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.