  Nitrogen interstitials (N$_\mathrm{i}$) have the lowest formation energy
among intrinsic defects of hexagonal boron nitride (hBN) under n-type and
N-rich conditions. Using an optimized hybrid functional, which reproduces the
gap and satisfies the generalized Koopmans condition, an N$_\mathrm{i}$
configuration is found which is lower in energy than the ones reported so far.
The (0/-) charge transition level is also much deeper, so N$_\mathrm{i}$ acts
as a very efficient compensating center in n-type samples. Its calculated
photoluminescence (PL) at 3.0 eV agrees well with the position of an
N-sensitive band measured at 3.1 eV. It has been also found that the nitrogen
vacancy (V$_\mathrm{N}$) cannot be the origin of the three boron electron (TBC)
electron paramagnetic resonance (EPR) center and in thermal equilibrium it
cannot even exist in n-type samples.
