nitride nanotubes (BNNTs) synthesis. We determine that DFTB+ cannot predict correctly reaction of boron atoms and boron dimers with nitrogen molecules. The first reaction produces BN$_{\mathrm{2}}$ molecule and simulations show it to be stable, even at T > 3000K. This is incorrect since BN$_{\mathrm{2}}$ molecule dissociates into B and N$_{\mathrm{2}}$ from the ${}^{2}$B$_{\mathrm{2}}$ state which has higher energy than BN$_{\mathrm{2}}$(${}^{2}$A$_{\mathrm{1}}$). DFTB+ is not able to reproduce transition from ${}^{2}$A$_{\mathrm{1}}$ to ${}^{2}$B$_{\mathrm{2}}$ state. Similarly, stable BNBN molecule is difficult to observe in these simulations, since the reaction leading to formation of BNBN has a high energy barrier and is kinetically hindered. Nevertheless, DFTB+ simulations show formation of planar B$_{\mathrm{2}}$N$_{\mathrm{2}}$ and BBN$_{\mathrm{2}}$ molecules and larger clusters (B$_{\mathrm{3}}$N$_{\mathrm{3}}$ , B$_{\mathrm{12}}$N$_{\mathrm{12}}$, etc). Finally, we analyze the thermodynamic feasibility of these reactions through minimization of Gibbs Energy of formation.