Quantum chemistry modeling of B$_{\mathrm{n}}$N$_{\mathrm{2}}$ clusters formation in reaction between small B$_{\mathrm{n}}$ clusters (n$=$2-4) and N$_{\mathrm{2}}$ molecule for boron nitride nanotubes synthesis.

We study precursors for the boron nitride nanotubes (BNNTs) formation that can effectively convert molecular nitrogen into boron nitride. The data have been obtained by using a DFT (density function theory) method with unrestricted WB97X-D functional with 6-311$+$G(2dp) basis set. Using quantum chemistry methods, we discovered that formation of linear BNBN, cyclo-BNBNB and cyclo-BNBNB$_{\mathrm{2}}$ species from B$_{\mathrm{n}}$ (n$=$2-4) and N$_{\mathrm{2}}$ proceeds through sequential steps, and activation barrier of the rate-limited step is near 1.1 eV for all considered B$_{\mathrm{n}}$ clusters. On the other hand, the highest barrier towards dissociation of BNBN, cyclo-BNBNB and cyclo-BNBNB$_{\mathrm{2}}$ species on B$_{\mathrm{n}}$ and N$_{\mathrm{2}}$ increases and equals 2.5, 4.8 and 5.6 eV respectively. Thus, based on our calculations we can conclude that N$_{\mathrm{2}}$ is able to react with small B$_{\mathrm{n}}$ clusters producing new B$_{\mathrm{n}}$N$_{\mathrm{2}}$ clusters with BN bonds, and these B$_{\mathrm{n}}$N$_{\mathrm{2}}$ clusters can be accumulated in the gas phase even at high temperature providing contribution in the BNNTs growth.