  Rhombohedral B$_{12}$ unit is viewed as a host matrix embedding linear
tri-atomic arrangements of elements (E) resulting in a relatively large family
of boron-rich compounds with B$_{12}${E-E-E} generic formulation. The present
work focuses on boron subnitride, B$_{13}$N$_2$ that we express in present
context as B$_{12}${N-B-N}. Within well established quantum density functional
theory (DFT) a full study of its electronic properties is provided. Also linear
triatomic arrangements in view of the existence in simple compounds such as
sodium azide NaN$_3$, i.e., Na$^I${N-N-N} and calcium cyanamide,
Ca$^{II}${N-C-N}, we devised Sc$^{III}${N-B-N} to establish comparison with
B$_{12}${N-B-N}. ScBN$_2$ is calculated to be cohesive and possessing N-B-N
isolated from ScIII with dB-N = 1.33 {\AA}. In B$_{12}${N-B-N} an elongated
dB-N=1.43 {\AA} is identified due to the bonding of N with one of the two B12
boron substructures, B1 with the formation of "3B...N-B-N...3B"-like complex
accompanied by a magnetic instability. Spin polarized (SP) calculations led to
the onset of magnetization on central boron with M=1 $\mu_B$ in a stable
half-ferromagnetic ground state observed from the electronic density of states
(DOS). The results are backed with total energy and calculations in both
non-spin-polarized (NSP) and spin-polarized stabilizing the latter
configuration over a broad range of volumes from M(V) plots. Further
illustrative results are given with the charge densities (total and magnetic)
and electron localization function (ELF).
